i TechnicalMemorandumNo - NASA · II I k i JPL TECHNICAL MEMORANDUM NO. 33-188 The xo, yo, zo, xo, y0, zo ecliptic are now rotated to the and the quantity o are then computed and

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i _ TechnicalMemorandumNo.33-188} :.

., PLOD I1:lf

_ Planetary Orbit Determination Program

[_":. _ -_ .. for the IBM 7094 Computer

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Charles J. Devine ;

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Technical Memorandum No. 33-188

PLOD I1:

Planetary Orbit Determination Frogram

for the IBM 7094 Computer

Charles J. Devine

H. F. Lesh, Moncger

Computer Applications Section

JET PROPUI. SION LABORATORY

CALIFORNIA IN'STITUTE OF TECHNOLOGY

PASA D|-" N A, CALIFORNIA

,=,pril ! 5, ! 965

1965019622-002

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IPL TECHNICAL MEMORANDUM NO. 33-188

CONTENTS

I. Introduction .................. !

!1. Development .................... 1

A. General ..................... 1

B. Specific ...................... 1

III. Method of Solution ............ 2

Appendix I. PLOD II Users Manuo' . ........... 6

A. Descript :on ..................... 6

B. Opera',rag :nstructions ................ 6

C. Descriptions of Input ................ 6

1. Orbital Input Inforr, ation ............... 6

2. Data Deck and C, ntrol Cards ............. 7

D. Descriptions of Oo put ................. 11

1. The Star'ring Values and Control Parameters ........ 112. The Inforrn_ .ion Printed at Each Iteration ......... 1i

3. The Final 'Jutput and the Summary Page ......... 12E. Flow Charfl for PLOD II ................ 12

F. Main Pro'oram and Subroutine Descriptions .......... 27I. PLGDMN ................... 27

2. FORTSZ .................... 28

3. XPAND ..................... 37

4. SMULT ..................... 37

5. SCAT,R ..................... 38

6. INTRP ..................... 38

7. TSTOP .................... 40

8. STINKS ..................... 41

9. SET32 ..................... 42

10. SETUP2 .................... 43

11. CORECT .................... 43

1._. TRANSX ................... 44t

13. DERIV .................... 45

14. EOSER .................... 46

15. ERRER ..................... 46

16. FORDV ................... 46

17. _TPRG2 .................. 47

18. ELEMTS .................. 49

19. OBLIQ ................... 5020, SPHER ................... 50

21. ARC'i-N ..................... 50 ,_

22. RUN ...................... 51

23. DPINPT .................... 51

24. DOUTPT .................. 51

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JPL TECHNICAL MEMORANDUM NO. 33-188

CONTENTS (CONT'D)

Appendix I!. Sample of PLODII Output ............ 52

Appendix 15. PLODII ProgramListings ........... 75

References ....................... 145

FIGURES t

1. Program PLODMN input and starting procedure .......... 13

2. Program PLODMN subroutine calling sequence .......... 14 _

3. Program PLODMN convergence and tape writing chart ....... 15

4. Flow chart for subroutine TSTOP ............... 16

• 5. Flow chart for subroutine FORTSZ ............. 17

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fPL T_CHNICAL MEMORANDUM NO. :33-188

ABSTRACT

This Repot t describes the double precision numeri_'al fitting program

for the IBM 7094 used in the computation of the Jet Propulsion Lab-

oratory" planetary ephemerides. The method of integration and the

least squares fitting technique is described in detail along with all

mathematical equations used in the computation.

I. INTRODUCTION

PLOD II is a double preeisiou (DP) program designed to determine a definitiveplanetary orbit by fitting known source positions for a planet in such a mannerthat the residuals in longitude and latitude are as small as possiMe in a leastsquares sense. The numerical integration used is a DP Cowell finite differencemethod.

PLOD II is intended to be used with a large number of "observations," i.e., asource ephemeris, and will compute a DP solution of the normal equations forosculating elements by linear stepwise regression, using these differential cor-rections to correct the epoch elements. It then repeats with the improved epochvalues until convergence is obtained, i.e., the sums of squares o{ residuals inlongitude and latitude are as small as possible.

il. DEVELOPMENT

A. General developed in order to compute a gravitationally consistentposition and velocity ephemeris of high accuracy.

In the space explor_tion field it is often required tohave planetary, ephemerides of position and velocity ofhigh accuracy. The errors inherent in presently usedtheories prevent the obtaining of accurate velocities by B. $peclfi¢numerical differentiation of tabulations or analytical dif- In PLOD II, all corrections are in the ecliptic system.ferentiation of the expansions. Therefore, PLOD II was In the first version of PLOD (called PLOD I) the residuals

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±x_-- _---v_- x_, (_ = 1, 2, 3) in equatorial rectangular, co- i,e., to fit the longitude, latitude, and radius vector in tordinates (x'o observed values and x_ccomputed values) the ecliptic system, with the option of eliminating thewere reduced 1,y least squares. The criterion of fit was influence of any one of the residuals by assig_dng appro- :

that _o[_1 1 priate values to ,_,, a_, and a_. _s an example, in fitting(2_x'_)z = min observations where distance is not known, it is sometimes :/ t

desirable to eliminate the influence of the radius vector,

In PLOD II, for purposes of flexibilky and display, it and fit only to latitude and longitude. It was also thoughtwas decided to change the criterion of fit to best to make eorreetions to _ := f_ + .,, rather than to co, _

( A__._)'- to avoid diflqeulties with small inclinations (such as the_,(cosflah)za, +_(Afl)2a2+_ a._=rain (1) Earth).!

III. METHOD OF SOLUTION

Given epoch conditions of either equatorial rectangular given ao, co, io, fro, .,,,, and M. in the ecliptic system, If

position-velocity coordinates x., yo, z_, ko, yo, zo, or oscu- they are in the equatorial system, they are rotated to 'fating elements a., no, eo, i0, 90, ,,o, Mo in the ecliptic or the ecliptic system by a solution of spherical trianglesequatorial s; stem, it is desired to determine an orbit (see Ref, 2). '-which most closely fits a source ephemeris in the least

: squares sense. If the orbit determination is started with This 3 × 3 matrix, together v ith the osculating ele-

position and _c!ceity as epoch conditions, they are trans- ments, is constant throughout the integration and cor-;ormed to the ecliptic constants of the orbit, i.e,, the rected at each iteration,direction cosines PQB of the three axes and the osculat-ing elements (see Ref. 1), A transformation is then made To obtain these elements as the independent variables ,,back to equatorial position velocity coordinates for of the integration, a transformation is performed which _.

FORTSZ. converts the elements to position and velocity coordinates .for FORTSZ, the integration routine, by a Newton-

If the epoch c,.nditions are already in terms of the Baphson' iteration which determines a value of E good •osculating elements in the ecliptic system, then the PQR- to full double precision accuracy.direction cosine matrix is computed by the following

formulas: Given the first approximation to Kepler's equation,

P, = cos o,.cos f_, -- sin _0 sin f_,_cos i, E = M + e s_.nM + l,fie_sin 2M (3)

Q_ = -sin _,ore_ _o - cos ,,,_sin f_,,cos i,, and kepler's equationII_ = sin fl0sini0

t'_ = cos _,,,sin fl° + sin ,,0cos _o cos io, ] (E) = E - e sin E - M (4) io

then E is found by iterating in the Newton-Raphson

Q, = -sin _o sin _,, + cos o,ocos rio cos io equation

R_ = - cos fl. sin i. f (E_) (5) _P_ = sin _. sin io E,..I := E_ f' (Ek)

Q_. = cos _o sin i. and x, y, z, k, _,, _,are found from the equations in Ref, 1 _"R: = cos i. (2) (p. 146).

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The xo, yo, zo, xo, y0, zo ecliptic are now rotated to the and the quantity o are then computed and the residualsequatorial system by premultiplying by a standard rota- in longitude, latitude, and 0 are for_aed from the follow-tion matrix, ing equations:

" 1 0 0 ] p cos/3._,\ = - sin XAx_ + cos ),_x_

R = 0 cos e -sine J (6) p/_/3 = - sin/3cosL_x_- sin/3sin L_x_ + cos/3Ax_0 sin e cos e-- 1 1 _ 3

pat, - x,ax, 4 x_Ax_ + x,±x, (9)

The equatorial pesition-velocity coordinates with the ele-For conven;ence in setting up the normal equations,ments as independent variables are then used t'_ se_ up

starting values for the Gauss-Jackson predictor ce-rt ctor the equations are stored in the following matrix form:

method of the Cowell integration seheme. (See Section IF B = CIL (10)of the Appendix for details and equations.)

where C is the matrix of coe_eients on the right side of

The equations of motion to be integrated are the funda- Eq. (9) multiplied by l/p, R_ is the residual matrix, andmental equations in Co;veil's method (Ref. 3, pp. 169-170). the last row of the matrix has been divided by p for

x' / x; - x: x_ "_ scaling.

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= -sin/3cosX -- sin fl sin X cos/3 ._x_/(r_)_= _ (xi)_ _ x_, ,,x_..... ,, ,, J(pj)-_= E (x;- x')'-' (n) .t=l

and where the x i are the position coordinates in the three- The _esiduals in Ax_ equatorial and cos/3A)_, A/3, Ap/pdimensional system, and m is the mass of the body whose ecliptic are now tabulated and the latter are used in set-

motion is sought, while mj and x_ are the masses and ting up the normal equations.! positions of the perturbing bodies. The positions of the

perturbing bodies are taken from the EPHEM tape gen- The iiategration yields position coordinates x_ (t, c) anderated by the Jet Propulsion Laboratory (see Refs. 4 and velocity components k, (t. c), (i = 1, 2,3), at time stop

: 13). This calculation and the computations involving the points to < t_ < t_ < • • • _ G. The computed coordi-relativity contribution for the inner planets are performed nates in general depend on some parameter set

[ in the derivative subroutine, DERIV (see Appendix). c = (c_, c..,, • ' • , c6), tile six constants of integration. Inthis Report, these constants will be the osculating ele-

During the in.egration of the equations of motion the ments mentioned above. This parameter set serves to: residuals are computed in the subroutine TSTOP at speci- fix the values of the coordinates and velocity components

fled time stops. The residuals are first computed as equa- at to. The c are chosen such that the sum of the squaredtorial residuals, i.e., residuals (S_) is a minimum. As _l PLOD I,

[

1' - ' (i = 1, 2, 3) (8) min (i 1, 2, 3)]=o

where x_ and x_ are the observed (the "observed" posi- ° (12)

tions being read from the source ephemeris tape) and or in the case of PLOD II,c,_mputed position coordinates in that order. The zxx_

, and ' " equatorialare then rotated by matrix (6) with So _ _t (cos/_/F_Zj)" + a2/_fl_ + _. a._xc, xc = = rainI

sint = -sine to ecliptic residuals _x_ and ecliptic posi- _0 ;_o _=, \ P_ /

tion and velocity. The ecliptic longitude and latitude, (13)iI

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The usual method of minimizip%S_ is to calculate the and i_

partialderivativesax_/_c,,,(i='/.,3),(k=l, 2,...,6), l_/_xl !_

for assumed values of the " and at the points tj, and to _:solvethenormaleqo'" .s B = Ay (18) _

' ";a,,ll-''"\_-_-_- J]_l - " I ,., / ,., .,_-=---t-'I/ack and all quantities are in the equatorial system.

(m = 1, 2, - • • , 6) (14) In PLOD II, since $2 is minimized: the rnatrix form ;is slightly modified. Recalling Eq. (15), matrix A is multi-

for corrections ACkto the values of ck. plied by the matrix

.. In PLOD I the partial derivatives appeared in a single 1 [ -sin X cosZ 0 l "_

equation of condition in matrix fol'rn (see Ref. 3, Chap. 9) C = --_ --sin t3cos X --sin/3 sin X cos/3 ] (19) ._where A is the 3 X 6 matrix of pa:";_.i derivatives. This o x/p y/p z/'_may be denoted explicitly by the following matrix wherethe traditional notation x, y, z is used for the position and obtaining a new matrix of parhal derivativesvelocity' vectors for convenience of expression: A = CA (20)

Pyz - P:y Q,z - Q.-y -_- + R,z - R..y x - _ t_c Hx + KSn

A= n_ P_x - e,z Q,x - Q,z -e- 4- R..x - R,z y - _

)l +l_y-Ryx z- t_ Hz+K_--_z P_y --P,,x Q,y - Q,,x _e 2 3_o:/

where and a new system of equations in matrix form

H = r- a(1 + e_) AX =B (21) _ae (1 - e_) where X is the column _ector _.

and X = (AMo q- Ar. A_,_./. car, aa/a, Ac) (22) i'

, r_ [" r ] and'B is now _he column v,:_¢.,"_ = (eos/3AA,Aft, Ap./p).... of the long_tude and lat:t't,..t': esidual_ in the eclipticK = a-r_n_Ll+a(1 e;_ %system. The position a,:d _e' _city coordinates for theThe actual matrix equation for one time pc'at ,vould be Set III matrix, i.e., the _, _ _, ix, are a],¢o_n the ecliptic "represented by system, Hence, there :, :_ :,t_nbolic notation a 3 × 6

matrix _ equal to the p._ ',.._ '_erivativesof X,/3,and p withAX = B (16) respect to the Se_ _': ,,_ ;-"ouwer and Clemence.

(x,/3,_) (23)wher_ A.. -'.C,,._A._.,_- ca(Set III)"AM,, + At"

Ap These pa_'tial derivatives wil] be formed at each of the

Aq n + 1 steps.x = (17)

ear

Due to the large number of points at which X is com-Aa/a puted, it is necessary to use a special method of solving

_xe _.t the system of equations obtained. (See Ref. 5.)

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,JPL TECHNICAL MEMORANDUN: NO. 33-188

Let the system of linear equations obtained after n + 1 The solution column vector [Eq. (22)] will then be thesteps be denoted by desired correct'.'ons to the osculating elements. The cor-

NX = F (24) recticns Ar, AMo, Aa, and _e are easily obtained in astraightforward manner from X, the solution vector, whilen is obtained from a unless the mean motion is held

where X is the solution vect,.r and N is defined by fixed, tit should be noted here that if the mean motionis held fixed, then the correction to the period is ignored.

N = _. ANs (25) The column corresponding to _a,'a in the overdetermineds_o system of linear equatioias is set equal t_,zero, and tJlere-

and fore, STPRG2 makes no attempt to solve for Aa/a. The'i - _ - value of a is then held fixed through Kepler's third law.)! i ANs : A_WAs (26) The only di_culty lies in obtaining corrections to ,aft, ai,_" and A_o,the longitude of the asee_ading node, the incli-

at each step. A*.is the transpose of _,s, and W is a diag-_ nation, and the argument of perihelion. This may be_." onal weight matrix, i.e., accomplished in the following manner:i,

W = 0 _ 0 (27) derivation of these results see Ref. 3, pp. 23&-239.)

!_, 0 0 as Ai=Apcoso,--Aqsin,_

The matrixW playstherole,-fexcludingtheinfluence siniAfl= Apsin_ + Aq cos_ (32)of any one of the residuals. If in PLOD II the longitudeand latitude residuals only are minimized, then the set An expression for A,, may be similarly derived, but inring of a = (1,1, 0) annihilates the contribution of the order to accurately determine A_ from a correction top residual. If a PLOD I type of fit is desired, the setting the longitude, it is more desiral_le to find the correctionof cx= (1, 1,1) will again make the p contribution sig- to Art = A,o+ a£, and then subtract the computed value

of g.q found from Eq. (32). By e'tarnining small rotat'_onsnificant and STPBG2 will correct accordingly. Ap, Aq, Ar and making trigonometric substitutions, it may

De found that a small change in A_ may be expressed asThe matrix F is defined by follows:

n

F = _ AFs ¢28) aTr -- sin is:o ' (1 + cos/) (sin_ap + cos_Aq) + ar (33)

where from which A_omay be computed after At2 is found. This

AF; = _,_WB'j (29) brings up the inherent difficulty of what to do with sin iwhen i is near zero. The problem is attacked by settingAf_0 whenever i < < _ e, or zero. Hence, from the

at each step. corrections Ap, Aq, Ar, it is possible to obt, in A,,, A_,

The equations NX = F are then solved by a DP step- and Ai and complete corrections to the osculating ele- _'wise regression program ea_led STPRG2 (see Section IF ments.

of Appendix), if the value of Sz as computed by The new elements are now computed ana used in

$2 = _ a_(cos Bs,_) _ + a, (ABs)i a aa(Apsy (30) Eq. (2) to compute new direction cosines, from whichs:o ' X--_ / new epoch values of position and velocity (x0yo zo,io YoZo)

may be computed and the inte[c'at_on may be startedis too hrge, or if TMA.'.. ,he maximum number of time again. The process is complete when Eq. (31) has a valuesteps allowed for the integration, has been .reached. The of SQ _ _, where _ is a predetermined number, or when

final .convergence test is performed oa the usual con- there are no further appreciable corrections from _he,t vergence factor least squares stepwise regression solution, i.e.,

i SQ=(SI/N)_t (31, ( _.__p_i 2 (cos#/AA)'a,+ _ (AB')aa ']_',\P/ as= raini whereN isthetotalnumberofintegratedpositions. (34)I

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APPENDIX I. PLOD II USERS MANUAL

A. Descr:ption C. Descriptions of Input

PLOD lI is to be us_,i ull the standard Fortran II m_ni- 1. Orbitai Input Information

tor system of the IBM 7094. It is a DP program employing _The basic h,:me of reference to which ;ill elements

DP sa_broutines to do most of the major computation, and rectangular position and velocity coordinates areThe storage req,:ired by PLOD II is considerable and the refe_ed is the fixed equator and equinox of 1950, Julianpr,,:gr_,,;q us_-'s ,_ ,,t: _h,, c '11-5av2.;!ab!e in _lae 7090 .94memo_- unit u_,der Fortran iI. Caution is therefore ad- date, 24332:52.-t2_3. PLOD Ii may be star_ed with rec-vised when new s_lbroutines are added or old ones modi- tangular heliocentric equatorial coordinates read from

cards, tape, or osculating elements, el:her in the ecliptictied. The follo-_-Mg user's manual is a complete description

or equ_,torial system read f:om cards. If the osculating

of PLOD II with all necessary information for ephemeris elements are in the equator/al system, a c-mtrol parameteret.mp"ta.'ion, and includes listings of the main programs, must be set to rotate them to the ecliptic system. Althoughq-he user _hould be particularly interested in the data the integration is alss avs carried out in ihe equatorial _'s-deck and control card Section. " "

t,:m, all othe: cornF _tations, corrections, and internalstartling values are in the ecliptic system.

B. Operating Instructions

PLOD II is a self-contained program that requires The oso_,lating ele.n,e:,ts a, n, e, i, .q,,:,, M, referred tono console monitoring. The program reads all control thrc:ighout the program, are actually the independent

variables of the differential correction procedure. Io an}"information from the data deck and sYiil call for tapeswhen needed. PLOD II uses five nonsvstem tape chan- case in the starting procedure, the rectangular coordi-nels. The seuree and perturbing body tapes are read on nares are foand from these values. In fact, an}" onper-hvo channels while the PV tape, the preconvergcd residual turbed orbit of a planet about the Sun ;s comgletely_pe. and the- cor,-:erged residual tape are written on the defined by six elements which may be chosen in various

remaining three channels. The user selects the channel, ways and which may be referred to an}" reference system.The elements t,sed by PLOD II are defined as follows:The source ephe,,teris tape and perturbing body tapes

are always calied immediately while the other tapos arenot called unless it is necessary to write an ephemeris a the semimajor axes of the orbit.

or residual tap- arid the integration has converged. (The n the mean daily motion, n and a are related byexception here is the preconverged residual tape. If this n:a _ = k: (1 _- m), where k is the Gaussian gravi-option is used, PLOD II will write immediately a residual tational constant and m is the mass of the main

tape for the first, n - 1, fferations.) The program prints body expressed in terms of the Sun's mass.out on-line, for convenience, the value of sigma and theJulian date at each iteration, and if there is no improve- e the eccentricity, of the orbit.

ment, the program may be stopped by requesting the i the inclination of the orbit to the ecliptic. 'operator to halt. !

9. the longitalde c" the ascending node of the orbit

It is to be noted here that the average run may take on the ecliptic, measured from the equinox. :

from 20 to 120 min for a 50-yr integration with three or o, the argument of perihelion. Even though o, is in-

four iterations, depending upon the bod.v being inte- putted to PLOD II, the corrections are madegrated, the integration step size, and the residual step in .-: = 11+ ,°, the longihlde of perihelion, inca-size. An estimate of the number of integration steps per sured from the equinox along 1be ecliptic to the _"minute s_ould be 2,50. node, and then along the orbit /rum node to

per-2helion._e order in which the subroutil_es are loaded is im-

portant under Fortran II. The subroutines FORTSZ, M,. the mean anomaly at epoch.XPAND, SMULT, SCALR and INTRP m,.st be loaded• :.'o

first in t_,_t order. This insures that all DP instructions The element n is not independent since it is related to a.refer to even locations. The others, including PLODMN, It may be input by cards to the program, but more com-mav be loaded in whatever order desired, monly is computed directly from a. There is an option :;

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to force n to be the input v'41ue vhen desired. When this a. PLOD !I data card format.is the ca_e. a is computed from n and the SET III matrixis computed accordingly, i.e., the .-'olumn vector on which Group one (Identi,ftcation).

a depends is set to zero. The first card (Format 214, 2A6) contains the wordJEND, the body nu_nber NBODY, and the name of the

The reciprocal masses of the p_anets are input to the planet being integrated. If JEND = 0, the p_ogram willmain prog,ram of FLOE' II. The,- are inverted in DP read only one data deck. If JEND = IX, where IX < 0within the program and the valu ; of/_ and _- is corn. or IX > 0, IX an integer, the program will read a newputed in DP also. "Ihe g_avitaional constant, k, is data deck. The bod,v number, NBODY corr,'_ponds tocompiled internally and k: is also computed in DP. the re,robe; of the planet which's to be integrated, i.e.,

Mercury =: 1, Venus -- 2. Earth-Moon - 3, Mars = 4,

t The value k := 0.017202 098950 ,)00000 is taken from Jupiter = 5, Satqrn = 6, Uranus =: 7, Neptune = 8, and

t Ref. 1, p. 58. The mass of the Earth is immediately set Pluto = 9. PI_.ANET (I = 1, 2) are the tv,o BCD wordsto zero along with the r,lain hotly of the integration, of storage fo_ l,__e planet name, i.e., Mercury, Venus,There is no i_er<l for the ma_s of the Earth at this time, Earth-Moon, .tc.

[ since ',ill work is done with the Earth-Moon ba_,eentre.

The second card contaius tape information for four

2. Data Deck and Control Cards tapes and the Fortran logical unit number for the precon-t

_: verged residual tape:The description of the data dee.k and control cards

will be outlined into four main groups. The outline in-1. COORD tape Format 4 (13. Ar, A3)eludes format specifications and control information and

all of the PLOD II options with explanations. The user 2. SOURCE tape where I3 is logicalunit number, A6 is

will be primarily concerned with this section, and it is 3. PLOD ephemeris write tape tape _umber, and A3recommended that some form of data sheet be set up for

production runs, since only a few of the cards will be 4. PLOD residual write tape is channel number.

changed for different cases. 5. Preconverged (n - 1) iterations residual tape logicalunit. Format (13).

The four main grL:ups are arranged according to thetype of input. Group one, the identification group, in-eludes general information such a._ the planet to be inte- Cards 3 through 12 contain BCD information and corn-grated, source tapes for the planet, PV write tapes, source ments on the PLOD run (in groups of two cards). Theretape for the perturbing bodies, and BCD identification will be 12A6 words on the f_r_t car,, and 10A6 words

records for the ephemeris and residual tapes. Group two on the second card. TI_c programmer may write a sen-is mainly input options and printing "_ptions for the tence of information with blanks wherever he chooses, asephemeris tape, i.e., PV tape generated by PLOD II, as long as he ends in column 72 on the first card, and inwell as infornmtion for FOI:iTSZ control options. Input column 60 on the second card (column i must be left

options include indications of what system the data are blank on every card). The followi':g is a specific list ofin, ecliptic or equatorial, whether on cards or _ape, and the cards taken two at a time:whether the mean motion is held fixed or not. Group three

consists primarily of convergence tolerances that are 1. Cards 3 and 4 contain the BCD record identification

iuput by the progr;_mmer. This includes the main con- for the PV ephemeris generated by PLOD II. Thevergence criterion and the step size for the normal equa- comment "nust end with the words "PLANET IS,"tions and the PLOD II ephemeris. Group four is the or words to that effect, since the v-"* word will beactual orbital information input, which includes epoch the name of the planet.

! conditions, i.e., either the osc_lating elements or position! and velocity coordinates. The reciprocal masses of the 2. Cards 5 and 6 comment on COORD tape.

planets, the mean motion, the mass increment for aug-menting the Sun's mass, the weight vecto," W, the light 3. Cards 7 and 8 comment on SOURCE tape.constants for the relativity contribution (at the presenttime, these are not used), and the Julian dates for which 4. Cards 9 and 1-0 contain the BCD record identifica-

the integration is desired are also input hf.re, tion for the PV residual tape generated by PLOD II.

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5. Cards 11 and 12 contain the BCD record identifica- NEPOCH = 1 Input by cards XYZ, XYZ (last two cards) ition comment for preconverged residual tape. It is DPINPT DP DEC 16 Digit. iadvisable to include dates and tape numbers in allcases. NEPOCH = 2 Input by cards a,,,lh, eo, i, f,0,o,o,M, (last

two cards) DPINPT DP DEC 16 digit.f

Group two. __:EPOCH= 3 Input by reading SOURCE tape for pt,- !-Control options: Input and ephemeris print, sition and velocity.

Card 13: Format (!414) NDOP = 1 (For PLOD II. NDOP is consta,t = 1.)

KAM = l Rotates source XYZ to ecliptic, computes Applicable to PLOD I only.

p,,i.,fl, prints, and computes Ap,A/,,a/3 NDOP = 2 PLOD I, NDOP = 1, normal matrix is '_for check. (3, 6), NDOP = 2, normal matrix is (6, 6).

KAM = 2 No rotation, print, or At,,aX, '_-Bcheek. Applicable to PLOD I only.

LAM -= 1 Prints _.]D, XYZ, XYZ, and AX, AY, AZ NECLPT = 1 If elements are ecliptic (no rotation). Ap-during itera_on, plicable only under NEPOCH = 2.

LAM :=2 No print during iteration. NECLPT = 2 If elements are equatorial, rotate to eclip-tic. Applicable opJyunder NEPOCH = 2. -NAM = 1 Derivative print during dates specified

for position, velocity, and acceleration. KAN = 1 Print X]D, XYZ, X-gT,,and AX, aY, AZ onconverged iteration (last).

NAM = 2 No print.KAN = 2 No print ofXID,XYZ,_7., and AX,AY,AZ

MAM = 1 Load COORD tape (MTAPE) only on converged iteration (last).

MA_; = 2 Load SOURCE tape (NTAPE_ only. i

MAM ---3 Load COORD (MTAPE) and SOUFCE FORTSZ Options.

(NTAPE) tapes (usual case). Card 14: Format (514, F12.6, E17.8) •

JAM = 1 PROG solves normal equations afterTMAX (usual case). MD = M 1 _- M L 15. Fixed point integer direct-

ing highest order of difference to be car-JAM = 2 Will be automatically set not to call ried (usual case MD = 8).

STPRG2 after co:wergence.JD = ] O_]LM. Initialization point ] = 0 place

K = 8 (Leave alone.) at end of net (usual case ] = 0_. '_[_

1NOBOD = 10 For COORD in DERIV (will stay con- ND = N = 0 No variational equations.

stant). Generally not used in PLOD II, NPT = OPT = 0

since it does not employ old COORD Gauss-Jackson open method.system.

NPq = OPT = J

KPOS = 1 Position only from CGORD (usual ease). Gauss-Jackson pseudo predictor coffee- ,-'Generally not used in PLOD II, since it tor.does not employ old COORD system.

KPOS = 2 Velocities only. NPT = OPT = 2Gauss-Jackson predictor-corrector (alwaysKPOS = 3 Velocity and position, used).

MEAN = 1 Mean motion is computed internally. IL = F = 0 FORTSZ computes only position atTSTOP.

MEAN = 2 Mean motion is inputted and remainsfixed throughout integration. IL = F = I FORTSZ computes position and veloeiW t

at TSTOP.ITRMAX = Maximum number of iterations allowed

(usually set at 8). H = Integration step size.

,, I _ I i i _m ii

1965019622-013

,JPL 1ECI-,,;qICAL MEMORANDUM NO. 33-188

ES = -0.1 X 10-:1cor,vergence test for NS'_'EP = 4 Reads neither COORD or SOURCEFORTSZ startin.; procedure (note nega-

t (Note: Leave at 3).tive value).

NEPHM = 0 Program goes through normal equationsControl options: Tape writing, normal equations, body and sf'er convergence sets NEPtIM = 1.

number, etc.

NEPHM = Some integer _0, if non-zero, simpleCard 15: (Format (1013) integration without correction of normal

equatim s.

MMAX = 3 !These remain constant for PLOD II. NEARTH 1 (leave at 2)NMAX = 6

NE,_RTH = 2MPRINT = 1 Will write a preconverged residual tape

for (n - 1) ,.'terations.MTEST = 1 Circle test, all masses set to zero.

MPRIN':'= 2 Preconverged residual tape not wl'itter.MTEST = 2 Normal case, only pnncipal mass = 0.

NPRINT = 1 Load _nd waite PLOD ephemeris andresidual tape (LTAPE, KTAPE). NREL = 1 Compute relati_ty contribution in DE-" RIV.

NPRINT = 2 Load and write PI OD ephemeris onlv(LTAPE). " NREL = 2 No relativity.

NPRINT = 3 Load and write PLOD residual only Croup three (convergence tests).(KTAPE).

Card 16: Format (4E17.8)NPRINT = 4 Do not load and write ephemeris or re-

sidual tap_. STEST = 5. × 19 _ iTest to see if residuals are too large (set

_PRINT = 0 No STPRG2 print, at whatever tolerance desired).SIGSQ _ STEST Correct orbit

KPRINT = 1 Print STPRG2 summary, final solution SIGSQ < STEST Continue to TMAXonly.

EPSILN* = 2. × 10-°

KPRINT = 2 Print STPRG2 summary, every solution. SIG < EPSILN convergeSIG > EPSILN iterate (Set at whatever

KPRINT = 3 Fu!l print of STPRG2. tolerance desired; 9.× 10-0is just a start-ing guess).

NSTEP = 1 For COORD tape only, reads two datesfrom COORD tape and computes tape CD = 1. × 10"_step size for DERIV. Tolerance in STPRG2 for relative reduc-

tion in magnitude of diagonal elementsof matrix.

NS'rEP = 2 Reads BCD heading on SOURCE tapeand positions tape. prints on line and offline BCD heading of SOURCE tape. SDOUT = 0.005

'_ Signtfleanee level (out) of STPRG2 (may

] be set at 0.0),NSTEP = 3 Reads BCD heading on SOURCE tape STPRG2" convergence (STPRG2 will al-• and prints same on live and off line, and ways give a solution if SDOUT = 0.0,{ positions SOURCE tape, then reads two SDIN -- 1XE.17).i dates from COORD tape and computers

tape step size for DERIV. "Thethreemaineonwrgeneetestsof theprogram.

9

1965019622-014

Jpt. TECHNICAL MEMORANDUM NO. 33-188

Card 17: Fonnat (2E17.8, 2F12.6) Card 0.,2:Format (DP1NPT)

SDiN :-- 0.25 > SDOUT significance level (in) of DEC xxxxxxx.x XTE

STPRC2. End print date for DERIV.

DEPSIL _ -= 1. X 10-1' Cards 23 and 24: Focmat (DPINPT)If epsiln is small, and if successive sigmasare not different in eleventh place con- DEC (DM (I),I - 1, 10)

verge. The programmer may select his The DPINPT reciprocal masses of theown tolerance after a few runs. :line planets including the Earth as mass

number four, i.e., there will be ten values

FSTOP1 --= Step size for n_rmal enuations, in the following order: Mercury, Venus,FSTOP1 _-_Step size of source tape. Earth-Moon, Earth, Mars, Jupiter, Saturn,

FSTOP1. FSTOP2 must be greater than Uranus, Neptune, Pluto. Any value mayor equal to integration step ,;ze. be used for the E:trth, since it will be set

to zero by the program.

FSTOP2 = Step size for PLOD ephemeris. At pres-

ent FSTOP2-_-- step size of source tape. Card "9.25:Format (DPINPT)FSTOP1, FSTOP2 must be greater than

or equal to integra.fion step size. DEC RM The DPINPT inputted mass incrementfor augmenting the mass of the principal

Group tour (i.,.put data values [or execution).** planet being integrated. This value ivustbe read in as zero if no variation in the

Card 18: Format (DPINPT) mass is planned. That is, it is c_mputedin the equation for _t at all times as fol-

DEC x.x, x.x, x.x lows:

Three dimensional DP, weight vector for,, normal matrix, i_ = k_ (1 + mi _- RM_) :

I-

W = (a,., ,._.,-.0, (0 _ -a -_ 1 9) where RM, is the mass increment and

m, is the mass of the principal planet.

a:, = 0.0 Normal case (p not significant). If it is desired to use this option for anintegration of the outer planets, similar

a3 = 1.0 o signiacant (PLOD I type), to lqef. 6, then the masses of the four in-ner planets on Card _ must be set to

Card 19: Format (DPINPT) z'_r°l

DEC 299773 CAR Card 26: Format (DPlNpV_Constants to compute velocity of light forrelativity. DEC The DPINPT inputted mean motion

XMEAN. Thi_ may be set to any value ifMEAN = 1.

Card 20:

DEC 149598845 AU Card 27: Format (DPINPT) '

Constants to compute velocity of light for DEC xxxxxxx.x X]Drelativity.

Integration epoch Julian date.

Card 21: Format (DPINPT) Card 28: Format (DPINPT)

DEC_xxxxxx.x XTS DEC xxxxxxx.x TMAX

Beginning print date for DERIV. Julian date signifying end of integration. '_

"For fmlnat desc='iptionof DPINPT and DOUTPT, see Section F-23'8

and F-24. Cards 29 and 30, • • ' N _

;0

10 ,t.

...._""_'.'_' '5"'..' '. .'

1965019622-015

| I

IlLL


The DPINPT epoch input data. Either position and ve- _utomatically prin_ed at every, iteration including thelocity or the seven osculating elements of the integration, first. Tile beginning of the iteration will be signified by

the comment "BEGIN ITERATION." Then the positionEND OF FILE. velocity coordinates at epoch are printed in two lines of

tluee DP words each-first XYZ and second X'_"Z. In the

first iteration, these will be the same as the input coordi-D. Descriptions of Output nates, but in all subsequent iter_..fions the)" will be the

PLOD II output may be separated into three main coordinates actually given to the integration routine, i.e.,the)" will have the osculating elements as the independent

categories: variables.1. The Starting Values (Epoch Values) and Control

Parametels The next line ,,f print will be the equatorial osculating

Here the position and velocity coordinates are listed elements computed by the subroutine ELEMTS from thealong with the direction cosine matrix and the osculating position velocity cx)ordinates in DP in the following order:elements. The osculating elements and the direction a,,, n,,, e,,, i,,, _1....... M,, followed by the computed equa-

torial DP direction cosines matrix, PQR. The P vectorcosine matrix are generally printed in the ecliptic system forms the first row, while the Q and R vectors form theand the equatorial system at the beginning of every, runand at each it._ration. For a typical ease where the epoch second and third rows. respectively. The osculating ele-position and veloci_, coordinates were read from the ments and the PQR direction cosines matrix are then

repeated in the ecliptic system, followed by, for the firstsource tape, there would be the following general out- iteration only, ecliptic position and velocity coordinates

t line of identification, with the osculating elements as independent variables

i that are rotated to equatorial position-velocity coordinatesThe first value printed is the resiaual weight vector, and given to FORTSZ to start the integration. In all

• defined by Eq. (_T/). followed by a printed tape identifi- subsequent iterations, the ecliptic position and velocityI cation of the main tapes that are loaded, the perturbing coordinates will not appear at this point, but will appear

bodies tape and the source tape, and the BCD beading just before the comm-,nt "BEGIN ITERATION.'"from the souice tape. The masses of the planets are then

printed in DP in the following order: Mercury, Venvs.Earth-Moon-Balwcentre, Earth (this will be zero for A comment is now printed identifying the ephemerisPLOD II), Mars, Jupiter, Saturn, Uranus, Neptune. and format to be us,._d. An ephemecis consisting of two lines of

information is printed on option at each iteration. The firstPluto. These are the actual masses of the planets, i.e., the line will always be Julian date, equatorial XYZ. ,((YZ,inverse of the inputted reciprocal mass. Next. the controlparameters for PLOD II will be labeled. The)' are de- and residuals AX,..xY,.xZ of observed minus-computedfined in the input section of this Appendix, Section C-2. rectangular equatorial coord!nates in single precision, fol-

lowed by ecliptic XYZ, XYZ, and residuals .xp, cos t?-x_.,After the control parameters, the BCD record of the pre-

converged residual tape is printed if the tape is to be and -x//. The residuals will have a fixed format of 7PF14.4.written. The epoch values are then read in and printed An addihonal check may be computed and printed byout in DP, and a comment is printed to the effect that setting the i_aput parameter KAM = 1. thus printing inde-all input data have been read in by PLOD II. The epoch pendently computed .xp, _x/3, and _x_,residuals directly.

values will in general be either the position and velocit Tread from cards or tape (the part;cular case being herein When the integration stops either by exceeding TMAX,described is of two lines of DP words representing XYZ, _r i)y exceeding the residual tolerances set beforehand byand X_'7,), or the seven oscillating elements a,,, n,,, e,,, i,,, input, the normal equations are soh, ed by STPRG2 and aft,,, _,,, M,, in the order read from the cards. A comment su,nma'T is printed hy STPRG2 indicating the order of

will be printed indicating what procedure was used and solution and the significance of each coefficient in the so-lotion vector. For KPRINT = 0, 1,2, or 3, there will be

whether the mean motion is inputted and held constantor computed internally, no print of STPRG2, a summar T of the final solution, a

, summary of every solution, or a full print of the matrix

t and a sununary of every solution prin_ed.2. The _nformation Printed at Each Iteration

The amount of output at each iteration is largely deter- This concludes the options allowed at each iteration,

mined by the user, but there are a few values that are with what follows printed at every iteration of PLOD II.

1965019622-016

JPL TECHNICAL MEMORANDUM NO. 33-188 _,

The subroutine CORECT which computes the corree, of the tapes used are printed for identiAcation and easytions to the osculating elements now prints the following verification. For complete detail of printing options, theinformation: The DP value of _ = _ + _ is printed first, user is advised to consult the data deck and control cardsfollowed by the uncorrected PQI{ matrix and the uncor- Section (C-2 of this Appendix).reeted elements all in the ecliptic s_stem and with the

same order as above. Next, the DP solution vector from The summary page printed by PLOD II is a referenceSTPRG2, the new corrected PQR matrix, the elliptical record to indicate the information necessary for dupli-corrections to the dements, and the new ecliptic DP ele- eating a PLOD II run. It may be torn off after eachmerits are printed, agai_ in the same order as above. The PLOD II run and kept in the access Ale for hture ref-final value of _ from Kepler's third law is printed for erence. The summr_'y page consists of a BCD commentreference, on the PLOD II run and a BCD comment on the COOBD

tape u_d for the perturbing bodies, followed by most ofA comment is now printed indicating whether the inte- the input options necessary to restart PLOD II. These

gration has converged or not, the Julian date, the elapsed are followed by BCD headings on the converged ephem-time in days, the number of integration steps, and the eris and residual tapes, if these were written, or thevalue of sigma and the sum of _he squared residuals, comment "NO TAPES WRITTEN," if they were not.A brief summary of statistical analysis is also printed The inputted inverse mc.sses are then printed, followed

: here. The mean deviation, the sum of the squared residu- by the weight vector described in the input Seetio_ andals, the standard deviation, and the maximum and mini- the angle of obliquity. The converged epoch values aremum of Ax, A_/, and Az are printed, plus the same then printed in DP, i.e., the osculating elements, thestatistics for Ap, coS_>,, and A/g. This enables the user PQR matr_z at epoch, and the epoch positions and ve-to have some idea of the least squares t_t at each itera- locities are printed, each in the order described above.tion. These values are also p_lted on the summary page The last printed output is again the summary of statisticalof the Bnal converged iteration, analysis of the converged ephemeris. This concludes the

output of a typical PLOD II run.

3. The Final Output and the Summary Page

The _nal and most important output is the ephemeris E. Flow Cherts for PLOD II

output after convergence. PLOD II will output at the The program PLODMN is the primary directing anduser's option an ephemeris tape and a residual tape after controlling program of PLOD II. It serves to controlconvergence is signi_ed by a printed comment similar input, output, and the order in which the subroutines areto the one described above. PLOD II _m write two tapes, called. All parameters will be set in PLODMN with theone of which will be a residual tape containing a BCD exception of a few convergence tolerances, and all sub-heading of 24 words (supplied by the user in input data), routines except FOBTSZ related subroutines will befollowed by one binary record of 7 words with subse- called by PLODMN. The one exception is the subroutinequent records consisting of the DP Julian date at each STINKS, which is called at each step by the subroutinestep, plus the corresponding equatorial residuals of AX, TSTOP, and which calls the subroutine SPHEB.Ay, zig and ap cos _AX, A_, in single precision, makingan eigh,'-word Fortran binary record at each step. Theother tape will be the PLOD II position-velocity (PV> The program PLODMN starts the integration and endstape which will again have a BCD heading of 24 words the integration. The flow charting will be in three majorfollowed by a binary record of 7 words and will consist sections: the input and starting procedure of th_ inte-of a DP Julian date, X, Y, Z and X, Y,_, all in DP, mak- gration (Fig. 1); the subroutine calls and the order ining a Fortran binary record size at each step of fourteen which they are executed (Fig. 2), and the convergence

flow and tape writing and output control of PLODMNwords. Simultaneously, at the user's option, the programwill print for observation at each step, the Julian date, (Fig. 3). A supplement flow chart of TSTOP is shown _th_ position and velocity, equatorial coordinates with in Fig. 4. The flow charts are not complete, and areequatorial AX, AY, AZ residuals, and ecliptic position- intended only to give the user an idea of the flow of thevelocity coordinates with the A//,/,p and cos/_A>, resid- program PLOD II.uals. These values may also be printed through each

_, iteration, in order for the programmer to observe the Figure 5 is a complete flow chart of the subroutine

:!. integration and its et_ect on the residuals. The numbers FORTSZ.

12

.7................ Hmrl I i . l _ IB . ,_7 ]1 I I I /_'_" _ " I' I

1965019622-017

.me,..


