DOCUMENTNO. TITLE APOLLO/SATURN V POSTFLIGHT …

DOCUMENTNO. D5-15560-6

TITLE APOLLO/SATURN V POSTFLIGHT TRAJECTORY - AS-506

MODEL NO. SATURN V CONTRACTNO. NAS8-5608, Schedule II,Part IIA, Task 8.1.6,Item 42

October 6, 1969

S. C. Krausse, ManagerFLIGHT SYSTEMS ANALYSIS

ISSUE NO. ISSUED TO

THE _IP_'_/_'_'_I#'G COMPANY SPACE DIVISION LAUNCH SYSTEMS BRANCH

D5-15560-6

REV I S IONS

DESCR I PT ION DATE A PPROVEDREV.SYM

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ABSTRACTAND LIST OF KEY WORDS

This document presents the postflight trajectory for the Apollo/Saturn V AS-506 flight. Included is an analysis of the orbitaland powered flight trajectories of the launch vehicle, the freeflight trajectories of the expended S-IC and S-II stages, andthe slingshot trajectory of the S-IVB/IU. Trajectory dependentparameters are provided in earth-fixed launch site, launchvehicle navigation, and geographic polar coordinate systems.The time history of the trajectory parameters for the launchvehicle is presented from guidance reference release to Command/Service Module (CSM) separation.

Tables of engine cutoff, stage separation, parking orbit in-sertion, and translunar injection conditions are included inthis document. The heliocentric parameters of the S-IVB/IUare given. Figures of such parameters as altitude, surfaceand cross ranges, and magnitudes of total velocity and accel-eration as a function of range time for the powered flighttrajectories are presented.

The following is a list of key words for use in indexing thisdocument for data retrieval:

Apollo/Saturn VAS-506Postflight TrajectoryPowered Flight TrajectoryOrbital TrajectorySpent Stage TrajectorySlingshot Trajectory

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CONTENTS

PARAGRAPH

REVISIONSABSTRACTAND LISTCONTENTSILLUSTRATIONSTABLESREFERENCESACKNOWLEDGEMENTSOURCEDATA PAGE

OF KEY WORDS

SECTION 1 - SUMMARYAND INTRODUCTION

SECTION 2 - COORDINATESYSTEMSAND LAUNCHPARAMETERS

SECTION 3 - POWEREDFLIGHT TRAJECTORYRECONSTRUCTION

3.13.1 .I3.1.23.1.33.23.2.13.2.23.33.3.13.3.2

POWEREDFLIGHT TRAJECTORYAscent PhaseSecond Burn PhaseTargeting ParametersDATA SOURCESAscent PhaseSecond Burn PhaseTRAJECTORYRECONSTRUCTIONAscent PhaseSecond Burn Phase

SECTION 4 - ORBITAL TRAJECTORYRECONSTRUCTION

4.14.24.2.14,2.24.34.3.14,3.24.4

ORBITAL TRAJECTORIESORBITAL DATA SOURCESOrbital Tracking DataOrbital Venting Acceleration DataTRAJECTORYRECONSTRUCTIONParking Orbit Insertion ConditionsTranslunar Injection ConditionsORBITAL TRACKING ANALYSlS

SECTION 5 - TRAJECTORYERRORANALYSIS

5,15.1 .I5.1.25.1.3

5.1.45,2

ERRORANALYSISQuantity of Tracking DataQuality of Tracking DataConsistency Between TrackingVelocity DataContinuity Between TrajectoryTRAJECTORYUNCERTAINTIES

and Guidance

Segments

PAGE

iiiii

iv

vivii

viiiix

X

I-I

2-I

3-I

3-I3-I3-I3-23-23-23-43-43-43-6

4-I

4-I4-24-24-24-24-24-34-3

5-I

5-I5-I5-I

5-25-25-3

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PARAGRAPH

CONTENTS (Continued)

SECTION 6 - SPENT STAGE TRAJECTORIES

S-IC SPENT STAGE TRAJECTORYS-II SPENT STAGE TRAJECTORY

SECTION 7 - S-IVB/IU SLINGSHOT TRAJECTORY

APPENDIX A - DEFINITIONS OF TRAJECTORYSYMBOLS AND COORDINATE SYSTEMS

APPENDIX B - TIME HISTORY OF TRAJECTORYPARAMETERS - METRIC UNITS

APPENDIX C - TIME HISTORY OF TRAJECTORYPARAMETERS - ENGLISH UNITS

PAGE

6-I

6-I6-I

7-I

A-I

B-I

C-I

V

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FIGURE

ILLUSTRATIONS

3-I Ground Track and Tracking Stations - AscentPhase

3-2 Altitude - Ascent Phase

3-3 Surface Range Ascent Phase3-4 Cross Range - Ascent Phase3-5 Space-Fixed Velocity and Flight Path Angle