_f READ IDENTIFICATION

r-m_ v_. INP;JT DATA CARDS J

PARAMETERS AND

-- -- "1 FORTSZvPTION S

I _ READ CONVERGENCECRITERIONi TI COMPUTE--------IC,LLOSL,Oj

J PROGRAM

I _ ICONSTANTS

II _ ip.,M/te_et¢"NEPOCH:t _ NEPOCH_ 3

,-- ,_oo... (-°°-)CARDS

V _.,TMAX : tCARD ELEMENTS TAPE - j

To TMAX AT To Xe Y_ Ze

x, Y,Zo _ _o P.z°_o_,,*o YEs _ NO T *L

ROTATE TO Pom_CLIPTIC MATRIX ITERATE

f,LEMENTS STORE MAIN LOOPPOINT

COMPUTE CALL TRAPdSX TOOSCULATING _ OSCULATING ELEMENTS FORDV

ELEMENTS ANDP 0 R MATRIX -_POSITION VELOCITY

CALL STINKS

l ROTATE TO, ,, EQUATORIAL

_.. IDENTIFICATIONPRINT//OUTPUT

Fig, I, Program PLODMN Input and starting procedure

13

w ,,,

i

1965019622-018

JPL TECHNICP.L MEMORANDUM NO. 33-188

COMPUTES STEP SIZE __ FORTSZ SMULT, DRIVES FORTSZ ]_ v I INTEGRATION

tNTRP

l ...... J DERIV

!! -I _I COORO

1

COMPUTE

_ RESIDUALS ICALL STINKS i

II COMPUTE

STATI STICS

WRITE E_ORMAL EQUATIONi

JL, , _ V

NEW JOB, TIME NORMAL MATRIXREAD SOURCE DECX J

l i SETUP2

!

oo,STPRG2

._ EOSER t INORMAL EQUATIONEND OF STEP J SOLUTION

ERRER _ CORRECTFORTSZ ERROR COMPUTES

d, LSo, _e, An, LSi,&_, &_, _o

NO TA IC g--.I COMPUTESTATISTICS\_ _ OUT RETURN FROM CONVERGENCE

)UT .'

L; Fig. 2. Program PLODMN subroutine calli,g s_quence ,.

_ _-- ,, .

1965019622-019

iI

'1 JPL TECHNICAL MEMORANDUM NO. 33-188

J

FROM CORRECT

:1 _ :4

REWIND AND l REW,ND [ REN_ND ANDREWIND POSITION / ONLY POSIT,ONCOORD SOURCE | I SOJRCE, COORD,

TAPE ONLY TAPE J I SOURCE TAPESL_.__ RD TAPES

i, I- _{COMOOTE_I---- L I- STATISTICSI l

/

SOLUTION<< B / STPRG2 _ SOLUTION >

2 EPSI'ON (< I Mn< _ SG A

k I c"" MuD

1 '- (SIGn- SiGn.ll<,_o"_ TEST_

INTEGRATIONL 720--I I _SIG n

CONVERGENCE (

BEGINS EPHEMERIS I ,.t)J : 4

: ,, (_ PR,NTS=MAZ T_'TRMA×

LOAO t LOAD 1 I LOAD I VALU, j. [_

RESIDUAL AND t EPHEMERIS J RESIDUAL

EPHEMERIS 1 WRITE IWRITE TAPES j TAPE ONLY L WRITE, TAPE ONLY _- WOT SIGMA _ OUT

I I i ' L. _.-_,_ATEjWOT I

INFORMATION COUNTERS I

I ' 1 'COUNTERS W(JT

STATIST iCS

I •I SET 1 1 RETURN TO MAIN LOOP=_POINT

EPHEMERIS WRITEII RETURN TO MAIN LOOP POINT

WOT "_ FOR EPHEMERIS INTEGRATION AND WRITE3TATtSTICS, JSUMMARY

Fig. 3. Program PLODMN convergence and tape writing chart

e

15

i

1965019622-020

lira I

,!. JPL TECHI_IICAL MEMORANDUM NO. 33-188!,

3

IENTRY READ _

L COMMON _FO_xYz, ,_k_

}

I ® .oTAPESSOURCE 1 @ ®

DAlE s < DATEc _,

i 1L TAPE -_K TAPE _

I COMPUTE ] 4.&x / !

I

'r ).=4 _ WRITE i'

i /. TAPE

I CALL _

" ROTATION _ _ _ '-SUBROUTINE '_

L

_ q

COMPUTE _

&p &x &B {

CHECK PRINT _-P_ _T._ -- "'

I i.

& ,CONVERGENCE

<"_ "" ""'_,,_f WRITE TAPES?

;;" =ili CON2' VERGENCE;_' RE"r IRN_4,

' Fig, 4. Flow chart for subroutine TSTOP

.%,,

p,,

. ; ,, _

1965019622 021

i ii _ I

im

T

4; .JPL TECHNICAL MEMOr, IANDUlV' NO. 33-f88P,

The Common Region Must": Contain M_#,N,OP_ -r,9, to, xt3:

.v,z, k,i,, _, _, (i),/ _(i) is,_;(/), i_l(i)lB

Save Index Registers I!

.'._: For Error Exit

i '

Compute and Store I

Const.nts involving ii , _,j

FLAG W0 Indicates IzMt FLAGI:First Iteration

Sat Gatel and indexing / ICompute and Store M I Pick Up o_d Store

for Chosen Integration L,.._ : Dependent Indexing i_ , Addresses of UserOption ] i Parometlri Provided Subroutines m

f :0 S=t Gates and Indexing_ to integrate Equation

of Motion 0nlySEM

Set Gate. and Indexing _ j., .o...oo. o, It¢ Integrate Variational _1 Tell Type Gates -(I-V) (u-J) '_BUFF 2

' IEquation LogiC.- _ I

DER2

Oarivatlvls at --------- _ .

50_COUNT Second Sum Computation "Inffiallzatlon Point

RLIST

i Fig. 51a). Flow chart for subroutine FORTSZ[ ",,"

1 17 ',_

t

] 9650 ] 9622-022


ST _$ 'J'*)] Compute T,-nes

BT (n) [ Neededfor StorhrRI i :0ill M L Nel

l -

l,TM

BeginCom_u,m Toylor's I -/¢ _mox

Series Coefficients ,r L 2.S_BDI+2= u mox 1

SEM.5 l

i -- TEMP r z _ BD1Vz _ T_._3_+2

?/r --_TEMP I c0:-2o:e _ 80 d -3o z (2oz-(I-FV.VIZ-4oal) -rz/_ 2 --TEMP +t, q --II _:-eos--eo+l- [ --eo+2

1c4 = -OzlOliI6OZ-_J.%.SlF--__, 40211 {O31 (157.5 1--_1z CS: -Os(35(r) 2 ,32o 2

�3.75(_Z2"_4oz)' }. (69.4) -t05(rV----:+ 4o,))-_ -15 ((-_) z .4oz))

1 --BO+4 l -233os) --aO+4 --BD+3

,,,:<,,/_- eo_._ os:-_,o,,,o+,',,,:,+<,ll:O I 1 ]

,,:o,I,-,o_.,o,:-<o,..o+.,v= -- °":'<°°°""°"='°"°'Y'°I,,.:.<.o._-=,>/_o _ '>°='<'°°'i""+"/"°

[ ""°r'--'°tCompute First Approximotion 0 _ i

|o All DependentVoriobles i

Fig. $(b). Flow chert for subroutine FORTSZ )i

i

IB [_

I

ill

1965019622-023

TJPL TECHNICAL MEMORANDUM NO. 33-188

I"; (t S -- tS)k

@4 _ (BT(,)-ts) k NOTE;"_ Vl .-_ 8D3(k) A Subscript S Denotes o

I K =- 1(1)5 Starting Point Value

6

= ok(,:-,,)' I ek=O g = :E bk(ti"fs)k

_.oz(t' _ts)z _lI k=0i -_ TEMP + 4---_TEMP + 5

S5

_! =0_ u(t,.) = T. us + gus

.! + _ (t; _ r,)2/2

, II

: I f:_'+°2 I luV,)Denotesx(f,.),y(fi),z(t;)

'; SVI_. _ [ Taken Each in Turn

-: [ 1_- 'f vk(ti): f " Vk(ts) + gvx(ts)'; [ J =, +1 F" k :t(1)18

>M xs, y_, zs, --P _ Save xs, Ys,zs,

_1 BX Array _;$,Ys, zs, in TEMP

SV2 I

' I vi(t s) "-_ Array LBV 1,i =!(1)18 I_

" Start Loop to GenerateDifference Lines for

Equations of Motion

Fig. 5(c1. Flow chart for subroutine FORT,4Z

i;19

1965019622-024


*as ,Vws Z#,

SLOOP,_ ' _- Arrays XOL,BUFF -_

---. x, g Z, r _.

oz. i_/ o_.comp.,..\ "

This Computation II SI3 ;

: ,BoadUponThoForrr.ulo ,/. ,i, _i. _ I| . HS_-V )m'v U , i: i+1

" :-Zn u.-V)'" .-a --- XDL.CUFFI !I ;i s28 -..

._,,,,v_,,,,on,v_,,, ,,.,,,,.Iv"_'_'_"_ I_ > -< _"Array XDL ';

L H 1-oI :0 (t)M ]"

,:. s3_, _

/u.eSCALRtoCo.p.t.\ __'0 '[ 1

• _V'_fi).V_'(,i),#(#i) _}__ > 0 "-" FLAG- _ Using the Relatmn /

. MAX(IVI,.V/.tU I) . as.ors..,.,onaz.t .AX(IV/_11 -- j Denotesitlrotlonthe _'....

I i _.-2_.* i' I ThlI CamlPutotto._is

,- u-.'--u"II .,.-., I:, _ .oca.ve,o.°o. _I u'= ' Z"I (4"-V| I ( C°nverw'r'ca r: _-

,_Converg..;" I Set Exit COte at S65 _ " IP

S43 _ -- *

Use SCAL_ to Compute,(t;_y(t,_,#(n) us,ng V_',V_y,_'_, ;-

: thaRetatio. _SSI ! /,-2(,)M

/-u,,-a-/"Hs(t-?}_._.v. I----OOArray .-z,,a--'-'_-W

' ISave Difference| for |

Convergence Test i_2

, Fig. 5(d). Flow chart for subroutine FORTSZ

_,o

1965019622-025

L

? JPL TECHNICAL MEMORANDUM NO. 33-188

X : Converged _ .

: _ X: Not Converged

Branch X

t Cc m-F

VAR

'i _ :p-- _fs_>, roo,,,,-r-,• - \._/ /-_cou.TI

, Ko[ io_" qegin Iterative Procedure

[_ Obtal'l Difference Lines I

i Lo._oo-"' @" UNT,!

_._ I The Variational Equations

_ DER4 Satisfy the Natrlx EquationDe :.4V Where Error Code' ,//GoToDE, W,th ,:.t. _ * MO

_;_ (/to Obtain Matrices A (ti) ___. O is The Derivative Operator, 2's Complement of : :J

Xi:O(I.)M and Save in / A is o3x3Matrix Frovlded by

_._i \\Array A if I_e(M-J)// WhoseDERand18YEiv,,,lntslso 3XGoreMatrixThe Error Address -I_AC

Compute the Second \ PETURN /

Derivatives at the Initial to

Point and Store In BDVI Main

' , Array

_* Fig. 51e). Flow chart for subroutine FORTSZ

-" 21

i-

1965019622-026


VS13 V S 2 0

i : 0 (1) M an_l _ _ _ Line Obtained inExcept i :M-J j:2(t) t.8 Previous Iteration

_BDV1 Array --- BOVL Array (

VS42

end ,.

_VIOL Array J : 1(1) 18 j=l(1] 1.8 -_VIOL Army -,_VIDL Array :.

vs48 ; _ !

V-zi'_; J : 1(1) 18 L 1 _VIOL Array Make Convergence _.Test

VS57 VS65

_E0 --1 Compute Convergence J Coen Exit Gate _i--I Test Element EPS I _ --| At VS82 "

I L

: It

q --," ---." COUNT -,

J

F o-!VS75 I r_

,,ssz V i

vs.,, ,_onva,,..c.T.,_; 1

V_(Tm. j] / : t (_,} 18 --_ V Vector _.- Y_'/ Y" zN-i Z! tu-i r 1

i

0 "_ $ _

M "_ STPCHG0 -" DTAPE

4M+4 -,4. 4M4

_i_ Fig. 5(ft. Flow chart for subroutine FORTSZ

.=

m

1965019622-027


SEAR

= "°'TS MIN I' iCurrent TSTOP Time

LESS

' IADDR (Subroutine TSTOP)

-_ TSTOP

1I lnterpolotion I

FIog--'_ FLAGI

o,i

, /Go to INTRP TO' _ Compute xltel,y(t'#) _

i \ ,(,.) /I

:: /Go .o,.....o\ _ t ..., ,, .,.. to

'1 _Compute _'(,;1 )_(t,) _'_ #: 0 Interpolate for

i \ i(ta) J Velocitlel

i I TSTOP

'[ _ Go Moke TSTOP_Exit TO Current /

'i TSTOP Routine /

:t,f

[i

Ii Fig.5(g). FlowchartforsubroutineFORTSZI

,Ii 23

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1965019622-028

JPL TECHNICAL MEMORANDUM NO, 33-188

• ti For Notutionol Convenience[, ^^c='_,... ,.J Define u/AI c 21-Element

\_.r/ --/Vector SuchThot.,.., .,: :,y [u a -" •end ul: vl.si: 4(1}2!

R_ 1: L00P T

l Go To RLIST

For New Step

Size

i [ IHelve Step "{he Step Size

Size Test If Possible

i I

...F I .P0S.T', o_ "

[ 2" DTAPE-M _ > _#0 =o _'_'- (DTAPE+M)//2

: "=. DTAPE -'=" DTAPE

' I 1I Hnew = Hold

t 1 'MAX 10, DTAPE) q

•-=- DTAPE

_os_r , ,

TheP,e,ioue*ySoy. Let,. BeTheI ( _os )-.--[ ".rido,,,up" ,,Derivotivee Are Reordered

On • Double Size Reetriction Current Time _ / Routine

, I

.,2 I DBLI

I_ > '

_Teb) old, i:-2111M iii(tn.l),i = 012) _ I t'-q"j--- BUFF 2M*2--,-.UFF2 _ I r _"

_ r_I_;(t_.,),,'.o(2)2m _ _"I +2 "*" XDL, BUFF1

DBLJ2 <. DBU.S

_ L+ / "-P j . _ /=1111 3 OR21_ -4,. XDL Arroy

'_ Fig. 5lh). Flow chad for subroutine FORTSZ

g o

_, 24

• ., ,, ,.' , .

1965019622-029

• L

,JPL TECHNICAL MEMORANDUM NO. 33-t88

DBL23

I Hol_

t DBL24

_-IUj j=l(1) 5or21;" ---" XDL Array

DBL32

l

_ XDL ArrayIDRL3B

i (/*Branch on Holvin'g_

_. or Doubling )

[

;[. MVIG_,[ Rsset Gate• _ At DBL50

• I:iHV30

_" RLIST1 HV18

et Next Hne_/ v - _ ,/'=1(1)_3BuFFor21

, >

_j(,..,),_=o(_)_,', j =1(1) 3 or 21

--4. BUFFI

DTAPE =MAX [t

Vl I

o,, i '''"' --Fig. 5111. Flow chart for subr,_otine FORT.C.Z

"! 251 •I ;4

1965019622-030

JPL TECHNICAL MEMORANDUM NO 33-188

HV4

HVt /Use SCALR°ridpra- \ _w.,,, �_.m

_-----_ Coefficients to Compute )\V",.,.,. ,':1el)M,j:lC_) / vl

- , \ , or2_ /

_ L2 _

HVSO Integrote One Step By Meons

_H_ _ 0 a'CSA#E J1 I ui(t*'l):/'/2"_' !tn! / of Th. Gau,s-dock,on 0p.n

v M DSTrJCHG| _ ('l-_)_nl(l-V) I .... Formula Define ta As The/:1(1)3or21 | Current Value of The Independent

l [ Variable .DER ' .

L9

Seco,:.t Dsrivutives At _ t_H:tn+H-4"T: tA ,� �.

I ') ,

L_O i_

Vldj (tin), i:-2(1)M, l Save Current Difference i

--_ _ Lines for CorrecterComputationj:t(l) 3 or 2t-'--_BUFF 3 _ :"

L22 1 L29

Ccmpute J Compute J

_7(bj• (',,,4) i:-2(1)-t _---_!'_idj (fn*z), i:_.(I)M

j =t3)3 or 2_.--_ X13t.Array _J"=1(t) :5or 21 --_ X DL Array

Use Gauss- JacksonCorrectar

Formulo to Improve Answers _ uj (to+l): H 2 u(1

DER 3 _ o_ _

, / DER Computes

\ Im_rovad SecondDlrivativoz _"

-, Jr_ ' - _.

I_l/t/ (tn.t), I:-2 (I)M

j=_(1)3or2_ _ XDL I i_

Array _ _"

Fig. 5(j). Flow chart for subroutine FORTSZ

:_ 26

. .,. ._;,y_.:.!.:_ m 3_',_

1965019622-031

Ii=


- M-_DTAPE of TheLo,_tSavedI SecondDerivative

;tO 1 IDTAPE-1 1_DTAPE _ _ 4M+2_ CSAVE

_ CSAVE

", , /.82

: L90 _,

• [• u],/ : 1_1130r::'1_BUFFArray

Fig.5(kl. Flow chartfor subroutineFORTSZ

F. Main Program and Subroutine Descriptions a. Purpose.

PLODMN is the main controlling program of PLOD II, PLODMN serves as an input/output program andwhile the main integration routine is FORTSZ. FORTSZ, driver for the subroutines used by.PLOD II. The pro-with its related subroutines XPAND, SMULT, SCALR, gram computes the needed constants for the integrationand INTRP for PLOD II has been modified for the procedure, controls the subroutine execution order, testsIBM 7094. That is, DPARTH and the macros f,_r the 7090 for convergence and number of iterations, and contro!s

versions are no longer used. the input/output. PLODMN is the primary logical frame-work or outline of the integration procedure and callsthe subroutines for special computation when needed.All of the major computation on the ephemeris integra-

l tion is done in subroutines called by PLODMN.I. PLODMN

l Multiple precision driver for tl, special perturbative b. Method.I integration technique. C. J. Devine, JPL1 The method of PLODMN is essentially thatof PLOD II,

i Machine: IBM 7090/94, Language: Fortran II and is described in the general outline of PLOD II.

" _ 27

1965019622-032


c. Usage. EOSER The er,d of step routine.

Given an ephemeris _f a body to be integrated and a ERRER The error routine called by FORTSZ.

source tape of perturbing bodies (generally the other FORDV The communication routine foreight planets) PLODMN reads the orbit input informa- PLODMN and FORTSZ.tion and starts an integration by calling appropriate sub-routines. It is to be used with an input deck (described STPRG2 The DP stepwise solution o{ normal

earlier) and the other general programs that make up equations routine.

PLOD II, which are described below. ELEMTS The DP transformation routine from

rectangular coordinates to elementsd. Remarks. a, n, e, i, f2, _, 1.

_, PLODMN is the logic of PLOD II and was designed OBLIQ The DP routine which computes theso that if there is a future need to change the control of obliquity given the Julian :]_tePLOD lI it can be done easily. Similarly, if there is a

SPHER The DP routine used to compute lati-need to cha_Jge the method of computation of PLOD II, tude, longitude and p. given rectangu-th;: may be done in the ;ubroutines called by PLODMN, lar coordinates.and thus leave the logic of PLOD II untouched. The

above description of PLODMN ._.snecessarily brief, since ARCTN "fhe DP arctangent routine, used as aall of PLODMN is essentially outlined in detail in the driver for FORTRAN library subrou-flow charts and description of PLOD II. PLOD II is tine.

: defined as PLODMN and its related _ubroutines. RUN Rewind and unload tape routine.

:i DOUTPT The DP output routine ,:ibrary tape).• e. Subroutines required. DPINPT The DP input routine (library tape).

: FORTSZ The Gauss-jackson DP equations of DCOS, DSIN, Fortran library routines.-.i motion integration routine. DSQRT

i XPAND The DP coefficient generator forFORTSZ. f. Storage.

SMULT The DP series multiplier for FORTSZ. All computable qaantities are stored in DP. The pro-

SCALR The DP inner product routine for gram communicates with FORTSZ through commonFORTSZ. storage, arid the description of this storage may he found

in _he following Section. The main quantities communi-_" INTRP The DP interpolation routine for cated by PLODMN in common between its subroutines

FOR I'SZ. and FORTSZ are time, integration step size, and position

TSTOP The DP residual computation and and velocity coordinates

ephemeris printing routine.

STINKS The DP system increments rotation 2, FORT_Z

r,aatine. Gauss-Jackson DP equations of motion integration !_SET32 The DP routine which computes the routine. J. H. Beeman, Computer Sciences Corporation,

matrix of partial derivatives. August 1, 1982

SETUP2 The DP accumulation of normal equa- Machine: IBM 7090/94 FAPtions ,'outine.

._ CORECT The DP routin*, which corrects the a. Purpose.:i osculating elements

*!_' TRANSX The DP transf_rmation routine from FOaTSZ is a closed subroutine designed to solve the"' equations of motion (in ret._angular coordinates) of a

"'_ elements to r_ctangular coordinates, body _n a grav'itational fieid, and, if desired, to calculate _: DERIV The DP acceleration rotdine, the first-_,rder variational eoe_icients of the computed *

_:: 28 ;,

2L,

, i

1965019622-033

L

¥


-_ trajectury. The integration is accomplished by either the ¢. Method,

Gauss-Jackson open formula or by utilizing the open A Gauss-Jackson procedure is employed to accomplishformula as a predictor and then applying itz closed coun- the integration*. Step size is controlled by a user-codedterpart as a correctnr, the formulas are in terms of back- subroutine, but step size changes must be limited toward differences. The order of the differences employed doubling arid halving. The following options are availableis optional within the limits 1 _ order of the highest to ,he us ,r:retained difference _: 15. The routine employs 7094 com-

'_ patible DP. and is intended for computation with the 1. Integration method._. 1BM 7094 as well as the 7090. Provision has been ma:le

for interrupting the computation at prespecified values Gauss-Jackson open formula.of the independent variable, as well as after each step. Gauss-Jackson open formula and improvement of

: the c6ordinates by one application of the Gauss-Jackson closed formula (note that no improvement

b. Restrictions. to the difference lines is accomplished).

1. FORTSZ will not integrate backward in the inde- Gauss-Jackson oper formula as a predictor ar.dpendent variable (the step must be positive), the Gauss-Jackson closed formula as a one-cycle

corrector to improve both the coordinates and the2. Change of step size is limited to doubling or to difference lines. A more detailed description of

halving, the numerical procedures is contained in the Section

3. Undertow and overflow are not c_:ecked internally, devoted to formr, las.

2. Order of integration protedure.4. The user must provide the desired interruption sub-routines, a prograr- to compute the de_.,redstep size. The order of the differences to be used mayand a derivative subroutine to compute the second b,z specified by the user between the limits ofderivatives of the equations of motion (and of the 1 _---M_ 15, where M is the highest difference re-variational equations, if required), tained in the calculation.

5. FORTSZ is a FAP coded subroutine which is not 3. Starting procedure.

_ Fortran com-_atible. If Mth differences have been chosen by the user,

_' 6. FORTSZ is intended for use with the IBM 7090 then the starting procedure must generate a net ofat.d, vfth minor modification, the IBM 7094. M + 1 points by utilizing the give_ initial, position

and the differential equations. The locatien of the7. The class of differential systems this program vail initial position in th_s net may be colatrolled by

;olve is limited in four basic respects. First, the the user t', maximize the accuracy of the startingGauss-}ackson equations are valid only for systems procedure.of second-order differential equations in which thefirst derivative term is absent The seoond limitation All calculations are performed in IBM 7094 com-concerns the starting procedure. A single precision, patible DP. The DP is accomplished in the 7090modified Taylor series solution to the two-body version by a special set of macros which simulate .

problem is employed to obtain a first guess to corn- 7094 DP instructions coupk _ with a DP arithmeticmence an iterative procedure for obtaining DP sab, o'_,tine.

i difference lines. If the solution of a set of equationsin the region of the initial conditions is not "sufli- d. Usage.ciently close" to that of the two-body problem, the 1. It is expected that this program will be embedded

•_ starting procedure will not converge. A third restric- in a system of the following general character: Ation is that only three primary and 18 secondary "driver" will call FORTSZ. Control will return to •differential equations may be solved by this routine. that program only if an error condition occurs. PriorFinally, the three primary equations may not involverl,e secondary variables. The restrictions contained to integrating each step, FORTSZ will sunender

in thi_ _a:_-gr.aph ,'_11have little meaning for the 'Jackson, J.,"Note on the NumericalIntegrationof d_x/dt_=f(x,t), ''user as long as this program's appli_:ation is limited Ro),alA3tronomiealAstronomyqoctety Monthly Notices,Vol. 84,

to the problem area ,'."orwhich it was desig:r_d, pp, 602-006,1924.

¢9

t

I

1965019622-034

JPL Tff.CHNICAL MEMORANDUM NO. 33-188

coutrol, first to one of a set of subroutines desc:'ibed ti_ from the data in T, X. Y, and Z (andbelow as T stops, and next to a user subroutine V(i),i= 1(I)18, if N=I). The corn-called the "end of : :ep" program. The first transfer puted values of these derivatives mustis made only at prespecified values of the independ- be stored in locations XDD, YDD. andent varip.ble,while the second _ansfer is made each ZDD (and VDD (i), i = I (1) 18, if N = 1).time a step is completed. In this manner, the user In the event N = 1, the following con-is _lowed to make use of the results of the integra- vention is to be observed. If S = - 1 (seetion in several ways if he so desh_. Section 5 for location), then DER need

compute and store only the second de-2. All numerical data used by this program are ex- rivatives of the positional varial_les. If

peered to be in FORTRAN I f compatible form. This S = + 1, DER must store the elemen_means that arrays are forward stored, that the low- of the matrix denoted as the A matrix

order part of a DP word is stored directly above its (in the later Section entitled "Variationalhigh-order part, and that fixed-point quantities are Equations Starting Relations") in theexpected as full-word integers, communication region array MATRIX.

If S = 0, DER must compute and store3. The quantities M, ], N, OPT, ES, T, X, Y, Z, XD, both the positional and variational sec-

YD, and ZD must be stored in the commut_eation ond derivatives in XDD, YDD, ZDD, and :region prior to execution of FORTSZ. A detailed VDD (i), i :---I (1)18. Whenever S _: 1description of the _orm and meaning of these quan- (S = 1 only while generating the initialtitles is contained ii_.Section 5. variational difference lines), ff,e array

MATRIX may be viewed as temporaryIf N = 1; i.e., if the variational coedlcients are storage allocated to the subroutine DER.

to be computed, the user must also supply initial

conditions for these coettlcients. Thus if N = 1, the EOS Th_ entry point address of the user'suser must also initialize the storage vectors V and "end of step _ routine. This program isVD. It is noted that once FORTSZhas been entered, called after each full integration step inthe user may not change any of these parameters order to return control to the user. Seewithout restarting the integration rontine, the discussion of DTAPE in Section 5.

4. Calling sequence: BLIST The entry point address of the user stepCALL FORTSZ or TSX SFORTSZ, 4 size control routine. The program must

PZE DER,, EOS leave the desired DP step size in the ACand MQ each time it is called. The most

PZE BLIST significant part of the step size is to be

TRA ERROR placed in the AC. The step size currentlybeing used by FORTSZ (except for the

PZE TSTOP1, F1, TS1 first entry after execution) may be found

PZE TSTOP2, F2, TS2 in location H. Step size may be changedby halving or doub.qng the ctwrent step

...................... size only..',_ the step size is changed,

FZE TSTOPN, FN, TSN FORTSZ will be unable to double thestep size within the next M steps. Re-

PZE 0 peated halving is permissible. FORTSZwill continue to halve the step size, with-

whexe the symbols are defined a_ follows: out advancing the calculation, until

DER The entry point address of the user sub- RLIST no longer signals a desire to re-routine to compute the second deriva- duce the interval.tives of the Jel_endent variables x, y,and z (and those of the variational coeflL NOTE: FORTSZ WIUnot detect an at-cients o(i),i=l(1)18, if N= 1). This tempt to change step size tosubroutine must compute these quanti- some interval other than twice

30

1965019622-035

; _r JPL TECHNICAL MEMORANDUM NO. 33-188

or half the current step. If the The logic used to execute the T stops isas follows:it,': user's RLIST routine makes

• _ such a step size change, an un- Let t,_, t,_, t,a, " ' " , t,_ be a set of values of thedetected error will result, independent variable for which interruptions are

;_. desired. FORTSZ sets t,, = min(t,,,t,_,...,to_).• ERROR Tiae address to which the user wishes Integration continues until the independent vari-

• _ coo.trol transferred if an error condition able, t,, reaches a value such thatoccurs in FORSTZ. The return fromFORTSZ will be TRA 3, 4 with the 2's t,_ _< t, _ t,complement of the location at which the

, error _._ndition was detected in the ac- The value of t,, is placed in T. The subroutinecumulator and a fixed point error .,x_de INTRP is then used to obtain the values of thenumber in the MQ. The error code is as coordinates (and the velociti_, if F = 1) at t,,. Con-follows: trol is then transferred to address TSTOP. A"ter

: control is returned from the user's interruption rou-Error tine, the values of X, Y, Z, and T are restored tocode Error condition the values corresponding to t, and the next value

1 X = Y = Z = 0 are illegal initial of t_, is determined as before.

conditions. Comments on triggers.

2 Either M or ] is out of bounds, a. Any nt:mber of triggers may be employed. The1 -_ M _--15 or 0-----] -/llf variable length list is terminated by PZE 0.

3 The starting procedure for the b. Whenever a T stop interrupt subroutine is exe-equations of motion failed to find cuted, it must update the corresponding time, T,,a difference llne which satisfies or inactivate _e trigger to avoid an obvious

logical loop. A trigger may be inactivated bythe convergence test specified by changing the PZE to an MZE. A negative signES in 50 iterations.

bit signals that a trigger is to be ignored when

4 Same as 3 except applies to vari- scanning the list of T stops.atiopal equations, c. INTRP does not allow extrapolation. Let to be

• ' the initial value of the independent variable. If ]5 illegal T stop time. INTRP will is defined as in the next, section, and if the value

not allow extrapolation, of any T stop, T,, is such that

The final strings of locations in the calling se- t_j > T,,quence are all of the form PZE TSTOP, F, TS and an error return will result as soon as initializationare defined as triggers. These triggers are the linkage has been completed. Similarly, if the T stop val-controls to user subroutines which allow the user ues ace being updated, an error will result ff anyto take action at a preset value of the independent T stop is recomputed so that it takes a new valuevariable. These triggers are also known as T stops, smaller than t - M'H, where t is the current

' The triggers each state that control is to be trans- value of the independe.".c variable.fewed to location TSTOP when the independentvariable equals T,, the DP contents of address TS. NOTE: The linkage to all user subroutines is

TSX SUBROUTINE, 4.If F = 0, FORTSZ will compute the values of thecoordinates x, g, and z corresponding to T, and Return is expected to be of the formTRA 1,4

i store them in X, Y, and Z prior to the transfer. If[ ' F = 1, FORTSZ will also compute x, y, and z and 5. Comnmnications region.; store these quantities in XD, YD, and ZD. T will be: _ set to Ta in either ease. No procedure is available to The communication region is an absolutely lo-•_ provide intermediate values of the variational coeffi- eated storage block established for the exchange of

cients. :lata between FORTSZ and the user's routines. All

31

|

1965019622-036

JPL TECHNICAL Mff-MORANDUM NO. 33-188

parameters needed for the initialization (see See- is indicated below. As the origin of this region is :tion 3) must be located in this block before control easily changed, the user must determine what abso-istransferredtoFORTSZ. The statusofeachcell lutelocationiscurrentlybeingemployedforthe i

-- when either a T stop or an end-of-step exit occurs definition of the program location COMMON.

ProgramLocation name Description

COMMON M The fixed-point integer denoting the highest order of difference to be retainedby"theintegrationprocedureinwhichi--_M -----15.

+ 1 ] The fixed-point integer ccnlrolling the location of the given initial coordinatein thenet of positions generated by the starting procedure in which 0 L ] _ M. ..l = 0 places the initialization point at the end of the net away flora the diree- ,-

tion of integration. ] = M places the initializatior, po/nt at the position for _.which the backward difference lines are to be generated. Intermediate valuesof I position the given point between these extremes in an obvious maimer.

J

+ 2 N This fixed-point integer flags the user's choice in _gard _o the variational equa-tions. N = 0 means integrate only the three positional differential equations.N = 1 means integrate both the positional and the variational differentialequations. +

+3 OPT This fixed-point integer controls the integration method. OPT = 0 denotesGauss-Jackson open method, =1 denotes Gauss-Jackson pseudo-predictor-correetor method, _aad =2 denotes Gauss-Jackson predictor-correetor method. "..

+ DTAPE This cell is set by FORTSZ as a signal to the user's end-of-step routine If theuser desires to save a covering set of difference lines, the end-of-step program

must save all desired lines every time DTAPE = 0.

+5 S This cell is set to a fixed-point integer by FORTSZ as a flag for the user's "_derivative routine (see Section 4).

+6 ES The single-precision floating-point convergence test factor for the starting pro- ieedure (discussed in detail later). Note that ES may be either positive ornegative, giving two types of convergence test. ES is used by both the posi-

tional and the variational equations.

+ 12 H The DP floating-point value of the step size currently being employed by the

integration procedure is located in H. This cell may not be altered by the user.

+ 14 T Storage for the DP floating-point value of the independent variable. Initiallyit must contain the initialization value of this variable, to. At any later time, thiscell will contain the current value of the indermndent variable ccrrespondingto X, Y, and Z. This cell will correspond to the velocities located in XD, YD,and ZD initially, but thereafter only for a T stop with F = 1 (see Section 4).The value of this cell will correspond to the diFerence hnes located in XDLand VDL for end-of-step exits.

+ 16, 18, 20 X, Y, Z Storage for the DP floating-point values of the rectangular coordinates x, y,and z of the body whose trajectory is being computed. Initially, these cellsmust contain the x_.,y0, and z0 corresponding to to in T. These cells alwayscontain the coordinates which correspond to the value of t contained in T.

32

q9650 q9622-037

_ JPL TECHNICAL MEMORANDUM NO. 33-188

Program_:_ Location name Description

i _ +22, 24, 26 XD, YD, ZD Storage for the DP floating-point values of the velocities k, _, and _ of thebody. These cells must originally contain the ko, _o, and r,0 corresponding to to.

, _ These cells are updated only if a T stop is executed with F = 1 (see Section 4).

+28,30,32 XDD, YDD, ZDD Storage for the DP floating-point values of _, _. and _,"which must be storedi in these ceils by the user's derivative subroutine as outlined in Section 4.

! +34--68 V Storage for the 18 _P floating-point values of the variational coefficients_'T v (i),i = 1 (1)18. Thes: cells are unused ff N = 0. Initially, V must contain

| the v, (i), i = 1 (1)18, which corresponds to to. V v,-ill contain the values of v• i corresponding to the t contained in T only for the end-of-step exits.

l

[ +70-104 VD Storage for the 18 DP floating-point values of the first derivatives,• ! 6o(i),i = 1(1)18 corresponding to to. These cells are used only during the

initialization procedure and if N = 0, are not used at all.

+106-140 VDD Storage for the 18 DP floating-point values of the second derivative,

l i_(i), i = 1 (1)18, which are computed by the user's derivative routine. These

• cells are unused if N = 0.

+ 142--158 MATRIX Storage for the nine DP floating-point elements of the 3 X 3 A matrix describedl in Section h-3. These elements are to be computed by the user's derivative

subroutine during the starting procedure for the variational equations. Thederivative subroutine may use this space as necessary at all other times.

+160-194 XDL The M + 3 DP values of the differences V-z_, V-'£, i, _7_, • • • , VNE

+ 196--230 YDL Same as XDL except that it contains the _ difference line.

+232-'266 ZDL Same as XDL except that it contains the _"diEerence line.

• + 268--914 VDL This block of the communication region conta_v,s the 18(M + 3) DP values of• the 18 difference lines V-_b',, _7-aiJ_, iJt, _Tb'_o'--, Vxb'i, i = 1 (I)18. The

array is not packed, i.e., the _7--'/3_,_term is always 18 DP locahons abovethe term V-2;_.

i +916--3100 BUFF Working space required by FORTSZ. It is noted that the block of storageactually used by this program will be smaller than indicated if OPT=l=2. Inthis case the user may provide for a smaller s_zed buffer region. If N = 0,the upper limit 3100 may be replaced by 2408. If N = 1, the upper limit maybe replaced by 2408 + 18M.

e. Space required, f. Coding.

i The IBM 71290 version of FORTSZ requires 2768 This program has been coded for use with the IBM(5320_) storage locations. The user must allow for the 7094 as ,_,ell as the 7090. The following changes must; communications region described under USAGE, Sub- be made in the source program to implement the 7094i routine SCALR. The 7094 version is smaller (4752_) as capability: Remove all macro definitions from FORTSZ,

one instruction will replace each two-instruction DP SMULT, XPAND, INTRP, and SCALR. Cheek that the"macro in the 7090 version. DP storage in these routines (and the communication

1

33 _,!'

_,o-._:,_ ,.,_-,c,__., ,,_,_y,,, u _; ';; _ , ',

1965019622-038


• i

h,(_- V)" .....region) is cempatibl_ with the final spedficatious for u(t.__) =-i-_n2_--L--_.u(t.)_ 7094 DP storage. It is expected that this will involve nomore than adding a spacer to insure that the DP storage

starts in an even cell. No other changes should be needed. = h'_ i f,.kV _ff(t,) (A-4) _The subroutine DPARTH will not be required by the _o-2

7094 version of FOBTSZ. where _7°/i = _, 7, is the step size, and n and k -_.

g. Subroutir_s. are integers. Equations (A-3) and (A-4) areeasily ,;derived by c_mbining the meth')ds _f Ref. 7 and _

FORTSZ uses the auxiliaxy subroutines DPARTH, the properties of the first and second sums. _.

SCALR. XPAND. SMULT, and INTRP. These programs It should be noted that k = -1 produces an 2,have been documented separately. In addition, tht, user - Lmust provide a subroutine to evaluate the derivatives, open integration formula, k = 0 gives a closed ,

integration formula, and values of k such that ""one to compute the step size, and an appropriate end- 1,L k provide formulas for computing past values !_of-step routine. The presence of T stop subroctines is of the variable u in terms of a difference line at t..optional. The requirements for these user-ceded programsis detailed under USAGE. : The coeSleients dl,k and f,,_ exist in this pro-

gram as prestored constants for all i such thath. Ba_ formu/m. -2 _ i _ 15 and all k such that - 1 _---k--_ 15.

I.Gauss-Jackson integration formulas*

2. Taylor series solution of the two-body problema. The Gauss-Jackson method is usually describedin terms of a single central difference formula It may be shown (see Ref. 3, Chap. 1, Section 30)(Ref. 8). The primary idea which sets this pro- that

eedure apart from other similar integration _methods is the definition and use in computation R = Ro _ aj (t - to)j +/_ _ b i (t - to)jof two inverse difference functions. For the pur- J: ° j=ol_wse of this discussion, any integration formula (A-5)which makes use of this inverse difference tech- / x \

nique will be referred to as a member of the where R = / g ) is a solution of R- -t_RGauss-Jackson family, _us enlarging the scope r_ 'of the more normal definition, z

These inverse functions are defined by the r ----lal, and/L is the gravitational constant. Capitalrelations letters are employed to represent vectors and

matrices in this section.

_7°_u. -- V"u._, = u. (A-l) By truncating this series with i = 6 an approxima-V-_u, - V-_u.-, = _7-_u. (A-2) tion to R is obtained. The coefficients aj and bj are

computed as follows:The operators _7-* and _7-, are called the first

and second sums. (Ro,/io) _ ;:oa. p- _.,

b. Two basic Gauss-Jackson formulas are employed" ro .

, in this program. These are: where (Ro,/_) is the inner product of Ro and R0.

h(1- _)_ _(t.) _ot_(t.__)= --_,,ff -v) h. r,_= p' = --

= h F, d,,_V'//(t.) (A-3) " " .r _.-_ c. p, = (Ro, Ro) _ 2__._= V_; 2_

i "ThenotationemployedinthisSectionis definedhadetailin Bd. 7. d. ao= b, = 1, a, = bo = b_ = 0A familiaritywiththis referencewillbe assumedthmugbout.Sec-

_ tion 5.5 c_ntainsa developmentwhich is very much like that P a, a:,neededto obtaintheabovefonmdas, e. a_= - _ as = -a_p b, = --if- b, = --_

._ 34.

mtr,m,_m_ -- : _ _: _-\_ _ __ ,

1965019622-039

L

.... JPL TECHNICAL MEMORANDUM NO. 33-t88

f. Co --_ -- _ or

,_ cl = -6a, m_R= -__R°_, aj(t - to)i

_ + _ "k,y'=obj (t - to)' -_ D (A-7)

_, c, = _- (p (157.spl- lO5p,)- z3_)! A first approximation to the matrix may be ob-

• _ - a= (a= (16a_ - 15.5p=) + 3.75p2=) tained by computing only the first two terms of

1 Eq. (A-7). No attempt is made to justify neglect-

g. a, = - -_- (coth + c=) ing the term D. D is deleted onl 7 to simplify thecomputation. It is intended that any first approx-

, 1 imation will b_ improved by a subsequent itera-as = - _(_ (cos3 + c_a_ + c_) tive scheme. This computation thus need only be

: _ 1 close enough to the actual solution to make the

: a6 = -- -_ (coa, + caas + c..a.=+ c,) iteration converge.

1

b_ = - _ (cobs + c2) 4. Starting procedure convergence test

An iterative procedu e is employed by this pro-b+ = - (cob4 q-ctb3--k cs) gram to generate an initial set of difference lines_7i/2i i= -2(1)M, ]= 1(1)3 or 21, where the 3will be used ff the variational equations are not to

: 3. Variaticral equations starting relations be solved. The dummy variable u, is thus defir_l

as ua=x, th=y, u==zandui=vi_ai=4(1)21a. The first-order variational coefficients 3R/'dwj, to simplify the notation.

where {wj} = {xo, go, zo, io, _)0,_}, may be writ-

ten as the 3 × 6 matrix After each iteration, compute for each difference

,V = (_,j)= (_RaJq_, _yo' _Zo'_R_fCo'_R_R_Rloyo""_ line generated, the factor

1_ E, = max I (v';j"'' - Vq/o'd) I; It is demonstrated in Ref. 9 that there exists a -"-"---_ I max _7_ Ii symmetric 3 X 3 matrix A such that i -_-,=i-_=

! _V = AW (A-6) over all applicable i. Then letI

t where .4 is not a function of the elements of W. E max (E_).f t

: I It is noted that A is the matrix which the user's,!

derivative subroutine must compute and store in This routine decides that a sufficiently accurate setI the array MATRIX during the variational e:lua- of differences has been generated in one of two', tions starting procedure, ways:

, b. Consider Equation (A-5). it follows that a. ES positive. The iteration will be terminated as:i

• _ _/_o _ soon as E < ES, where ES is the input parameter

.: _R _ _Ro _ a, (t - to)' + _ _'=obo (t - to) defined earlier.

_. _ b. ES negative. The iteration-will be terminated ff1 + Ro _----o_w_ (t - to) _ E < IESI and ff E._a - E,,, = 0. The second

' - condition permits the user to obtain, in most

• _b_ cases, the best difference lines possible withoe •+/l_ 2 _-- (t - to)'_=. Cto_ needing to pree2sely specify ES.

1965019622-040

_" JPL TECHNICAL MEMORANDUM NO. 33-188LF

5. Changeof step Once thesenew differencesha__ been computed,a schemeidentical to that used in doubling is

a. Doubling employed to obtain the new first and secondThis routine doubles the integration step size sums. The formulas are

by saving enough of the previously computedsecond derivatives to allow a straightforward V;_ _, (t.) = 2 V; 1//j (t.)computation of the double interval differences

M

V/_hi/j, i= I(1)M, and all ], by differencing. + _, dk,o(2V_it'j(t.)-"_/.,iJjt.)This means that the last 2M + 1 second deriva- _=otives of each variable must be available before

4u_ (t,,) ua step size increase can be made. As M + I see- _77,_.,;2s (t.) = _ [_,o V_t_//s (t.)ond derivatives are implicitly contained in the '- h: k=.difference lines, this implies that M steps mustbe taken after the initialization or after each step i. Method.

change before the step doubling procedure may 1. Fi:st approximationbe executed. Any attempt to double the stepwill be ignored until the requisite derivatives Equation (A-5) is used to obtaha a first approxima-have been computed, tion to the positional coordinates and variational

-. coefllcient_ on a net of M + 1 points. The varia-i ..

Once the double size differences V_ uj (t.), tional coefl_ei_"_ts_.re generated under the approxi.'-i = 0(1)M, all i, have been obtained, the first mation noted tn Section h-3 by.replacing Re and Rosums are computed using Eq, (A-3) and the fact "inEq. (A-5) by _l:to/_W_and aRo/_U"that the first derivati-ze of a variable at t_ must

z. Coordinate improvementbe the same when expressed in terms of eitherthe old differences Vi t_t (t_) or the new differ- The first approximations to the M + 1 vaiaes fences _7_,//iLt_). The actual relation is x, y, and z allow the compatation of the second

! derivatives of these quantities at these M + 1 points.! 1 , T'- second derivatives are used to compute the

V:.,]i/i(t_) =_Vg //j(t_) required _ifferences _TiZij i = I(1)M, J = 1(1)3.Let _,- .nitial values be denoted by uj (t,) and

+ E ,tk_ g V_ii_(t,) - V_ iljt. ;_(t41;=0The first and second sums of u_(t_) are then given

Finally, the second sums are computed using by Eqs. (A-3)and (A-4)asEq. (A-4):

V-q/_(t_) =- t_(t,) E d, V'ii_(t,), i = 1(1)3uj(t.) _ _=.

VS_ fit (t,) = 4h_ _ _, oV_, _i_(t,)=-_ and

b. Halving _7-_ii#(t,) u_(t,) u= h_ 2 f,.... v%(t& i=_(_)3Halving is accomplished by computing the half i=-t

step differences, Thus a complete set of differences is obtained foreach coordinate. Equation (A-4) is next employed

i V_,,: _ (t,), with k = 0 (1)M to generate a next approximation

: i = 1 (1) M, all _, from the following subtabula- to u, i = 1 (1) 3 at each of the M + 1 net points:_ tion formula (see Ref. 7, Section5.7): The convergence test described above determines_" whether the iteration is to be terminated. If the itera-_ tion is not to be terminated, a new iteration, is com-_ //1 1 1.3_:,, VI/_ u'_ = _,2 _ + _ _7_+ _ VI_, menced. If it is to be terminated, the program will

_,_ begin to generate the difference lines for the varia-1.3.5 _ tional equations or, if they are not required, begin_'_' the integration procedure,

.%_ 3e

• _ ff:,'L d "_'

1965019622-041

L

"_ JPL TECHNICAL MEMORANDUM NO. 33-188

t3. Variationa| coefficientimprovement, a. Purpose.

"_ This subroutine generates the first (i + 1) coefficients-- The user's derivative sJbroutine is called to pro--_ vide the matrices A, discr_sed it; Section h-3, for in the expansion of (1 - _7)_ using DP arithmeH_"

;. each of the M + 1 points o the net. A_the matrices b. Method.depend only on the coordinates and the time, and

i_ as these quantities are, at this point in the compu- The expansion of (1 - V) _ is given by

tation, well known on the ne t, this procedure has (a - 1)'_ been adopted to prevent the generation of these (1- V)"--= 1- a_7 + a-------_ _7'-'< matrices more than once. The relation (Eq. A-6) and 21

the first approximations to the variational coefficients _ (a - 1) (a - 2)-- _Ts+ • . .: generated are used to obtain the values of the sec- 3!

ond derivatives of the 18 elements of W. The itera-

tire improvement procedure for the variational Let this be written as

coefficients difference lines is, from this point,/den- (1 -- V) _ =/30 "_-fl_' + #_V "_+ flsV 3+ • • •tical with that used to obtain the difference lines

for each of the coordinates. When the convergence Then

test indicates that the difference lines are sufficientlyconsistent, the integration is commenced. /3,,= 1

(_- i + 1)/_,_, i>0' 4. Integration procedure. /31= i

The integration is accomplished by one of three c. Usage.methods:

Calling sequence:

z, a. Gauss-Jackson open procedure. 7 CALL XPAND or TSX $XPAND, 4-_ Equation (A-4) is used with k = - 1 to advance: the calculation. The new values of the dependent Y+ 1 PZE ALPHA, , N

variables are employed to update the difference y + 2 PZE BETAlines.

+ 3 Return

b. Gauss-Jackson pseudo predictor corrector proce-dure. where

: ALPHA = the location of a (floating-point, DP).'_ Equation (A-4) is applied as above. No further

change is made to the difference lines, but an N = number of coefl;cients in series BETA._, improved value of each of the variables is calcu- BETA = the first of 2N locations where/3o,/_, • • • ,/_i

lated by Eq. (A-4_, with k = 0. This procedure will be stored as DP numbers.

"! requires only one entry to the user's derivative O_' subroutine per step. d. Storage.

_i 104_locations,c. 9auss-Jackson predictor corrector procedure.

,_ Equation (A-4) is used with k = 1 and k = 0as a standard predictor-corrector scheme. The 4. SMULT

"_ corrector is applied only once. This procedure John Van de Wouw, Computer Sciences Corporation,requires two entries to the user's derivative sub- April 26, 1962.routine per step.

a. Purpose,

'_ 3. XPAND This subroutine generates the coefficients of the first nJohn Van de Wouw, Computer Sciences Corporation, terms in the product of two series of _ terms each using

Apt'i! 26, 1962. DP arithmetic.

37

..... c,, .... . ....

] 9650] 9622-042

!


. b. Method.' be two vectors. Then the innerproduct of A and B is the: number

Let series

A = (al, c_, • " " ,a.), and series (A, B) = _ aib_ (A-8)

B = (bl, b=, • • • ,b.). Tken A*B = C, where ,=1This program forms (A, B) by summing the DP products

C = (e,,c_, - - • ,c.) a,bz inthe order i = N(-1) 1.

cl = alb_ c. _'lestrictions.

c,: = a,b..,+ a..,b, This is a FAP-coded sub-outine which is FORTRAN IV

- c,, = v a;bj over all i, _such that compatible. Acrays must be forward stored. Fixed-pointi + j - 1 = n variables and constants are stored in tile address of their

storage location. The low-order part of 8 DP floating-e. Usage. point quantity is stored directly above the high-order

Calling sequence: part in an array.

a CALL SMULT or TSX $SMULT 4 d. Usage.

a + 1 PZE A, , B Calling sequezt_:e.

a + 2 PZE C, , N CALL SCALR (A, B, N, ANS_ :',

+ 3 Return where :

A = the first location of 2N cells which contain thewbere DP floating-point vector A.

A = the first location of a block of 2n locations con- B = the first location of 2N cells which contain the

ta,;ning a_,az, • • • ,a, in DP. DP floating-point vector B.

B = the first location of a block of 2n locations con- N = the fixed point integer giving the number oftaining b, b2, • • • , b, in DP. elements in _ectors A and B.

C = the first location of a block of 2n locations where ANS = the DP floating-point storage location assignedthe series c_,c,_, • • • , c,, will be stored in DP. to the quantity (A, B).

N = n, number of coe_eients in A, B and C. e. Storage.

d. Storage. IBM 7090 version: 40 (50_) locations.

52s locations. IBM 7094 version: 32 (40s) locations.

f. Coding.

5. SCALR The IBM 7094 compatibility of this routine ,,ay beDP Innerproduct Routine. J. H. Beeman, Computer implemented by removing the six DP macro instructions

Sciences Corporation, August 8, 1962. from the 7090 version.

Machine: IBM 7090/94. g. qubroutines required.

a. Purpose. IBM 7090 version: DPARTH, a 7094 DP arithmeticsubroutine.

This subroutine computes the innerproduct of two vec-tors in DP. IBM 7094 version: None required.

_, b. Method. 6. INTRP ILet: DP Derivative Interpolation Routine. R. J. Krekemeyer,

A = (aa,ah, • • ' , a_)and Computer Sciences Corporation, August 10, 1962.

i B = (b, b._, ' • ', b,) Machine: IBM 7090/94. .38

1965019622-043

b._


!._ a. Purpose. 2. Extrapolation is not allowed. If t, n, and M are as

![ Let V-zfi',, V-1/i,, ''. ,Vx//, be a set of DP Gauss- defined under PURPOSE, t must be such that_, Jackson Mth order backward differences in terms of the t__ t _ tn-x.' I second derivatives of a variable u. If t, "; tile value of 3. This program has been coded for use with both the

. i the independent variable corresponding to this difference IBM 7090 and 7094.! line, the routine will employ these differences to inter-

I ! polate for the value of u (t), t'_(t),/J (t), or 'tY(t) for any t d. Usage.such that t,_t_t,__.

! i Calling sequence:

r_. : b. Method. CALL INTRP (T, TS, D, H, N, M, ANS, ERROR)

'.i The differences, V;/2,, i= -2(1)M are provided by where, i the user. The difference interval is uncl.cistood to be h, i.e., T = t_. the double precision floating point"_ (DPFP) value of the independent variable

Viii, = _'ii(t,)= Vi//(to + nh) corresponding to the difference line D.

It may be verified (see Refs. 7 and 8) that TS = t, the DPFP value of the independent vari-

i i able for which the dependent variable:_ f,-_ = f(t,- ah)= (1- V) _f, = _ pk(_)V_f,, designated by N is to be computed.

! _'=° (A-9) D = DPFP array of at least 2M + 6 locationscontaining V_//,. = _7'//(T), k = -2 (1) M.

"! where a is a real number.•! H = h, the DPFP value of the interval on which

hz

:i u. - In (1 - V) _-//"= _ al'Vk/i" (A-10) the differences D have been computed.:! k=-_ N = Fixed-point integer designating the variable

-h _ to be computed by INTRP."i"[ t',, - in (_--- V)/i_ = _k,,x7_ii, (A-11)_f _ N=0 compute u (TS)l;, i/, = ii,, (A-12) N = 1 compute _ (TS)

!. t 1 N = 2 compute//(TS):_ _', = - _ In (1 - V) i/, = _ ckV_/J,, (A-13) N = 3 compute ii'(TS)

M = Fixed-point integer giving the order of theMultiplying Eq. (A-9) by Eqs. (A-10), (A-11), (A-12) and differences contained in D.

"_ (A-13) produces interpolation formulas for u.... tl....

ii _/"-_ and i_'._oin terms of the available differences of the ANS = DPFP value of the variable returned by

second derivatives of u. The coefficients ak, bk, and c1,, INTRP.• k = -2 (1) 15 exist within INTRP as prestored _nstants. ERROR = Name of the user's error subroutine. This

Subroutine XPAND is employed to generate the coefl_- subroutine will be called if TS does "_otfall

[ cients of Eq. (A-9). Subroutine SMULT multiplies the in the range T_TS_(T-M.H). Note

i_ c:oefficients of Eq. (A-9) by the coefficients of the user- tha ' an F card must be included in the call-

t selected series £qs. (A-10) throt, gh (A-13). Subroutine ing program to define ERROR as a sub-: SCALR multiplies each computed coefficient by the eor- routine.responding difference and sums the resulting series togive the interpolated value of the desired variable. All e. Storage.calculations are made in DP. IBM 7090 version: 340 (524_,)locations.

c. Restrictions."_ f. Coding.

1. This is a FAP-coded subroutine which is FORTRANThis routine has been designed for use with the IBMIV compatible. This implies that arrays are forward 7094 as well as the 7090. The 7090 version may be altered

stored, that the low-order part of a DP word is storedto a 7094 program by:

directly above the high-order part, and that fixed-point quantities are stored as full-word integers. 1. Removing the macro definition.,.'from the program.

; 39

c

JPL TECHNICAL MEMORANDUM NO. 33-t88-

2. Insuring that the DP storage (TEMP and below, c. Usage.

including the prestored coefficients) is compatible (:ailing sequence:with the final specificatSon for 7094 DP storzge. T'l_i_should involve no more than relocating the progra,_ CALL TSTOP (NTAPE, LTAPE, KTAPE, DELTA,address TEMP to an even cell. TIME, DELT, COSOB, SINOB CMAT, XLB,

XJDO, XYZ, VXYZ, KLM, LAM, KAN, NWI_ITE,g. Subroutines required. NPRINT)

IBM 7090 version: ERROR, SCALR, SMULT, whereXPAND, DPARTH

IBM 7094 version: ERROR, SCALR, SMULT, NTAPE = the user's logical tape unit number for theXPAND source ephemeris tape, 'r'be subroutine ex-

pects the following tape format: READERROR must be provided by the user (see Usage). The TAPE NTAPE, ]D, x_ (i = 1, 2.3), _i (i =remaining subroutines are documented separately. 1, 2, 3) where all quantities are DP, with

the most significant part fi:'st.

7. TSTOP LTAPE = the user's logical tape unit number for the

,. DP time stop routine for the computation of residuals ephemeris write tape. The format is theand ephemeris printing and tape writing. C J. Devine, same as above.

JPL. KTAPE = the user's logical tape unit number for the

Machine: IBM 7090/94. Language: Fortran II. residual write tape. The format of thetape is ]D (DP), _x_t,._Y, and ,_Z (SP),

. a. Purpose. ap, cos/3_X, and AB (SP).

This subroutine is intended to obtain the integrated DELT = the 3 × 1 matrix of ecliptic longitude, lati-coordinates of an ephemeris from common storage, read tude, and _,re¢iduals, i.e., cos/3_X, _I_, _,pa source tape for source coordinates and compute resid- supplied by T3TOP. This quantity is com-uals of observed minus computed coordinates. It lill also puted by the rotation matrix STINKS.

call a subroutine to compute residuals in latitude, longi- TIME = the total elapsed time, t, - to (DP), _om.tude, and p from the coordinate residuals After the above puted by TSTOP.computation, the subroutine is used to write a convergedephemeris tape and/or a residual tape. TSTOP will also DELTA = the 3 × 1 DP matrix of equatorial resid- ;write a preconverged residual tape of n- 1 iterations, uals of rectangular coordinates computed I

corresponding to n- 1 files of information, by TSTOP.

COSOB = the DP cosine of the obliquity supplied byb. Method. the user.

- Let x!, be the observed ephemeris coordinates SINOB = the DP sine of the obliquity supplied by(i = 1, 2, 3). the user.

Let x_ be the computed ephemeris _ordinates CMAT = 3 × 3 DP matrix supplied by the rotationmatrix STINKS for r, ultiplication by SET(i = 1,2,3).III matrix.

Then the residuals in rectangular coordinates are Xr_B = the 3 × 1 matrix of ecliptic p, longitude,formed by and latitude frorr reputed XYZ.

v

_'r aX _----X_-- X_ (i = 1,2,3) (A'14) XJDO = DP starting i,te_ation date supplied by_ the user.

_._ The residuals in longitude, latitude, and p are formed by XYZ = DP 3 × 1 matrix of ecliptic position co-"_'_ calling the subroutine STINKS, which also rotates ordinates computed by TSTOP._il position-velocity coordinates to the ecliptic system.' TSTOP will also print the ephemeris and residuals as VXYZ = DP 3 × 1 matrix of ecliptic velocity co-

!_ outlined in Section D-2. ordinates computed by TSTOP.

', _ 40

1965019622-045

'%


KAM = integer flag supplied by user for separate 8, STINKScomputation check of Ap,AX,A/LKAM = 1 Yes DP system increments rotation subroutine. C. J. Devine,

-_ KAM = 2 No JPL.

ii LAM = integer flag supplied by user for pri,ting

of ephemeris during iteration. Machine: IBM 7090/94; Language: Fortran I1.LAM = 1 YesLAM = 2 No a. Purpose.

I KAN --- integer flag supplied by use, for printingThis subroutine obtains DP zotation of position-velocity

coordinates, residuals, and computes p, longitude and

_[ of _phemeris on final converged iteration, latitude from the rotated coordinates. STINKS willKAN = 1 YesKAN = 2 No also compute the 3 × 1 residual matrix (cos pAX,A/3,Ap)

I and the special C-matrix described in Section Ill of theNWRITE = internal integer flag set by dr_ver program descnptive text of this Repox¢.for tape writing. NWRITE = 2 during

_ iterations, NWRITE = 1 for convergence,-_ tape writing may proceed, b. Method.=;

NPRINT = integer flag supplied by user for choice of Given po._ition-velocity coordinates xt, x i and residuals,. tape writing. Ax_(i = 1, 2, 3), they may be rotated by the follow_g

NPRINT = 1 Wlite ephemeris and matrix multiplication:residual.

i NPRINT = 3 Write residual only. _= = 0 cos e ±sin • x= (A-15)

ii NPRINT=4Notapestobewritten. _ 0_sine c°se / xs

The quantities in the calling sequence _t_st be dimen- _sioned in the driver program as follows: where _ are the transformed quantities.

D DIMENSION DELTA(a), TIME(l), DELT(3), Then the matrices (cos #AX,A/3,_p) and the C-matrixCOSOB(1), SINOB(1), CMAT(3,3), XLB(3), may be computed by the followinS equation: /:

'[ XJDO(1), XYZ(3), VXYZ(3)f

the user's program at each tim,., stop in common in the A/]

following order: .xp/p

r',I_ENSION DUMMY(4972), VZL(1),

! VZM(1) • • • , VXM(1), ZL(1), ZM(1),. • • , / -sinA cosA 0 ! /A_x:! ,

i XL(1), XM(1), JDL(1), JDM(1) = 1 -sinflcosX -sin/SsinX cost ;=P

i.e., starting with velocity in descending storage order, x_/P x=/P x_/P/ "

withtheleastsignificantpartfirst. (A-16)

d.Remarks. wheretheAx_aretherotatedresiduals,and A,_,and p

A flowchartof theTSTOP logicmay be foundin have beenfoundfrom thesubroutineSPHEB by the

Section F of this Appendix. usual spherical coordinate methods.

:, e. Su/ _.flnes required, c. Usage. _'

,¢ STIN S Described below. Calling sequence: 'i

SPH; I Calledby subroutine S'HNKS (described CALL STINKS (XYZ,XIDOT, DELTA, _

below), XLB, CMAT, COSOB, SINOB, NBOT) i"

I,

1965019622-046

JPL TECHNICAL MEMORANDUM _40. 33-188

. i

_" where b. Method.

"_. XYZ = the DP positior, vector supplied by the user. Given the ecliptic osculating elements ao, no, eo,/o, fh,_,o, and Me along with ecliptic position-velocity coordi-

X1DOT = the DP velocity, eetor supplied by the user.nates and .r, PQR-direction cosine matrix, it is desired to

DELTA = the DP residual vectol, sapplied by the user. compute the follo_Sng ma_.x:

_(L,#,p)XLB = SPHER.theDP vector of p, t, and X, computed by .X..... ---"CMAT.-,._ * (SET III)_., - ?(SET III)

CMAT= the DP 3 × 3 C-matrix described in Eq. (A-17)

(A-16). or as in Eq. ('9-23)of the text,

COSOB = the DP cosine of the obliquity'. A = CA (A-18)

SINOB = the DP sine of the obliqu/ty, where C is the C-matrix described in STINKS and A is

NROT = 2, the integer flag for rotation only; or the SET Ill matrix of Ref. 3 and Eq. (15) of the text.

NROT = 1, rotation and matrix eomputa- e. Usage.tion.

The user must pro_qde DP storage capability in the Calfing sequence:driver as follows: CALL SZT32 (PQR, XYZ, X1DOT, A, ;

• -- E, XN, SET, TIME, CMAT)

D DIMENSION X_ (3), X1DOT (3), DELTA (3), whereXLB(3), CMAT(3,3), COSOB(1),SINOB (1) PQR = the DP 3 × 3 direction cosine matrix sup-

_ plied by the user..The P vector is the first

If it is desired only to rotate position and/or velocity, row, the Q yeetor is the second row and the

the_ all that is required is to set NROT = 2, and supply R vector is the last row.

the desired coord/nates, including appropriate dummy XYZ = the DP _liptie position vector supplieddimensions for the rest of the calling sequence, by the user.

d. lleraar_. X1DOT = the DP ecliptic velocity vector suppl.iedby the user.

The rotated values of the position and velocity eoordi-

_- nates and the ne_ residual vector cos flAX, Aft, Ap are A = the DP semimajor axis of the e:lipse. '

returned to the us_ r in the same storage locations, i.e., E = the DP eccentricity of the ellip _e..i.:. in XYZ_ XIDCT, ar_ DELTA, respectively. " i": '_ YN = the DP mean motion of the osculating ele- i

• n. ]_. Sulfroutines required, ments.

SPHER. Described later. SET = the DP matrix A computed by SET32. I

TIME the DP elapsed time t_ - to, supplied by the I9. SET32 user. I

Th _ DP SET III matrix of partial derivatives of the CMAT = the 3 × 3 DP C-matrix described above, i

oseulr :,_g elements. C. I. Devine, JPL. The arguments in the calling sequence must be dimen- i

! ,,_aehme: LBbt 7096)9t; Lang_mge: Fortran I1. sioned as follows: ]

_ D DIMENSION PQR (3,3), XYZ (3), X1DOT(3), 1

: a_Purpos¢. A(1), E(1), XN(1), SET(S,6), t

i . To compute in DP a modified form of the SET III TIME(l), .CM/_T (3, 3). 1"

partial derivatives of the osculating elements of Brouwer d, Remarks." and Clemence (Ref, 3, p. PAl), i.e., to Comput_ a 3 X 6

matr;_.xof pa-tial derivatives of k, t, and p with respect SET32 is a modification of the original SET III matrix

to the SET III of PLOD I. of PLOD I, called RED 3. Essentially, the diffe_ enee _or _

.4a

............................................ :2L .....

1965019622-047

Ik

t


PLOD II is that all quantifies are now in the eclipt2¢ c. Usage.

_' system and there is a last multiplication by the C-matrix.Additionaliy, RED 3 had an acceleration _pability that Calling sequence-SET32 does not have, making it a possibie 6 × 6 partial CALL SETUP2 (SET, DELTA, XaNUM,

° derivative matrL:. SIGSQ. AMAT, BMAT, MMAX,

e. SubroutineJ required. NMAX. NCOSOL, STEST, WT)

None. where

SET = the DP matrix computed by SET32 (SETI0. SETUP2 lIl matrix.

DP accumulation of the normal equations. C. J. Devine, DELTA = the DP residual matrLx (cos fl_Ut, Aft, Ap)., JPL.

XNL'M = the floating point DP number of integra-i Machine: IBM 7090/'94; Language: Fortran II. tion steps.

a. Purpose. SIGSQ = Xa_ (cos flA_,)" + _.- (Aft)'- + a_ (Ap)'-,the DPThis subroutine accumulates the equations of condition test value.

obtained from the SET32 matrix, and tests for solution bySTPRG2. AMAT = the DP matrix, A_MAT = N, in E,q. (A-19).

BMAT = the DF matrix, BMAT = F, in Eq. (A-20).b. Method.

MMAX = the amber ef rows of the normal matrix,• i Let the system of linear equations obtained after n + 1 SET.

steps be denoted by NX = F, where X is the solutionvector and N is computed by SETUP2 as follows: NMAX = the number of columns of the normal ma-

N = E aNi (A-19);=o NGOSOL = the solution parameter set by SETUP2 on

where the STEST, if NGOSOL = 1; no solution,r

I AN, = X_,W_, i (A-20)

2 solve.

at eac], _ep, _,'_.is the transpose of _,j, and W is a diagonal STEST = the DP number, _, in Eq. (A-23).

, weight matrix, WT = the DP weight vector WT = (1,1, 0) for: PLOD II type rum, (1,1,1. _ for PLOD I

(o,00/ type rims.'[ W = a_ 0 (A-21)|

\ 0 0 a,] The above quantities must be dim,msioned as follows:

if The matrir F is computed as D DIMENSION SET(6,6), DELTA(3), XNUM(1),

| N SIGSQ (1), AMAT (6, 6), B,'.tAT (6), :t

F = Y ±F, (A-29) STEST(1), WT(3)

I j=l

• ! where d. Subroutines required.

i .2iF; = _. WB. ,None required.

'i at each step, and where Bi is the residu_ vector. A test

J;l ismade at this point to determine whether 11. COllECT :The DP computation of corrections to the osculatingS = _ [a_ (cos fliAAi) t + et2(Aflj)= + a, (Ap/) 2] -_ _ elements from the solution vector of the, normal_equa-

j=o

-!' (20----- k---_ n) (A-23) tions. C. I. Devine, JPL."- .- j

If it is, a solution is called for immedia_dy. Mgehine; IBM 7090/94; l.anguage: FoA_ran II. !.

-| j !

i - 4a :

-: ;-_

] 9650 ] 9622-048

/-

JPL TECHNICAL. MEMORANDUM NO. 33-|88

_ a. Purpose. d. Subroutines req:dred.

_ This subroutine _ intended to compute corrections to DOUTPT DP output. At JPL, this is a library syst_the osculating elements given the solution vector to the subroutine. !

normal equations. COKECT will then compute- new oscu-lating elements and a new PQR direction cosine matrix. i

b. Me_md. The DP t_ansformation from elliptic elements to rectan-gular coordinates using a solution of Kepler's equations. ,.

Given the solution vector X = (AMo + Ar, Ap, Aq, eAr, C.J. Devine, JPL. Machine: IBM 7090/94; Language:Aa/a, Ae), and osculating elements _,, r_,, eo. i., .q,_,_,o,M_, Fortran II.with a direction cosine matrix

a. Purpose.

This subroutine provides a DP transformation from _

(PQR) = Qz Q, Qz (A-24) elements a, n, e, i, f_, _, Mo, and direction cosines PQR toIL I_ IL r_.gular position-velocity coordinates Using a solution

: of Kepler's eouation.computed from the osculating elements, COBECT will

: obtain corrections aa, An, Ae, Ai, A,q, a., AMo from the b. Method.|.

vector X and add them to the osculating elements. These Given the elliptic elements of the orbit, a, e, Mo, and |new elements are then us_ to form a new directioncosine matrix, b = a cos _ = a (1 - e_)_ and direction co._.nes I'QR, then |

the position-velocity coordinates are obtained frovi t'._._ ;,

• c. Usage. _ following equations: _

Calling sequence: Xo = aP.(cos E -- e) + bQ_sin E ],

CALL CORECT (XSOLVE, MEAN, Yo = aP, (cos E -- e) + bQ, sin E IXMEAN, ELM, PQRN, XMU) Z, = aP_ (cos E - e) + bQ, sin E (A-2,5) i

where ._

XSOLVE = the DP solution vector supplied by the Xo = [(bQ_cosE - aP, sinE)/ra_] I,_

user. _'o = [(bQ, cos E - aP_ sin E) /ra_ ] p"_ ]

MEAN = the mean motion integer control flag. 7-o= [(bQ_ cos E - aPz sin E)/ra_] _ (A-26) != MEAN- 1; mean motion computed (An

is computed from/t = n_a'_), where E is determined from Kepler's equation.MEAN = 2; mean motion held fixed (Aa - _,

. is computed from _ = n_a_). M = Mo + n (t - to) = E - e sm E (A-27) _'

L XMEAN = the DP value of the mean motion suppled by a Newton-Rapbson iteration. ,__- by the user for MEAN = 2. _"

ELM = the DP seven osculating elements (in- c. Usage.

!_ eludes mean motion) supplied by user in Calling sequence:,_ _ the following order: a, n, e, i, l_, ,,, and M.

": CALL TBANSX-(PQR, DPXYZ, ELEM, XMU)_ PQh N = the DP direction cosine matrix PQR.

XMU = the DP value of _. where

The 3 X 3 matrix PQRN is used to supply the old PQR = the DP direction cosine matrix :.,pplied by -,-

!_ I'QB matrix and to return =the new one, similarly the the user (P, Q, and R are row vector_ o_ the_' - vector ELM. The dimemions must be as follow_: matrix).

'_: D DIMENSION XSOLVE(8), XMEAN(I_, ELM(7), DPXYZ :--the DP position-velocity vector compt_ted_ _ PQRN (3,3),XMU (I) by TBANSX.

. _ _,,_._., _ , ._., .. _ • . ::,_.,, . .:. _-_ ,__._._.... -,._,_r _ _:_.,_.__-__:_, _._ ,. - _ . :,, :, . : :___. _

9650 9622-049

JPL TECHNICAL MEMORANDUM NO. 33-188f

• l

ELEM = the DP elliptic element vector supplied by c. Usage.

i the user, i.e., ELEM = (a, n, e, i, f_, ,, Mo). Calling sequence:

XMU = the DP _ supplied by u_er for the sealing CALL DERIV (MTAPE, NOBOD, KPOS, XDS,[factor in the veloeity solution iz= k' (I + m), XDE, DM, XLITE, XMU, AKS, NAM, NREL,

! where k is the gravitational constant and XDSA, XH)! m is the mass of the body. Quantities are! dimensioned as follows: where¢

l| D DIMENSION PQR(3.3). DPXYZ(6), MTAPE = logical tape number of tape supplying

I ELEM(7), XMU(1) COORD, the perturbing body tape.NOBOD = the number of bodies on the COORD-

EPHEM tape, which will be 10 (not used[ 13. DEBIV in this version).

• [ The DP acceleration routine. C. J. Devine, JPL.- _ KPOS = integer flag for COORD (when old version

I Machine: IBM 7090/94; Language: Fortran II. of COORD was used).• _OS = 1;position coordinates only from

a. Purpose. COORD.KPOS = 2; ve!ocity coordinates only from

This subroutine provides a DP numerical evaluation COORD.

of the fundamental equations of motion in Cowelrs KPOS = 3; position-veloc/ty coordinatesmethod of integration, from COORD.

b. Method. XDS = DP starting print date for DERIV ff print-,_- ing is desired.

Civen the DP position-velocity- coordinates of the mainXDE = DP end print date for DERIV if printingbody, x i, _i (i = 1, 2, 3) and the DP mass (m) of the main

i body, with the position coordinates x_, and masses mj is desired.(i = 1, 2, 3) (i = 1, 2, • • " , 8) of the perturbing planets, DM = the DP masses of the main body and the

•[ then the equatlons of motion are evaluated as Earth, with the main body and Earth sett to zero before entering.

• I _/_= -k _(I + m) -..#-+ :2k'mjj L 0'_)" (rJ)'_J DM(1) =. Mercury DM(O) = JupiterDM(2) = Venus DM(7) = Saturn

(i = 1, 9. 3), (i = 1, 2, • - , 8) (A-28) DM(3) = Earth--Moon DM(8) = Uranus - .

where DM(4) = Earth = 0.0 DM(9) = Neptime

r" = _ (x')",r_= _ (xJ)',and(p,)_= _ (._- x)' DM(5) = Mars DM(10)= Pluto

t J=, _=, i=_ XLITE = D.P value of the velocity of light supplied

On option, the equations are modified for the relativRy by the user in All per day.contribution by modifying Eq. (A-28) irt the following XMU = DP value of p for the solar term.

" form:AKS = DP value of the gravitational constant

_x i 3R (squared)supplied by the user.

i _' + _ + c * xl/r" = ._, (i = 1, 2, 3) NAM = 1; print aeceleratic_,_ -- ..

_print flag set oy user. !2; no print(A-29) Printing will occur only at time t,

where _ = k_(l + m) and aR/?x _ is the last terrain the XDS_-t--_XDE"

i right hand side of Eq. (A-28). (This option is no louger NREL = Relativity flag se_by user. ".

in use, and will be replaced by equations in Bef. 10 in = 1;relativity

! future versions of PLOD.) = 2; no relativity. _}

• 4e ":_ :

- . _ " " "_' ._ _ _ _ "' . ..... . "__._ ,,"---'t_._ -.._- _.,_ ::r "',,: _.

1965019622-050

_L

JPL TECHNICAL MEMOFIANDUM NO. 33-188

2;

XDSA = DP date set equal to zero by user before c. Storage.

entering DERIV. Common storage:

XH = DP step size of COORD-EPtlEM tape DIMENSION DUMMY(4984), T2(1), T1(1)computed by MAIN.

where the current Julian date is ol:.tained from T2, T1, _:d. Storage. the least and most fignificant parts of the DP number.

The above quantiti,.'s must be dimensioned as follows: Storage for TMAX:

D DIMENSION XDS(1), XDE(1), DM(10), D DIMENSION TMAX(1) .XLITE(1). XMU(I), AKS(1),XDSA(1),Xtl(1)

The subroutine reads from common storage the value 15. ERRERof the DP Julian date and the position-velocity supplied

-- by the user. It must be dimensioned and stored in com- Error indication subroutine for FORTSZ. C. J. Devine,mon as follows: JPL. :

DIMENSION DUMMY(4966), XL(1), Machine: IBM 7090,/94, Language: Fortran II 'XM(1), • -. , ZL(1), ZM(1), XL(1), ;,

-: XM(1), • - • , ZL(1), ZM(1), XJDL(1), a. Purpose. t

XJDM(1) This subroutine provides an error print routine for

DERIV, after t_mputing "_i (i = 1,2,3), will store the FORTSZ. I:

value in common in the above location for the user. ib. Method.J

e. Remarks. At any time FORTSZ indicates an error, ERRER is i"

; The analytic relativity contribution is not included in called and a summary of possible errors is printed. Thethis Report. The next version (PLOD III) will be pub- integration is then stopped and the progr/an is halted.lished in the near future, and will contain this information.

c. Usage.

f. Subroutines require&. Calling sequence:

DOUTPr DP precision library, s_utput routine. CALL ERRER

14. EOSER,. 16. FORDV

End of step test for TMAX. C. J. Devine, JPL. Driver for FORTSZ and subroutines used by FORTSZ,bfachine: IBM 7090/94, Language: Fortran lI C.J. Devine, JPL.

* Machine: IBM 7090/94, Language: FAPa. Purpose.

: This subroutine is called after every time step and tests a. Purpose.

for TMAX, indicating this by printing a statement that FORDV acts as a logical link between PLODMN and: maximum time has been reached. EOSER then sets a flag its subroutines and the integration routine FORTSZ. It . :"

for the end of integration, also computes the step size for FORTSZ. ,_

b. Usage.b. Usage.

i Calling sequence: Calling sequence:CALL EOSER (TMAX, J) CALL FORD_ (IFLAG, IFL, TS(2))

where wherei TMAX = DP end date supplied by user: IFLAG = integer flag set by FORDV for calling of

,: J = flag set by EOSER for MAIN program, subroutines in PLODMN.%

2

46.p -2

q9650 q9622-05 q

1,p

,JPL TECHNICAL MEMORANDUM NO. 33-188

t

IFLAG = 1 CALL DER1V a. Purpose.

IFLAG = 2 CALL TSTOP This subroutine provides a DP solution of the normal

IFLAG = 3 CALL EOSER equations of a linear least squares regression problemusing the stepwise procedure of M. A. Efroymson.

IFLAG = 4 Ch LL ERREBThe subroutine is particularly intended for use in least

IFL_tC. = 5 HALT squares problems in which the user is aware of a largenumber of basic functions which might bear a linear

' IFL = integer flag for FORTSZ to indie_.te whether relationship to the object function but expects that onlyvelocity is desired at the time stop. some of these basic functions make a significant contribu-

: 1; position-velocit T computed by FORTSZ. tion to the determination of the object functioa.= 0; position only computed by FOBTSZ.

b. Method.TS(2) = most significant part of starting date sup-

plied by user, i.e., user must set up the fol- In an n-parameter problem, this subroutine provideslowing instructions in his program (in this successively a 1-parameter fit, a 2-parameter fit, - - - , a

: case the program PLODMN would h_.ve k-parameter fit, where the new parameter introduced atinstructions): each step is the one which will make the greatest reduc-

TS(2_ = XJD(1) tion in the sum of squares of residuals. This criterion isequivalent to the requirement that the new parameter be

TS(1) = XJD(2) selected as the one which will have the highest statistical -_DIMENSION TS(2), significance in the sense that'the ratio of its magnitude

D DIMENSION XJD(1), where'IS is stored to its standard deviation will be largest, or equivalently,in common to insure an even location, its "F" value will be largest.* The termination level, k,

which will be _l, is determined by the subroutine on the

Several ether quantities needed by FORTSZ are proc- basis of tolerance parameters SDIN, SDOUT, and CDessed in FORDV. Because of the discrepancy between provided by the user.

Fortran II and FAP, several integer constants are #ored For an expnsition of this procedure, see Ref. 1._. For a

h=com,aon by PLODMN, shiited to B35 by FOBDV, and complete single precision regressiol_ package which incor-restored in common. They are _tored in the following porates this procedure in its system solving subrou_ne,order: see Ref. 12. Lawson also discusses the procedure, inelud-

COMMON BOOL 65652 ing details of its implementation in this program."

M EQU COMMONJ EQU M + 1 c. Usage.

N EQU M + 2 Let the overdetermined system of linear equationsOPTION EQU M + 3 which expresses the linear regression prob]em be de-DTAPE EQ_r M + 4 noted by

S EQU M+5 Gc=fES EQ_ M+6H EQU M + 12 where G is an m by n matrix (m > n), c is an n-vector,

and f is an m-vector. The elements of G and f are knownwhere quantifies are those defined in the subrcatine

and the coefficient vector c is to be computed as a

FORTSZ. Hts the DP step size supplied by the user, and weighted least, squares solution.will remain constant for each integration. %hen FOBTSZcalls the step size routine, FORDV simply gives it the The normal equations Ae = b are formed from the *value of H stored-in common. - 0verdetermined wstem by premultiplication by G*W

:. (* denotes transposition), where W is an m by m non-

negative definite weighting matrix (W may be the iden-17. STPRG2 tity matrix),

Double pr_ecision stepwis_ solution of normal equations.._ C. Lawson, W: Thomas, JPL, January 1, 1963. "Lawson, C. L., Computation ot the Most Stgnt_.ant Coefficients

in Lemt Squares __:lmatton, Jet Proptdsion Laboratory InternalMachine: IBM 7090, Language: Fortran'II Document, August, i932.

47

i,!

1965019622-052

e"

JPL TECHNICAL MEMORANDUM NO. 33-t88

This computation,as well as the computationof the will later be removedfrom the solutionif this prob-_calar quantity s = f'Wf, is to be done by the user's ability falls below 90_.program. STPRG2 may then be called as follows:

If SDIN-----0 all significance tests will be skipped.D DIMENSION A (8, 6), B (6), S (1) This permits use of the program with meaningless

DIMENSION INOUT (6) data in B and S, as may be the case when only matrixCALL STPBC2 (L, B, S, N, M, SDIN, inversion is 2esired.SDOUT, CD, NIN, INOUT, KPRINT)

The parameters are defined as follows: CD Tolerance for relative reduction in magnitude ofdiagonal elements. The ith coefficient will not be

A (I, J), I = 1, N; J = ], N entered into the solution if the ith diagonal elementbecomes smaller than CD times the original ith diag-On entry: The matrix A, computed by the user as

A = G*WG. On return: A-_ if NIN = N. If NIN < N, onal element of the matrix A. If, e.g., CD = 10.**then only an NIN by NIN submatrix of A will have (-12), then a potential pivot element will not bebeen inverted and the elements of this inverse will be used ff it has lost more than its first 12 significant

in the locations A (I, J) corresponding to thos_ values decimal places.of I and J for which both INOUT (I)= +1 and NIN On return: The number of coefficients in theINOUT (J)= +1. The other A(IJ) locations for final solution.I _N, J L N will contain zero.

B (I), I := 1, N INOUT (I), I = 1, N On return: Flags to indicate finalstatus of each coefficient:

On malay: The vector b, computed by the user as +1; included in solution.b = G*Wf. On return: The solution vector cff - 1; rejected by diagonal test.

• _ lglN :=N. if NIN < N, then only NIN components -2; rejected by significance tests.of c will have been computed and they will be those

in the locations B (I) for which INOUT (I)= +1. KPRINT Flag for control of printing:_, The other B (I) locations for I _ N will contain zero. 0; no printing.: S 1; p_int summary, final solution only. ;

2; print summary, every solution._ On entry: The scalar s, computed by the user as 3; full printing. ,.

s --: PWf. On return: The weighted sum of squares;" of residuals: The summary printing is all single precision. Listed

for each coefficient in the solution is its value, its standard(f- Cc)*W (f- C,e)= (f- C.,c)*Wf deviation, and the ratio of these two quantities. Listed

"_ = PWf- (Ge)*Wf for each coet_cient not in the solution is its predicted'_ ratio of value to standard deviation or the word DE-

_-' "-- PWf - e*b PENDENT if it has been rejected by the diagonal test.Also printed is the sum of squares of residuals and the

N The dimension, n, of the normal system, unbiased estimate of the standard deviation of the resid-

M The dimension, m, of the f vector, ual function.

_'_ SDIN, SDOUT. If SDIN > 0, these two numbers will The full printing includes all of the summary plus the* be tt_ed by the "significance." logic of the program, full augmented symmetric m_,trix_ in DP for every_" A coefficient will be permitted to enter the solution solution.

__ if the ratio of its magnitude to its standard devia-i_,' tion will exceed SDIN. If thi_ ratio subsequently

drops below SDOUT, this coe_cient will be removed d. Remarks.

_ from the solution. Toavoid looping, SDIN shoald The internal output of this subroutine, namely A, B, S,_•_ exeeed SDOUT. Typical values for SDIN and NIN, INOUT, was provided in case the user e.hose to

SDOUT might be SDIN = 1.96, SDOUT =1.64, incorporate this subroutine into a more complete regres- 'which c_uld.be interpreted as meaning that a coeffi- don paekage. For many applications this is hot necessary

.,_ eient will be permitted to enter the solution !f there and the user's program can ignore the internal output, -"._ is a 955 probability that it is different from zero and employing the flag KPRINT to obtain the external output.

'_ 48

i

1 N

1965019622-053

JPL TECHNICAL MEMORANDUM NO. 33-1B8

This subroutine uses storage rather extravagantly in wherethat the given data is moved to locations which are local

• _ to the subroutine before processing and finally moved COSOB* = the DP value of the cosine of the obliquityback to the user's storage locations. This could be supplied by the user for rotation to the

" changed if storage becomes a problem, ecliptic.

The first version of this subroutine was called STPREG. SINOB ° = the DP value of the sine of the obliquity

STPRG2 was written to provide more complete and supplied by the user for rotation to the: flexible printing, ecliptic.

; e. Storage. DPOS = theDPposition-velocityvector, suppliedby

the user DPOS (1) = X, - - • , DPOS (4) =2947,,, = 5603_ locations. X, • • • , DPOS (6) = 7..

f. Subroutines required.XMU :-- the DP value of/_ supplied by the user.

• DOUTPT for DP output under the full printing option.

Otherwise only standard Fortran 1I library subroutines DPQR = the DP (3 × 3) PQR direction cosineare called, matrix computed by ELEMTS, where

(P,, P,,, P-) is the first column vector,

(Q_, Q,,Q..) is the second column vector, and

18. ELEMTS (R,, R,,, R-') is the third column vector.: The DP calculation of the elements from the position-

velocity coordinates at a given time. Specified and pro- ELEM = the DP (7 × I) osculating elements vector

trammed by N. Block, JPL. Subroutine description by computed by ELEMTS in the order a, n,C. J. Devine, JPL. e, i, f/, _, and M.

Machine: IBM 7090/94; Language: Fortran IIMEAN = the mean motion integer flag supplied by

t_ the User. MEAN = 1; a is computed by thea. Purpose.[ equations in Ref. 3, p. 48. MEAN = 2; a is_. This subroutine provides a DP transformation of the computed from the DP XMEAN value ef_ position-velocitv coordinates at a certain time, t, to the the mean motion supplied by the user.

elements a, n, e, i, _/, o,, and 3,1,where a is the semimajora_s, n is the mean motion, e is the eccentricity, i is the XMEAN = the DP value of the mean motion supplied

inclination, .q is the longitude of the ascending node, by the user (used primarily when the mean,u is the argument of the perihelion, and M is the mean motion is held fixed in PLOD II).anomaly. The (3 × 3) direction cosine matrix PQR is also

computed.d. Storage.

b. Method. The quantities in the calling sequence must be dimen-Given the DP position-velocity coordinates of the body, sioned as follows:

X, Y, Z, X, Y, Z, the numerical value of Kepler's third law,

t /_= k2(1 + m) (where m is the mass of the body), and D DIMENSION COSOB(1), SINOB(1), DPOS(6),

the sine and cosine of the obliquity, then ELEMTS will XMU(1), DPQR(3, 3), ELEM(7),i compute the seven DP osculating elements of the orbit XMEAN(1).• along with the direction cosine matrix PQR. The formulas

_ and the explicit method used are outlined on pp. 48--49 e. Subroutiues required,': of Bef. 3.•_: ABCTN (Section 21).

e. Usage. "If no rotation is desired, i.e., if the position-velocity coordinatesCalling sequence: are in the equatorial system and equatorial elements are desired,

or ff they are in the ecliptic system and eeliI_ie element_ are de-CALL ELEMTS (COSOB. SINOB, DPOS, sited, then setting COSOB = 1, and SINOB = 0 will suppress _ _r.

XMU, DPQR, ELEM, MEAN, XMEAN) the rotation.

, 49 '._.

1965019622-054

!-

?

' JPL TECHNICAL MEMORANDUM I_O. 33-168

2

19. OBLIQ c. Usage.

_, The DP computation of the angle of the obliquity. Calling sequence:Specified and programmed by N. Block, JPL. Subroutine

CALL SPHER (x, y, z, p, ;t, r)description by C. J. Devine, JPL.

Machine: IBM 7090/94, Language: Fortran II where

a. Purpose, x, y, z = the DP values of the position coordinates sup-plied by the user.

This subroutine computes the angle of the nbliqui_'

given the Julian date. p = the DP value of the radius vector computed byOBLIQ. _.

b. Method.

Evaluation of polynomials in T, the Julian date. k = the DP value of the longitude computed byOBLIQ.

c. Usage. fl = the DP value of the latitude computed byCalling sequence: OBLIQ.

CALL OBLIQ (XJD, EPSLN)d. Storage.

where

XJD = DP value of Julian date supplied by the D DIMENSION x(1),y(1),z(1),p(i),_(1),fl(1)user.

_ EPSLN = DP value of obliquity, computed by e. Subroutines required.OBLIQ, which must be multiplied by 27r ARCTN (Section 21).by the user.

d. Storage. 21. ARCTN

D DIMENSION XJD(1), EPSLN(1) Interval reduction of the argument for calli ,g the in-verse tangent function. Specified and programmed byN. Block, JPL. Subroutine description by C. J. Dexdne,

e. Subroutines required. JPL.None required.

Machine: IBM 7090/94, Language: Fortran II

! 20. SPHERa. Purpose.

The DP solution of spherical coordinates. Specified and

programmed by N. Block, JPL. Subroutine description by This subroutine provides interval reduction of the argu-_, C.J. Devine, JPl,. ment for calling the inverse tangent function. The fi,ne-

tion subroutine _1._o tests for zero, negative, or positiveMachine: IBM 7090/94, Language: Fortran II x and y for an expression of the type Arctangent (y, x).

a. Purpose. b. Method.

i This subroutine computes the radius vector, the longi- Sets up the interval reduction logic and calls the For-_ tude, and the latitude given the position coordinates_, tran II library subroutin,.- ATANF (Y/X) and returns the_, X, y, Z., value of the function in a function t_pe _tatement.

_i b. Method. c. Usage.

I Given x, y, z in DP, then p, X, and fl are found by the Calling sequence: '

usual trigonometric reiations. An interval reduction is

i also pedormed, with tests for zero values. VALUE = ARCTN (Y, X)

SO

JPL TECHNICAL MEMORANDUM NO. 33-I88

where ARCTN is defined in the furlction subroutine as This would cause the subroutine to read in 10 DP num-

" i ARCTN = ATANF (Y/X). bers and store them in array X (the Fortran programcould refer to them as X(1),X(2),...,X(IO) in any

d. Subroutines required, statement in the DP mode). Then the subroutine wouldread in three DP numbers and store them in Y(1), Y(2),

Fortran librar/function ATANF. Y(3), and then one number in Z, and then two numbers' in A(1), A(2), etc.

22. RUNData card format:

Rewind and unload tapes• Programmer: C. Orozco.d

Machine: IBM 7094 Each card must have DEC in columns 8, 9, 10, with ablank in column 11. The data field starts in column 12.

a. Purpose.Several numbers may appear on one card separated by

This subroutine rewinds and unloads tapes by a For- commas, but the first number called for by a new pair oftran II type calling sequence, arguments (X, N) must start a new card.

: ! b. Usage. E-type numbers are permissible, i.e., 0.100, 1.0E-01 areCalling sequence: equivalent.

CALL RUN Space required:

1331(s)or 729(_,,).23, DPINPT

DP input. 24. DOUTPT

a. Purpose. DP output.

This subroutine reads DP decimal information from a a. Pumose.BCD tape, converts to binary and stores the results in This subroutine outputs DP numbers in a fixed format.core storage.

b. Restrictions. b. Restrictions.

Output is to tape A3.Input is from tape A2 (logical tape 5) and is limited to

a complete singly subscripted array (i.e., if X is dimen-c. Usage.

sioned X(20), then all 20 values of X must be computed at

i once). Only the first 17 significant digits are converted. Calling sequence:

' CALL DOUTPT (X, N, I, Y, M, 1, • • ' )c_ Usage.

Each triplet of arguments is examined separately. TheCa!ling sequence: first number of the triplet, X, is the name of the array to

CALL DPINPT (X, N, • • • ) be written on tape for printing. '___te second, N, is thename of a fixed-point vaii.'ble or constant indicating the

where number of double precision numbers to be outputtedfrom the array Y. The third, I, ,.'s the product of the

X is the location Of an array to start storing DP dimensions of X.numbers.

• N is the number of DP numbers to be stored sequen- If N is positive, N double precision numbers X(1)tinily starting at X (and ,he dimension of X). through X (N) will. be written on tape A3 for printout in

floating point form, four to a line, ending in columns 30,The number of arguments in the calling sequence is 60, 90 and 120. The numbers when printed out m'e in

variable, consist;ng of ordered pairs (X, N). the following form:

Example: CALL DPINPT (X, IO, Y, 3, Z, 1, A,2," " " ) SX.XX,_CXXXXXXXXXXXXXPEEl

rail m

1965019622-056

+C

+_ JPL TECHNICAL MEMOIRAP,IDUM N_. 33-188 .....

where and 120. The format would be similar to using a Fortran

format 4F30.12 (except, of course, the Fortran formatX is the char.eteristic+would not give the results with the DP accuracy).

S is the _ign of the number either blank (for positive)

or -+ (for negative). Each new triplet (X, N, I) begins a new line.

P is the sign of the exponent either blank (for posE- Accuracy:

tire) or - (for negative). The output is correct to 17 significant decimal digit.E is the exponent.

If N is negative, the numbers will be printed in a fixed- Storage requirements:point format, four to a line ending in columns 30, 60, 90 1566_A_or886,0_.

i' I

1965019622-057

JPL TECHNICAL MEMORA:_DUM NO. 33-188

:- l--m+d

IPL TECHNICAL. MEMORANDUM NO. 33-T88

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p< JPL. TECHNICAL MEMORANDUM NO. 33o!84_

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1965019622-063

IPL TECHNICAL MEMORANDUM NO. 33-18;B

XSOLVt

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e,e* STATISTICAL ANALYSIS FO_ R_SIOU_:S _ ..... RADIUS V_C;_ C05A OL OLAr-OS_ D_VIATIO_ ................ #C°SU_(_LTAI/N _"o5_373863£-01 0.1365_359_-0_ b.115330S_E-_8SUPS CF SQUARES _ESIOUALS ...S_-SU_(OELT_oe21/N C.3_tl_qlE-l_ 0.3;_$6_0E-13 _.S$_8_9_lE-17SrANOJRO OEVI_EION .............. SO-SQ_TFtSR-_9-'?) 6.5_6_0965_-_70.115JTq_E-_6 0.261923_6E-¢E_AXlX_ _ESI_JAL ................................. _,79,_428£-07 O.30_gAA61E-_6 :.6_58992E-08NINI_IJ_ A[SIOU_L ................................. -_.1C_61761E-06 -0.47_88_IE-07 -:.Z83606_IE-_S

ECLIPTIC P¢S-_EL F_O_ TRANSX A_O _QUATO#IAL POS-VEL AFTE_ AOTATZO_ F_O_ ECtIPTI¢

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BEGIN ITE_ATION

EPOCH VALUES EQOATC_IAL 2_32|_._0

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59

1965019622-064

+.

_+ JPL TECHNICAL MEMOC_ANDUM NO. 33-1884-

4

EPH|P_t|3 FORMAT FOR E&CH JUL|M40ATE IS

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2453310.S-4.47633088 2,6|294440 |,L60444TO*O*_O415_T*O*OO540??O-O*OO_LS45_ 0,_|1 0.1650 0.05_|-4.4763300_ 2*9629442? 0.05050340"0o_0423037"0.00_04004 0.0001100_ O*_tlS "0*0_00 -0*0034

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1965019622-065

i JPL TECHNICAL MEMORANDUM ;NO 33-t88-_.23714650 1.43772302 0.11Z13334-0*00203873-0.00693020 0.00007320 0.3062 0.0531 -0.0044

-0.:426 -0.0432 -0.0200Z4 _$800 • 5-5.31_08550 C.9047q731 0.55232 ?? *-0.00164755-0,00647715-0.00273045

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2455000.5-5.41107505 0.4610297o 0.33042140-0._00_5557-0.0_650403 0.00200363 -0_0298 0.2005 0.J036

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1965019622-066

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1965019622-069

; IPL TECHNICAL MEMORANDUM NO, 33-188

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Z_3T_40.S°O°61389Bg_-_.8_52695-2._S_2'_TB O°O07_I67_-O,OCO_IZS_-O-OOQ_5_2 -0o_55$ 0.2_5 0.0119-O.61_ngb_-5.2_2_3176 0o034_98F0 0.0_7416_6-0.00_137-0.0001_56 -0o3_S_ -0o03_1 -O,0O25

2437010.5-G.31639632-_,8320_$t-2°O65226_? O._T45_O-G, OO¢O2231-O_OOOIgI7g -0°_66g O.lg?_ O,OT_-_°316_96_2-_°25_a0920 0°_278_37_ OoO_145_O°O-O00_g6T_-O._OOI670B -0o_580 -0.03_1 -O,OO20

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0.5713_1-5.1og1_233 O.OO?5O25O 0._,_1_2_76 O,O011g_O_-O.O00171_5 0.0115 _.00_7 -g.O04__43?Z_0._ O.ST_lZ_2_-_o?O_2163_-_°O_63650 0,0_?36103 0°0615596_ 0.000_1915 0.5J95 0°021_ -O.0096

0,17_292_°5.t3273782 0.0_063_82 0o03?36105 _o_6_9-3.00017178 -O._gOl 0o0_75 -O.OO35Z_?ZO0.5 1.166_3377°_.6359_5_-2o0116_600 _.0)T2?_96 _,0C195_$ O°O00660Zg 0°1695 3.1_gO 0o0596

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2._7566?_.?_625660-0.¢2_61715 0._¢686_12 0.0_3517_9-0._0016710 -0._754 O.020! -O°OOT| "

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2_37520.S 2oI0521T_-3°lg"_J2-1.T396_lS8 0,6_OZ2600 C°0_419|11 0o0016_15_ -0.1969 O.OSIg 0.,_006

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_.2_20_697-_o_155725_°0._5|_Z1_1 0._56_g0_ _,0_2515_-0.000|_126 O_OS_ -Q.OII5 -O°OO562_3?6_.5 3°5_12_lO-J.331_6566-1°51*'_3_g6 0°_53?t03 ¢._¢51T65T 0,00_089_ -0._148 0°0_05 -0°0165

3.S_317310-3,65913379-_.06_2_253 _._537|_3 _.O_$SaOS_-_°OOO1426g -0.0_1! °0.0050 -O*O050

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1965019622-074

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'*: JPL TECHNICAL MEMORANDUM NO. 33-188

I

_fPRGZ STCPWISE R_GRESS|UN PROGaAN

N MTOTAL SOlN 5OOUT D_AG

6 l_O LOoOCOOOOf-ZO Oo lOoO0_OOE-O9

NO. OF CO_FF$ tN _EGRESSIUN - 0 SU_ OF SQUAAEO R_StOU_L$ • 3.42265E-L_ $.D. UF UATA = _._a09[-C9

COEFF$ IN _E6AE_$10_ CO_FFS tlQr ZN R£G_kS$10N

t_OEX COEFF $.0. COEFF/_,D, I_EX P_OICTEO ICOEFF/S.O,)

3.106GE-OT3 1.50_6-0?• h5005_-055 r°L_e_[-066 1.313_[-0S

NO. O_ CO£_FS t_ _G_ESSZO_ _ l SUM O_ $OUA_£O _IOUALS - 3°_Z_6SE-I_ $.D. OF OArA - _,_0362£-09

_O£FFS IN R_GR_SStON COEFF_ _01 IN RE_[SSt_

I_EX ¢OEFF SoD, CUEFF/$.Oo _NOEX P_OICTEO tCUEFFIS,O.)

3o168_E-07

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_0° OF _O£fF$ IN _EGR£$$1rI_ • 2 SU_ OF $Q_O RE_IOUAL$ - 3._Z26S_-15 S.O, OF DATA - _o62_S0£°09

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1965019622-075


XSOLVE

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2.ZAb_I8ZI52272_Vl-CE 3°9_SEblbSOuSOA_S7-03 9*9973qEblSlEOEZSL-OlELLZPTIEAL CCRRECrlONS

!

1.757210_2412u2_86-1_ C,000000_0O0G0_£_0 O0 E.E10394316378_272-1_ -|.0718030179981090-16-1.090_299533199Z10-1_ |.8_qqq_TIIT686_9-13 -I°_ABAIbIS9961_ItS-11

NE_ ELEMENTS

S,2¢26_5_20575q239 O0 I._$327T39]AE_581Z-_I _,EVlOTSBE_'lll_88_-Ol 2,06|OOT_IVIObS_EI-Ol_._6TlE198327909 OO _,TTT385014_VTOS76 _ 5.27qbAbVlE_662_lq O0

KEPLE_S t _D LA_ _u

2._619_T_115_C7876-0_

l_ DIFFERENCE N_GLIGIE_ER_S|I*Ilx 0._5T808_[-08R_S_I) • U._5780866E-O_

PLCO HAS CENYERGEO _T S ITEm&TICkS

eND _ Sl_X_ wtuE OF ....... O._STeOfl_VEO_

dULIEN _ATE .................... 2617b10._0

ELAPSED T[_ l_. OAYS ......... _O0.O0

_UV_K _F Ir,lrGKAT_ON STE_S.. IlO.

51GX_ SOU_RE X N............. 0.3_22*_E-L_

x • 3. SCILZ31O Y - -3.331_6366 Z - -1.51483896

_LDC _IL_ _EGI_ TC _RITE A_ E_H_EalS

e.ee STATI$IICAL _NACY$_S FOR AES'_UALS IN ..... DELLA X _ELTA Y D_LTA Z_EA_ OEVllTlOt ................ _-S_MfOELTAIlN -Uo63_B36CBE-08 -OoA36_|?BE-09 -O.LT6BIElOE-OtSU_$ CF S_U&RES R_S|_IJILS ...S_vSU_IDELTAt-EI/N _._2_TbtlE-1S O°IZT_QT_E-I_ O.7T6769_-I6STANDARD OEVlkrlOh .............. SC_S_RTFISR-_O_-E) _.lTASOETAE-_ O.lO6b_689E-v_ G.861_Z|SCE-08_AXINU_ KEEl DUAL ................................. C.EqOSTIVIE-CT O. S2SOTABEC-OT _.|9|lbBASE-b?mINIMUM AESIOUEL ................................. -C._125ZT_OE-O? -O.AA+bTD23E-+? -0.23o76101E-07

leee STATISTICAL IN&LYS|S FOR RESIDUALS |k ..... RADIUS VECTOR COS_ UL DLATIOB_EAN DEViATiON ................ HO_SUMIDELTA)/N -C*I_)_O_&?E-G8 0.33336370E-[_ -O.EE710_3_E-OqSUPS CF SQUARES R£SIOUALS °..SR_SUN(DELTEeeE)/N C.181126_3E-16 O°|ZBTbqITE-|6 _.|25AT[vqE-18STANDARD D_VIATIO_ .............. SD-SQRTF(SP-_D_tEJ U°_&qAobzE-G8 0,3S886622E-08 O.237466EKE-09_AX_MUP KES|DUAL ................................. 0°783_77C2E-08 O. lG66E?SbE-O_ O.ALbTT_4_E-39,IN|NU_ RESIDUAL ................................. -_.913_73_E-OB -OoASTAAAJ_E-;E -O.E_IALAbVE-OV

ECL|PTiC PDS-V_L FRO_ TRENSX AND E_IJATORIAL P_S-VEL AFTER ROTATION FRO. _¢LIPT[C

_o3_9356648772_82_ CO -t°812_q_bSASITl_68 GG -6.02126_b_T335_26S-OZ5°_856_4918763_42-3) _°34_23548gq199_69-¢3 -1.46606_686_!0_CA-0_3.3_93566487TZ_823 0.3 ..3._TT?bS99T_60|ISE C_ -I.STEIbIEO252I._Q9 COS°58565_qTET634_?-¢3 _.qbZE_Ob71193_OIE-_ hVg226608GAO193q_-C3

8EG|N ITERATION

EPOCH VALUES LDUATOK|AL _3728_.S0

_.3_93_66_8772_23 DO -3._7_TbS997_6011_8 _ -1.$721612925Z12609 DO5,_es6s_raT_3_?-o3 _.q_2?_EbTIT_)_O?2-_3 |*9922660806OlgS93-03

ELEKt_.ATS CHECK FRU_ SUEK ELEMTS

_.2:26_5420_7_q039 DO I.._277393_G_sq_o-cJ _,8q1075O6_9333613-02 4oOSEq71AbT314E_5_-OIS.b_1)05207S6_8_5-02 I.EbbOE_82E2CSg7EE-GI 5°2796_b?38166ZIA6 00

TAAhSEDS_ PO_ P&TEIX CHECK

q. T134?_qO1782*16-Ol 2.263Et7382127ARES-GI T._E_yKOA29OEIE71"-02-E.S65916A93_70_II-_I 8.q_7qqTOTE_Y675_q-oI S,E79AEb_bY_?SI069-O|Z°E_6_|_2152_72|2_-O_ -3,q_lSlbI31_ETE_HT-Cl 9.18768275TOC3_A3A-OI

ECLIPTIC ELEMENTS

5°202655_2357S9039 00 1.45_ETT3936¢_SYEO-G) _.EVIOT_BAAVS33613-O_ E,2810079291063491-02I./_AATSEI9832Tqll O0 A,?773E_O1A_qTOgZ2 05 S,OTYAAAq_E1662t_b DO

ECLIP_[C PeR MATR|X

9,TI3_Q_qOtT82_16-¢I 2.3656)380?_072339"-0I -2,275993806133E15S-02-_.365916A90770_81[-_1 q.716080_TOS_IZIA-GI I.AEI)gZS_TISTIEOE-O)Z.2_b_iE2|S2272|ES-02 E.q_SBAIAEBb_O_CE-O) 9.997398_ISI20605T-OI

i 71

I

1965019622-076

JPL TECHNICAL MEMORAN,'_._,_ NO. 33-188

EPHEMERa> FCRNJT FOA EACH JULIAN OATE IS

JUL-UATO EGUA. X EQUA. Y EOUA. Z EOUA XOOT EOUA YDOT _OUA ZDOT 7PFOX 7PFOY )PF02ECLP. X EOLP. Y E_LP. Z ECLP XDOT ECLP YDOT ECLP 2DQT 7PFOP TPFOO$ODL 7PFDO

2633280.5 3.06933662-3.47376597-1*5t216120 0.0_$38565 0,00406224 0.00199226 0.2E02 0.38_2 0.1_793,_493_662-3,0124946_-0,0602|264 0.0_5§0563 0.00336523-0.000|_661 -0.0266 0.0950 -O.O03T

2433320.3 3.$6656304-3.269087|1-|.,896_344 0.0_$27_99 G*0_526898 0.00213154 0.2218 O.OOgT o. teD1_.56636304-3.$9189036-0.0639_602 0.03522099 0*00368202-0.00U140B7 -0.0430 9.1065 -0.0069

2433360.5 3.77024730-3.05242233-1*A017208? 0.03493460 0.0_'.$5800 O.00ZE_ALC O.l_lT ).3231 0.19123.77074730-].35817105-0.02142_64 0.0_403_6B 0.00600069-0o000|$436 -0.0_24 _.tO|l -0.0024

2433400.5 3.961062|6-2.02462026-l.3036336_ 0.00_?770 0.00583023 0.00238922 -0.3062 _.6622 0.16173.96106216-3,11209905-0.07672230 0.004577"0 0._0629952-0.00012773 -0°0007 0.0355 -0.0080

2453640.5 4.13670254-2.S0631227-1*21369J23 0.00_29_|3 ^.0060_190 0+00230645 -0.1091 0.29u2 0.11534.13670254-2.85440430-0.C, _BSSB 0,004E_IL5 C.0_657703-0.000120_6 -0.0539 0.0400 -0.003_

24E3600.5 4.296911|8-2.33830801-1.1_+23224 0.0038._635 0.00631242 0.0026_0c -_.1539 o.20_J 0.02726._9691118-2.S0624080-0.00_J4436 0.00300633 0.00683]tl-0.00011267 -O.O_qO _.0220 -0.003_

2433320.3 _._4098241-2.00L62171-1.001613_4 0.003)9678 0*00652052 0.00271436 -0.1466 0.1_4 0.03354._098741-2.30022981-0.00067906 0.0033_70 0.00796220-0.0001061_ -0.3368 _.00_4 -0.0032

2433500.5 4.56027089-1._1702371-0.89121273 _.00296798 0o006?0522 0.00200601 -0.0_75 _*076" 0.022|4.36029089-2,021603_2-0.09663115 0*09296790 0.O_T26TZB-O,OOOU953T -0,3t1_ _*012. -0.0021

2633600.3 4.03026343-1.54053043-0.77742817 0.00232761 0.0u686037 0.002883_8 0.9647 _.092_ 0.03014.6382_3*3-1*72725000-0.09830306 0.09252761 0.00744003 0.00008619 O._OS5 0.0226 o0.0017

2_33640.5 4.2703_0_8-1.20813509-0*66067500 0.03207§33 0.00700O02 0*00205232 0.0O37 _./2.1 0.0432 ""6.7703_096-1.42630_46-0.10156130 0._20_33 _.00759_79-0.00007662 O.OCA7 v.02q6 -).0007

24336B0.5 4.06413050-0.90_7618-0.5_138952 0.001_130J 0.00710043 0.0030101_ _*0336 0.2_ _.09974-84413050-1.11908Tq3-0*10442916 0.0_i61303 C._0721020-0*00G06621 -0.:_53 O.O_OO -0.00|2

2_33720.S 4.89727614-0.o0982120-0.+2001037 0.0011_267 0*_0718076 0.003036_[ -0.0466 J.3266 0.11736*8q927614-0*80913024-0*10689_67 0.00_14267 0.00781228-0.0000565J -0.0205 0.0673 -O._O_g

2633760._ 4.93547|_9-0.4||06296-0.2970243_ 0.00066620 0.00_263_Z 0.003091/2 -0.10_3 _.2331 0.C9006.93347139-0.49530476-0.10094600 0.00066629 C.00781_1-0.g0004606 -O._O2B _.0351 -0.0_)61

Z433O00*3 6.90252673-0.12071150-0.1f282_00 O.O00|03qS 0.00726937 0o00311403 -0.10_3 0.1273 0.03304,932_TO'O*17933044-O*llOS/e_k 0.0@518595 0.00T90_21-0.00003539 -0.0362 _.0231 -O.OGc,3 +"

2633840.5 4.95032227 0*17011061-0.04800066-'0.00029631 0*00726701 0.0031248_ -0.1723 -9.053! -0.03_6.93032227 0.13694333-0._|17764_-0.00029631 _.00791034-0.0000_36 -0.3331 -0.0116 -0.002 _

2433880.3 4.72082407 0.46027210 0.07&0_589-0.30_77038 0.00723602 0.00312345 -0.1720 -_.22_9 -0.10304.92082607 0.60208602-0.11206063-0.00077838 0.00780163-0.00001362 -0.0393 -0.0660 -0.0021

2433920.5 4.88508244 0.74E6305_ 0.2016_207-0.00125811 0.00317326 0*00310905 -0.1190 -0.205[ -0.0877 _*4.8|8082_4 0,76706204-0*11L86530-0,00123011 .*0_282204-0.00000261 -0.0309 -0.0608 -0.0003 ,"

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• leo le SUPNARY eeee e_e •ewe eJe l, • ,GENERAL ICEhTIF|CATI r , FOR PLO_

PJ.O0 t! EPPE_EKIS FIT* _ PV TAPE 10 50URCE fIP£ £9005, 40 UJY RESICUJLSA_O 4 ©aY I_?EGRJY 51£Pt NRITT£_ 6,'23/64 8Y CEVlk£ FOR JUPII_CCOROTaPE IS Ege dRITTEN 8Y OROZCCBY PRE-EPHEM FRON ¢[RR[CT£_ OATJ_|TH J 2 lAY " SIZEt I&PE _RtTIEN 41_8164

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6oC_2C61_L_279Q_6°O_9.tT_6_522_Og_TL_-Ol

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e_a_ STA11STICAL AN_L¥$1$ F_R RE$|O_AL$ _N °...° OEL1_ X CEL_P Y DELTA Z i_-_EAN OE_IATIC_ .°.o ..... °°,o°°o_O-SUN(_£_TA)IN -0°_)C8_¢92E-C8 -C.03_5L_22£-C9 -'.1768_14E-05SUMS _F $¢_AaE5 RESiO_JLS ..°SR_SUPICELTAot2)IN ©°32_37Se6_-L_ _o42_60|26£-1S 0°77676q_-_6STJNO_AC CEVI_TION,o°o°° ..... oo.S_mSQRTFIS_-_O_Q2) OoLT4_O270E-¢7 _o2C_637CC_-C7 0o86_2L?_-00_JXiNUM RESICUJL °,°o ....... ooo°,_°..°o-°o,,oo.o,° O°39Q_718_E-_7 C°_075C_£-C7 0.|_1_8E°C7_|_!MU_ R_SZC_AL • ..... ..,.,°°.o°...°oo°,o° oo°o° _0o6|_5_7_7_-C7 -_o_6466_3E-¢7 -0o2C676¢0_E-07

oe_o $TJTISI]CJL ANALYSIS FOR _£$_DU_L_ IN ,o.°. RAD|U$ VECTOR ¢CS| CL CLAT-C6• N_A_ O_¥1A?lO_ °,.ooooo°.°° .... _-SUM(OELkAIIN -Oo_S_4C_g4E-GO Co_]_76701£-_ -0o_87_05_7E-0_

SUNS OF $_UAR_$ R£SIO_JLS o°°$R-SURI_LIA,e2|/N 0o_8112659E-_6 C.L_76_I|£-L6 OoL2S672C_E-_8_ $TA_OA_C _£_IAfI_o.oo°.o°,,°oo,_-$QR_F,$R-_DQe2! 0,3969|C50E-¢0 C.3588_413£-¢8 0o20746_88_-09

_XlNU_ AESICUkL ..... o.,°o°..°o.* ......... *oo°°_o O.?B357_IOE-_8 ¢.1_6_075_E°07 0.4_6777_2E-09 __|NI_U_ RES[CUJL °.ooo°*oooooooo.o...o...°°.ooooo. -0°913473_£-_| °C.6_76_62_E-C6 -0°6_1_L692_-0_ t_

[,74

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1965019622-079

_1 J illI I _1 nl

JB_

.JPL TECHNICAL MEMORANDUM NO. 33-188

APPENDIX Iil. PLOD II PROGRAM LISTINGS

PLOOMN HA|N PRCG_AN FOR PLOD CHARLES J. OEVINE t/Ol/6_ PACE |

CCC o..I*o.._e.._DIHEN_'CN STATEHENrS •O'.*001DIQOOO.Q*IQOIW6gOOI4OOQtOm'_Illl

C

C_|_ENS|CH _HAX(6),UHIN(6),_AX(6),FH[NI6)

_|M_NSIC_ XDSA(I| ,RH(I|_g_qSICN _FLT(_

_ CIMEN$10_ YSTATS(tI3}_|uENSICN XTSilJ_(TE(LJ

_ C|HENSInN DH(IOJ_I)_$|IO|_DTEHP(II_ ' I_SIDN CAR|I},,_U(I|IXLIT_I)D C|_E,_S|ON XSTATS|3,3)

_ DIH_NSI_N YTIHE(II

ClM_SI_k INOU_L,_|D CIN_NSI_N _K|I_,AKSfI_

C_ C|_ENSION XLB(_),I,_T(3,3)_WT(3)

O CIM_N$I_N P_RT(3,_)_COSOBII|,SI_O_|I) ,XJDO!I)

_ _I_ENS!ON ELEM_?)_EP$_|I),OPXYZ(6) , X_U(I)

D DI_N$1CN FSrOPI(_|tFSTOP2|_)_STEST(_)_SIG|II_{SOLV_L_,)1 _ _PSILN(L)

_|PENSI0_ PLANET(_|t_WCR_(2_|_NWDRD(2_),LW_R_(2_)_ KWORDf_?)

_ CIMENSIDN UELT_(3),XNU_|I),SIGS_(I| _SLIL_ ,XMEAN(I)

_ DIH_SION Hll} ,TM_X|I_

C _I_EN31_ S'_TENE_TS (FROM _B)P C[WE_SI[_ r_ATE (l) t XJD|1|

C CIM_NSIC_, FOR _w CU_H_

_I_ENSIC_, DUMYI(27201:CUMY_(ZZ_bI_Z2UL'(IIIZ2_N|I3_Y_(LI_Y2_|I|,1X2rL(I|I_ZDHll)oZDCIL(I|,L_CTW(II_YDCTLllJ,YCOTM(I)_O_TL(I)_2_TM(I),,VZL(I|I_Z_II_#_YLfIJ,VY_|II_VXL(I)_VX_[L)_XJDL(L),

pt_CMN MAI_ PRdG_A_ FOR PLCO CHARLES J, CEVINE 7/0Z164 PACE .'

J_O(1),_'ODII}._S(2)

C o_t_iit.,totlo,ENp DIMEN_IO_ $TATE_ffNTS t*_oQi_itoli_.,_•o_•_•1*o,

C •_ C_P_CN SI_TE_E_TS o,_C_HON L)'_YI._b4V2_Z2OL_Z2DM,Y2DL,Y_M_X_LtX2_M LD_JTL,L_OTH,

IY_C|L_YD.T_,X_C_L,X_CINtVZLpVZ_tVYL,VYH,_XL,VX_XJDL,_JD_tHSL, H_ ,2_UPY_, [i,S_t_IP_N{_PT,NOD,JOC,MOO,TS

C EC _A0 |NPbr _ FOrMaT S_AIEM_NYS

J_Ip_:-. _ _ .....

1

+y+ii

i


_ ptt,'_.-A pl|_ PtO_, _ot pLCD C-_LCS J. CEVI_E T/¢1/6_ P*GE _

41FCINA||_I|_.A6,A])*I3)

_ c dtfA0 |kP_T TAPE _,II_,IhVOICIIIglcI+IZ |*llulJm0111*|_l,22 1,

l ILbCICIII.ImI+Z_ )+llb310ll)lltl+ _lgIlbl_l_lllel*Ii_lll;_ F;IIATI_2A61|QI6|

£_0 GIC+_P 0_£C

t • eee • * • o_eoe • • *Q • •C _.

• $ CC_Y_qu_tE&O IqPbl TAPE $1_6I_Lq*LAP,RAqI_I_*JA_._*NCBC0.

| I_ i P_Jl2q • l TIPA_ IkEPCCH* _IP*O_e_gLPT ii_

46 FCIJ_I| ; l'.l_ !

E_O gl_'P ThO

CGs.OUP .** T_A_E

C47 CCkTInSJ_

C PAeA_tTEI5 F01 FCI_TS_I_CLN_$ SI_P SIEE,DIFF _ASL[ CCmv.,CrC.

PEAU lmP_l IA_£ _e_lt_£ *JC .II0 +q;_ :It o_-P3• l FCI_&TIS|_Fll._e_I_+II

C _C_*JIr'b_lSCltt_P_eAdE _|_ IN pOII_A_jS_ ,IUk_ _HJPTE_ TO _ IN ¥_PGV

4_ CCkIINUE

R_AO INPUT _P_ _,_O_MCAX*IqA_&II_I|_T*N_AIkI*KPIINTtNSTE_EP_I_* PtlNTOPT1 q_l_,PVES_,_tet .

: 2 STESI-_PSitN,CO,SL'CAT, SCi_,CEPSIL*t 3 FSTOPI.FSTGJe_ _I_ OPI _.

50 FcIrArlIOI]/4EI?.I/2EIT.I. IFIZ.GlC"C [_ _kOu_ T_t_EEC_eeoo_es e_ # eeetoeee-te • • • eeeee_e eeeee • • • •e_e • ee_ • eesteee • eee eeees • seeea • e:ee_: eeC

PL_'JNA ISLE&PllUGqAp FOR PL(.r) CHAItt._S J. r'EVlNl_ 7/'011S_ PAGE 4

_.JLL I_lkPl IkT,3t_111_ OUTPUT TAPE _w_Oll

20IT _¢I_;_TIi[*OI I$_ WEIGI_; F_TOA/J |CILL _IPT[_T, 3,3) ,_CALl. O_lJ_PfAC_ I_ IU,I !_[LITE-¢ £&L.*I&4_O* )1 AUCALL OP |NPT | _.IS* _I][TI_ 11_0_, _tlr II, | I]_PEA_I*1 !I_OP 1_3. IAlSq_6S358979_ *2.0

_) XXJ*Z_3328Z*A23¢ £1LL O_LIG I*_IE FOI EPSILO_

CALL OeLIQI_XJ*E-St ! _."D EPSI.-I_PS I oT_OPi _,D CCSO|_COSF| EPSLI

S IkO$-S |_F(EPSL !

OC 1_0 I-|,GUPIX I I | -- 1oOE_I|

1_) UPINI I)*L*OE_$|UIFCND'*I_ |XTsZ_(T|-LXCCI_IR+|*0

0 XC_.&*O*Ox|_olr-l,0 _ *=XN|OOYINSOOYNWPlI_-Z

0 _PSO*O.O <rITEGAX_O ZIUt¥'|I*k;LA_2GG YG 1211ZZ_$hI_4_

Z! CCOCTII_JE tSIIIITE OUTPUT TIP[ 6*6_*_IAPO_NCHAN

GT FOR_ATIEAH LOAO TJPE*A6_ISk ON ¢1_AI4. +A$///)P_INT GTwNTAPO__¢_AllP_USE ??T??C_LI* S_q_ |RT&PEIREM|llO NTAPE$C TO 24

_ _17 C_rlNUE•_ _IIT_ _T|_T TIPE 6,ATgHTAPO,_HA_

_ PII |NT 6T,_TAP,3+ _KAN

-, U

J

+\..+/

"r _ -- II II++++ + _" IU+ + + + "_" , ......... , •" .--'_+ ml_' I

1965019622-081

JPL T_,CHNICAL MEMORANDUM NO. 33-II98

PLC_N PAIN PROGAAPFOR PLOD C_ARLES J. DEVINE 7101/AA PAGE

P-USE 77?77CA.L $DN_ I_TJPE|

RENINO NT&PE Err.GO TO Z423 CONTINUE

_I|TE OUTPUT ?JP_ 60?EEINTAPCtPCHJNI_TAP01_ANPRIN_ ?Z81PTAPCwPEHANoNIAPGvNChA_PAUSE ?7777CALL SDN_ ImTAPE|CALL $DNP |NTAVE)NEkIN9 MrAPEREW|ND NT&PE

24 ¢CNT|_EGC TO 1_5,Z6,2;._gllkSTEP

25 CENTIMEREiD TA_E _TAPEm_H|REA_ TAPE _?AP_IXHZ

_ X_mXHE-X_I6C TO 29

_6 CENtimE135 FO_AfI3_H NCC FR_ $OUNCE tAPE HEAOI_I$11X,|EA6 I!

qE_D TA_E _TAOEINGIL_R|_E OUTPUT T_PE 61|35_NGILPRINT L3S_INGIL (TI_I_L_E_|NE_ TAPE _TA_EthBE0kCGC TO Z9

27 CENT|_JEREAD TAPE NTAP£_Ik_R_TE _UfPUT TAPE 6tl_tNGILPRINT _35_INGIL t|l_|x|0Z_lREAD TAPE NTAPE_N_C_DREAD TAPE MTAPEtXH|qEAD T_PE _TAPEtXH_

0 XPIXHE-X_I2_ CCNTINt_E

E¢OIQ_e_IIOO_O_eOOI_OQOJe_eOBQO_*JOlei_OOOOD_I_e_i_Q_O_O_OOOOoteDOeOaOeem¢CC GROUP _Qo FEURC_gIoQiII_I_Qoom_oeo©I_o_oeome_oOo_oeeo_to_QQo_I_oeB_teo_Q_o_o_oIQQ_IOe

PLOO_N M&IN PNOGRAN_OR PLGD CPJNLE$ J. _EVINE T/OIlS& PAGE &

CCPPUTE PASS DF 9L_NLT_oFON T_ANSFEN TO CERLvoANO OTHERS°119 CCNTINUE

NPLAN_NECD_£C

_C LL7 Iml,L0D |FlO_ll1333*332o333

333 C_$111_L,_ICP(IIG_ TD LZ?

_17 _E_fI_UE¢

IF|_-NPL_N|2Dg_2C_|L2G_ GC fO (2CE_91_EART_20_ CC rc Z|_20_ NPLA_mN_LA_|2_| C¢_fII_U_

_ A_-9.0L7_DEC_89SCODD_

_ $CRT_UISCRTF|X_UI¢

C TP|$ IS _Pr|0_ FOR TEST RUN kITH ALL PERIU_GING PA$SE_ ZERO wGC TO (_,2Z_h_T_ST

r£ 2L_ I-Ltl0£ ?|_ r_$|:)10°0

C_mllE OUfPUT fJP_ 601L

tL FCAX_rlL_Dt Al_ CONP_IED _ASSE$ kiTH P^I_ _0DV A_0 EARTH sEr| TU _R||lll

CL_8 C_TI_UE

C

77

1965019622-082

JPL TECHNICAL MEMORANDUM NO. 33-_.q8

PLUCU_ WA|_ PROGRA_FOq PLC_ CHARLES J. C[Y|_E 71C|16_ PAGE $

C _C$1"¢OSF(EL_F(_I)C

_C TO _I302,|3_IIt_CLPT

¢ _E_ ELEPENT$ N|LL B_ T_A_$ FR_ EOUATC_IAL TO _CL|PTT_1301 ¢C_I_UL

C CASE _NE.SCLVE FGR LCNG A_CC£.|_CLi_ATi¢_

$W-$1NOeeCOSI_CCSOS.$1Nf_COSLP SL-_CSO_CCSI*$1NOSeSI_I.COSLC¢D CILL $P_R(SX.$Y_SZ._H_G.XLN.XLAT_

_ i'aFPl_3o|_L_2653_Sq793Z_/_.

_ £LEM¢5)'_AFPI-_LN_LEk(4)-_AFP?-_LAT

_ CJ$_ TWO SCLVE FCA PEAIHELICNtI_CLINAT_0k¢

P SY_CCSQS_SI_I-$1NCBeCOSI_£OSLC SZ'COSOB_COSI_I_O0"SINIoCOSLC_ CJLL SP_SX,S¥_SI,_CG.XLN,XLAT!C_ C_EGA-HAFPI-XL_ :

C _ECK-_I-XLJT_<IT_ OUTPUT TAP_ O.1303

1303 FC_AT 1_0,_O_ ELF_£NTS RCTATEO I_¢LU01._t.- ! CHE¢_II)CALL _OUT_ritL_M,?e ?_C_ECK_itl)

CC NG_ CO_P_TE NEW S|NP,$1NL,SINIg&NC CQ$C S|_P-SINF(ELtP(6|P PER|HEL

¢CSP-COSFI_LkP(_)} PEI|HEL• $|_La$|NFltL_NlbI) _ONGASNP CGSL'COSF(EL_M|_}) LONGASNC S|k|_S|_FLELE_(_)! INCLIq_TC CO$|,COSFIcLE_(¢)) INCLIN_T

1965019622-083


PLQDMN MXIN PAOGRAY F0R PLCO C_4-LES J- 0EVlNF 710[164 PAGE q

C1)O2 ¢'._T|_E_R_ELE_EhT$ _AVE UEE_ q[AC IN [_L|P ([_ONt. Y COMPUTE PG_C ¢C_PUTE PeR

0 _CRI_ .)-C0$P*C0$L-$1NP*Sl,4t'¢C_I PXC PCRIZ_II--$1NP*CCSL-_GSPoS_NLI_O_I =X

O PC_I3,11"$|NLeStNI RXC PCR(LgZ}mC_$Pm$|_L*$'NP_C0"L°CC$| PYO P_R(2w21--SINPe$1NLIC_$P*£OSL*CO$1 0Y

_ p_R|),2).._GSL_Slp I qYPC_|I,)I-$1_P*$1'_! Pl

_ PCRI3*3)e_OSI _

C _GW CA_L T,.AN$_ TO _ TO XYZ,XDOT,YOCT_Z_Of

C

r

C T_h _ILL AL_O 6£ _AIN P_Q6_A_ _ET_R_ POINTC

C ***_e*65 CC_T|'_E

£C $2_ I"q,3

U-AX_I)--_.C(*)8

:C _24 J'L,_

0 YSTAT$_],J)-_.C£ $24 x$_ATSt|,J)-Q°¢

WR|T_ OUTPUT TJPE _1)C4Lt64 _CP_TILP_,90H ECLIPTIC P_S-VEL "_0_ TRA_$X AN_ _QU_TC_IAL PO

I_-VEL AFTE& q_fATICN FRCH ECLI_T|C//I

CJLL _'2U_Pf IXCLC,_,_VOLD,)I_!

PLOO/<_ _&l _. PROG_t&I _ FOR PLCO CHARLES J* CEVI'/E ?ICIIG4 PAGE /,O

C qFTER TRJk'_$X_Ot<LY KGTJI_ x'_Zv_lqr_T'2

C _'_ SET UP TRJ_$ _Ce' EQUA TO ECL;.'I"IC$ IN8--$ |_Ct_

I_LL ST|t_e,$ (XCLC_VOLLI_OELfA*XLtS,CI*_.T* CC$_eISI%C tkPCT)r.iLL OOtlT;_T t Xt_LO* 3, )* VCLII_ _ i ) )

C _CW Xot.n,vc1._qb I_1 ECUAT_I41:L(;C IC *,

C

_ _-E_ q_A_i TAPE AT _PCCH FC_I INIflAL v_L*J_$C _|APE-IS" _AC _-APE _TAPE THIS IS T_]_ID |_I_.IT CHC|CE

CC_LL OPINPT tXJ£,1,T_AX,! |

_, XJ£O-_JO

| (VOL_(_I, V_LD (_ �!_)vH-l, 3 }P, 1_ UBATE-XJO)), ?,_

5 k_lT_ OUT_'UT I_P£ _,8,C04T_

P_ I_lf 8_CBAT[It _C_'_AT!|P_,2$_" $OU_ICE TAPE STA_IIS A1 FIC.I,Z_ I_IT_'GRATIC_

ISTCPPE_ISO_ CPCRATC_ Rr _CVE rA_E$ , W_IT f_ SEE IF PRI_GRA

L_ CALLS FCR _c_ _AP_$/I)GC T(I 1077

2 CC_T I_IUEPICKSP_CE _I_PE

4 CC_ f I_IU£

_£ fO (ICO_tI_C))tK_YLeO2 CCNT I,IuE

£

_ [_E_TIF fCAftC'I

_qlfE Otl11_T TIPE _,543,_pSILtX_EA,_EA,_KA_ILA_tKAN_'_'%_STE_t

2 'tECLr'T, 't11_ L, J_

I

_ 79

1965019622-084

m

JPL TECHNICAL MEMORANDUM NO. 33-188 ,

PLO_V_ _tik PROGRA_FOK PLCO C_AHL_$ J. CEVINE 710|16_ PAGE |1

9 2_H DEP$_L _E_b,812AH MEAN mCTICN INPUIT *LIA.e126_ _A_; *14126H KAP2 Jl_126h LA_ wlRI26H _N

tlRIZA_ I_AP mI4126_ NSTEP,14/26_ _P_I_I t_4/20H JAN

*14_26_ N_CLPT ,1_126_ _

cC _C _A _RIT_ A RCaI_UAL IRPE r_ IN-t) |_TE_RArIO_S

G_ TG IICq*IIOI_RINTtO_ C_L S_N_IITA_[)

REbIK_ |T&#_

uCCN_4.0_RITE TAPE IIAP_tI|dCKCI_)_I*I,Z2I,IPLAN£Till_I_I,21

i _ellc liP_ iT_E,_oG_YiUC_eXJ_G,TX_XiFSTCPZ,X_C_Y,FST_P2K|2_RTAPEKI_NPRINTKIRmKA_KTA_£_|TAPL

xtk=_

L XBODY_UCd_ *XJCC,TMA_,FSTGP_tXN_O_Y_FSI CP_|LO _CkT|_K.*E

cC

EP_C_ 0PTICN$ _N_ REPRINT OF EPOC_ _TArPLU$ _FAN OPT|_

_ TG ¢IGOSt_O|C_ICI_NEPGC_C

.- iC08 ¢C_TII_[ _PINPT• _#l_k UUTPu! TAP£ _,IOIS

101_ FCR_ATlJPOtS6_ INPUT OATA IS _Y CAR_S IN DOUBLE _P_ECISIONI C_C/II)

CALL DOUrPEiACLC_3_3$¥GLD_3_)IGC TU 1030

PLODNk PAIN PROGRAPFOR PLCO CHARLES J. _EVINE 710|16_ PAGE 12

Ceaeeee*eeeeeeI*ee_*e_*ee*eeueee*e_e*eeeee*wIe*e*eee**e*eeeeee*_eeeeeeee_eeeeeC

LC10 CC_TINUE C_LZPTNRITE OUTPIJT TAP_ 6t_O|? OP|NPT

10;T FORNAT_IP_*46h INPUT OATA iS BY CARES O.P° ELLIPTICAL///ICALL OOUTPE(EL[NITtT__R|TE UUEPOT TAPE A,|O|8

_C 1019 I_|*_0 PP[I)=PQRII_||P PC|II=PQR|2*|)010_9 P_|I)IPQR|3,1)

C_LL OOUTPT|PPt3_3,P¢_3t3,P_*_3|C

kR|T_ OUTPUT T_PE 6t1021|¢21FORmATII_O_36H TRRN$FO_RTIO_ _CR XYZ YYZOOTI/II

CILL OOUTPT(OPXYZ_6_ )GC T_ 1030

_Q_eeeee*_eeee_oeee**Qeemeee*ee_*_e_t**eee*_*oee_Ieeeeeoee*_*_e*_*_e_eee_*eeeC

LOIZ CCNT|_UE T_P'_RITE OUTPUT TAPE 61|OZ3|C23 F2RNAT|I_OtRUH INPU! OATA FRO_ SGURC_ TAPE EPOCHIIll

CALL OOU_PT(XOLOm3_3_VCLOt_3|C

1030 CCNTiNUENRITE OUTrUT TAPE 6_1016

|016 FORNAT_t_O_2_H END UF INPUT O_T_IIII)GC TO |I_32*|034)_NEAR

1032 _RITE OUTPUT T_PE 6_|0_5|02_ FORNAT|IkOt2$H PEAN POTION IS CO_PUT[OII/|

GO TC _00]10_4 WRITE OUTPUT TAPA 6,|02_,RREAN|OZ6 FCRNAT(|_O*37H _£AN ROTION IS HELO _|XE© AT EIE.81//I

GO TO 1003|UO_ CCNT|NUE

NRITE OUIPUT TAPE 6.|02TIOZ? FCINAT(|_O*|R_ BEG_N |TERATIONIII!|0_0 CC_TINU[

_R|T[ OUTPUT TRPk 6_|O_|,XJO0


PLOOKK PAl| PROGRAP FOR PLCO CHARLES Jo CEVIKE Tl011_ _GL L3

lO_l FORMAT(I_OtZqH EPO_ _ VALUES EQLATORIAL F12.21#_)CALL OOUTPTIXQL_t3,1e_LOtlt))

_eeeoeelemooeoeeeeoeeJeeete_o_eeleeoobHtaaeeJloloeeeoooomeoeeeeooeeu_eoo_eem_!

CT EONTINUF

PSPaHtI|_SL-H(2)

XJCM-X_Oll)XJ_L-XJ0(2)VXV-_OLP{I)VXL-XO_.O(_|

VY_'_.LOIZ)

VYL-XQt. O{S|VZP-XOLO(3|V_L-XOLD(6)

XCCTMvVOLOIL!XCCTLmVOL_(4)YCCTM-VOLO(2)

YCCTL_VOLOI5)ZCCTK_VOLO(3)

ZCCTL'VOLOIb)CCoeeeeoooeeoe,,e,*eeeleke ee*pe_ee_,e_eoe_eee eee_eee_moeeeaeeke_e_oeer_e_e_

C SUBK TO COMPUTE PQR _ATA[X ANO TRARSFORN XYZ TO _LIPTIC

_C 6 I_lt3C CPXYE(|)-AOLO(||O 6 CPXYZ|I*3)-VOLC||)O $[ OBa O°0

C CC 08_ 1.0CA'L ELECTS (CC O_tS] OBo0P[fZeX_U _PQRT_ELMeM_ANeX_EAN)

_RITE OUTPUT TAPE 6e2OOAZOO6 FCRMAT||_Oe37H ELLKENIS CHECK FRG_ SLBA ELE_SII/ |

CALL OOUTPT (ELNeTw7|

_RITE OUTPUT TAPE 6o20052005 FCRMATLI_O_]}H TRANSPOSE PQR _A;RIX CHECK _/I)

CC 1120 Iml,3C PP(/I_PQRT(i,I|

P_III-PQRT([,2)

C|120 PR|I)-PQRT(|,3)CaLL _UTPT(PPe3e3oPGo3_3oF_.3_3) ECL|PT|C

20:_ CCNTINUE

PLOOM_ _Aik P_OGRAM FOA PLCO C_AKLES J* UEVINE 710|166 PAGE |4

CALL _LE_T$ (CCSC_$|NOB,OPXYZ_PU tPQRYtEL_EAN_XPEAN)ItRITE OUTPUT TAPE 6,UCO

IIOC FC_NAT|IPO_ 20_ ECLIPT|C _LE_ENT$// )CILL DOUTP; (ELN_7_7)

n_ltE OUTPUT TAPE 6tllCll|Ol _C_AT ||H0,23_ _CLIPTIC POR PJfRIXl/ |

CC 20ZO (_1,3D PP|I|'PQRT(It||n P_¢I)-PQRT||t2|

C2020 P_(I|-PQRT(I,T!CaLL DOUTPT|PP_ )o3,P_3t3,P_t3e 3)

GC TO LTSo2OCRtqC_|tPNFLkG_00_ CC_TIqUE

rC t22 1"1,3

CC 122 J-_,3

12_ PCR(J_I)nPQRT(IeJ)CC 201L I=L,7

UZCII FLENIII_ELP(I)

_-FLE_II)C AN"ELE_|2)

CALL ¥_JhSX (PCR_PXYZ_ELE_oX_U)CC 1350 i'h3

C X_LO(I)-EPXY£|I)Pl3b0 VCLO(I)sCPXYZ(It3_

kRlT£ OUTPUT T_PE 6o|305,XJCC

1305 FC_ktll_0o28_ ECLIPTIC EPOCh P_S-VEL _FIZ,It/)CALL OUUTPf (XCLC_VULD_,_)

C AFTER TKANSX_CNLY ROTATE XYZ_NRQT_?

C PF_E _Ef UP TqiN$ FRCM tQU_ TO ECL|PTKC

P $lN_e-$lK0flCALL $TIhK$ LXCLC_VCLOgUbLTAoXL_tC_ATo CCS_6_$|NU tNROT)

C hCk X[)LO_VCLO* _RE IN ECUATORIALV *-X_LOIII

V_L_AULO(A)VY_I_OLU(2)VYL "X'._._| _)

VZF-X(ILfl(_)VZL'XOLO|6)

XCCTPaVCLO(I¢XC£TL*YOLC|_!

r II I I I I III , , ,......... . ........... _" I

1965019622-086

II"q_lipP_..,_ --,*._- _ ........ . __

JPL TECHNICAL MF.MORANDUM NO. 33-188

YtCf_-VCL_IZ)

YC£TL-VCLClSIZ££T_VnLCf_)ZrP;L-V_L_Ib)

_lfE OUTPUT TJ_E _,IJ41,XJCC

_C1 CC_Ti_UE

• !ZPH J*L-_TE EO_A. X E_. Y C_UA° Z ECU_ XCQT ECUA Y• CCT E_U_ _CCT 7PFOX 7PFDY 7PF_Z /

• [2C_ ECLP. X _CLP. _ _CL_. l ECLP X0C! FCLP Y• CCT E_LP ]_Qf 7P_0 p ?P;C_SbOL ?PFOB I/ )

_ "£_ C_LL F_P _C_C¥ TC '._0 AND OP(_JT_ FLR_Z

J£C_JO

_CC-N_

IFL=ILC

'. JSET U_ IFLJ6 ICBRk5$ J_O SE[ IfL=_,_;T XJ[)=T$

TS(I_-XJC(2)C

_O2 CaLL F_CV(_L_6_|FL*TS¢_]

90_ GC TG 12GGt300,4C0,5_0,6CO),IFL_£ _Ug_G_IT|NE CALL $T_TEqFN_S FCR OE_,1_T_P,ECS_ERR¢

C 5UB_ OLRiV CO_PU;ES _CCEL_RaT]_ J_ STC_E_ i_ C_'_ 6570_-L2

_REL,XOS&,XH_£JLL SP_T

C _ST_P _.C.T. TtX_Y,Z,X_.YC,ZD_ANO ,_CR£P(NT$ XST_P_C0 £SLL TSTCP ( N1a_E,LT_t_f_P_, OELTA,YTf*E,

CC 52_ I=1_3

• PLOi';Mh _41_ PR(_GRAW FO_ PLLD CHAR_.E$ J. OEV:NE 7101164 PA£,I t_

_'JX( I la_'A_(IF(LJ_AX| | )_C:ELTa{ I I)F_'_IX | I* 3 ) _'JX LF ( UM_,X ( | * 3) . OEt. f (1]|

_/*1_| ! )ll'lNlr |_kflk¢_ ! ),_icLI"A| | | )

U_'AX| | )=F_I,X¢ | |

" U_'IN( ]*3|_FI_IN( 1'31

XSTATS( | t 1 | IX .STATS( !. 1 | _'OELI"J ( ! IP. YST_IT.S( ! t _,|-YSTAf$| |, 1 | *OELT | | |

D YSTA_.S( | _;_|'Y$TATSt | ,2 )_'| _If:LT |[|*e2)r_ 'J25 XSTATStI,2_XSTATS(|,2|'C'(DELTA|||e*2)

C _:LAC, FUR TSTOP |NCR° FOR kR|T|NG EPIC4.! F | NEPH_' ) )03. 303_:SCZ

c)OZ CC_.T | _JE

XJP_._ JG `!À�@�TC]PZ

T$(II-XJC_2)TSIZ|-_JC| 1|CJI.L $PCT

£1LL $f: T _2 ( P_R, XY;P, X |8(_ T. 4. E, XN _ .S_T j ¥T IME t Ct_/IT )

C/_LL .S_fUPZ(SET,CEI. T ,XN'JM,SIGSGeAMAT,6MAT.MI'AXeNMAXvNGCECI., STEST,I,T |

GC TO()$C,'_02,402 |, iqGG$6L38(_ CCkTI_UE

C XJ(_'XJO*F._fC r _f$| 1|'XJ£|2|

lr$| _|.>_JC| 1 |CALL $P_T

C, E£$t:A TESTS FOR XJ_ _'AXe T LLS$ _AX R_'TURN_ i' C,REAT(R NiX I_U'i" _"C" T_JX IS RcAO iN _lT CE.S|REO CI;T QFF T|NE

4{_ t'JLq EOSEIt|T_AXeJ|_q|

GC TQ |4C2,4_,_05),Jll.402 ¢CNT _UC

G£ _0 (_(;ZI*6OO|,JAN4CZL £CK T| r_qJE

O SL-SI;Sq

A+TAmXNU_ ,

NCPUKmN_IXCC _9| Zshb

1965019622-087

k,

_!L

.¢


PLOP.PI_ MAI% PR_G_AP = FOR PLCD CHARLE$ J. 0EVINE 7/01/64 PAGF 18

_C 10 L2_31_'_ CCNTi_UE

_ E_,INO PfAPE

|2C_ £CI;T l NU _"

t:C _2_ J'|o2D '_STAT$1 | o JI,Y.CT_TS! |, JI/XNP

P._23 XSTAT$11 ,J |_ _S fATS( i, J |/X_IRr_ YSTATSI | I 3|_S_RTF|YST_TSI | ,2)-|YST_TS( 1 ,_ I _o2| |

_526 _(STAi'$( | t 3_$_RTFI_ST/*T$1 | _2)°| _,$T_TS| : BLlom2| |

C TP|$ |$ STPI_G? CCfiV_iIGE_CE T_STwREGUI.AT_ _v _OCUT, _.0|r¢

£C 4t_ [rl,6

_Rtf_ OUTPbT f_PE _,_3_

_}_ Ft:RMAT| 2_H CCNV_RGEkC_ _ty STEPRG//||F( I TERAX-21_,3_t 720 t 72C

_3_ CC_ _ It.rUEC $ IGS_N-$ i GS_/X_,UP

?L5 CC_ f 1"¢u£C TP|$ |_ P_ T_ST

(" _PSI_$|C,

| F ISt_ALL-CEP$ |L | I|o07_.7| 771_ CCRT |*_RJE

_ttlfE OUTPI_T T_PE 6,71_1_¢1_$1,_P,$C?L8 FC'_MAT(II-0_ _81, RP*$ BIF_E,t_RCE _EGLI61_LE/

| ILl_ _tPS(| �D�|,EL_°_/|LH_$( |1 I'_.lb._///|66 ?_ 72C

7L7 ¢Cr_T |'¢U£

_IPSOIRP$1IFI IfRMAX-lf_JXI?20, _4_75{]

J

83

1965019622-088

:, JPL TECHNICAL MEMORANDUM NO. 33-1E38 ......

PL_O_ _Al_ PA_AV FOR FLGO CHARLES J. DEVINE 7/01/64 PAGE 19

54_ frR_ATII' %_H SIGMA ,EIN._t2t_ tn_ JLLIA_ DATE tFt?._l/)C ELAP_T=XJ_-XJ_C

_RITE OUTPUT TAPP 6elAGtXJCt_LAPSTtX_UNw$IGg_IG$_V_.VY_V_M

[_6h P_QC _S EXCEEO[O fOLE_A_C_ ,IT _ILL _0_ CORR

2ECTI/SEH _PCCH VAL(E5 AN_ _Edl_ A hE_ ITLR_T|ON.///

_ ELAPSED ll_E IN CAYS .... ....,,P12.2//

_Z_ NUmBeR OF IkT_G_AI_CN ST_PS,._FIZ.C/_ 1b_ZP SIGPA ............ *.. ............ *ElA_RI/

7_P SIGPA SGLA_E X _ ............. eE|6.A//_1_ X _P|6.E_6H Y =F|EoE_bH Z xF_6.§l///)

_7 _RIT£ OUTPUT TAPE 6-_

_ FCPMAT(LPO_ PLCC PAS EXCEEDED PAX ALLO_[D ITE_ATION_ _1 j

• T_CUT CC_VERGENCE _C ThATS TPE EqO _RCTHERf/)C_ rE 60C

_6 CC_TINU£C _ACK |_ _ PLACE AFTE_ $1G TE_Te JUST _EFCRE COPR.

CC TLO J-_*6

T|G AVATII_J|_OoOP 71L H_ATII) _0.0C SZG$O-DoO

C XNU_O,OXJ_'XJ_O e

VkFLAG=3

|_CLUO[ ALL CCUNTER$ A_GVE• 7_0 _C TD TRANSFORNAT]ON _BROUTINE AND $Tk_;T _V_R

_RITE OUTPUT TAPE b_S_8,IIXSTAT_(I_Ji,i_I_3I,J=_3]Z ,(F_AXil]_l_Lt3hiP_I_(ll_i'l,3)

kRITE _UTPUT TAPE _5Z9_(( YSTATSI3_JI_(YSTATSII_itI_I_Z|))_-[_3)

L_F_AXIb)tIP_AXI|)_I_AeSI_F_I_IN)IIFP[N(II_[_6_)GC ;U b5

£

C kRITE ()UT ELL _ANTEC _UA_T|F$T_O CCNTI_E

_Tu2

CC I0 fl_|lbIePPR|NTI|E CCNT]NUE

KTAPE=K|2

NPRiNT=K_

PLOOMN MAIN PRUGRAV FOR PLCO CPARLE$ J. DEVINE T/Ol/Ak PAGE 20

KJ"'KI_

CALL RUN(|TAP_II|6 CChTINUE

GC TO ITES,126tT27,?3C),NPRIhT

725 CCNT[NUECC_e*o**ee_eo_*_eQe**It*ee*eIte_*_*e_eeo*II_*I*I*eIeeweete*o_e_*_*o=*Q**_ee*_C

NR_|k OUTPUT TAPE 6_TEE_LTAPCILCh_N_KTAPC,KCHANPRInt 72RtLT,PO_LEhANtKTA_OtKChAN_T=l

T28 FCR_ATIIhOtA6.|2_ GN ChAN_431AT_LEH ON CHAk. A3// |

O'USE T7777CALL SDNF (LTAPE|

CALL SUNk (KIARE)REW[ND LTAPEREkIN0 KTAPE

C hEAO[NG COP OOT_ KTAPE;LTAPE

_R|TE TAPE LTAPE_IL_CRO||)_I-|_22 | IPLANETIII_I_|_E)

_RITE TAPE XTAPE_|KN_RCII)_I-_t22 |_(PLkNETII),i_Ie2|_RITE TAPE LTAPE.XBDCY.XCONTR.XJDO.T_AX_FSTOP2.XN_OOYtFSTCP2_RITE TAPE KTAPE*XBOIJ_'tXCONTR*XJOO_TPAX_FSTPPEtRNBOOYeFSTQP2

NR_TE OUTPUT TAPE b,/_C_NRECRO thBOOV_XJOO_TPAX_1 FSTOPT.ILkQROK|I_|_teZ2 ),IPLANET(_)tI_IeZINRIT_ OUTPUT TAPE 6_?AO_NRECRD _NRDDYtXJOOtTPAX_

FSTOP2_IK_OROIII_]-|,2Z )tIPLANETII)_I_IeZ)GC TO 130

C

C726 CCNT|NUE

_R|[E OUTPUT TAPE b_ET_TAP_LCHANPRINT ETtLTAPO_LCHAN

PAUSE T7777CALL SDNP (LTAPEI

REkiNO LTAPEC eCO HEADING FOR EPHEMERIS TAPE

_PITE TAPE LTAPE_ILNCRCIII=i_|_Z_ )_|PLAN_T(IIt]=[_2I_RITE TAPE LTAPE_XBOCT_XCONTRtX,IUDeTPAXePSTOPE_XNEODY_FSTOPZ

kRITE OUTPUT TAPE btTNC_NRECRD ,hEOOY,RJDO*TPAX_|FSTO_2_ IL_ORCII}_|=I_2 )_IPLANETI[)_|=|_2_

T_O FCR_AT|20H ECC YAPE HEAOING/II22H RECORD LENGTH _|N/

_._ _...............

1965019622-089

•JPL TECHNICAL MEMORANDUM NO. 33. 188

PIODMN MAIN PROGRAM FOR PLOD CHARLES J. DEVINE 7/01/64 PAGE P_

122_ 8DOY NUMBER- ,14/ 25H NUMBER OF 8COIESI 1/

2 22H START OATE_ _FlO.2/22H ENG OAYE"3,P10.2/

4 22H STEP SIZE" ,PIO.2//IX,12A611X,LEA_HI/)GQ TO T30

le Gel .m.eel** * e*e * Q****_***

C

727 O_TINUE_RITE OUT"tIT TA'E o_6T*KTAPOtKGHA_

PAIN! 6?,_iJPO*KCHAN

PAUSE TTT71

CALL SD_ (KTAPE)RE,INn XTAPE

! C 6CO _EADING FOR EPHEMERIS TAPE_RI[_ ;APE _TaP_tTWGRCtiZ_I-_,22 )t(P_ANET(i),I'I,Z)kRITE TAPE KTAPEtXBOCY,RCONTRwXJ_QvT_AX*FSTOPE,XNDOOYtFS_D_

IWRITE OUIPuT TAPE 6t?4C,N_ECRO a_eOO_*XJOOeTPAX,FSTOPE_IK_OROIII,I-_,22 ItIPLANET(I),|'I,2|

_***********wI*_**lee_e****j***D_jl**m_***e**_•*_o_•I**_*_eI**e**el*e*_**metC

730 CONTINUEC ELAPSY'XJC-XJDC

_RITE DUT=UT TAPE 6t732_TERAX_SIG,XJO_ELAr'STwANUM,SIGSQ

1 , VX_,VYM,VZM_ ?32 FOR_ATI28H PLLD HAS CONVERGED AT _1_, L_H |TERATICNS//

_ 1 3)H AND _ SIGMA VALUE C_ ...... ,Ei6.81/342_ JULIAN DATE......,*,, .......... ,F12.21/642h ELAPSEC TIME IN DAYS.. ....... _FIE*EI/

542_ NUMBER OF |NTEGRAT|UN STCPS**_F_2*D/ItAZb SIGWA SQUAR0 X N ......... ,,,.eEIB*_//814_ X uF[b. Bt6H Y IFZ6.Bt6H Z =FI6.B//

• 2 45_ PLOD WILL BEGIN 1_ kRITE JN EPHEVERI_///)

C SEI ALE FLAGS FOR _P_M WRITE AND RESIDUAL WRITE_EPHMJ_JAW-2

D RJP=RJDOW_FLAG-3

%kRITE=_

PLUCNk _]_ PROG_AP FOR PLOD G_ARLE$ J, CEVINE T/0_/bA PAGE 22

LA#'2PPRINT'2

C

_RITE OUTPUT TAPE 6*52EoIlXSIATSll_Jl_i-lt3I_J'l*3)

[ tIFMAXI|)_I'|e3i_IFMI_I|)t[_Ie3)¼RITE OUTPUT TAPE 6tSZD,({ YSTATSI3_JI*IVSTATSIItJ|tIxItZIt*J_1_3|

|+F_AX(6ItIFWAX(IIt:_4tS)_FPI%(bI*IF_INII)_['4_S)DC TO 65

CC_________________________________________*_____________i_______________________

C600 CCkTINUC

¼_[TE UUTP_T TAPE 6t93• ee

_ 9_ FCRHAT|IPttTq_ • _*_e_,_*| SUMMARY eeevelati_*_/ )kRlTE OUIPUT T_PE Ot[OC6*Ik_EROIlJtI_|_2? IvIPLRNETII}_I_ItE)_

I(_WGKOII),I'_Z2 )t_REC_D_N_OCY*XJ_CtTMAX_htFST_P_I

: 2FSTUFE,_ . tO tES_STEST,EPSILN_G¢*S_OUT_SOINoMEA_*SIG_CC6 FERNAI_3B_ ,;_NERAL |DENT|F|CATIOk F_R PLOD/

_" 12(IA*|EA61)*_X_I_¢_/|X_IOA6/126H REEORO LLNGTH el|4_2_5_ BODY NUVBER _I15/

_' 326_ START OAIE tF|_.2_26_ M_X LATE F

4t¢.2/25H INTEGRATION SIEP SIL_,F|5._Z_H RE_IOUAL STEP SIZE5 ,F|b.2/2_H EPhEYE_IS ST_P $1E_ _F|_.Eo25H N(INB_R 01FFS.

- _ ,115125_ INITIAL PT. _115.20H DIFF CONVERGENCE_ ,_ZOo8/[Ah SI;SQ TEST ,E2_,e*|_ R_S TEST ,EZg.P TH CO "E33

R_R_HH SCOUTaE3,?,8/TP S_INsE_3.E_ ' HEAN MOTION FLAG ,It5g/E&H COMPUTED SIGMA [_ *E16.8//|

GE TO (g4_qA_OOZ,gSI_Pql_T9_ k_iTE 0UIPUT T_PE b_3GC|,(L_CRC_II.,=le22)*IPLANETIII*I'hEI_

i 1 XB[,OY_XCQNTRtXJOC_T_RXtFSTCPZ_XNBOOYtFSTOP2ICUI F_RHATI_H FIRST K_GDR0 §E0 EPPE_ERIS TAPE Hr_l_g/

¢ I _(IX*IEA6/I_IEP 2NC RECORD/B% _CDIES*FB.I_|CH TAPE rYPE,Fq.|o• 2 6H START_F_,I_H T_AXeFIG.I_O_ STEP SIZe,FS*I_H BODY _C*_F_.|t

t IPH STEP SIEE,F_.ll/)

OC TO ()C02_30CII*NT

_002 _RIT_ OUTPUT *APL _3GCA_lK_0RGllI_|_|,221uIPLANETIII*I=|_EIt[ XDOOY_XEDNT_XJOC_TMAX;FSTEPE_XKE_0Y*FSTCP2

t leO4 PER_AT146H FIRSt _rGCRO SC_ _ESICU_L taPE HEAOING /I 2(IX_IE_b/I*IEH _NC REGQRCI8h dC_IESeEA.I:IOH TAPE TYPEtFA*|_2 6P STA_T_FIO.I*S_ T_AX,FIO.I*|O_ S_EP SIZEoFS. I,qH B_CY NO._FAoIt

) |OH STEP S|EctFS.I//)

:!

" '( 85

r

] 9650 ] 9622-090

JPL TECHN_C/_L MEMORANDUM NO. 33-188

PI. ODNN PA|N PROL;RAt'_ FOB PLOD CHARLES J° DEVTNE 3/0116ff PAGE 26

O XSTAT$_ | _2)'XSTATS( |, 2]/XN_0 'TSTATS; |, _]_$ORTF_Y$_ATS{ [ _2)-(Y_:.TAT$( |, 1)*'2) |D_'_ XSTAT$(],_|=SQ_T_(XSTATSt|,Z|-_XSTAT$(I,I}wJZ))

'_R.[TE OLJTPUT TAPE 6,5;)_8,((XSTATSII,J_,|_I_3)_,J=I,?.|

OUTPbT TAPE b,$29p|( YSTAI$(3,J|t_YSTAT$(|,J_I-112_|_J_It3)

C

C CALL RAU A_D _IE_OV_ TAPES AND EX._C

GO ro (IDTO,I07L,IO_2_IOT3),_PR|NT1010 ENO FLLE LTAPE

ENC F[LE KTAPEC_L RUN| LTAPE]

CALL _UH(KTAPE)

_7t E"D FLLE LT_ECALL _UN(LI APE)GO Tn I0r3

1072 END F_LE KTAPECA_._. RUN[KTAPE)

_07._ C_NT LNUE

107; CONT |.HUE

_3 CQ_ LNUE :CALL RUN(HTAPE)

£ALL KUN_NTk_E __.R |HT .lO

_0 FORPAT||HO_34H PLE_$_ RENOVE TAPES1CALL E_|T

I

86

A_

|I

] 9650 ] 9622-09 ]

JPL TECHNICAl_ MEMORANOL'M NO. 33.1q8

I*FCAT_,/I* _C_IFIrL MY C. LAunCh A_O • )EVXNE JLJ_ Iq6_ 71Cbl6_ °AG, l

('RI_I_ALLY _RITTEN PY BE_AN, CSC 196_O00AO i

P_L_RA_ TO !_TECUAT[ [_E c_A1]O_S or _UtJ(N Ot A O008O_CI_Y ]_ A GRAVt/ATIrJN_L FI_LO° THE STa_T;_; PROCEDURE 00C60

CVPLCYS _ TAVLF'R_ SF_IES '._Lt,tlC'_ TP ?DE TWI] e_y 00070pnC_LEP ;OLLC_f 0 tl_ AN I;LRArIV_ PRO,-ECUR_ 10 IIAPR,_VE 00080IPE UIrF_REN_= LIN_S GE_c_TE_ r_w '_L tAY, UnS SERIC_. OGOqO

TH_ (ALCbl _TICN _S At_v_CE_ U_ING THE G_IUSS-JACKSCN OOLCO

rI'FF_NCE SC,,_E. A CCRR_C'CR rnRMbLA _AY _LSO 8 ¢ 00110_PL(Y_O TC IP_R(_VE l_ S_LUlt_N. _J120

e_ 00130

,_ CALLING _L_LE_CE OCIAO

T_

1_A ER_ C:1_0• vyy ,STCP,F,TS O_JX_O_ YYY TSTCP,r,TS O_?CC

................. 002|0

vyy T'Trp,L,TS £02J0

'i PI_ 00230'_ 30240

d_rRU.olJE°'h00AEE_ C,_ ThL US[R_ [,E_IVATIVE ROIrTINE 002 '0_. ECS=Ar_RE$S LF END OF STEP 8CUTI:,E_IIST-A_CRESS r_F STEP SIZE _OUTIhE 002?0

E_-APO_SS OF E_RO_ RETUR_ 09280YYY-PZE .... _CTIvE T_[GCE_ _32q0

=Hi[ .... I_ACTIVE r_lCGEk 003_0

T_TO"_A_DR_S_ CF CURPEN_ TST_p R_UTINE 00310E.r INTt_P_LATE ¢OR PO_ITIt_N ONLY 00320

z'_N ZE_C*,.INT_RPOL4TE F_R PCSIflO_ 003_0A%0 VELCCITY 003_0

TS'TIWE C_ 1 STEP 003_O

NCTE ..... _HF FINAL PZE I% USEC TO FLAG TFE EN0 'IF 00360 [THE T%TC_ lIST O_TO '

00380C_C_ ENTRY FC_T%Z 03390

• 00A90

00670• *_ee_**I_ITIAL1ZATIC_me_e**H* O06P)

|Ir_RTSZ*I MCDIFIEC _Y C. LAWSON AND C. DEVINE JU_ _ [q6_ 7106166 PAGE 2 _-

i TRA'_SFER VECTO_

BINARY CAR_ NO. FI_ $ZnO00000 67_72_52460 XP_N_OGOU| 624_4363_0 SMULT

0000: _2232X_35.60 SC_L _

i OOC_ 31_56J5_1_0 INTRP

00004 06J4 O0 X 01303 _08ISZ SXA X]_] 006900,$005 0(_ 00 2 0130_ SX_ X2,2 00700

: C0006 0_ CO A 0|305 SXA _,_ OOT|O03007 0500 00 0 _4720 CLA -15 00720

00010 0802 O0 0 65682 Sb_ _ 00730OCO;L Olzu _ 00_OX3 TPL t_? P (CG LARGE GREATER TPAN X8 00740G0012 _07_ O0 4 _1277 TSX STS,_ 00780

OCOL3 0500 O0 0 65652 CLA _ 007_000914 0_02 OC 0 _?L3 SLB =1 00770O00X_ 0]29 00 0 00017 TPL *+2 00790

OC01b _rTA O0 _ C1777 TSX S/5,_ V LES_ THAN ONE O07QO000L7 0500 O0 0 E5_82 CLA P 00800

00020 0_02 O0 0 65683 SLJ_ J 0081000021 O_OX 00 00_LIT SIG _J 00820

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• 01_60O01Ge C_O_ O0 0 04722 CLA 036 SET I_EXlNG PAB_JqETE_S 0137000107 0402 O0 _ 03114 S_u 21 0131000110 073! C0 1C0000 PAL 0ol -138-2_) TC Xi 0139000111 -J6_4 _0 I C2620 $X_ L_.L 01_0000112 -_6,/4 00 ! 02761 SXC L?_,l 014100_113 I 0_002 I _I14 TX| _*I_1,2 XI'-I_'-ZR| 0142000114 -0_J4 06 I 01425 SXU vSZT.I 0_430

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e_Foq;520* q00|FIEC BY C* LA_5C)0 4_0 C. I)EVIHE JUIIE 1964 '/._¢%16q PAGE 4

0_!i6 -0_ O0 C2165 $XC UtLlt*lrt 01440G_I!T -CA J4 O0 02_4_ S_O C8127.1 01460_7120 -06J4 O0 02344 SXD _V_,I OIATO0:i21 -¢_4 CO 02_4_ $X0 _VTT*I 014800-_122 I 39_04 03123 TXl J*1,1.4 XI'-13C-2Pl 01AqO0_i25 -06J4 00 011TZ $XD 542.1 0!.500_124 *0434 O0 01224 SAC SAS.I 015_00012_ -06J_ O0 01364 SAC _$62,1 015200012. _ -0634 O0 02550 SXO L14,1 01330eTIZT I T,/74_ 0._L30 TX| *,1,1,-32 11--162-2_1 31540 --001J0 *g_4 O0 0116_ 5_0 $41"1,1 01550CC'131 -06_40_ 0122_ $X0 S_5,1.; 015600_132 -._14 O0 L 0155T SZC VS61"1.1 015T000133 I 7'/77_ 00134 TXl *,1,1.-4 Xl.-(6_-2_! 015800_134 -0634 O0 C2166 SX_ C#LII*Z+I 015400_!35 _063_ O0 02245 $X0 0a127*',1 01600_i56 °_6_4 00 0_345 S_O hVTel,| 0161000157-06_ 00 02446 SXO kV33*l,l 0162000_ .'_ 1 T?YT6 0_141 TXl u*|*L.-2 Xi"-165-21I 0|6300_1_1 -0636 O0 01424 SAC ¥$2_,1 0164000142 0534 C') 05114 LX4 _X*I 01650 qr"0_143 -06_ c_ c0150 $x0 lq.l 0166000164 -¢6_4 _0 c0156 sx_. 1"40,1 01670 -0_I_5 -0634 oo _ 03235 sxc iqll,i 01610

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1965019622-093

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JPL TECHNICAL MEMORANDUM NO. 33-18R

J

i **FORTSZ_* RGO|F|ED BY C* LAH$ON AND C. 0EV|NE JUNE 1964 1106164 PAGE 5

• 0187000170 -0100 O0 0 00175 TNZ |q3 IF PIE PCDE SET L|MI_$ TO SAVE O10|0

I 00171 0774 90 | T7_2_ AXT -10011 THE CCRIECT NUMBER OF 01FFENEN00 0109000172 0520 00 0 65654 2ET N LINb;* THIS 0EPENC£NT 0r N_THEN OLq00

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01930

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00237 0774 O0 00025 |AT 21_1 02280

eeFQRTSZ*_ MCGIF|_C UY C. LAk$GN A_0 C. DEV|NE JU_ 1964 7100/6_ P}_E 6

002_0 C6J40c 02113 SX_ C_L15*1 02290

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0024& -_534 C_ 03121 LXC _aA_GP_I 02)5000247 -CO)4 O0 _1654 SXC VS_2,1 CLCSE vARIATIONAL CCNVEKGENCE GATE 02360

C02_C 0_J4 CO 03121 LX_ T44NOP,I 023700_2_1 -063_ OO O_t_ x_12 S_C Lo*t SET TRA/_CP GATES 02380_0252 -06_4 0I_ 02367 SXC L24.2,1 02390002_3 -9634 O0 02o44 SXC L46*1*1 02_00

0_254 -06_4 C_ 0267_ SX_ 156_1 02410002_5 -0634 00 02730 SXC 16_,1 02420

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• 0253002540

• _ol****e*ST_RT SCLUTIC_ FCR EGN. OF P_TIO_ 02_002_60

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[ G0275 0500 09 _|22 _E_ CL_ LCGIe| S_T LC_I TC COMPUTE FIRST SUN 02620Qu276 0_01 3¢ 72t22 ¢TC _FFZ,| 02630

_27T I 7T777 CC30_ TX| _[tLe-_ 02640_J0 _ ) 00_0_ 0_27_ S_H.I TX_ SE_*I,*. 026500_301 0774 00 OJZ34 AX[ _'2.1 02680

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1965019622-094

r_


**FURTSI*• _COIFICC RY C* LANSON AND C* OEVINE JUNE 1964 710_,156 PA_E 7

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00324 0560 O0 0 _3117 LOt 2PJ SUM COMPUTATION. 0286000325 0200 O0 0 04721 MPY =IP 0?870

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00361 OnT4 O0 6 00000 _LIST TS_ •e,4 PICK _P STEP SIZE FROM SUB. RLIST 03930

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START _OLUTION USING _AYLOkS SERIES EXPANSION. 03080**570RE C SCALES IN 00 A SERIES IN 6D1 § SERIES IN 002. 03090

• 8C3 MILL BE USEO TO STORE PONEAS OF TIRES* 03100COMPUTE A_O SAVE TINES AT STARTING POINTS IN 0T* USE 03130

• 8Xt BY* 4f_C 5Z_ TO STOKE COPPI_¢_ 7_|7I_NAL COORO* 03120

**FORTSZe* MODIFIED _Y C* L3kSOH AND C. DEVINE JbNE 1964 7206164 P&GE 8

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00355 0301 O0 0 65630 OF&C 7 03220 ?_

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00362 | 77776 1 00363 TXi •_1_1_~2 0327000363 3 O00CO I 00353 $71 TX_ ST*I*** 03280

• 03290 (00364 0_60 O0 0 6567_ LO_ x FIN¢ PAX OF 6BS, VALUE OF X, Y, Z 03800

00363 0500 00 0 65674 CLA V 03330

00366 0760 CO O 00003 SSF ABS(Y) TO AC 0332000367 0765 O00 00000 L_$ C 0333000370 0774 O0 I 00001 AXl 1,1 SET X3 FOR Z MAX 03340

O0371 0040 O0 0 00376 TL_ SEN3 TRAMS, If Y MAX 03350 _"

O03TZ 0500 O0 0 65676 CLA Z X |$ LARGER THAN Y 03360 ,_00373 0760 O00 00003 SSP 03370

00374 0040 00 0 00401 TLG SIP4 03380003?5 | 00006 1 00603 TXI SEM6_ 184 SET X| TO 3 AS X IS MAX 03390

00376 Ol3I O0 0 00000 SEN3 XCA Y GREATER THAN X 0340000377 0500 00 O 65676 OL6 Z 03410

00400 0760 00 O 00003 SSP 0342000401 0090 00 0 00403 TLQ SEN4 TRANSFER IF Z=MAX(X_YtZI 03430

0_402 0_4 O0 I 00003 a_r 3,1 yuMAX(X_y_Z) 0364000403 -0520 00 3 63617 SEN_ NZ_ 1*1,_ 03450

_060_ 0074 O0 2 01301 TSX 580_2 ERROR RETURN AS R-O 0346000405 05OO 00 I 65712 CLA 200_1_1 0347000_06 0241 O0 I 55677 FOP 281-1 0346000407 0?60 00 0 04723 FPP ==5 03490

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1965019622-095

_

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**FGRT$2 "t _C01F|EO BY C* LAhSON AND C. DEVINE JUNE 1964 7,06/64 PAGE 9

004|5 0560 00 1 65677 _tP5 L00 1_|11 03350

004[& 0260 00 1 65677 F_P Z*ltl 0356000417 0300 00 0 67602 F60 601 COPPUTE Rel2-Xee2tYoeE_Zee2 035?0

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00422 _0260 CO 1 65677 FMP 1"1*1 COffPUI6 0360000423 0300 O0 0 03062 F60 "E_P _*8007 03610

00624 0601 O0 0 E306_ ST_ T_P _|IeXD elO!03620"_ 0-425 0560 00 1 65705 L03 Z_ºl,l 03630

00426 0_60 O0 1 65705 F_P ZO*hl 03660

00427 0300 00 0 03066 FA0 TE_P_2 0365000430 0601 O0 0 03064 $T_ l_P*_ _VELOCITYa.2 03660

00_32 0241 O0 0 67602 FOP _01 -Ve*2/Nee2 0368000633 -0600 O0 0 03064 57_ TEmPt2 03690

": 00434 0500 O0 O 03062 CL6 _EMP 03700J 00635 0241 00 0 676_2 FOP 801 03710

DU436 -0600 00 0 03_62 S_G TE_P =RDGT/R-ROCT-RIR_*2 03720._ 00437 0260 O0 0 0306? :_P TEPP 03730

,_ 00440 0601 00 0 03063 570 TEPP*I u(ROOTIR|**2 0374000441 0560 00 0 67604 LOG 001+2 03)50

_ 00642 0260 O0 0 04?30 F_P -6. 0376000_43 0300 O0 0 03064 F40 TEMP @�-[V*e2/R*º2*NA2)OR 03770D0444 0601 O0 0 03_66 $;0 IEWP*2 "(V*e2-ZNI*IRI/R*_2 03780

00445 0560 O0 0 676_4 Lg_ 80|_2 03790

00646 02_0 00 0 ¢3062 F_ T_Up 0306u• 00447 0760 O0 0 00_C2 C_S 03810

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" 00452 0260 00 0 04763 FNP _-2. 0384000653 0601 00 0 _0012 STU 80 C0"-2_A2 03850

00654 0560 00 0 67605 LOG B01_3 0386000655 0260 00 0 04744 F_P --6. 03870q0656 0601 O0 0 700_J $TU BOil C1"-6*63 03880

_06_7 0560 00 0 6760k LC_ 001_£ 03890C0460 _2&0 CO 0 04726 FPP ._* 039_0

004_1 C_01 00 0 03065 SIC TEXP_3 -3*62 0391000662 0560 O0 0 67604 LC_ 001_2 03_20

00463 0260 O0 0 04725 F_P "2. 03530: _0464 03(,2 GO 0 03064 F_6 TEffP*2 0'940

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: 00466 0260 O0 0 0306_ FMP TE_P_3 03960

"_ o_FORTSZ'* _CDIFIEO BY 0. LANSON ANO C* DEVINE JUNE 1964 7206166 PAGE 10

00467 0601 O0 0 03065 $TO TENP*3 m3eA212*AZ-T21 0397000470 0560 00 0 03062 _OG 1E_P 03980

'; 00471 0260 00 0 67605 F_P U01+3 0399000i72 0131 0U 0 00000 XC4 04000

0_473 0260 00 0 04731 FNP "15. 0601000474 0302 00 0 03065 FS8 T£NP*3 0602000475 0601 O0 0 70016 $70 80*2 -C2-15{RDOT/RIA3-3eA212_A2-T21 04030

0047_ 0560 O0 0 03063 L00 TEPP*! 04040

00677 0260 O0 0 0473& FPP -35. 0405000500 0601 O0 0 03065 $70 TENP#3 0406000501 0560 00 0 67606 LOG 601 �D�06070

00502 0260 O0 0 06733 FNP -32. 0408000503 0300 O0 0 03065 F_0 IEMPe3 0409000504 0601 00 0 03065 $10 TEKP+3 04100

00505 0560 O0 0 03064 LDQ 7EMP_2 0411000306 0260 O0 0 04766 FMP m-_5. 06120

,, 00507 0300 O0 0 03065 F80 T_qP*3 0413000510 0131 O0 0 00000 XCA 0414000511 0260 O0 0 67605 FNF 001*3 06150

00512 -0760 O0 0 00003 SSN 0616000513 0601 O0 0 7001_ STC 80_3 C3m*A3(35*IROOT/R}*e2_32.A2-15T2) 06170

00514 0_60 O0 0 67603 LOG 801_3 04180OO51S 0260 00 0 04737 FNP -253. ONl_O00516 0601 00 0 03065 STG TEmPt3 04200

00517 0560 O0 0 03066 LDG TENP_2 0421000520 0260 O0 0 06735 FMP _105. 06220

00521 0601 00 0 03066 _T0 TEMP_4 0423000522 0560 O0 0 03063 LOQ TEMP_| 0424000523 0260 O0 0 04736 FMP "157,5 04230

00526 0302 O0 0 03066 _$8 _ENP_4 0426000525 Ol3l O0 0 00000 X06 04270

00526 0260 O0 0 03062 FNP TEPP 0628000327 0302 O0 0 03065 FSB TENP_3 04290

00530 0131 00 0 00000 XCA 0430000531 0260 O0 0 67605 FNP 801.3 0431000532 0131 O0 0 00000 XCA 04320

00533 0260 O0 0 04723 FMP .5 , 0433000534 0601 00 0 70016 STO 8D_4 P1-,563((157.5*T1-[05*T237-233*A31 04340

00535 0560 00 0 03066 LOQ TERP*2 0435000536 0260 O0 0 03066 FPP IEMP_ 04380

00537 0131 O0 0 U0000 XCA 0437000540 0260 O0 0 06727 FMP ,3.75 04380

91

1965019622-096

JPL TECHNICAl MEMORANDUM NO 33-188

eBFORTSEee MGOIFIEO 5Y C- '.Ak30N ANO C. DEVI4E JUNE 1984 7/06166 PI;E 11

00541 0601 O0 0 03065 $70 TE_P*3 -5.75*T2*e? 06SqO0C542 05'60 O0 0 6T6_4 LOO 801"2 0440000543 0260 O0 0 04?32 FHR =16. 0441000546 0601 O0 0 03066 STO TEMPt4 0462000543 0560 O0 0 03064 tOO TEP_2 0443000548 0260 O0 0 04?4? FMR "-15.3 0444000547 0300 O0 0 03066 F6© TEqP+4 0445000550 0131 O0 0 0000 _ XCA 04460G0551 0_60 O0 0 87606 F_P B01*Z 0647000552 0500 O0 0 _3065 FAO TEWP_3 0448000533 OLSL O0 0 00000 XCA 044g000554 0260 OC 0 676C4 FHP 801 D�0450000535 -0760 O0 0 00003 SSN P2*-A2|IL6*A2-13*5•T2)A2_3.Tg*T2e*21 04510005_6 0300 O0 0 70016 FAO U_*4 04320C0537 0601 O0 0 70016 $1_ 8_+4 _4-_1•P2 04330

• 045_0• _OTE.°.THE _IRST I_IMPLE) TERHS OF A 6_C 8 04550• ARE 4CX STCAEO OR USEO 04_60

04570C0560 0600 O0 0 67604 £LA 801"2 0458000561 0241 O0 0 04726 FPP _3. 04590C0562 °0600 O0 0 62621 STG _02+3 83=6213 0460000563 0_60 O0 _ 67605 LOQ _C1•3 0461000364 C260 00 0 04723 FH_ m.5 0462000565 0601 O0 0 67622 STC 802,4 84_3/2 066300_566 0560 O0 0 67604 L0_ 801+2 04640_0567 0260 CU 0 70012 F_a 80 0465000570 0300 O0 0 70014 FAO SC*_ 0466000571 0241 O0 0 04745 FOP a-1_. 0467000572 -G600 00 0 67606 5TJ dDl_4 64=-(62*C0+02)/12 04680005T3 0_60 O0 0 67605 LO_ 801_3 046900_514 _260 O0 0 70012 F_P EG 04700_0_25 0601 O0 0 03065 S[O T£NP D�04710005?6 gS60 O0 0 6760_ L_ _*_ 04720C9522 C_60 O0 C 70013 FP_ _C*_ 0473000600 0300 O0 0 _065 FAC TEH_*3 04?4000601 0500 O0 0 70015 FAC 80*3 06?5000602 0241 O0 0 04?50 FD_ _-Z_* 0476000603 -C600 OC 0 67602 ST_ _1 �@�AS--(J31CO*A_*GI•C3)/200477000606 0560 O0 0 10012 LO_ EO 04780_605 0?60 O0 0 67606 FHP 801•4 04?900U6_6 g60L O0 0 0J065 STO _E_P D�C4800

!

• oF_RTSZet HCOIFIEC 8Y C. L&NSOh &_O C. OE9|qE JUNE 1964 7106164 PAG_ 12

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• 050_0• _AVE TAYLOKS SE_I_S OOEF* GOPPUTE FIRST JP_ROXIMATIONS 05060• 05070

050800_637 C53_ 0_ 4 0311_ LAC 2_7_4 2_2_2P �D�050qoC_640 -_4 O0 4 GC?4? SXC $6t4 051000364_ 054> :_ 4 03111 L_C _J,4 2_J=_IH-J_ 05110_642 _34 00 c 031_5 _X_ T_5_,4 0512023643 0774 00 4 0000_ _1 C,4 05130

LOOP TU COMPUTE FIRST APPROXIMATION5 05_40 i• T_ THE keL STARTING P0XNTS C5150

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• _647 1 ¢T776 • G0747 TXI 56,4,*_ PRECI$1_ VELUE 67 ST* SO CCNT CO_PUTE 05190• 06200

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1965019622-097


eeFOkiSLee M_O|FiEC 6Y C. LAMSON AND C. OEV|NE JUNE 1964 7106/64 PAGE [3

00.652 0601 O0 0 07_33 STO 803_1 I(T-TOI 05250C_653 077_ O0 ? 000C5 AXf 5B2 05240

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60_63 _60 00 1 6T_|[ S3 LC_ EC1_7,1 0532000664 C260 O0 L _641 FPP B_3_7,L 0_330OC_S C303 OC _ 03065 FAC TE_P_3 0554G

0_66H CbO| 00 0 03_65 ST_ fEMP*3 -$UM(A||)*DT*e[I,|m3tl_b 05350C_b7 05_0 0_ | 67G2_ LEG _C_7,L 05360_0670 0_$0 00 _ 67641 F_P B_7,1 05370

0_6_1 0300 00 0 0_066 FA6 TEMP_4 053d0q_672 OHGL 00 0 0J_$6 5_0 TE_P*_ I$_MIB|[)_Te*[),|-_II|b 053q0

C0673 L 00_01 t G0674 TX| e_1_1,1 05400_067_ -_ 000G4 | C06_ TXL $]1114 0_4_0G0675 0_0 00 _ _76_ F_C 603_1 G$4_G00676 0_0_ 00 0 63_6 ST3 TEMP*4 "GIT]'SUWlB_J)eOT_e|},J"O_I)b 05430

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egFO_TSZe* PCD|F|EC _Y C. LAhSCN ANO C. OEV|NE JUNE 1964 7106/64 PAGE 14

C_7_ -_Z3 00 C 65_5_ _ZT _ TEST FC_ VA_|AT:QNAL E_UAT|CN$ 05660L_72_ ! 03_L2 4 0074? TX| $b._,202 SET X_ TU TWO LESS THAN QR]G|N&L VALUE 05670

V_RIATICNAL _G_ATIE_$ P_ESENT° USE SANE T_YLO_$ 05_90

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1965019622-098


**FORTS_u* _CG;F|_C 8Y C. LA_ON A_O C- _EV|NE JUNE 1964 7/06/66 PAGE 15

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1965019622-099

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JPL TECHNICAL MEMORANDUM NO. 33-188_

**FQRTSZH MGCIFIEO 8Y C. LAWSON AND C. DEVINE JU_E 19A4 7/06/6A PAGE 19

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_' **TORT;_m_ MCOIg[E_ _Y C. LAkSON A_D C. OEVINE JUNE lg6_ 7106164 PAGE 20

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1965019622-101


• .FC_TSZ*. MCCI_IEt _ C. L&_SOd A_P C. OEVINE JUNE 1964 710616_ PAGE 21

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1965019622-102

L--_

?

TECHNICAL MEMORANDUM NO. 33-188

*,FORTSZi* MGDIFIEG 8( C* LAWSCN ANU E, DEVINE JUNE 1_64 T/06/64 PAGE 23

Cl427 -0520 O0 0 03123 NZT 2_N2 IF M=I THF DIFFeReNCE LINES HA/E 09430

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e_FORT$/*s MC_IFIEI _ _Y C. LAWSON AND C. nEVINE JUNE 1964 7106166 PAGE 26

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1965019622-103

JPL TECHNICAL M_MORANDUM NO. 33-t88

elEO_TSZee MODIFIED 8Y Co L_kSO_ AN_ C. OEVINE JUNE Egb4 1106/64 PAGE 25

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1965019622-104

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• eFORTSZe• _CC_FIEC _Y C. L_SCN AMOC. DFV!'AE _NE 1984 71061f4 PAGE 28

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1965019622-105


**FORT$lJ* XDU|F|EU BY C* LAb$ON A_0 C. OEV|NE Jt_%E 1964 7/06164 PAGE 29

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• 1196001774 0131 _3 _ 000_ TS.5 XCA 11970OL7f5 -0603 00 0 030_2 f$ 051 I£_P SAVE T|_E J_0 C_RRENT POSITION 11980CLT16 0T7_ 00 | 0ODDS AXT $*L LL990C1777 _3 00 1 6567? T$_ qLC l*lmL 12000

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1965019622-106

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:._150' -_63. 00 Z C2143 SAD 0BLS,2 13160

• _FORTSZ_ NCOIFIEO BY C. LAWSONAND Co _EVINE JUNE 1964 7106164 PAGE 32

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1965019622-107

JPL TECHNICAL MEMORANDUM NO. 33-1_313 |

teF_Rl$Zve MCC|FIED BY C. LAkSC_ ,Nil Co DEVINE JLNE |966 7tQ6/64 PAGE 33

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0230'. 1 77776 1 02305 TXI _*'_th-2 1412002305 3 77773 1 02267 TXH 06L32,1_-S 1_130023C_ G020 00 0 02327 QBL38 FRA 0bL50 TN_ REPLACED BT MOPFOil VARIATIONAL EOU* 14140

02307 0774 00 I 00000 AXT 0.1 14160

02310 0634 00 2 02313 O6142 $X6 08144,2 14170,',2311 [ ?7776 2 02312 TRI *.1.2,-2 COMPUTE $ECON0 SUNS FGR VAR. EQU* 14180C_2312 0636 00 2 02J23 $X6 06L45,2 t.*iqO02313 0074 00 6 0000Z TSX $¢AtR+_ 1420002314 0074 CO 0 O3_36 TSX P0*2+O 1421002315 0074 00 0 00000 05L66 TSX *.,0 1422002316 0074 00 0 03112 7SX 1_2,0 1423002317 0074 00 0 03070 TSX fEPP*6,¢ 14240_2320 0443 00 1 65716 0LQ VIii 1625002321 -0241 00 0 03100 OFDP MS(; 1626002322 0303 00 0 03070 0FS6 TEilP*6 1427002323 -0603 00 0 00000 00145 0$1 ** 1628002324 I O00_6 2 02325 TXl *+112*38 142B00_323 I 77776 [ 02326 TX! *.1,1,-2 143000_326 3 77734 I 02310 TAM 06L42,1,-36 14310

02327 0020 00 0 02474 CBL_0 TiT6 HV_014_30

'32130 0535 O0 " 03113 HV LAC 2N2_1 HALVING pilOt'.[DUNE [435002331 -0636 O0 I ¢2340 SXO I_V2:l 16360C2332 0774 00 I O00CO ART O,l 1437002333 0774 O0 20QOGQ ART Q_2 143000233_ 0443 00 l 66116 _Vl OLD X01._4,t 14390

02335 -0603 UO 2 67F42 DST 6U¢;:'_3602 SAVE CLO OIFFEREk_ES 14400

103

. .,

1965019622-108

J

_" JPL TECHNICAL MEMORANDUM NO. 33-188

eeFORTSZeP MOOIFIEO BY C. LANSON AqO Co 5EYINE JUNL 1q64 "7100/6_ RAGE 35

02336 1 77?76 ! 02331 TXl **1111-2 1441002337 I 77776 2 02360 7Xl s*1,2,-2 1642002340 3 00000 1 C2334 h¥2 TXh hVltl,5* 1443007341 -0534 G0 4 02340 LXD _.2*4 1444002342 I 77734 4 02343 TXl o*1*q.-36 14450_2343 -0634 00 4 02340 SXG _¥2.4 1446002_4_ 1 00000 1 02345 HV3 TXI "'1*1, le *t*-I34-2_} 144700234S I 0_000 2 02346 TXl e*h2*** **_166-2N) 1448002346 _ _0_00 1 02334 TXH _Vl*lw_o *e'-1O_ OR -756 14495

02347 0500 OC 0 03111 CLa Vl 145100233_ 0601 00 0 03066 ST0 YENP*4 1452002351 0774 00 4 00036 AXT 30.4 14530C2_52 0724 00 L 04332 AXT PMl,) 1454002353 0?74 O0 2 661_0 6ST XCL*6,2 1455002_54 -_634 CO 4 023?4 HV4 SXO hVLEo4 FDR_ NEM OIFFERENCES USING 14565_2355 0_34 00 4 0306_ IX4 f_NP �Ð�H�PRESTCREOCOEFFICIENTS FOR 1457002356 I 77777 4 02357 TXI **L,4*-1 SUSTABU.ATION 14580_2357 0634 00 4 03066 SKI T£MP*4,4 1454_02360 0_34 O0 L C7364 kV5 $x4 _vT.t 1460002361 0634 00 2 02365 HV_ SXA _V_,2 14610_2362 0634 00 2 02379 5X_ PVE,2 14620 .02361 0074 00 4 000_2 rsx SCA_,_ 1463002364 0074 00 O q0000 hV7 7SX **.C **aPhl[) 1464002365 OOTa O0 0 00000 HV8 TSX **_0 _*_IFF. LINE 14650 IC2366 gC74 0_ 0 03066 ?SX TEMP*4,0 14650C2367 C074 00 0 03070 TSX TE_P*6,C [4670C2370 "0_0_ O0 0 00000 MY9 _T _$ _4600_2371 1 00044 2 02372 rXl **1_2:36 14690_2372 -3 00000 2 02361 rVl0 IXL hv6*2o** _XGL*IO8 OR XOL*?56 1(70002373 1 000_0 2 O237_ hVll TX! _*lt2,e* _*_-106 OR -7_4 1471002374 I 0_000 I 02375 hVl2 TXl *_l,1,** 1472002375 -0534 O0 4 02374 LXO hv12*4 14;3002576 I 77776 4 0237? TXI **1,4,-2 147400237? -3 00000 2 02354 PVI4 IXt _Vq,2,** ***(XCL*4_EM+LI 14750

• _LYE_ _XIT FRON FIrSt ANg 14770SECCN_ SUV CGMFUTAT|CN IN 1_700

02400 0774 00 I 02403 AXT MV16_1 00_LING Pq0CEDURE. bSE Yh_T 147900240£ 0634 CO I _2327 Sx_ CflLS_*l COOE TC N_KE FIRST _NO SECOND 14800C2602 _023 00 O 02216 TqA 05123 SU_ C_MUI6TION FOR hALtING 14610

m**kO_TSZ** MCCIFIE_ _V C* LA_$O_ ANO C. DEVINE JbNE 1964 7106164 P)GE 36

j 02403 0774 _0 I C247q _V16 4X_ PVSG,I 14830024G4 0634 O0 I 02327 SXA 0515011 RESET [JOUBLI_ PROCEOURE 14840 -I

. 02405 0074 _0 4 00000 RLISTI TSX *e,_ *o_CPRISU_RCUrlhE RLIST) 1486032406 0120 O_ 0 0241J TPL _vL_ 1487007407 034_ O0 0 6_666 CAS h H NEGAflVE. TEST FOR ;URTH_R AEDUCrlO_ 1488002410 _020 O_ 0 0_416 T_A MV2C _EDuCE STEP AG41N 148q002411 _C_O CO 0 02431 TR_ MY30 STEP CK 14?00_2412 0_20 C_ 0 C2411 T_ _V_D STEP C_ 14910

0Z41_ 0_40 CO 0 03666 PV18 C_S _ H PCSITIVE. TEST FO_ FURTHER REDUCTIO_ 14q30C2414 0020 O0 0 _2431 ?A_ hV3C SfEP O_ 14940C2415 0020 O0 0 CZ431 TR4 _v_O STEP C_ 14950724L6 -0520 00 0 656_6 beE0 _¢T CLAP: REObCE SFEF _GAIN 1496002417 00_00C 0 C23_0 T_4 PV DTAPE,C DENT NEE_ TO CHAN_E 1497002420 0500 O0 0 65656 CLA O?4PE COMPUT[ N_M CTAPE L4980C2421 0767 CO 0 00001 4LS 1 1449002422 0402 00 0 65652 3_ p 15000024_3 C601 CO _ 65656 $7C CT4PE _2_T6PE-M 15010C2424 0100 00 0 02427 TEE EOSI 15020C12425 0120 O0 0 C2330 TPL _v 15030_2420 0600 00 0 65656 STZ CTAPL OTAFE LESS THAN CR ECURL ?O 15040C24_7 0C7. CC 1 00C_0 EO$I T$X oe_l Z_RGt IENCE NEEO EOS TAPE CUNP* 15050C,24_0 OOZOO0 0 C2330 FRA _V SF70(_PE_O _ND GO 70 EOS 15080

02431 0SJS 00 _ 03ll$ hV)C LAG 2_2,l 15500 ¢02432 -0634 O0 1 07_41 SAC Nv32*/ MOvE qEM O_FFERENCE LIKES TO L50qO0_433 0774 O0 I C_000 6XT G_l STEc C_UBLING EUFFEP 15100,'_..' 0774 O0 2 _0000 _x[ 0,2 15110_2435 04_ O0 t 66116 hv3l OLD XDL*4v! [5120C24_6 -0603 OC E 67476 DST BUFF,2 15130¢2437 ! 77776 1 02440 TX[ _.1,1,-2 1514032440 1 ?7776 2 C_441 TX[ *_1*2_-2 13150024_I 300GO0 I 0_435 _V)2 7XH _V_l,l,-* 15160¢244_ -0534 00 4 01441 LX0 hV32,4 151700244J l 77734 _ 02444 TX: -*1,4,-36 15_80C2444 -Cb_q O_ 4 02441 SXD hV32,4 1514002445 I 000_0 1 02446 HV33 rXl _*1,1.** **_-I34-_hl 1520002446 I 00000 2 02447 TXl _*1_* *_--;66-2_I 1521002447 ) 00000 I 02435 7X_ _V)ItI,** eo,-lOS =R -?$6 152Z0

}

......... :: ' l | -

1965019622-109

+_JPL TECHNICAL MEMORANDUM NO. 33-185

**FOq_SZ** _SClFIE _ _V C. LA_$D_ A_0 G. _EVIN_ JbNl 1964 7/06/64 PAGE 3T

"Z&50 _f7_ C_ | _50_ PVI4 _X_ .owl ++*ACCRIBUFFeDW+|I 1_2_0524_I _774 _ 4 _SCD_ PV15 6xr it,4 +t+3 _R 21 15250

'_2657 _3_ _ 4 DZRf2 _V36 $X_ _V_2,4 15260_ _6_4 _ 1 C2461 SXA _V_qtL 1_270+Z454 C-_4 0_ I _2464 SXA _V4C,I 152B0

_24_S I 77776 1 C24_0 IXl ,+1*1*-2 15290_2456 06t4 C_ I C2_C2 SxA _V16,L 153C0

_Z4_T 0_,14 O_ 2 0311_ LXA Z_,2 15310_0 -C_4 0C 2 C2466 _17 _X_ _v_1,2 15320

_61 37I_ 2: I :50_I AXT I,I 15330"Z_6_ _93 GC i DIC_ _V]_ DL_ ++,1 U_OIFFLR_CE NC_ 0;FF[RENEE LINE 15340"_a_S C_1 9_ I _C_ P¥19 5F$_ *+,1 TO GENERATE 5_EONC DERIVATIVES FOR 15350

_246_ -_CI 9_ I C_CC_ .VRC DST *+,1 STE_ C_USLING 6RCCEDU_E. 15360_;465 I 30_02 L 32_6 ;X| *+1,1,2 +* $ 5T_ED AT HV36 TO H_36*4 15370

CE_6o -3 _0_ l 024_Z _vRI tXL PvOe*l*+* +* 5TC_E_ _T HV 37 15300CZ_6? 2 CDOC2 2 C2465 TAX .Ct7,Z,2 15_90_2470 C_ D_ 1 02463 LXa .V_9_, 15400

"lRll I 33154 1 _247_ TXl "+I.I,6E 15410C2472 077_ C0 4 D _3 hV_2 AXI *..4 15420

. C2474 C_0_ 0D _ 03_5 _VS_ 5TZ CS_VE 1545002475 D_33 D0 0 65652 CLA v USE _ 15 _AXE STOC_G NG_ Z_R0 1546U

,'2476 Cb_t CO C _3L_4 StO STPC_O USE _S_ TO PA_E STUCCO _ON-LE_O 15470

* 15490• 15500

?2477 0774 _ 2 66112 12 A^t X'_,2 I_TEGRSTE C_E STEP _lTh C#EN FOrmULa 15510

_2500 0774 CC I 50003 AXT D*l THIS L5_P FCR P0_ITIENS 15570725C1 C634 C"_ 2 _25:4 L3 Sa_ L4,2 SET 6CCRIO[FF LIKE) :N GALLING SEQ. 15530

_2502 _14 DC _ _02 7SX SCAL_,_ 1554002501 CCT_ O0 C _111_ T_ P_t,_ 15550

CZSC4 5_74 O0 C C_OCO L4 TSX **_C' 15560_2505 _C7_ dO O 03113 TSA _3.C _-P+3 15570

'1250_ 3_74 -+_ 3 65756 TSX VlS,0 USE V16 AS _UR_y STORAGE 155R0_25_7 02_I C_ 0 _31_0 OP_P _SO !555002510 -5_D3 0_ 1 6_672 OST _,1 15600

:2511 I 3JO44 2 02512 TXi *+1:2,36 1561002512 I 71776 1 _7513 TXl "+I_L_-Z 15620

CDSll _ 77772 1 D25_1 L5 TXP L3t_.-6 15630r2514 _CL5 C_ _ 0Z53I tb T_6 L _ TR4 IS REPLACE_ EV NOP IF hAVE 15640C2515 _774 D0 1 CO_ 6xr C,1 VARIATICN_L E_UkTIDNS 15650

**FJRTSZ*+ VCdIFI_C 6Y 0* LAkSCN A_O G* DEVINE JU'.c lq_C 7/06/64 PAGE 3_

CZSI6 C634 00 2 C2521 LT Sxi L_,2 15660_2511 0074 _ 4 00C02 TS( SCAL_,_ !NTEORA_E VARIATIONAL EOUATIONS 15670

02520 OCT +, OO 0 ¢3166 TSX P_I,O 156R0C2521 _074 O0 _ _0DC0 16 SX +*,_ 15690

_2522 _07_ _0 d 01113 TSX _1,C 157000?523 0074 DO J 65756 ISX VI_D lS710

C_Z_24 _261 0D b 03I_0 OF_F rS_ 15720_25_5 -_6C_ 0C I _5714 OST Vl*l 15730_25._6 _ 03044 2 +2527 TX! *+1,2,36 15740

r2527 I 77776 I _2530 TXl +*1,l,-_ 15750025_': _ 71734 I 02516 TX_ tT_lt-36 15_60

15770

_2531 _4_3 O0 0 6_670 Lq _)LO I INCREASE TINE TO T*H 15780

r2532 _C'l OD 0 65666 OF_C _ Is7qo02_:33 -06_3 D0 0 65610 OST T I_BC0

15S10

(_2534 _74 00 40_O_D CER TSX ++.4 E0_PuTE NE# 5EGON0 0ERIV6TIVES 15820*+-60CR IDE' I 15830

02535 0rZO D0 0 02552 19.2 T_6 L20 NOP STORED OVER TR6 IF OPTICN-_ 15Q40_2536 _535 C_ 1 03116 t.lC 2_'6,1 .*.*SaVF CURAENT DIFFERENCES FOR 15850

0_._37 -56J4 O0 1 02_44 SXC LlD,I PREDICTOR CORRECTO_ _OCE 15860e+2540 +J774 C0 I _O_ _XI 0,1 IS870P,2tRI 0443 O_ I 66112 LIO OL_ XO_,l 15080

C254-' -5603 O_ 1 72322 OST _UF_J*I 1569002543 I 77776 I 52544 TX| *+hi*-2 15900

C2544 3 000CO l _254L t12 TXH LI0_I_-* 1591002545 -0534 00 2 02544 LXC L12,2 15920

C25_6 l 77734 2 02547 tXl **1_2_-36 15930_547 -C634 00 2 02544 SX_ L12,2 15940_255_ I O000O 1 C2551 L14 TXl *el,l,*+ .*=-130-2_I 15qsn

r,25_1 I 77624 1 G2541 LL6 _X,_ L19,1,-105 -3e36 IS REPLECED BV-21+36 FOR VAR. 15960• 15970

02562 C774 O0 I COOOD LDO AXT C,l CO;RPUTE FIRST RNO SECC_,D SU;_5 15960_2563 0774 0O 2 C0000 qXl 0,2 Aq0 FIRST OIFFERENCES '.599002554 0463 CO 1 65706 L22 OLC _0P_1 16000

02555 C301 0_ 2 66114 0F_O XDL+2_2 loCtOC2S56 -0603 O0 2 6611_ 0S1 X(1L+2.2 IPiRST SU_ 1_C70

02557 0301 0O 2 66112 0F60 XCL,2 16_002560 -0603 00 2 66112 OSt X0t_2 =5_COhO Sb_ 16C4_

02561 0443 00 1 65706 OL0 XCO_l 16050C2562 _303 OC 2 66116 DFSD X0L+4,2 16C60

. _ 02563 -5603 _0 Z 66116 OSl .0L64,2 -FIRST OIFFERE_CE 16(_70

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elEUAfSZe* _COIFiED WY C. tANSCN AND C. DEVINE JUNE L_6R 7106164 PAGE 39

02564 I 77776 I C2662 TXl **lmI*~2 16080

- 02565 I 77734 2 02566 ;Xl **]12t-]6 |6090OZSbb 3 77772 1 02654 L24 TXH 22,1,-6 16100

• 16110DESb7 0020 L)_ 0 62605 124*2 IRA L2fl TAR REPLACE0 BY NOP FOR _AR. EQU* 161_0_25/0 h?l_ 00 1 CCO0_ AXE Owl 16130

02571 077_ OO 2 COOOO aX7 O*Z 1616002572 04_3 DO 1 o602_ L25 OLD vIDC, I 161500_573 CJOI 0_ 2 56270 DFAO VIDL+2,2 16160

02574 -050J 03 Z 66270 D$f VIOL*2_2 =V6R. F|R.,T SUM 16170

_2_75 C_01 O0 ? 6o266 3F_ VtDLt2 1618002576 -0603 _O 2 66266 DST VIOL,2 mVAR, SEE|NO SUM 16L90_2577 C_6_ O0 1 60924 01_ VlODtl IbZO002600 03_3 00 2 6_27Z DF$B VI_L*4*Z 16210

rEbEl ~C605 OO 2 60272 OSf V|DL*RvZ "VAR* _IRS _ DIFFERENCE 1122002602 1 77776 1 02603 TX; *.I,1,-2 162)0

P2603 _ 777_& 2 O26_ TXI *_1e2.-_6 _62a0r2604 ] 7773_ I _572 IXh L25-I,-_6 16250

16260r_05 _5 r_ 3_11_ L2_ LaD 2_,1 I6270

_2606 -063_ 0 _ C262_ SXO t_O,l 16250P2607 077_ O0 77776 AXT -2_1 162_0

02613 3443 C9 6_!1_ L29 OLD XOL_2,1 COWPUTE NEW 3[FFERENCE LINES 16_C00L611 C303 CO 6611o OFS_ XOI+4*I 16310 ?D2612 _C_05 CO 6_116 USE XOL <�16320

C2613 I 77776 C_61_ TXI " Z16330_2614 3 DO0_O 0_10 L30 IXP L2_,1,** *. LOADED 6T 12_*I 16340

r26i_ -05J_ O0 0261_ LxO 130,2 16350_261f, 1 77734 C2617 TX| *+1_2,~36 16_bC

C2617 -0_4 _0 G261_ SXC L)0_2 16370_262P _ 3000D E262[ L32 TAi * �|�0�@�_*'-{38-2_16380

UZ62_ ,_ 9000C C2610 L_3 TX_ LEqel_ee *e_-108 _R_-TS_ 16390 i16400

",2622 _ 077_ O0 I C_CC_ L34 AX[ **tl -*-AODRIXC_ 16410

0262_ _634 O0 I 02633 L_6 SX3 L)9el RESTORE CIFFERENCtS _642C_2624 1 77776 L C_25 TXl *.1,h-2 IN C0_ECT LOCATiCNS 16630

; _2625 CW_4 OC 1C2_27 SX_ L_R,L 16440 _"C2626 077_ C'_ 2 OvOJl AXE I_2 16450_2627 _3 _0 2 C_OCC L36 0L_ "*,2 16460

C2630 -Oh03 00 Z C(CCO L39 OSl co,2 1647002631 1 O00G2 Z 02632 TXI **I,2.2 1_4_0 :

C2632 -3 O00_C 2 C2627 L6O rXL L38-2,** _**2N 16490

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1652C_ .-C26JS 077s _0 1 C003; AXT C.1 NISW DIFFERENCE LINE CCNPUIATION 165_0:Zb_6 377_ O0 2 O30_. _ _X7 0,2 *VE hEW CEnlVATIVE$ TE O[FF L|NE 16540 "e_C2637 0463 O0 ! 65706 145 ELO XDO.I 16550 F"

02640 -OhO_ O0 2 66116 _)$7 XI,_*_.L 16560_2641 1 77776 1 C26_2 ?xl _.1.1,-2 16570

:7642 | 77734 2 026_3 TX! . 6L6580D264_ _ 777? 1 02637 LA6 TXH L_5,1,-6 16590 i;

16600 a0264_ CCE_ 0 _. 0 O2664 TR_ 150 ERA 4L,LRE _ TO NCP F_A 16610

C2645 0774 O0 L OCC_ AXE O,l VARIaTIONal E_UAIIONS 1662n ,__Z646 0774 O_ 2 C0903 AXE C,2 16630C26_7 0_,4_ _,C I _02 _* L_70L_ VI_C.I 16640

_26*_3 -C_O_ O0 2 66272 DSI VI_L+4,2 16650

026_1 I 77776 I C2652 TX[ * 216660 :_02652 | 77?34 20Z65J f_! .41.2,-36 16670

[

t_26_ 3 7773_ I 02647 L_8 TX_ l_7,1,-36 16680• 16690

M

C2_* -35¢0 bO _ 6_655 L_O _ZT OPTION [F CPTICNsO THE PROCEDUR'_ IS COMPLETE 16700 _L026_5 0020 O0 0 C276_ TRA L@O 167|0

16720C2656 077_. DO I COOC_ _X! C,I 16730 --

_2657 077_ O0 2 6_L_2 AXT XOL.2 16760_2660 063_* ('3 2 02W6_ L53 SXA LSN*_ IMPROVE CGDRCIN_TES WITH 167_0",2oal 007_* CO A DOE02 7SX SCaL_t,_ CORRECTOR FORNULA le_?60

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02676 C_7_. O0 4 DOOC_ TSX _C:,LA,4 168g0

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l:

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,_"' 106 L

1965019622-111

IL

,JPL TECHNICAL MEMORANDUM HO. 33-188

mekORTSZel HCC|F]EC BY C. LAkSCN ANO C. _EVINE JUhE 1964 7/06164 PAGE 41

C_?O! 0C7_ O0 0 0311J T$_ _3,C 1_q20CZTOZ OCT4 O0 O _756 TSX V|_.O 16R30r270_ GZ&l CO _ C3100 DF_O _$0 16940C27G4 -0603 O0 1 65714 05[ V[*I 16950_ZfO_ _ 000_4 _ CZTP_ T_ "_ltZ,_ 16960C2706 I 7777& I _2_ 1 TXI _*l.l,-Z _697_C2707 J 77734 I 02_ _ TX_ L_7,1,-36 16980

• 16qgOCZTIO _C20 O0 0 02?63 L'9 TRA L_8 TRA REPLACED BY _OP IF OPTICS.2 17000

LTOtC_2711 0C74 O0 _ COOCO CE_3 TSX *e.4 P_EC|CTCR-CCRRECT_ _GCE.°°**-OER 1?020

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• 1732002746 05_5 O0 I 03114 L60 _AC EHtl 17330

**FGRTSE** _CDIFIEG 8Y Co lAwSON AND C. DEVINE JUkE 1964 7106/64 PAGE 42

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• 1746002763 050_ O0 0 65656 180 GLA OTRPE OECREASE TAPE OU_PlNG FLAG 1747002764 -05_0 O0 0 65656 N_T CTAPE 17430_2765 0500 O0 0 65652 CLA _ 174g002766 0402 O0 0 U4713 S_B "1 1750002767 ObOl GO 0 65656 STC CTAFE 17510

• 1752002770 0500 O0 0 0310> GLA CSAVE INCREHENT STEP OOUBL]NG _1530_2771 -0100 O0 0 02773 TNZ •t_ DERIVAT!VE LOCATCR 11_4002772 0500 00 0 03106 GLA 4H4 17550_Z773 0402 O0 0 G471_ SUB "E 1756002774 0601 O0 0 03105 SfC CSAVE 17570

• CYGLE 1756002775 0520 O0 0 03104 L_2 ZET STPCHG 175q002776 0_20 O0 0 03007 TRa Lq5 IF STFCHG NON ZERO GO TEST IF REAOV 70 17600

• DOUBLE YET _761017620

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1965019622-112


t*FORT_Ze* _ODIFI_C 8Y E. LAbSON JNO C, DEVINE JUNE _R66 T/06166 PAGL 43

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1965019622-113

l

JPL TECHNICAL MEMORANDUM NO. 33-188 i

/"

**FORTSZ*_ NOO[FICO _Y C* LAWSONAND C° OCV|NC JUNC *964 ?136164 PA(,E 47 t

03204 +17_42727g_7 0C_ 175_27272727p142272727273 +.682043650T_365C793e_ _1 PMI 503209 +I_2272727273 _O_Ob +17_414212_ OCT 175414212_34,I_2545004634 +.654957561720395_617_P=C! PMI

03207 +162_45004_J4 _032|0 *17,402477052 OCT 175402477052_142565544603 _.63_4043_09 7_3_0_80-C1 P_! ?0321L 5544_0303_[Z +17476_235204 0_1 174764235204_141726027044 +.610T2_49_q, 1712_bl_217-Ol P_l03213 Z602705403_14 +174_45230736 OCT tT47_523073_*X_I60LSZS074 0564123_76623_7_0-0LP_I0_2_5 *14L6_1_2307403216 +_747277C70_, OCT , _27707¢74tl414_Z25473_ +.576036258_1453135733_-01 o_l 1003217 *141_322_73303_20 +1747_3642150 OCI 174713542150_141071270345 _*56|29980d84507_7418gD'O| P_l II03221 *i_1071_?0345

03222 v1747007G0221 OCT 1747007C02_1,141104773324 _.5_7945791070711471390-01 PMI 1203223 +141104773324 _'_03_24 66714412OCT 1746_6714412.141767161_03 *.53576593744466381926D-01 PML 1303225 +14'76716_303_32_6 5502L6_OC[ 1746556C2164_141040342421 _*_2460247680248_648110-01 _NI 1403227 +I4_C 03424_103_ *17_ 251190 OCT 17_6452_I150_14127275113_ +o51431942901177079223D-01 P_I 15

• _323L +141212751L5_03232 +2C1400000000 PO O_T 2014000G0000_14600_000000 +olO000000000000000000D �X�<�P0-i03233 +l_60000000OO032_4 -201400000C00 OCT 6C1kC00C0000_546000000000 -,iO0_O00000000000000nC+ol PO -_C3235 -15O¢O00COGO003236 +£75525252525 OCT 175525252525_14225252525_ +_33333333333333333330-0| PO 00_7 +14225252525_0_240 +00003000000_ OCT 0COOC00C000C,000000000000 -.71746401373430634031D-42 P0 10_241 +OO00000COCCO_3242 -sT142LO_2}04 OCT 5714_1042!04_536210421042 -.4166666666666666666_0-02 PO 203243 -i_ZI0421042_3244 -_71421042104 O_T 57_4_104210_*536210421042 -.416666666666666666660-02 P0 3_3245 -136_|04_L0_203246 -17 73b/46422 OCT 5_oT]_T464_2,535_4136747 -.365410052qt005_910050-02 PO 4r_32_7 -L351l_7_6747 _._ _aF-?3250 -1706_3_10633 OCT 570633610633,5356106_3611 -.31415343915343_15_430-02 PO 50_251 -135_063361103252 -170543013_2_ OCT 57_543013525,535275121757 -.2708608906525573L4220-02 PO 60325_ -135_75t217520325_ -17¢464557076 OCT 570464557076_53_752001_11 -.235532407407407407400-02 PO 7

**FORTSZ_* _CDI_|EO FY Co |ANION ANO Co _EVIN_ JUNE [q64 7106164 PAGE 48

03256 -170_17016410 OCT 5704_702641C,53_525447047 -.20677822370930'038640-02 PO0325? -13_25_47C470326C -16774021232_ OCT 56774_212305t534_1_176415 -.1832085738335738_57r-02 PO 90326| -134_14176415_3262 -1676550721Cb UCT 567655072106,534_52306044 -.263623_28592348764300-_ PO lO0_263 -1_435_306044 •03264 -16700223_216 "T 567602235216,53403"2|7. _ -.1473644952945_61543_D-O2 PO II_3265 -13_037217_G20_266 -1675_6075_7 OCT 567536C75337,534_[3641C'34 -.133560177743602705020-02 PO 1203267 -134213641034_3270 -167477120304 OCT 567477170304t5"4670501037 -.1217785J6_1042652132_-0_ PO 13032?L -134670501C31C3272 -1574445t1335 OCT 5674_4_|_335,534330733076 -°ll;634606471761111_6D'O2 PO 1403213 -134330733076_32t4 -1674!5440_66 OCT 5674254_056_534257452131 -°L02830472907168555B30-02 PO 15_327_ -1342574521_10)276 C3C0000_l _C' _CI_O00C_Ct_6000000000 _.100000000000000000000+01 Pl -20_277 _lNbOO00CO000Ol?CO -202_000¢0_00 OCT 6C24CCC_0C00,_7000000000 -°200000000CO0000CO000D X�@�Pl-!C_301 -[5700C0000CC03302 2526UCT Z_2_5_2525_1_o252_25253 _.108_3_3_3333333333330+02 Pl 0P330_ _25_5303_C4 -175_25252_2_ OCT 5_525252525,54225252_253 ".83333333_33353333330-01 Pl l_33C5 -[4225252525_03306 -171421042|04 _CT _21_10'2|04,5_62_0421042 ",416666666666666o6666D-C2 Pl 203307 -1302104_1C__331C +O_O0000CO00_ OCT O000(_OrnO00,00CO00000000 _2406_6715317¢150-42Pl 3O.311 _OOO00CO¢O00003_12 *1_64i4566?_1 _CT 106_1_5667_1_1_3420414567 t°51256613756613'56613D-03 P_ 40331_ +l]3420424367_3314 *1564145667_1 OCF 1664145667_1,_33420414567 _.5_25661_66137_6613D-03 P| 503_15 +12_420414567,_1_ +165?05751_6_ OCT 165?05751063,132135116572 +.432q254eS_P88183,_215D-03 P_ 6(_3_7 +1321351_637_r33_ +165562344263 _CT 26_62344263,1322322_3406 +,353284B_245149_11_160-03 Pl 7C_2t +_322_1203406C_22 +16_4554C_o:2 _CT 1e54554c4662,132243323413 _.287541837021003687670-0J P| 8

'_" 0332_ 323_1303124 _64756225l,,_ OCT t6425622514C_131362175020 *o2356q6498717332u_0660-C3 _ q_3_25 _1_3.1175020_3326 L2Ct7_6()cr 1646322C1766_1314_6703_1_ +.lq51474524t225069267C-O_ P! lo0_3_7 67035|1

1965019622-115

=eFORTSZe= PC{]IFIE_ BY C. LAhSCN _ND C. D_V|NE JUNE 1964 7106166 PAGE 50

0_402 -1616Z2606276 OCr 561422606276,52633720331"_ -.16377x17946t137383800-O_ 62 1403403 -126_37203317_3606 -_0_016_0055 OCT 5_0T01440055,525655177163-.133980111_i216572338D-04 P2 15'_3405 -t25435177163C3606 000000063 E}CT 201_00000000)146000000000 +._00000000000000000030 �\�8�P3-203_07 +146000000000 r03610 -20_,00000000 OCT 603_Q000000Gt55C000000000 -.6000O000000000000000G+01 P3 -1G361L -15000000000003_12 .2_3605252525 OCT 203605252525)150Z52525253 +.60833333333333333J33)+01 P3 00_613 252525303_I_ -20_420000000 OCT 603420000000,55000000000_ -.42699_9999999999qgq9D+Ol 63 103615 -15000000000003616 6735673OCt 201616735677,146567356736 5833333_3333333330+0163 2034_7 +[4656735673603420 -1754631463_4 _CT 675_63166316,562631663146 -.75000000000000000000D-,'II P3 3

1 03_21 -I_26314631_6G36_ -I?J7_67_66_2 UCT _70736746422,53_i16736_47 -.3654100529100529_005_-_2 63 603_23 - l J51_7367670362_-16641_566731 OCT 566_I_566731 53362041(567-.51256613_56613T566130-03 63 503_25 -1334206[_567

03626 -163516022777 CCT 563516022777)5_0617653717 -°7964065_5573192239R5D-0_ 63 60_%c7 -13_6176537t7d36_0 +000000000000 UCT 00000')0_0000,000000000000 -.16162qSR3090218926570-61 P3 7

03631 +000000000000o 036_2 +1607Z22_7734 OCT 1607222_773_)I_5701537410 76571_6823793690_-0663 8

03_3 + _2570t 5374t0-_ 03634 *160722267734 OCT 16072__2_77._4,12570153",I0 765TI_6823793_900-0_P3._ l_3635 +1257015376t0'" 03636 73026663OCT 160573026663.12_163611767 _.l12962g199BSeCZTgO130-O_ 63 I0

03437 +t_5163611767 m

03440 +16044360155! OCT 160443601561 125665264365 +.B59_92687035676653660-05 P3 It _k_'_03_6L *1256657.u_34503642 +1576731_6317 OCT 1576_3,36317)1244345453_4 9619671-_298785600-05P3 I_

" G 3_'_3 _126636565334

_" 0344_ +15752_072_?_ OCT 15T521072_73, iZ4_350[1460 397288918948971BD"05 P3 1303_45 _[660

i_r 93646 2260566OCT 137_0/260546,|2_312106736 966223_'5569182_620-05P3 I_

'_ 03467 12_106734_ C3_50 62615OCT l_6617¢_6ZS?6,123105036252 06_028971660416D-05P3 15

03651 +12_105036252_ 03452 00000000P6 0£" 20|'_000C0000,146000000000 _.lO000000000000000000D (X�<�P6-2

_i 03_53 _146000000_00

] 9650 ] 9622- ] ] 6

;3

Ji=L TECHNICAL Mr.t,COR_NDUM NO. 33-188

ecFOITSZ** KO_IFIE0 SY ¢. LAk50_ ANO C- 0[Viii JUIF la64 T1¢616_ PALE _l

0345_ -Z03SOOO00000 OCT 5034000_00_0._S000000n000 -*SOJOO00000_OOOOOOOOOD*C| P4 -1

03_56 _201502525Z52 O£T 2045025_525Z_15152S252525 _°Z¢08333_33_333333333G*02 _4 O !_34ST ,_5_$25_S_$ZS

46_ -Z0_51ZS25252 0¢1 60451Z5252_2 $$15_#252525 -*]05333}33_33333335530,02 P4 |_46| -tS]$2_252525O_62 -203537_8T_5_ OCT 203S37567356115G_35_T356T *.54958333_333_3135333D*0| _A0_63 _15013_673_6703_64 -201522104210 OCt 60_$221G421_ 5_64210_2_01 -*l|20q$3}333333333333D*01 P_ 3

0546& ,1?5_167141 OCT 11$4_167144114216_144167 **_134_qq_T01SqAT08qqD_01 P4 40_46? "L_2167144_6?0547_ *_70633_|O_33 OCT 170633_10633.1356106_3611 _*31415343qLs3_3q|534_O_02 P4 $O341_ *_3_6106336|1O_ATt "1_57057S1063 _CT %657C_751_63.132135116372 *°_3Z9254_SO0¢0113_2_5¢_-_$ P_ 60_AT_ *13_1_5116372_3471 ,1635|602ZT77 OCT 16_516022777 |3C_17_53_1T O65_$ST_Lq22395_0"-04P_©3_$ *_3G4174S371?0347_ ,15C7222qT734 OCT 16072224??3_I125T0|S374|_ *._3|q_b_¥I?68z3Tq3_OG_04 P_ b0317? ¼_25TG1537410_3_O_ *0000OOOO0000 O¢I C00G¢0_00_00 000000000000 -°_22BSqt66_8OA_¥_14_-_l P4 9

03S0Z -_$6_35_1_346 O¢1 5_5535114346.5Z3470526105 -.260_]65120233514476.D-0_ P4 tOi _JSG3 -_;347=$:_G_

_3_04 -1_6_S114346 OCT _S653_114346 523_?0_Z6|05 -°Z&_36_I2e_3_|_?69D-05 P4 1|0]_5 -_Z3_705251050350_ -156430_12007 OCT _430512007.52]13_C06?36 -.2¢q0_64qO322_?_66_05¢-¢5 P4 1203_7 -1Z313_0C6_36O3510 -155650_1_117 OCT _SSbS02_T11_ _22_?_55¥35T -o158_564_¥_21403188420_C5 PA 130_511 °122376557_5703512 -1554730_;_25 _CT SSS473_41$_5_2_!13412_17 -.1_7_755U$136OO3072550-05 P4 [__3_13 -_22113_12_1703_14 -1_7Z3213_76 OCT 554T2J273¢?6 521_74b76073 -._?O_360316bLTS220A$qo-¢b P4 15_3515 -121_74_76_T3_3_16 *2014OO0_0_ P$ OCT 20140C_¢0C0¢.1_6OOC_O_00_ **L000_0¢00_000OP_0000D*_! PS -2

01520 -2C3_000_0000 OCT 6_6C_0_0COC 55_000000000 -.60OOC0_00_0C000_00OOD*¢1 PS °_"* : 3_21 -I_3GC'_0000C

_Z2 -2_74252525_ OCT ZC4?425_2.1515:_25_$25 *.1_033333333333333330_2 P5 0_3_23 _l_LS2525_5_v$SZ4 -2C$S_5_2525Z UCT :.05"_6525Z52 SS252525_525 -.2G41666_66666666b_560*C2 P5 1_35_5 -|$25252525_5

**FORISZ** nCCIFI_C Ox C. LAmSCN AND ¢* O[VINE J_KE 1964 I/C6/64 PAGE 5Z

r_526 "2(_772_|_4_ OC! 2C4772_1¢42w1$1104_10421 _*l_82qlb666666_,6666660_OZ PS 203527 "1511_2;_.__35_0 -_C3b_21342_ OC! 6_56642|O_21,5_CG_2104211 -°6|16666¢666666_66656_Cl _S 3_3531 -1_00_21042|1_532 *?¢15_313_5b OCT 2¢|54_315_$6.146630_LO314 *.1392119_3200_232_420*C1 P5 __3533 *t_b6_O410_140353_ -175427_,2_2 _ G_! 57542727272115422777_2¥3 -*6bZ043650?q3650,q365b-Cl PS 5_3535 -1422727_7273

_3536 -170545013_Z_ OCT 5_05_3013525.535275121752 -.270_608q0652_573tq220-02 P_ 6

0_540 -1_5bZ3_42_ _CT 5_SS623_4263,$32_312G)ACS -*35_20403Z4514qq|lS|60-C3 P5 ?r_41 -13223|_C340_ BC3542 -163_23576003 OCT 56_123576¢03.53¢727277756 -o6_?_2qq5430_95430_qsc-OA P5 0C3543 -|3OT272??TS6_3544 -160722247_ OCT 56_72224??34_52_?01_374_ -.138q?6571Z6$23_q34_OC-04 PS qC3545 -12513153?_10_546 -iSb_1_346 OCT 5_6_3511_34_1523_7052_]_5 -.Z_O1365!2_23351_4?690-_5 P5 10_35_? -12347C5_6105_3550 *0C00000_0000 OCI OC0_C0_00C,COCO¢000_O00 -°_Ob_l_!IS_4_Tt2;793D-42 P_ 11O3_51 *0_O0000QO00003552 _5_42201157_ OCT 154_22C1157_,___56_-7_634 **$|040_22500_737?9633_-G6 _5 I2_3553 "121562_74634_3554 "1_422011575 OCT 1_442201157_,|Z15_2474634 _*_1040022500q737?_633_-C_ P5 13_3_55 *121bb24_4631_355b _153664_3_?S| OCT 153_6463_751,12C314623577 *.40680_23_54OC_1_065G-06 P$ __557 "1203146_357;_35_C "1S3_O_45032! O¢_ 15_¢$453327,12C264255705 _.30521qO226q8275520_?O-¢6 P5 tS

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1965019622-118

"PL TECHNICAL MEMORANDUM NO. 33-188

2meFOLTSlee I_DIF|E_ 6Y Co LJ_SON 6KD Co DEVINE JUNE 1964 7j06/64 PAGE 55

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JPL TECHNICAL MEMORANDUM NO 33-188

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115

1965019622-120

JPL TECHNICAL M3MORANDUM NO. 33-188

t*FC_TSZ** VCCIFIEC dY C* LIM_O_ AICDC* OEV|NE JUN[ |966 ?10616_ PAGE $9

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0411_ -2C_47_S_|_$Z OCT 6_5473_71_12_$226_55_340 -.19_5_7306_6_4_61_*_2 Pl] 110421L -1522b_3_634_

0421) *|_64113_2631_214 -174666714412 OCT 574_667|4412_|767161_01 -.535765_7_966_819260--01 P13 13

_4_15 -1417_7161303_16 "_t74t._5|1333 _CT 5624_451I]}_53_3_733_7b -.III63_6064?I76171146D-C2 Pl_ 14

_2_ -1_3561213101 GC! _356!211161,53C223_17112 -.8_0412E5645931526274_-04 Pll IS_4_21 -130225_1711204ZZZ .2_140CC000_0 PI_ 0C1 Z¢I_C00GOCOC_I4eO30000000 **t0_00000000C000_00000tGI Pit -204223 *|4o0000_0CC_4214 -204_0000000 3C! 6_4_4g0C_000,551000000000 -.IS00000C0C0G00000000D*02 PIt -I0422_ -151000_C00_e_2Z_ +_C764_2523_ _CT 2_264_2_Z_23,1_42_25252_) ".1CS08_33331_333333330+03 P14 0C4_27 +1_25252_042_C -_1171_1Z_2_2 OCT _1i71012_2_2_6_25_2_2_ -+4561_6666666666_b_b6D_C3 Pit |

_32 _2|_$2711_1;4 OCT 2_5271;2l_,16_2|0421042 _.137ZS79166_666666666_4 PI4_4233 +160210421_C4_34 -21_73121673 0C7 614_121_73_$61567356736 -.3_332791e.6666o6666_04 PIt 3_423_ _161_6233673__42$6 _15476_27_6 O_T 2134260C2_,162207346207 _.508809217_232804232_D_04 Pit 4_Z37 *1622073_62_7C424_ -21_634_4565 0_7 415634_24565,562656563632 -.660064P_17460_17_60_C_'C4 PIt 5C4Z4I -i62_65656_7_4242 e2_641511$76 C_T 21641_I137o_22_3677776 _.6682_045_30$776014100_04 P14 6C424_ *I_22Z362727604244 "215_122_77o5 _; .155122_7265,562766_1C6_ -._283_¢q_8_S_3_8641q?O+C4 Pit 7_424_ -I_276£31_6C2

• _FG_TSZ'' _:CIFIEC 8Y C. LI_SOk X_O C. G_VI_ JU_S |_64 tlC6164 P_G£ 60

C4246 -21_62362o_67 OCT 2|r62362_262,161_0165_213 ..3_6_4q353a99861_12_D+C_ P|4 8

_4230 -213$7$2|16_? OCT 613_?S2116Glg_CZ6_56323_ o.15_076283gB3185024_0+04 PIt 9

0_2_1 o160261563;SCC42_2 +2124126_042_ OCT ?124126G0_,157606101232 +.$33502;11!53_3Y_Z?0_C3 P14 |0r4253 +1$76061_i2$Z_4264 _2|_411_6Z74 _CT 6104113_6224,5_557411-C_ -.|3_7249_937_IC6630890+0J P14 1|_42_$ -I_S_2411403204ZS6 .2_$$3|6205_2 OCT 203_31620572,152141_32_2 +.216|141_92_3266_8800+_2 P!4 _204237 .1321412_24_2042_0 -201236_43_G5 OCT 6C_56_45_0_,5_667106625 • -.192,4_73797_428_6_59C*_1 PI4 13_26l -|466210662_7_4262 +1746556021_4 GC_ I_63_6G2164tI_104C342_21 _.$24602476_0_48764a1|_-01 _14 14

,263 _14104_342421C_64 +16241$440566 O_T le7413440_6_,1342374_t31 +.10283047790716835883Do_2 PI4 IS_426_ +134257452'1!04266 +2014000_ PI_ OC! 2C14¢_C_0CC,146000_000¢0 *olOCO_OOCO0000_OCO000D_OI Pl_ -2

C4270 -2_$40000_0C_ OC! 6_54C¢C1"_¢0C,5520C0C00_00 -.16000_0000000000bC000_02 Pt5 -1

04212 +20774025252_ _C_ 2_?24_25252_,13+252_23_$3 *.120083333333_333333)0+03 PI_ 0_4223 +1542325252_3042;4 -2124305_000_ OCT 6|243_5C0_00,55700000000_ -.561_99_99_999_99990.0) Pl_ 1042?5 -1_70000¢00=004276 _2|37|1137336 U_T _1)?11137336,16C7_5623$6_ +.18287_83313_3333333D_C4 PI_ 2042T7 +t_07336233_704300 -21b_23273356 _:T 61342_22)3_.56273567_567 -._40385_)3333_333_3330+0_ P15 304301 -162735673_67_4302 +2|$7734_3704 t_CT 21577345370_,162103;_536& _.8121371_899_708_940_ P_04303 +162105|3336_04304 -21653_2_$6 OCT 61653_21_S_,56_0_3_5o033 -.1168873999669312169)g*03 Pl5_305 _1630330_6033C4306 _21_637037122 OC_ 236_3PC_7172,1630_123272_ +.13282932400518077601D+05 P|3 6

_4310 -216566000672 OCT 61_366C¢0672,56_1C510_300 -.11968_$3971_b0846560_+05 _1_ 7_43|1 -16_10$10430004312 _216412301450 OCI 2104125C1430,1u_?1331754_ +.853209_24240294813210+04 PlS 804313 _163213512_440_|4 -|15_52133_7_ OCT 6154_2155423,362315263500 -°_??1423637_3_4613720+04 PlS 90_315 -16251526350004316 +2t_12430_1 0_! 214_C1243011,101072312237 +._038378403|30_24_6610_0_ PI5 IC04_1; *161022J1223_

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0432_ -_]_15072104 OCT _12_15072104,_577_5L24261 -*666ZZ?CaMSZ834607_[6_*03 e15 110432| -|_77451Z4Zb_04322 "2104645303_ OCT 2tO46453?_4.15SOIOZ37302 *.1543361_76652_q2qsT?O+CJ P15 L2C4323 *15501023130_0_32_ -205570537C46 OCT 6_STC537C4_*_2q34676C05 -.Z_$4Z_87Z26_9545_60*02 Pt5 130432_ -152434676_C_

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04334 "17_4000C000_ _C_ 17640¢C_000_,14300000_000 _.IzSOOO_PO00000000CO00*_O _! 2C4_35 "143000000000

04337 .14_00000000004344 _174300000_C OCf %74500_C0000-141000000000 *.3_06_500000000000000D-01 PH| 40434! +14_000000000C4342 _:7370000000_ OC! 1_3700_000_C.140000_0_000 _.2?3_3TSOG_OOOCOCOOC_D-CI _1 S

0.34_ *t4000CO0_O0043_ _17341CC00000 OC! _7341:0_000_,14:000060000 c-I_11328t_5000000000C0-0_ PHI 7

_43_0 "1726_50_0C0 GCT I_Z6_5_CO600,13700GO00000 **_30q204|0_$6250000000-01 _HI 80_351 _137000_C0qC_C43_2 "172_45460000 OCT 172_454GOCOC,i_7000r.OOCO0 _.I09tOO3417?_BTsCO0000-6_ _1 q04353 ¢137000000_C0_4"5_ *_72_7700_G3 301 1724_7700000._37_0000nc_0 **_27_52_CSZ73437500PO0-02 _HI 10_43F5 .1370000000000_3_6 -1724063_0000 OC; 172406340000,;37000000000 _.SCC_q56qoqI?qbB7500_D-C2 P_! 11

_4360 *|TI_13ZlO00C OCf 1f171_21000C,_6000003CC0 +°TOO3e372q_532226_250-02 Ph_ _2

_4362 _TI_Z_2|40_O OCT I?162b_140GCf|360_O00_O00 _.6|qq2406B_50q2773437D-02 P_L 13"4363 _13600000$G000436_ *_?155Z57_00 UCI 1?155257500_,136000000000 *._350_63_54_711q1400-02 PHI 14_4365 .13O000G00000O_bb _171_063_0400 0_! 1?|_Cb360_00.1360_000_C0 _°47BI532_q29092407Z26D-02 PH| 15_30t -11600000000_

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o*FQATSZ** P_C|FIE_ aY C. LikSC_ t_O r. O[V|N[ JUSt 296_ TlOb164 9AGE 62

C4_72 _t7640_0C0CC_ OCT 1764000¢00Ge,1430_0_00000 +°12500000000000_000000.00 PH2 3G4_?3 +143000000000043?_ _1755_0000003 OCT ItS_C_CCCOOG,142000000000 +o7B12_00'_000000000000_01 P_2 4_4375 _142000000_G0_43_ J_000000OCT 17_ ?C0000000t_41000000000 _.346BT_OOOOOOOOOOOGD-01 PH2 $04377 .1_0_0000000C, 40_ -17_2000_G_ OCT _745200000_Ct141000000000 *.41_L_6_50000000000000-01 PHZ 604_" *1_,10000¢0000_440Z .1;4410000000 001 _7_10000000,141000000000 _.3Z226_62500000000000_-01 PH2 704403 _14100000000074404 _73655000000 OCT 173655000_00.14_00000P_00 *.261840_20312500000000-01 PH2 8044_ +t40000_O0000C4_06 .173_45_C0_0_ OCT _7_545400000:140_00_000 6B35q37_O000000-CIP_2 _C4407 .140000_G0000_4419 *L7345770_000 OCT 1734517COOGC,14000_OO_GO0 +.tB_705810_q68750000_-OI D_ _0044_L 000000CO34412 .1734063_000_ OCT 173406_000G,140000000000 +o16017q1381B3_93730000-01 PH_ 1104413 _140000_000_0C4414 +1727137t0000 OCF 1.'?_3210000,_3100_000000 +o140%56745qtO64453|Z_O-01 _H2 1204415 +_37000000000_4416 262t400¢OCT t726262i4000,L37000000000 **_23'84R136_018_546871_01 PH2 _304417 *L3_OOOPO00_OC44Z0 +172_2_7500_ OGT 1?2_5257_000,|37000000000 7007_650_Oq42382eO-OLPH2 1404421 _3700000_000

04422 e_?2_Ub3_¢4_ OCT 17Z50636_400,137_00000000 _.qq630653858186814453p-02 PH2 _0442_ _13700000_0_4424 .176_0_00000_ P_3 OCT 1?_40_C_00C 143000000000 +.125000000000000000000+00 PH3 30442_ _1_3000000_00_4426 _17_6000¢0000 OCT 175b_OOCOOOG*I4_OOOOO_OUO **_)7S00000000000000000-¢1 PH3 4

_430 +|75440000060 OCT 17_4400_.000,_42000000000 *.?0312_000000000000000-0t PH3 5

_4432 _t747000¢0000 _C; _7 _C0000000,141000000000 _°546_?_0000000_0000000°01 PH3 604433 0000000004434 _74550000000 OCT 1745_000000,14_000000000 +._3_4_125000000000000-_| PH3 704435 *14100000000004436 *1744S1000000 OCT 1744510C0000j141qO_O00000 *,36254MS2812500000000D-OI PH3 B04437 *141_0000000004440 64400000_GT |737_440000Pv14C0000(0000 **}05480937031250000000-01 PHI 904441 *14000000000006442 +|7t6h500000_ OCT 17365§_00000_14000000_000 I_408_O3|_50000000D-OIPH$ |00_443 *140000000000

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eeFQRTSZeo MGOIF]EO §V C. LJ_SCN AND C. DEVINE JUNE L96& 7/06/64 PAGE 63

_44_4 _[73$64740000 O_T [?3556_ 140000414C000_00_00 _298558398437550000-01PH3 L|C44455 _140000000000_4446 _17355L0030000 OCT ]7351003000C11400000000_0 *._OOZ23922f29_921875500-OL PH3 12044_7 "1400000000C0 m_44550 _17346_35Z00_ OCT 173443_5Z000,1_C000000000 _.1778_12_44Z_O488Z_120-01 PH_ 130_551 .1_0000000000_4q552 55_3ZG00OCt 17340543Z000,1_0000000C00 *.1559409066173095703120-01 PP3 4404455_ _440000000¢0_044554 _172727_Z_00 OCT _?Z?27442_OO,_3700GO00000 _.1_3910944_61822_09760-01 PH3 15504_555 _70000000C0C_556 .115_000_0000 _ OCT 1_400000000,Z42000000000 _.62_0000000000C000000D°01 PH4 40_? .142000000G0004460 _1 _S_O00000_ OCT t_ 554CC000000v1_2000_00C00 _.6_55000000000000000000-01 P_4

0_462 _17_?00000000 _CT 1747Q00_000C,141000000000 _.5546875000000000000000-01 PH4 604465 .14_00000000__6_ _17_60C000000 OCf 1?4_CC00000C,141000000000 _.46E7550000000000000000-01 PH4 7

• 466 _17_5512000C00 OCT 17451Z000000,141000000000 _°40ZE)Z03_250000_O0000_O| PH4 $74_67 .1_1_300C00C00_I_ .1/4_360C0000 OCT 17_4_6CC000C.14|000000000 _.3_121093T550000000GO0-01 PH4 ?04_71 _1_1000000000_472 6_400000OCt 1737644C0000,1_0000000000 *°_0554809557031Z550000000-01 PH4 10

C4_7_ _175672000000 OCT 17367Z0¢000C_1_0000000_00 _.26977555590625000000000-01 PH4 L!044?55 _l_O00000qOCOC4476 _l?_bll_ZO000 OCT IT_61[_20000,l_rO00000000 _._402687012753qO6Z55000-Ot PH4 120_477 _|400000CO00D_45500 *173_[220000 OCT 17354]_200GC,44000_000000 _°_1_6255T629394553_255000-01 PH4 13045501 .14¢0000000000450_ *17_7_1556000 OCf 1_477156000.|_0000_00000 _.[9_83327865560_5585595570-01 PH_ 140_03 -1_000000000004_04 .113_214_000 OCT 173_214400_J._40000000000 _.17712116Z414_0751255_-01 P_ 155

_45506 _17_000C0000 P_ OC! I74_00_C0000,1_10C0000000 *.31255000000000000000013-01 P_5 55

045510 _lT_O000000C OCT 1_55¢COC00GC,1_1000000000 _°39062550000000000000_0-01 PH_ &C45511 000_4512 _74_00C0000 OCT 17_500000000,|_1000000000 _.3906255000000000000000-01 PH5 ?0_5513 _t_lO000CO000045514 _174_554000000 OCT 1_40C0000_14[000000000 *.3662109375500000000000-01 PH55 550455155+141000000000


**_u_T$l** PCCIr|¢C 8Y C. la_FN AkC C. *EVI_E J_k_ [qE4 71067_4 P_GE 65

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,_ +17_443_5200_ OCT 173_52000,1_000_0_000_ *,1?7_12544;594_82_12P-C1 P_7 15

0_0_ _|_lq_900_0_ _'_ OCT 1714COCC000,.,13_OCC_CCO0 _.3_06250_G_00000000000-02 _8 8

¢4604 _1774_000_C_ 001 1_Z_CCCC_0_C,1370,_090_009 *o7_!25700_000000000000-CZ F_C46u8 +137000000_0

£_60b *17_403_?C_ _ 1,Z5400_0090,137000000000 **IC74218!5000000000000-0l P_8 10

C4_10 *172_C_0¢C0 dCT i7_CC_00_,I_70C_0COC0_ _.1_6_5]1_5n_0000000000-C1 PH8 11_4811 +l_Td_0000C0 _,_ +I_)T_:'_0,'C _ _01 1_2707"C_0_C,1_7_C_000000 _.1_854_046_7_0000000-C1 PH_ 12

C461_ "13_00£000_CC_614 _17273_00000 _CT 17_73_CC_C00,137000_000_ *.1_526_071875000000000-01 _H8 [3

_4615 *IITOC_0CC__Stu _17_.4400J0_ OCT 17Z74_4CQ00_,I3700000£C0 n *.1_7_57_6_015_250000_O-CI P_ _4

C46 7 _!_TCC_CgC*CC0_6.0 +1721_4_,_9_C_ _C; 172744_C000_,137000_C_C_ +.1_785766_01562500C000-C1 aP6 15

r_621 _1370_09_C_n40Z2 +1"_4_0_0_0_ _h_ _CT 170_CCCC0_00,13500000n000 *,I_5312500000000_:00PCU-C2 PH9 9r46Z3 +1_00_00000_

_Z_ *17!_4000_000 OCT I?I_C_000,13600_CCC0_C _.43945_125000_G00_0000-02 PH_ 10"4625 +13o0C_0'_00C

C_26 _lTJbbO0_ClOC 0C_ 171_,?CCOCC_,I_6000_0_000 7_6878009000000_U-CZPHq IIC46Z_ _136000_0009_630 *I_4ZIOCO_C0 OC_ 1?_421^0300_*13700_0000n0 _o83312q8828125¢0000000-02 PH9 IZ

_4_3_ _17_7_00000¢ OCT 177_Tl_CQ_C,1370_000000_ _.9_130_710937500000000-CZ PH_ 13

04_3_ _137_0000010__46J4 _17Z5_200000 OCT IT2_tC_C0300,13700CC0nC00 _.IC505_76_5312S_000-01 PHq 14

"46J5 _1370G00_0_C0_630 +177_3300_C$ OCI 1725_3300000,137000000000 +.11069124_511718750000-01 PHq 15

C4_37 +137000000_C0C4_0 +167_00_0000 P_10 OCT 1_740_CC_00_,1_400000_000 +.976562500000000000000-03 PHIC 10

_641 +I_400COC0000

*1FORTS?** PCOIFIEC BY C. LA_CN AND C* OEVINE JUkE Iq6q 7106/66 PaGE 66

_4e4Z +170_00000000 OCT 170SC000000_,135000000000 *.Z44140625000000000000-02 PHIO 11"40-, _ +13',000000000

C,4bt4 +171404000000 OCT 1714_40000001136000G00000 +.396728515625000000000-02 PHIO 12

04645 _13600000000004846 '171530000000 OCT t?1_36000CU0_136000000000 +.53405761718750000000i_02 PHI0 15

0_6_ +136000000000

_465C +171651000000 OCT 171651000000,136000000000 *.64849853515625000000D-02 PHI0 14

04651 +1360000000_0

C465_ +1717_44C00L0 OC_ 171744400000_136000000000 +.7392883300781250_000_-0_ PH10 1504653 +13600000000_

04654 .166400000_Cl PHIl OCT 16640000_000_133000000000 *.488281250000000000000-03 PHll 11C4655 *1330000000_0

04656 +1675400000_0 OCT 167540000P_0,134000000000 +,134_773437800000_0000-02 PHI1 1204657 000000

r,4bb0 +1704_4000000 0C; 17046_000000,135000000000 +.234985351562500000000-C_ PHIl 1304661 +135000000000

04662 +170670000000 0CT 1706700C0000_13_000000000 +.3_569335g37_000000000-02 PHIl 14

04663 +135000000000Okhb4 '171430400000 OCT 171430400000.1_6('_0000000 +.428009033203128000000-02 PHil 15C46_ *1360000_000004666 +165400000000 PHI2 0C, 185400000000,1320000_0000 +.246140625000000000000-03 PH12 12

04667 000000

04670 +166600000000 OCT 166600000000_133000030000 *.7_Z4_I87500000U000000-03 PHI_ 13C4671 +13300000_C000467_ 00000GCT 167550000000,134000000000 **1373291018625_0000_0-0_ PHI2 14

04673 +13400000000004674 +1704200000U0 OCT 17042_000000,135000000000 +.20751q53125000G000000-02 PHi2 15 •

04675 *13500000000004676 +164400000000 PHI3 OCT 164400000000,131000000000 +.1'207031250000000000_-0_ PH13 1304677 +131000000000

n4700 *165640000000 OCT 155640000000,132000000000 **396728515625000000000-03 PHI) 1404701 *132000000000

04702 _166640000000 OCT 16664000000Ct133000000000 *,793457031250000000000-03 PHI3 1504703 +I_3000000000

04704 *1634000J0000 PHI4 OCT 163400000000,13000000_000 +.610351562500000000000-04 PH14 14047_5 +130000000000

04706 +164700000000 OCT 164700000000_131000000000 _. _ [ 36_0_667_000000000-0_ PHI4 15

04107 *13100000000004710 +162400000000 PHI5 OCT 162400000000t|27000000000 +,3G51757812_0000000000-0_ PHI5 15

04711 00000000ENO 23390

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i 121

1965019622-126

,r

JPL TECHNICAL ME_C_RANDU,V NO. 33-188_--

• *DOUBLE PRECIS[C_ I_;NER PROCUC1RGUT|kE BEE_AN C$C 20 APR6Z 7/01/64 PAGE 1

BINARY CARCNO. SCALRO00 ,'00000 ENTRY SCALA 00300

• 00060CALLIN_ SEQUENCE 000_

• CALL $CALR|A_BBN_JNS| 00_60_HER[ A=D_UBLE PREC|SIDN VECTOR A 50070

8"DOUBLE PRECISION V_CTOR 0 O00BON=NUMBEA OF OoP° ELEMENTS IN A ANO 8 00090

A_S=D°P° |_NEAPRO_UCT=IA,B| 00|00• NCTE_*°oA AND E ARE STOREOFOR_4RD 00|10

N 1$ STOREb NB3_ 00120• OOt30

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, 122

1965019622-127

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7/01/64 PAGE !

IBINARY CARC NO, $_ULTO00

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7/01/64 PAGE 2

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T.-*

Jpl TECHNICAL MEMORANDUM NO. 33-188• IS

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i JPI.. TECHNICAL. MEMORANDUM NO. 33-188

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,,+-

JPL TECHNICAL MEMORANDUM NO. 33-188 ........

*tlqTlP e* JeCOIFIEC aT C*JoOkViNE*C.L.LARSON, JPL* JU_ 25*106_ 1/01/64 PAGE •

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004_7 C COg_O 0 ¢_22 _ PZ[ _SEqlJt t* 016400041J C_GO O0 I 0000_ CL_ 3_1 01650

C0411 0400 00 0 G_476 4CC "_ 0166000412 C_21 00 0 C0415 ST_ 16_I.2 01670

00413 C074 00 4 00002 _AT _ALL SCAL_*ffS_R|***_NCOEFeTE_P 01680

BI_A_Y C_C kO. _k_P_ll

00414 C074 O0 0 002_70_415 0C74 00 0 COCCC

-*iI*TRP *e JeGOIFI_C 0_' C.J*OEVINE_C.L.LAkSCNo JPL: JUN_ Z5_1904 7101164 PGGE 8

00417 0074 O0 0 00157

C04ZO 0534 GO | C0472 LX6 XR_*I 01670CC42_ 05C0 CO I O00C? CL6 711 01700

00422 C621 O0 0 00427 STA CCldXS 0111000423 0500 O0 0 003_0 _LA SIEP n1_2000424 0621 O0 0 O04ZS $16 Q•! 011'30

0042_ 04"*3 00 0 COOCC DLC ** 0174000426 C261 _0 _, OOL_7 OFPP IE_P 01750

00427 -0603 _)0 000gCO C,_leh5 DO! •* 01760• _: 00430 0020 O0 0 00472 TRA XR_ O|TTO

• * - 01790

I_EN N • 3e ._OPPUTE xOOO|N _ PU_ *• • 01810

XO0016 - _'U) • |-LkI1-OELTAIQ|I-OELTA|*•FUIN *• * 01830

• XOO(N| • 0|$40• * 018'_0e***l *_** • • * * D**** _ * ** e***et**l _1. O|P_O

00431 C500 O0 0 C0273 h3 CLA NCOEF 01870

004)2 076? O0 0 0_'022 6LS te 01 ,_000_33 0622 O0 0 00456 $70 **3 0109n00434 0_'76 O0 400CCI lrsx 3SI_LT,_ 039r', :

00435 C 00163 0 000C3 PZE LCG_tBSERI 01q:

00436 0 00000 0 01227 PZE I_SERI._a* 0112L00437 0500 O0 4 00003 CLA 3,_ 01930

I BINARY rGR_ l_0° INTRPOI2

00440 0400 O0 0 00501 6CC -6 0194000461 0621 O n- 0 _0444 ST6 N4.2 01950

00_._2 0074 O0 4 00002 h4 CALL 506LR._SERI,_*oI_._EFwlrEI_p 01q60C0_43 0074 O0 0 C0227

_1_ _1044_ 0C14 O0 0 00000

:_ 00445 0(.74 CO 0 C0273

00444 00?4 O0 0 0015700467 0534 O0 I 00472 LXl XR4.1 01970

(10450 0500 O0 ! 00007 CL4 ?_1 0198000451 062! O0 0 00456 STA 66 01qO0

(_06S2 0500 OO 0 00330 CLA STEP 02000

00453 G621 00 0 00455 S[6 _5 020100C454 0443 00 0 00157 0L(" TEI_P 02020

_. 00453 -024t 00 0 G00C0 N5 Of_ _* 02030

In ] I I I I n I ii i I II n iii 11 i n I nl]l Illl - . 3 - i I

] 9650] 9622-] g2

_! JPL TECHNICAL MEMORANDUM NO. 33-188

"_, e*I_TPP ee NGClFIEt 8Y C.J*DE_INEIC.L.LAk$CN, JPLp JUkE 25*i96_ 7/02/64 PAG = 9

-_ 00_6 -0603 00 0 C00¢0 _6 057 _* 0Z040_- 60457 _020 00 0 00_7_ 7R4 XR4 02050

leo eoe.a • • • • .meg• oe • we•.• e_eo_ • ; ••• • 02_60• • t ee•_ • • • ace••e•1 ee le • o • • •••••OSG_

_- * • 02070• d_% h • 2* COPPbT_ XDD(N - Pb) *

• * 02090 l• X00(N - rU| s |(2 - 0ELT_}•_U) • XOC(k| •

• • 02110_" • •• • •4•• •4 • •••••qee• gelel e• 4ee • • ••tee • 02120

00460 0500 ¢0 | 00G03 h2 :LA all 02130004_1 0490 O0 000$CO AC¢ •4 0216000462 C_21 O0 0 00466 $74 $0*1 021S0

OQ&b3 0530 00 2 00007 £L4 7.1 02_60

0|NLRy _AA£ N0. ;NTAP01]

0096_ 0621 00 0 00471 ST4 SG*& 02170

00_bS 0074 O0 * 00002 SO CALL $CALR_•e_ESERI,NCOEF,•_ 021_0Q04_6 007_ 00 0 0000000_62 G014 O0 0 001e_

0_470 C074 03 0 0027 _03471 00?4 00 0 00000

004?2 0774 00 4 00000 X_ 4xT **._ 0219000473 C774 00 2 00CC_ 4_2 AXT ••_2 02200

¢_7_ C774 O0 1 00C¢0 X_I AXT ••_1 022100047S 0020 GO 4 0032| 7R4 9_ 02220

_0

LI¢_RAL$00476 00000000_002

00477 O000000COOC_00500 0000000C00C4

0050| 0_00000000C&OGS02 2330000_0000

J_

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128

• _L

1965019622-133

[.

: JPL 'TECHNICAL MEMORANDUM NO. 33-188

I TSTOP RESIDUAL CO_PUTATID_ CHARLES Jo DEVINE 7101/6_ PA_E |SUBROUTINE TSTGP ( NTAPEmLTAPE_KTAPEv _ELTA* TI_E_

| DELTjCOSOgtSINQB,CPATeXLBt XJCO tXVZ,VXYEf. 1 KAMoLANtKANo;_WRITEtNPA|NT )

I 0 _IPENSION XLBliJI tXJCitl tXk8(_!O CIP_NSI_N CGSGBIIItS[NOEILI,DELr(SI.XY_(SItV'YZ;SI,CPA'|),SImXJUG(

It|

D DiVE,SIGh OELTAI)!D CIPENSIOk VCLD(3IO CIPENSINk CGATr;II,XCLCISJ

£1_ENSIQk DUR;I4966)_$UMEIbI,V3LIIIeVS_IIIttZLILIIVEPIIhIVILII)IVI_IlI_YZLIII,VEPII),VYL(LItVYRILI_V, Li|I,VX_(Iiq2XJLll_*XJ_tII

CCMMD,_OUR1 t DUPE • VSL,V=PtVZLJVE_tVI_tVIN_VZLtVZ_9|VYLtVYboiXLmYX_XJL•RJ_

C FLIP STORAGEFROP FAP _O FORtrAN BE.XJC(II-XJMXJCIZI-XJLXYZIII_VX_XYZI_)v_XLXYZ(2)_VyPXYZ(_I_VYLXYZ(_IaVEPXYZ(bI_VZL

VXYZ(_JsVLLVXYZ(EI=¥EMVXYLIS)'VELVXYZISI'V)_VXYZIb)eV)L

O TIP_XJD-XJOO5 REAU TAPE NTA_,CDATE(II_DC_TEIE),IXCLD(_EI,XOLOIME+3I PF'I,31t

1 (VCLOIME)_VCLC(ME+3]_NEmIt_IO IF(DOATE-XJD)5_,_

CCNTI_JE3C0 ECkT['_E

EC 13 IsI*3D CELTIII=XCLCIII-XYZ(|)C 13 _ELTAII)eOELTII|

GC TO |21_26|oLAP12 FCRMAT| F10.1_ 6FLl._o TPSFIA.4 |

21 kRITEDUTPUTTAPE 6tlEm XJM_ IXYZIIItI_I_St_

TSTDP RESIduAL COMPUTATIGK CHARLES J, DEVFNE 7/01/&_ PAGE 2

!V_YZ(II_I-1,3I,2 |CELT |I),I'I_3I

26 EE_TI,*_UE_qETulCRLL STINKSIXYZ _VXYE_CELT_XLE _CPATtC_B_b! EBvNRDr)GC TO EAR,St||LAP

69 NR|TE GUTPUT TAPE 6t_Oo | XYZ(i|,I=It31_(VXtZFI)mlml_3)•I CELT 13)o|DELT 'I|,[=I*2I

50 FCR_AT(ICX_6FII°_,/PIF_.__I ccNrI_E

_C TO (ICO,2001tKAPIC0 CONTINUE

hRCr=2CALf STI_KS(XCLD_VOLCtCELT_XL_B_C_ATo_DSERoSINCBINRCI)£C 15 I11_3

C 15 XL_u|||=XL_B(|I-XLO(|)_RIrE OUTPUT TaPE b,Lb,(XLee|1|vIi|,3)

Lb FCRMAT(T6Xt7P3FI_°4)2C0 CCkTINUE

E EPHERER|S kRITE PEtEG£ TO (_O,A61,N_RITE

60 CCNT|_U_GC "0 (AI,6Z_63,_4|,hPR|NT

61 _ITE TAPE LTAPE_XJH_XJLmVXPtV_LtVY_VYLtVZNtVZL_VI_tV|LIVEMmVZL_V13P_V3L

WRITE TAPE KTAPE,XJO(L)rXJC[2|,IC_LTA|II,I=I,3), _ELI|3I,[ |CELT (I)_,2!

6¢ TO 6_b2 _RITE TAPE LTAPE_XJMIXJL_VX_tVXLtVYP_VYLeVZM_VZLtVI_tV|LIVEMoVELmV

I_V3LGC TD 64

63 W_ITE TAPE KTAPEtXJD(1),XJD(_$,|CELTA|I)t|=Io3), OELT(31,I |CELT (|)_I=L,21

6_ CChl;NUkGC TO (_,5_6),KAh

65 CENTIMEWR|TEOUTPUTTAPE6_IE_XJP_fX_V_M_VZVtVLPIVE_+V3_

2 |CELTA(IImI=1131W_ITE OUTPUT TaPE _SGt |x¥_ (I|,I=I,3},(VXTZ|I|mIm|,3),

I £ELT (1)_(OEL! |I)tIiltE)66 ¢CK_|NUC

RETURN

TSTQP RESIOUAL COHPUTAT|DN CHAR_ES J, OEVINE 710tl6A PAGE I

_NCIL_OtCoO,OtC_1_OmOtltO,C_CtCmOl

129

• ;

i ii lit . n in , _ _-':._ " ;" _ T u nilinn _ _ W _7 ;" T T _- _ _""'"- L'x- TT "_7: T "' " ................. n

1965019622-134

t

_; JPL TECHNICAL MEMORANDUM NO. 33-188:__

STINXS ROTJTICN SUBROUT|N£ CPARLES J. cEriSE TIO1164 PAGE l

_ 5UERUUTINE STINKSCXYZ,XIDOTtCELTAtXLB*C_AT* CO$Oee$|NOEw_ADT

C

_- _ SUERCUTINE STI_K OOES THE FCLLC_[_(ll ROTA/ES xvZ AND VELGCITV TC ECLIPTIC

_ C (2I ROTATES UELT_KXYZ) TO _L[PT[CC 13I CO_PUT_S RPO, LC_GItaL)E, L_TITUDE I_ ECLIPTIC, BY CALLING $PHE_' C f4) CO_P_TES CVATRI^ mANL NEk DELTA kHlCP I$ B MATRIX, THAT

C (_l [S_ COSIBET_)eCELTALt ,,_LTAIRETah JhO OELTAIRHGI0 C[VLNSIO_ XYZI3I*XLCOTI3I_CELTAI31fXLBI_ItC_ATI3*3IICOSCBII)*

| $[NC_III_XI3IeDI_SeRHCIII*XLI|I*_B[|I_DEL[})C ROTATE P_SITIC_ ANO VELOCITY A_O DELTA

5 CC lO [=1.3GC TO [7*8e_)*_S

C 7 _II)'XYEIIIGC 10 10

C 8 xIII-XZOCTIIIGC TO lO

C 9 _[[_'CELTA[I)to CCATI_JE

;" _ C(||:X[|)C{21" XIZIeCOSCB-XI3IeSINO_r C{31*-XI2IeSINC_*Xl311CO$O_

GE TO (15,20e2$)_NS15 CC lA I_l,a16 lfZIl_=O(ll

_- C U=CIIIO V_CIZ)

C k.CI3lCAL. SPH_RIUeVe_RHO,XL_XBIC XLEILI'RPC

XLBI2I'XL

C XLBI3)-XE_S-2

,_ GC TO• 20 CE 17 I-l_3

!_ C L7 XICUI(I)-CII|NSu3. GC TG S

,_ STIN_S ROTATION SUBROUTINE CHARLES Jo DEVINE T/Ol164 PAGE 2

r c25 CC 18 1'_1_3

O 18 CEE II_=CII)/RFCGC TO IGC_)_N/CT

40 CCNTJtUEC NC_ .OMPbTE CVATRIX

S Cr_,lNUEO $INXL_SI_FIXLI

: D $1NXE=SIhFIXOIO CCSXL_COSFIXLIO CCSXE'COSFIXR)

CPATIL_II=-SINXLC_RTIL,2I_CQSX_O C_TII_3)=0.0O CPATI2_II=-$_NXReCO_XL0 C_ITIZ*2I_-SINXBeS|NXLO CP_TIZ, 31_CCSXB

, 0 r _0 Rule30 3_ ¢+JP(_tlI'XY_III/RHO

• 0 32 CELTA(II-O,OCC 3_ l=1*3CC 35 J_l*3

0 tS CELYA(I)-OELTRIII I,J)_C[LIJICC 59 I-1,3OC sq J.h3

59 C_ATI|,JI*CMAT(I,J)IR_C_S CCNrl_JE

RETURNENCII*O_C*OeO_C*I_O*C*L*O*OsCeC_OI

i

"_ i_.. ii i, i2i ii r ,liiiiii ._ .................. :_,. _: _JJl I III II IILI_I , ........ " . . : ;--_r " nil IIII _ :._:.-:--- i

1965019622-135

L

4


SET32 NORMALEQUAT|OMS CHARLES J, CEV|NE

SUBROUTINE $ET32|PQRtXYZ_XICOTwAIEeXNwSET_ TIMEBCMAT)

S¢T32 IS I MO01¢ICATION 0¢ NEO3;IME_SION A|I)_E(Z).XN(IIwTIMEll)0 01NENS|ON $ET3{3t6)tVELN(3)tPGR(3t3)tPQ$|31tX|0UTI3)_SET{6o61t

1 XYZI3JtCMAT(3031CC 178 JC,lt3

0178 PCS|JnI-RYZ{JO|0 RROOT_POSII|eXIOOTIII_PQSI2)eXIOOTI2ItPQSI3)e_IOOT{3)0 O'E0 r+lQ ESQR-GeQ2

B-Fe:IoO-ESQR)R*SQRTF(FOS|IIea2+POSI2Ime2*POS(3)ae2|

"_ _ AB_OeB• X_OulR-Fe(I.O+ESQRI}/A 8' O AR-F*e2

XNN,XNIIZ

_ C|VIAR°X_NeGCIVRmRROCTIOIVD RB-RIOC RB_=L,O+R50 XK0aC|VR+RBi

CC 20 l'|t3O 20 VELNIIJmXICCT(I)IXN

IX-IIYm2IZ-)

21 l-IX

J-l+3C CF PAGES 23712_1 IN 6RCUMERR,*O PRI_ITE CO_MLNICATICNC SEr31I,|)=+VEL_IIX|0 SET3LItZI-+PQRILtIY)o PO$( ZI-P_RIL,|ZI* POS(IYI0 $ET3IIt3Im+PQRI2tIYI* POSI|ZI-PGR(2eIZI* PCSIIY)C $ET3/I,_)- + POSiIXI-I.$eTI_E.XIO_TI[XID SET3|It4)-I-VELNIIXI_PQRI3t]¥)_ POSlIZl-PCql3_ltl+ POSIIYI)IGO SET3IIt+)'XHOePOStlX)+XKO_X|COTIIX)

IF fiX- 122_2t,22Z2 ||EMP'I'

lX-EYIY'IZ[ZxITEMP

$ET32 NORMALEGUATiONS CHARLES Jo CEVI_E

GC TO 2123 CCNTINUE

CC _0 I'1,3CC SO J_llb

0 S_ S£Tt[,J|-OoOC CC_PUTE C * S_T [I[ MATRIX

CC 40 J"l,3CC _0 L-1°6I:_ _0 K-|,3

0 _0 SET(J_L|-SET[J,L| J+K|ISEI3(K,L)qFIURN£NC[I,O,GtOvO,Ce[_O,C_I,O*O,C+_,O|

131

in l iii i] i i i i i i lUl i iii ii i i i i ii i ,,,,,,,,

1965019622-136

_:- JPL TECHNICAL MEMORANDUM NO. 33-188__ ,

_" SETUPZ SETS dP NCRMAL_AYRIX ChJRLES J° DEVINE ?IOL/6_ _AGE 1Y_', _U_POUTINE SETUPZ(SETtCEL_AtXNUM*S[GSQtA_ATt_NATtM_AXt_PAXl:*_ 1 N_DSOLeST_STtWT)

CC TP|S $USR LIILL FCRM 6*6 MATR|XeAX=BekNERE _ ANO B ARE LEJST SQIIARES*

$_ O CIFENS|ON kT(3)

CIVENSIC_ STEST(IIC|_ENSION SETI6v6lfDELTA(IIoXNU_(Ilg_IGS_IlI*APATt6_6I_SNATlb)lell6obllU|6)PC IO |altMPAXEIlI=O_LTA(I)CC I0 J-I,NMAX

CL_ _lhJ)sS[lllvJl_kTll)0 XNUhmX_U_*l,O

CC 40 |IC_-I,6CC _0 ICCc_L__ _0 KmlIMPAX

O a_TIIRDk,ICOL)aANA_IIRO_ICCL|_A(K,IRO_)eSET(_ICOL]IF(I_O_-_9_O,30,_O

C 30 BPAT([COL) =BV_((ICCL| +_(KoICCL)eE|_?40 CCNTINUE

CC 20 [m_,_O ZO SIGSQaSfGSG �(BiI)*a2IeWTI[)C TEST IN SETUP hOR NS[GS_ GREATE_ THA_ lO-_e IF Y_S SOLVE*IF NO,CONC TIhUEC [F|SIGSQ-STEST)7C_6O,6C

60 CCNTI,4UEC [F{XNUM-20,)TOt61_bl

61CCNTINUE_GCSDL=2GC TO EO0

70 CCNTINUEhGCSDL=IGC TO 20C

200 RETURNENCI_eO_C_O*O_C_I_O_C_I_O_C*CeC_OI

i/


CCRECT CORECTSN_AN ELEMENTS CHARLES J_ DEVINE T/Oi/64 PAGE !

SUBROUTINE CORECT(X$OLVEtMEANtXNEAN £LMtPQRNw XMU )uC_oe_e_e_AJ le 0|MENSION _TATE_Er_TS te eteee_ oooeee

C0 ClPENSTON _L_7)

C!PENSION XPU(I)CX_ENSI0N QPP(3_tG#QI3loDPRll)

0 CI_ENS|ON XSOLVElblvXMEANILI_ELEPI7ltEI.|PTITlwPQRI3t3loP_AN(3e3!CI_ENS|ON PP(I)tPQI3)_PRll)

C

¢C COMPUTE CELTA |NCLINAT|ONtDELTA LCNG.ASCENO,NODEIDELTA JRGPERINELoC

CC SO 1_1_7

CC 60 _I_3

D bO P_Si|tJ)=P_RN[IIJ)

£[LP-XSOLVE(21_ELQ-XSOLVE{3)0 _ELRmXSOLVEI_I/SLEM[3)

C _EGAiELENIb)SINQM-SlkFIOMEG/) PERIHELN

0 CESO_=COSF(O_EGA) PERIHELNC SINI_SINFI_LEP(_!I |NC_|NAT

C_S[=COSFIELE_(_)) 8RObHER .P._39 FOLLO_XNG EQUA.0 CE_|IOELPeCGSOP-CELQIS|NOH INCLNo

0 AB_IN-AESF(S!N|]0 CCNST=L,CE-L60 IFiA_S_N-CGNSTIISO, 150,15SOLSO _ELN=_.O

GG TU 16001_ SICELOm_ELP*S[NQ_DELG_COS_ _0 CELNmSIDFLO/SI_[

|60 CCNT|NU80 CSLPR_DELPI-_SLN

_|TE OUTPUT T_PE _eL6||6[ FCRNAT(|_O_ch LITTLE OMEGA rILT_//)

CCREGT CORECTS ff_A_ 8LEHENTS GP_RLCS J. DEVINE 7/011oA PAGE 2

C_LL _UTPT|OELP|,I.I)CCG ELE_I"A,ELEV2m_,E_E_3=E_ELE_'t0ELE_S'LCh._SC*_ELE_6"PER[_'.ELE _7"C _PEAN Aft.CC0 kEN CO'PUT8 SiX ELtlPT[CAL ELEPE_IS

_ EL|FT(I|-XSOLVEiS)*ELE_ftt SEP[I:AJ.

_ EL[Pf(2)=O.O _EAN_OT.ELIPT(3)-XSOLVE{6) ECCENToC ELIPT(_)-OELI INCtIN*_ FLIPT{5),OELN LNGASON0 ELI_f|b)_D_LPR ARSPER!

_ EL[PT{T)_XSOLV_II)-OELR _EANANO_ r

C _[TE OUT _QR,ELEMlXS_LVE,EEIORE £C_T[ONS

C _R[TE OUTPUT TJ_F 6oBO80 FC_:_TI_P ,25_ tfl[S "$ POR PaTRIX///)

r_ 82 1_1,30 PPlI;,P_g(1,1)_ PCt|I-P_R(2,11

* _ 82 PRil)IPQR(3_]|CaLL OOUTPT(PP.2.3.P_o3.3,PR._,3)_RIT8 OUTPUT TAPE 6,84

E_ FORMAT(|I, .13_ ELEMT_///)CJLL OOUTPt(ELE_7_7)WRITE OUTPUT IJP8 6o_6

86 FCR_AT(I_ tLO_ X$QLVEI/I!¢JLL OOUTPT(XSELVEt6_6)

CC NCk CONP_TE N8_ ELEMENT5C

CC 10_ J=l,T_ 1_ ELEV{J).EtE_(J)*EL|PT(JICC_ NCk TEST FOR _EAk OAIL_ NOT|ON CA_¢.¢

GC TO (|IO, I||)_PEAN

133


CCAECI CCt_CTS PEAk |LE_EkIS C_iILES J.f._Vl_£ 710|lA_ PAGE 3

IIG C(_rt_EC CLE_tI|a°_oJCLEm{I)ImSCATF|Ir_UICL_PIll)

C_ TC 01_¢

I_i C(bT_IIUE¢ £L£R_21oZPE_C Jl_ptlqJl_VkA_me_f ETPONQI°I_.C ELF_ILI"JIGeQ_IPCN

LI2 CCW" qfJ£¢C _Cu CCIIPt,TE PC_ ]¢NICb 1S ¢Ca=_CT££ PC; PATAIAC¢ S_NIw SllEtELEFIAII¢ CCSll C_SF|£LEPI_I!

D CCSPI COSF_ELEPIAII¢ $1¢L" $|kF¢£LE_¢$11_ CCSL" COSF_LEPK$1J¢ P_I|L,LI_ ¢GS_CCSL - _I_Po$I_LeCCSIC PCAa|_2|- ¢CSP_SINL * $|_Pt_C$tICC$1

_ PCPfZ*L|_ -$|kPeC_SL - C_$_SI_L_CCSI£ PCP[2o21--SI_P_S|'qlL • ¢_$PeCCSL_CCSI¢ _CII2*)|o CCSPQSI_I

0 _CI_)t21J-CCSLISI_I

Cwlir_ _IPUT TAP_ 6_1Z¢

120 ¢C_w_TIL_ ,|2P _ PQ_III|

0 PI(|_-PGI _;_|1

C

_IJTE _TPUT TAPE &,!2_125 FC¢_!_|P o27M ELL|PTICAL CGIII_CTI_SI/II

Cm_L _U_Pf|_¢IPT,7_7|

CCAECT C¢IECT5 _JK EL£PENIS C_JRL_S J. _:V|NE _10116_ PAGE

kll_E OUTPUT TJP_ 6,|_C150 F£RmAT(|P ,19_ ME_ £L£P£_TSIII|

CALL OOUr_!_LENo¥,?ICC

_IIT_ GUTPU[ TAp_ A,13S|_S FCRMAT_|P 126_ IEPLFRS J R" L_ _U_II|

CALL _OUTP/|X_U,|tll

0 8_0 PCRq!I_JtmP_R!|,JI£C I_L |-1,7

m_TCI_NE_C|l_0wO,0_0,C,l,_lCt|lO,_,C*Ct©D

f34l

i ii u i i ir an I I I ]1 n i I I i --_-: -

1965019622-1


TRA_SX I&4qSFCIPS £L£P_N|$ TO XYZ,V[L_ITY ¢_IIL[S J. 0£¥1k£ 7/0!16_ PaGE |

5UeROUTI_[ TRahS_( _GAIOPXYZ,_LE_,X_U!( eeae_m CIME_S|Gq STATE_E_TSototoo

C molFhC)}l$ClXUU"SCRfF(X_U)

£ X_CCe£LEP(_)

C X_'£LE_I2)C Xe_X_mS_F_L--(X_CCel21)

C XEk-X_'O

)0 XEqI"X£_IX_-X£_)_ZE_CeSI_FfX£NI)I(L--X_CCeCOSF(XE N)!

XT£ST-|.CE-I_

C 4_ X_k'Xk_

42 6C ;C _0

C CC$_OSF_Xt!

r _TENmCO$£-XECC_C 60 |_|D3

0 _0 CF_YZI:)'X_*PCII|I|IoXT_X6oP£AI2,1)B$1_RSCAm(DP_YZ(II_)_ICPXYZ(2)_o21*I_PXYZ(_)*°2)

_ R_SGITFEaSGA!_AS_ITaReXJ$¢ICC g0 J'|,3

I-J*)pXy_II).IX_oP_I2. J)tCOS£-XaOPQ_I_J)ISIN_|I_aSQ_T

90 CC_I_UE_£TUA_

£_(|,01_tCo_.C,hOJC_eGoc.ctC.0!

E

135

1965019622-140


SUER_qJTI|,_ _EAIV(NTAPFwNUOODfKPOSI XOStJr.OEeONeJL|_EIXMUIAKSo 112S/65 PAGE |

SUEAGUTINE CEA_VIMTAPEmNOD_OBKPOSI XDS.X0EvDM_LL|rE,XNUIAKSt

• NAMtN_ELoXOSA,_HICDEAXY C_NPulrES ACCELERAr!ON CHARLES J. DEVI:"t_£ _eeeaee* C_NMENT_ eeeioee*

CPRINT OPTIuN FUR ACCeleRATION *XJO IS _Arqa_j

C _ PRXNT _EQUI_ES NA_aZ,GIVIN_ _ET_NC _ER[V PEADS CO0',Ot TO _dT_ POS|I_(3_ UP PERTL_ING PLANETS

CC

C_**H**_*COMPO_ SrAT_ENIS FU_ POSITIOn, _CELERA_;OII_ VELQCITVe A_D TIN_******

C_i_E_SION L"_Hh4qb61eA_L( |I*AZMIIIoAYLI LI+AYMIIJ*A_LII)eAXN|II +¥ZL

IIII,_ZPlII.VYLIII-VYMILI,VXLIII,VI_f_It_LIII+LM[_I*YLII)oY_°II*XLI

CC

C****,°***** BEGIN CO_ON **********C

C

CONMCq OUN|,ALL+A_N_AYL,AY_,AXLIAX_*_ ZLeV_P,VYLIVYM,VXL,VX_,IZL*ZN+YLwYN_SL*XMoXJ_tXJ_MCOPNCN HL,h_

C

Ceeee'ee END COCHIN eeoee_eC

C_ee_eeOI_EN$|CN STAFENENT_ FU_ COUELE PREC* QUANTITIES* e_eteeC

C eeeeeeeee&_eeD_G|N O|MEhS|ON ¢_A:cRENT_seeee_e_eeeeeC0 0IPEN_ION X_SA(||, D&T_IlJ ,RHII)

O OlrEh$lOk P_;|)IeACCI)|,VELI]),DMI|:I+AKSI|I.XLJTEI!I_X_UI|]

CINEkSI0_ XCITISel_|,Ri_! )+AHL, AII ),All ),KHOI| )Cl_EkSIOk CIREC(St 1_)*XJNDIR( 3*L0|tDIK_U_d_ ]_X|NSUPI3 |0 O|PE_SION P_NT#0_ 3 ),SOLAR IS)

CINEIIS|ON XJO||l ,XOSI;I,XOE(1)OIP_KSIOk RLIIItA2ILI_R_(t)D CIPE_IQN C(3,i_|

C0 OINEf,SION XJDTDLIgI,CTAELIS*ID*?I

D CIPEPS|Oh HSTEPtZI )+

SUER[SUTI_E _ERIVINIAPE,NOBUDtKPOS, XDS*XOEt_NeXLITE.XNU*AKS* LI?SIbS PAGE 2

CC*******_** E_D _|KENSION *********+

CC

C FIAST CEFIN!NG FUNCTIONS TGR RI'[),RCU_E,ETC.C

O STACEFIUeV,H)iIUoo_ItIVee_|_|_etZl _CUEEO CUOEFIU)'U_SQRTF(U|

***_ND FUNCTION STATEMENTS_**C

Ce* SETUP PQSZIICNeVELflCITY_ AND TIHE F_OR CO_ON **=JC|I)uXJ0_XJCl2)-XJ_L

PQSIIIaXPPO$IAI-XL

FCSI2|-YPPOSIS|*YLPOS(SIuZP

POSI6)-_LVELI|)-_XM

VELIAI*VXLV_LI2)_VYN

VELIS|uVYLVELIS,_VZNVEL(bI-VZL

C HQTE KLINE-_t;NITIALLY FAUN SYSTE_ LOADI_AIFIKLiNE|20L,12Ot201

¢ NEfl£ IF _JOTBL hOT YET fILLED TO 9 POSI(IONS|_0 KRTN't

H$_EFIIIiHN#SIEPI2I-NL

O XOSA-XJO1Z1 GO TO 4_22 KLINEeKL|NE_I

DO 123 IPLAk_'L_ 10

0123 CTADL(ICCAtlPLAN_KL|NE )-CII¢ORIIPLAN)O XJDTBL(KL|NEI_DATE

!FIKLINE-gIL24*LZStIZ9012_ XOSA_XDSA_HSTEP

GO TO L?L


SU_AI_TINE n£NIVINIAPE+NOBODIAPOSt XDSI+_EsUN,XLITE_XMUtAKSe 1/25/6S PAGE 3

125 KRTN-2201 JLINEmg

0202 IFIXJD-RJOTB_IJLINEIIEO3,ZOS,EC?203 J_,NE'JLINE-_

I_I_LIhEIE¢_.2_,202204 CALL DUMP

ZCS DO 20b )PLIh+LBIODO 2C6 ICOR'It3

0206 _IICOR_IALANI'CTARLIICCR,_PLAN,JLINFID DATE'AJO

GO TO 2_q

207 CONTINUEC READ PREPRRR_U CODRD TAPE

IF IXJD-X_J 2_ 3,2Z X_SAAX_

REJD TAPE MIAPE_DAIEIII_OATEIEIelICIICDR,|PLRNItC(ICOR,[PLAN+|G)t• ICOR'It3)tlPLAN+|IIGI

W=CATE-XDSA0

D IFIMI _o3,SS U" ABSF|M)

|FIU-I_*) 818wgR N-XFIXFI_/RHIt|

DO 6 J'|*N6 BACKSPACE M[APEGO TO 4

9 RE_|NO NTAPE

GO ?O 43 COKTI_UE

208 GD Te 11_2,209I,KNTN2Og CDkTZNUr

C

O AZ-STACEFIPCS(II,FUSIEItI+OS(3))O R3-CUBEFIREI

GPTION TO CONP_¥E RELATIVIYY CONTRIgUTION

GO TG (20+2_),PREL20 CONTINUE

GO TC 40

SUDR_TINE CfRIVINTAPE,NOBUDt_POSt xOSwADEIDNsNLITE wXNUIAKS_ |/2_/65 PAGE 4

2_ CONTINUEC

Ce_eeleeeees CDwPUT_ S_.IR ?ERR USIhG NU AND GRAV CD_TAN[ FRO

C

SOLAR l_lN

CO 35 1"1,3O 35 SDLARIIIu-XNUePUS|I)/R_

60 COKTINUEC _ER_ C_HPUT_ 31RECT AND |NDIRECT T£RNS

C

CO IG ICCR_|_3

CIRSUNIICOR)_O+_XIK_UN(ICO_)'0,_O 70 P_RTRB|ICORI'O.C

CO 3C5 I_LAhm|_|C

CO ]0O ICOR'I_3D 300 XDITIICDR+|PLANI_CIICOR_IRLANI-POSIZCOR)

O RA "STACEFICI|elPLANIeCIE_IPLANI_Ci3_IPLAN)_

RHCA -STACEFIX01Tll,IPLANI.XDITIE_II'LA_IeXDITIleIP_NI)R -CUUEFIRA )

D RHC =CO_EFIR_OA )CO 30S 1COR=1_3

O DIRECIICCRI|PLAN_DNIIPLANIe(X_IT(ICORI|PLANI/RHO |.' O XIADIRIICDR_IPLA_I'-ONIIPLANI_IC(ICURt|PLAN|IR )

D DI_SU_IICDR }=DIRSUNIICUR )¢OIRECIIGIIR_IPLRN!

030S XIkSUNIICOR )=XINSU_IICDR I_X|NDIRIICUR.|PLAN)DO 3_6 ICOR-|,3

O PERIRR{ICOR )mDIRSLINIIC_ I_XINSUHI|_ON )0306 ACCI|CCR )sSOLAR||CDR)_RRSePERIMBIICDR |

320 CORT|NLE

AXAsRCC||)AXL-ACrl6)

AY_CCI_)

AYL=_CCIS)AZA=kCCI31AZL*ACCI_|

; C PRINT CPTIDK• GO TO (SOlS_OIeNANi S0 CORTINUE

C PRINTS OK D_TE DESIRED

O IF(XJD-XCStS00_52_52

SUEP "UTINE OEREVtNTAPE_NOBOO_KP_S, XDSeXD_DN_XLITE_XNU_A_Ee |_}_ PAG_

C

D 52 IFIXJD-XCEISS_SS+S_0SS CONTINUE

_7 CDhTINUEMRITE CAJTP_T TARE 6_?3_XJD

33 FORMATII_O_tSH JULIAN DATE-FLE,2 lRRITE CUTPUT TAPE 6_62

bE FO_NATI A_N ACCELERATION COORDINATES FOR MAIN BODY/)

CALL DCUTpTIAGC_3+3ISO0 RETURN

137

........ .......................... : ................................... , .:: _i '_ .7 1 1 111111

1965019622-142


[¢SEK EHO OF STEP SUORObTENE CHARLES Jo OEVINE ,'1011b_ PAGE 1

SUBROUTINE tOSERtTMAX,JIM}

CI_EN_I0k CUMN(_98_ }tTZlL|wTltl|¢O_lq0N 0UMNIT2jT|

O CIPENS|O_ TSTPIIIIT_aXtll

TSTP|||=IiTSTP(2)-T2JZ_=2

O IF ITMAX-TSTP) 3Ct3CmZC20 RETUXH

30 _RITE OUTPUT TAPE 6_31,TSTP _T_AX)L FCRMAT(LPO,2F9*II 46H POLO YOUR h&Tt T_AX _AS BEEN lEA

XCP_OIIII)

JI_aLREIVRN

E_CIIIOIOeO+OtC,ItO,Ct|,O+C,C_C+C)

ERRER RICKS Cb; iF FCRTSZ ERROR CHARLES Jo OEVINE 7/Clr66 PAGE |

SU_ROIITI_E ERREK

mRITE OUTPUT TAPE 6_i01C FCRWAT¢|_ .71P YOL I_JCT, GCOC ULD FORTSZ HaS GIVE_

X AN ERROR RETURn/ r

X72_ FOR T_E FQLL_.ING SIMPLE R_AS3NS_ tHAT IS _f"HEXR °o .... / ;

X_¥h C_E o°X=Y=Z_C iLLEGAL CCKOIT|_NS/ iXSSP T_G o°_ M_St 86 GRC&T[R 11LESS THAN 15/KSIP J _R_ATFH 0 LESS TPA_ O_ =_/

T_RE_ .°S?ART PROCo FCUNC NC D[FF _|hE/X_PXS_ FOUR .o_0 6IFF L[_E VKR. EQUAIlO_S/

X61_ F|VE °°|LLE6AL T STOP II_t _O _XTAAPCLAT|CN/)RET_RN

_, 138

.¢, ", i ._ [ ILJ. J!J ill i i I _1 ._ II Jlllllll_il link mi _ _ - , I. m im man I I I I!Jl _ mm

1965019622-143

L

JPL TECHNICAL MEMORANDUM b_O. 33-188

CALLING SEQUEhCE I$ CALL FONOVIIFLAGnlFL*TSi 110116A PAGE 1

OOCCL ERIRY FON©V

00046 ENTRY SPOT

TRANSFER VECTOR

OOC00 264651636271 IORTSZ

00001 0634 O0 | 00042 FORCV SXA XR|II SAVE PAIN FOITRAN00002 0636 O0 2 00043 $RF XR2,2 INDEX REGISTERS00¢03 0654 O0 * 00044 SRA RRA,4

00006 0500 O0 400CCL CLA Ii4 STORE AOQRESS Of IfLAG RETURN00005 E62i O0 0 00036 STA IFLAG

00006 gSOO 60 4 00002 CL_* 2,400007 0771 O0 0 00005 AR5 3

00010 0625 O0 0 00034 STT PLACE_3 STERE AOORES$ OF INTERPOLATE00011 0500 O0 4 00003 ELl 3,4

00012 0767 00 0 00022 ALS 1000013 C622 O0 0 00034 $70 PLACer5 SIORE INITIAL JULIAN OA[E00014 0500 O0 0 65652 CLA00015 0771 O0 0 00022 ARS 1!

00_16 060; 00 0 656_2 STC

00017 0500 00 0 65653 CLA J00020 0771 O0 0 00022 ARS 18

00021 0601 00 0 65655 $10 J

C0022 C500 O0 0 65654 CLJ00023 0771 00 0 00022 AN$ •

00024 0601 O0 0 65654 SIC00025 0500 00 0 656_5 CLA CPTION00026 0?71 O0 0 OOC_2 ARS I$

0CC27 C601 00 0 65655 STG CPTION

00030 007_ O0 4 O00CO TSX sfORTSE,400031 O UOObO 0 00052 PLACE PEE _ER_,EOS00032 C 000_0 0 00054 PZE RLI$T

00035 0020 00 0 00062 TRA ER_00034 000000 0 00056 PZE |SICPteDwee00035 O 00000 0 OOCCO PEA C

00036 0601 00 0 C00C0 IFLRG SAD **00037 E634 O0 I 0C046 SAVEF SXA XRA.l SAVE FORTSI INDEX REGIS'ER$

OOO_O 0636 O0 2 00047 SXA XKBi2

00041 C634 O0 400ESO SxA XRC,400E42 0714 O0 _ 000_0 RRI ART *e,1 RESTORE PAIN FORTRAN00043 OT74 00 2 000¢0 XR2 ART **.2 INDEX REGISTERS00044 0774 O0 _ 00000 X_4 AX! *e*A

CALLING SfDUENCE 1$ CALL +=OROVI|FLAGtIFLvTS) 710|/64 PAGE 2

00045 0020 O0 4 OOCE4 TqA 4t4 REIURN TO laAIN00046 0??4 O0 I 000E0 XRA 4_T e+_l RESTERE FORTSZ

00047 0_74 O0 2 00000 XRB AN" ***2 INDEX REGISTERSOOP.50 03?4 O0 4 COCCC RRC P+RI **t4C0051 00E0 O0 4 COCCI TRA 104 RETURN TO FORTSZ

00052 0500 O0 0 00064 GER CLA "1017 SET IFLAG00053 _+020 O0 0 C0036 TRA IFLAG SET AND RESTORE XRSB GO TO I<A|NG0054 0443 O0 0 65666 RLIS? OLC h EO;_PUTE STEP SIZE

00055 COCO O0 A 0000! TAX i,4 RETURk TO FCRYSZ00056 0500 O0 0 0_065 TS;CP ELl -?B_7

00057 OC_O CO 000C3b TPA IFLAG SET AKO RESTCNE XRS, GC TO NRIN00060 0500 O0 G 00066 EGS ELl -351700061 00_0 O0 0 00036 TRA IFL_ SET JNg RESTORE XRS. 00 TO NAIN

00062050000000067 ERR CLA '481700063 UOZO 00 0 00036 TRA I¢LAG SET AND RESTORE X&5_ 00 TO NRIN

RETURN POINT FRQN PAI_00046 SPCT SYN XkA

065652 CO_'NCN 0001 E5:,5265652 N [G_ CO'YON

6565_ J Eel,, P*I

65655 _TPT ICN EDU N*3

65656 E/APE EGb V+465657 S EGb P+5

65660 eS ECb N*665666 H -_0U _J412

ENC

L I [ERJLS

00C64 OCO0010COCCO00065 0OG0O20GCCC0

00C66 CCOO030COCCO00¢67 0000040C0000

139

1965019622-144

_: JPL TECHNICAL .MEMORANDUM NO. 33-188_.

STPRG2 7/0L/6 _ PAGE L

• 5_gKCUrIkE ST_RG2CAP,FPoSLJ_tMTA,SOi_tSCC_T,COAININA_IkCLTAtKPRINT* TI

C; C aPl_X% I'PbT

_ FM-F VLET_RSL-SU d CF SCUJRES

C N-i,_PUT SiZEC _TmT:TAL _C OF POinTS

C SCIN m [N THR_SHHLC FOR A_SFiCGEFFliS,C. OF CCEFFI)C SCCU/ • OU_ T_RcS_DLC FOR AESF[CCEFFI(S,_, OF CCFFP))

_EN F TESTS ARE TC EE USED FINC SMCULC EXCEEC FOUT A4C FP ANC SL N_SI

C CCNT_[% LEGITAMATE CATA.

iF FIN•O. ThEN THE F TESTS MI;.L _ESKIPPEC _N_ NC rESTS CF [ME CONTENTS

C CF FP A_C SL _ILL BE _ADE.C CC_DIAGONJL CCEF'iCIE_TC klhm NO. OF PaRAmETERS [_ FinAL SCLLTION

_HL A_RAV INC_T[) i_CICATES THE STAT_SC EF EACP PArAmETER AS FCLLC_S-

+_ P_A_ETE_ IS [ECLUCEC IN SOLUTION.-! P_RA_FTER REJEETE_ _V DIAGONAL TEST,C -2 PARAPETER REJECTED BY F TEST_£

_PRINT • 0 NO PRINTING• ] PRINT S_MMARYt LAST STEP ONLY£ • 2 PRINT S_MVARYo _ACH SfEP

C " 3 F_ L PRINTI'_GC

C _•NURKINC AREA

G CPA;_GE TE C_MMCN OUNPT CXXXXI_Pi2_,21) TE SAVE _AI_2 LCC

E[_b_SICN A{ 7_ ?}tAP( 6o 6ieFP( 6l

PINENS|O_ B( _),INO_T( 7)_[NCUTA( 6)CI_E_SI_N _C_2)KPR_KPR[EI

PT_MTA

_--1 F i_-SDI q H2

STPRG_ T101/6¢ PAqE 2

FCUT• SCCUT_*2CC_CCA

NPI=N ,�P A( i _NPI )_FP[ [ )

CC S AiloJI_APlItJIAINPI_NFII-SLINCur 111_-1N[_O 1

_G |0 l•loh

I'KINCUTi , )=-1

BIRI=AiKoK)eCO• CO, 10 J•l_K

{J LO A(I_JI'AiJ_I)£ eeeBEG IN OL.TP_JT _4_

IFiKPRI 4Or) _ _OC_ a,Ol

601 MqlTE UUTPUT TAPE 6eIOCO

1CO0 FORMAT( LI'I_t_CX_bPSTPRG2,IOX*,2THSTEPkISE REGRESSION PROGRAM)

kR[T_" OUTPU _" TIRE _IOC2_MToSOIN,SCOUT,COI_O_ FC_4ATi IhOt 9X, IHN_4Xt 6hMTOT/hL t 1 IX, 4NSD IN, lea t SHSOCUT

*_ 11Xt _HOI_G/[IsC_2I IO_ IPSEZS°6)

IFiKPR-31 400o402_400602 EG IS I=I,N

_S _R]TE OUTPUT TaPE 6_qO2_I_BI[!

gO? FORMAT IIM _Zhei_12t2h)',Ei6.S)400 CENT INUE

C e_ENC CUTPUT_ee

UI_OoO

K•O

C BEGIN NAIN LOOP20 CCNT lNUk

C _BEGIN O_TP_JT_e

.- [FIKPR-3) 406_40S_406 L*"60S CGNT i NUE

kRITE OUTPUT TAPE 6_903_UI_L_2_IL_I2_KeNCCUNT_NIN

_.' gOS FORMAT i IHU_31_UI_ vE |6+IIo'_HU2_ tEI6,I_.4HIL- _ IZ_6H|2 • + 12_SHK_ _ I_t_, IRPN COUNTu _ISeSPN[N_ ti_)

_c_,_. 140

• ' ., ,_) ' r

1965019622-145


_TP_GZ 710Z/64 PAGE ]

CE 25 J=I,NPI

hRIIE OUTPUT TAP_ bl_O4tJg04 FCgMATI/FOC_Lb_NtI_/[X)CALL OOU|PT!aII,J) t NP[ * 64|1

i Z5 CONTINUE

i 4Cb CC_TINUE• C _eeENC CU TpUTeli

! IFIFI_) 2CGt2CC,ICCC BEG|h PIVCT SELECTION (FIN NOT 0.)

C ***EEGIN CLTPLT,**_FIKFR-2) 6C_tR0_,_C]

403 $_OAtAtSGRTFIAINPIJNPI_/FMT)F_TItFeT-I.

WRITE OUTPUT TAPE _*[OG3*NI_AINP|jNPI)tSOGATA

! LOG3 FCRMLTI3C_Ct_TI* OF CCEFFS IN REGRESSION •• 13,SXu26PSUr CF SQUAREC RESICUILS =IP_13._,_X

• ,14._.O. OF DATA =1PE13.5

• IIII_X*ZCPEUEFFS IN RCGRESSICN,55X_• ?4PCUEFFS NET I_ REGRESSION

i// t_H |NDEX_Xt5HCCEFFIZX_RHS._.,6X*ICPC_EFF/S.D.*33X_HIN_EX,3Xt2_hPREOICTEC ICCEFF/S*0.]/IX)40q CONTINUE

C • e_FkC CUTPUTiee

IFIA(NPItNPI)) 9C0,qC0,_0

_0 UI=O*ITL*3_U?=O.O

I CC 53 1-1,_. U=A(I,NPIItR(I,_PIIIR(I,I)

IF(I_OUTIIII_5,43_N]63 CCNTINUE

C .*_BEGIh CLTP_Tee*

IFIKPR-2) 40R_407,_07607 Sf=S_TFI_II_II)eSPCATA

_ WRITE OUTPUT TRP_ _,IOC_,I,RII,NPII,SO,R_TIO

• _ _C04 FCRMATIIX*IS**PEI?..7_2_I6*_)

i 408 CCNTI_ULC ***ENC CUTPUT***|gIU-U_)4ReS0*_0

ll=l

STPRG2 7/C _./64 PRGE _.

GC TO 50C O)AGCNAL TEST

65 [FIA(leI]-e(II} lOle[OltNblot INCUTiI )=-I

C 4_eOt.Glh Ot _PUTe**

If" [ KPR-Z) S01e 50CeECC500 WRITE OUTPUT TAPE 6,I007-1

!. IC07 FCR_RT[ Ig _._ IoxtgI_OEPEN_ENT ]501 CCf_T INUE '*

C **'ENC CUTPL'Tee,

GC TO 5066 INCUT( I )=-2

C ,*-BEGI _, OLTPET'**

_: )FIKPR-2) kLO_OgekOq

40g RATIO • S(_P_PIUeIFWTI)/(AINRIt_P_) - U))WRITE OUTPUT TAPE 6_ICC_tItRAT|OXOOq FCRMa r_ 195, IPEI9.4)

4_0 CC_'_ I_UE

C _.eENC COTPbTeeeIFIU-U2)50*50_47

i 67 U2mU12=1

50 CENT INUEIF( .NCOUNT )52, _2_5_

$5 NCCUNTuNCCUNT-IIFIUI-O, ITE+39158_SZ, 52

._ $8 I F ( UI'FMTIR ( qP l *NPI )-F(_UT ) E9 _'_2, _259 KuI_

t GC TO 6552 IF I UZ ) 900:goo,sa*

54 I F( A( NP I _NP I. I-U2 }60 _6O t 654_" 6SR I F( O2e( FffT-I.*0 )/( A( NP [ _NP 1 I-U2 )-F IN) 900 e_;0_6C

_" 60 Kul2

INOUTIK)- *[

GC TO 67

C END PIVOT SELECTION (FIN NOI 0,)

¢ BEGIN PIVOT SELECTICN (FIN'O.I

_' 2_.0 SIZE-O.CC 201 I=1_k

_ IF_ INOUT{ I ) ) 2C2_201_ 2G1• 202 TEST=A(],l)/fi(I)

i'i 141

=t

I I I I II I I I 1 11 II I11[ II 11 I I.I III I II I I I llll I _ I - -

1965019622-146

i

?


STPNG2 7/01164 PAGE

IF(TEST-SIZE) 201t201m20_

205 SIZE-TESTK-I

' 201 ¢ENTINUE

C DIAGGNAL TESTIFI$IZE-L.) ?coiqooJ65

C END PIVOT SELECTION |PIN'Oo)t

C BEGIN JORB_N PIVOT65 INCUTIK)--INOUT(KIbT NIN'NIN*INOUTIKI

C eleBEGIN OUTPUTiewIFIKPR-2) 4IZl411e411

411 IFIINOUTIK)) 415*415i_

B 414 BCOI1)-60t145635146B BCOIZls246423314527

GO TO 416

B 415 8cr,11I=606060602425B 6COI21-4323633L452T

416 NRITE OUTPUT TAPE btLOCbiBCCo!_|006 FORMATII_Op44Xv2ABw20_ COEF_ NO.14I

4|2 CCF:T[NUEC el*END OUTP_Itel0 AIKtKI_I.O/AI_tKI

CC TO J'I_NP|[F(J-KIbbITGI66

0 b6 A(KiJi=AiKiKie;fKtJ)0 AIJIJ)'AIJw-I;-A(Jt_ioAIKvJ)

]F(NiJ,Jl_oew?C,?OC 68 AiJiJI=_.O

70 CCNTI_dEDO _6 Iw_INII|l-K)71,76i71

71 IPI'I ´�CC 75 J-IPiINPI

IFIJ'KITZITSwT20 72 A(ItJIaAII_J)-AIIgKIiAIKi'J

IFII_OUT(II • INCUT(J))'Ji?3*?4

D T3 A(J,II--A|hJ)GC TO 75

D 74 ilJwII_AlIpJI?S _CNTINUE

STP_G2 7/0LI64 PAGE 6

76 CC&TINUE

OC qO II_eN_IF(INOUTIII • INEUTIKI)85185tSC

0 B0 AIIIK)=AiK_IIGO TC _9

0 B_ A(IIK)--AiK_Ii

90 CONTINUEC ENO JORCAN PIVOT

GO TO Z0

C END _AI_ LCGP

C COMPUTATION FiNISPEC960 CONTINUE

IPIKPR-II 41B.417i418C REPEAT LAST PASS T0 OBTAIE CUTPUT

41? KPRI_GC TO 20

41R CONTINUEC BEGIN-STORE FINAL RESULTS

CC 920 [litN

IF£1NOUillllqlliqlil912

GC TO 915

D qi_ FPliixAIilhPiIql5 CO 9ZO J-[,N

IFIINOUTIIIIqI61_ITigI7O ql6 aPil_Ji-O.G

GO _U 92_

ql7 IEilNOUTlJliQieiql_lql8O ql8 APII_JI-AIhJI

_2_ CENTIIUESL-AINPiiNPIININA=N_N

_C 360 [=liN100 INCUTAIIIzINUUTII)

C [NO-STORE FINAL RESULTS

RETUKN

ENClilOiO*OiOtO_ltCtO,llO_OiCIClOI

_ 14,

k

Iq

1965019622-147

m.Ld|

i JPL TECHNICAL MEMORANDUM NO. 33-188

SUBROUTINE ELEVTSICOSOBIS|_CBtCPOcr_P_tOPQRIELEWjHEANvXVEA_) 7/C|166 PAGE 1

SUOROUT|_ LLEVFS{COSOBtS!ToGB,CPOS,X_U_OPQRPELEWr"EANtX_EJN_CELE_TSC PRCGRANNER--N, R_KIJFL)~-I_64 FEB 27

CIVLN_!C_ CPOS(6]_POS(6!uV_L(6)wX_!II,PGqlt3t3)tPOR{3t3)tELEW(7_CI_ENS[g_ CCSOEII),SINCO[I)

_ _IPENS[CN TE_PI(I)tTEMP2(I)CI_ENSAGN _P_R(3_IEGU[VALE_CL (POS!4)IVLL(1)I

C NCTE THAT XVUI!GAUSS**2Ie(I.*X_ASS)_ SGRT_U-S_RTF(XVU)

CC 10 ICCR-I,9C PCS(ICOP )'SPCS(ICO_ )

P RSGR_POS(II_2_P_S(2)*_2+PCS(3)**2 _D GS_-VEL!I)t*2+VEL!21**Z+VEL(31t*2_ P IPUS(lI*VEL!I] }_gEL!2)+POS(39*VEL|_I_ _S_TFIRSGR]_ RECAs2.0/R-GS_R

_ S_RTA-S_RTF(A)_Tb_h-A*SG_TAC Xk_S_TN_/JTH_F

GC TO (A_8},_E_N

_ X_=X_EAN49 CCNTINUE

_ ESINE-H/S_TA_ _COSbs_*GSQR-I.O

i P ECC_ARCTN(ES[NE,EC()SE)_ S|kE=SIN_(ECC)D CCSEICOSF(ECC)C r_FSINE*S!_L_ECO_E,CCSEC P=A*_ORTF!I.O-E*_Z)

! _ FK|uCOSb/RFK_.-S_RTA*_[NE

CC II ICCR-I,3

i_ 0 P_R[IlCOR,II-EK|,_0S!ICORt+_2*_ELI|COR|rill P_RI(ICOR_2)=FK_eF0_(IC0_!*FK4eVEL(ICQR_

-i


ARCTN 7/C1/64 PAGE !

F_hCTIUN ARCT_(¥tX)C FUNCTION ARCTNlv_X) OCUSLE PR_.|$IO_ !P PI_oI_159265_'_TQ_

IF {A; eC,6 _ JCbR IF IY} _ .7CC bq A_CTw#+_ O[

GC TO •C ?0 ARt _,31pl

lobPTI _TN-O.C

_d A_CIN=ATANF(Y/X)IC4 [F IX) 1C5,106,1C6

Q |0_ ARCT_sA_CT_eP[ICO IF IARCTh) |07tlCSeLC8

ICH ?'TURN_,C(LtC,C,O,O_,.,_fC,L OtOtC,C.C_

SPHER 1/2_/65 PAGE 1

C SPECIPIEC AND PROGkAMMEOBY N.OLGCK IJPL)SUOPOUTIN[ SPHERIX,Y_Z,RHOwXLONtXLAT)

6 C|MENSlOh X(1)tY(1)_ZII},_LUN(I),XLAT{I)_R(I)_RHO(I)o|#_.|_15926535B97_3

D _ALFPI-Plt_.50D R_Xol2+Ym_20 RHC • $QRTF{R*Z_o2)D IFl_| 3,3,_D2 XLC_I AL_Cr_IY_X)D R-SQRTFtR)D XLATa ARC A(ZtR)

IF(XLAT-I.b)Z5,2_,2_D24 XL_T'XLAT'2._*P!

25 RETURND3 XLEN I_._D %LJT-S|GAFIHALFP|,L)

_ETU_NENCII,I,0,O,O,O,I,.,_,I,_,O,C,O)

OBL_ 1/2516E PAGE l

C $PI C IFI_C AAO PRt}GRAMMEt_8Y N.BLOCK !JPL !SUB'OUT |_E CBL IQ(XJO,r_PStN)

D _ !AJU-2415 ZO.O )/36E_E.O _0 EPStN" !i(+ t.8IE'3eT_5.q£°3). T-_6. $_5) _T_A_28.2_! 41296G_0.¢

RETURN __ FND( l, 1 ,C,O,Ot_, I, t, Ot It O,O,Ot O,_I

,_, I' 144

_,,

lg65019622-14g

,_ .JPL TECHNICAL MEMORANDUM NO. 33-188

REFERENCES

1. Planetary Coordinates for the Years | 960-1980, National Almanac Office, 1958.

2. Chauvenet, W., "A Manual of Spherical and Practical Astronomy," SphericalAstronomy, Volume 1, Chapter 2, Dover Publication% Inc., New York, 1960.

3. Brouwer, D. and Clemence, G. M., Methods of C;lestial Mechanics, AcademicPress, New York, New York, 196_.

4. Peabody, P., Scott, J., Orozco, E., JPL Ephemeris T_lpes E9510, E9511, E9512,

Technical Memorandum No. 33-167, Jet Propu!sion Laboratory, Pusadena, Cali-fornia, March 19_

5. Plackett, R. L., Principles of Regression Analysis, Clarendon Press, Oxford, England,pp. 33-41, 1960.

6. Eckert, W. J., Brouwer, D., Clemence, G. M., "Coordinates of the Five Outer

Planets 1653-2060," Astronomical Papers, Volume Xli, 1951.L

: 7. Hildebrand, F. B., Introduction to I'lunlerical Analysis, McGraw-Hill Book Company,Inc., New York, New York, Chapter 5, 1956.

8. Jeffreys, H. and Jeffreys, B. S., Methods of Mathematical Physics, Cambridge Uni-

versity Press, pp. 300-301, 3rd Edition, 1956.

9. Holdridge, D. B., Space Trajectories Program for the IBM 7090 Computer, Tech

nical Report No. 32-223, Jet Propulsion Laboratory, Pasadena, California, p. 80,

: March 2, 1962.

10. Kuiper, G. P. and Mid_lehurst, B. M., Editors, Planets and Satellites, The Solar• System, University of Cb_cac_o Press, Chicago, Illinois, Vol. 3, pp. 43-44, 1961.

12. Stepwise Multiple Regression with Variaf_le Transformations, SHARE DistributionNo. 1194, October 1961.

13. Peabody, P., Scott, J., Orozco, E., Users' Description of JPL Ephemeris Tapes, J

Technical Rel_ort No. 32-580, Jet Propulsion Laboratory, Pasadena, Californi% rMarch 2, 1964.

o,_ 145

1965019622-150

Documents

i TechnicalMemorandumNo - NASA · II I k i JPL TECHNICAL MEMORANDUM NO. 33-188 The xo, yo, zo, xo, y0, zo ecliptic are now rotated to the and the quantity o are then computed and