Ascent Phase3-6 Total Inertial Acceleration - Ascent Phase

3-7 Mach Number and Dynamic Pressure - S-IC Phase3-8 Altitude - Second Burn Phase

3-9 Space-Fixed Velocity and Flight Path Angle -Second Burn Phase

3-I0 Total Inertial Acceleration - Second BurnPhase

PAGE

3-73-83-9

3-I0

3-113-123-133-14

3-15

3-16

3-11 Available Tracking Data - Ascent Phase 3-173-12 Antenna Locations and Center of Gravity 3-18

3-13 Azimuth Angle Tracking Comparison - AscentPhase 3-19

3-14 Elevation Angle Tracking Comparison -Ascent Phase 3-20

3-15 Slant Range Tracking Comparison - AscentPhase 3-21

4-I Orbital Acceleration Due to Venting 4-44-2 Ground Track 4-5

5-I Estimated Trajectory Uncertainty - AscentPhase 5-4

6-I Ground Tracks for S-IC and S-II Spent Stages 6-2

7-I Slingshot Maneuver Longitudinal VelocityIncrease 7-2

7-2 Trajectory Conditions Resulting from Sling-shot Maneuver Velocity Increment 7-3

7-3 S-IVB/IU Velocity Relative to Earth Distance 7-4

7-4 S-IVB/IU and Spacecraft Relative Trajectories 7-5

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TABLES

TABLE

3-I3-113-1113-1V3-V3-VI

4-I

4-114-1114-1V4-V4-VI4-VII5-I5-115-1116-I6-117-1

7-11

7-111

Times of Significant EventsSignificant Trajectory ParametersEngine Cutoff ConditionsStage Separation ConditionsTargeting ParametersAvailable Tracking Data - Powered FlightTrajectorySummary of Orbital C-Band Tracking DataAvailable

Orbital Venting Acceleration PolynomialsParking Orbit Insertion ConditionsTranslunar Injection ConditionsCSM Separation ConditionsParking Orbit Tracking Utilization SummaryPost TLI Tracking Utilization SummaryTracking Data Spread Ascent PhaseTracking Data Spread - Parking Orbit PhaseTracking Data Spread - Post TLI PhaseS-IC Spent Stage Trajectory ParametersS-II Spent Stage Trajectory ParametersComparison of Slingshot Maneuver VelocityIncrement

Comparison of Lunar Closest ApproachParametersHeliocentric Orbit Parameters

PAGE

3 -223 -233-243 -253-26

3-27

4-64-74-84-9

4-104-114-12

5-55-65-76-36-4

7-6

7-77-8

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REFERENCES

•

•

•

•

NASA Document SE 008-001-I, "Project Apollo CoordinateSystem Standards," June, 1965.

NASA Document M-D E 8020.008B, "Natural Environment andPhysical Standards for the Apollo Program," April, 1965.

NASA Document MFT-I-69, "AS-506 G Mission Launch VehicleOperational Trajectory," July 14, 1969.

Lockheed Document TM 54/30-150, "Manual for the GATEProgram," September, 1967.

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ACKNOWLEDGEMENT

The analyses presented in this document were conducted bythe following Boeing personnel:

G. EngelsJ. GrahamJ. JaapJ. Liu

The analysis presented in Section 7 of this document was con-ducted by the following MSFC personnel of the S&E-AERO-MDivision and is included for completeness in terms of spentstage trajectories:

D. McFaddenC. Varnado

Questions concerning the information presented in this documentshould be directed to the technical supervisor:

R. D. McCurdy, AG-13The Boeing CompanyHuntsville, Alabama 35807

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SOURCE DATA PAGE

The following listed government-furnished documentation wasused in the preparation of this document:

Exhibit FFLine Item DateNumber GFD Title Received

R-AERO-P-#35c OMPT Format 6/16/69R-AERO-P-#17 Tracking and Network Specifica-

tions 7/9/69R-AERO-P-#35b Transponder Locations 7/9/69

N/A Operational Trajectory CertifiedData (MSFC supplied) 7/18/69

l-MO-#4a Insertion Point and/or OrbitalElements 7/17/69

l-MO-#4c Six Seconds Raw Radar 7/17/69l-MO-#4f Meteorological Data (Final) 7/25/69I-MO-#6 IP Raw MP 7/17/69I-MO-#9 Pulse Radar 7/25/69l-MO-#17c Final Significant Time of Events 7/25/69l-MO-#18a Preliminary Guidance Velocities 7/18/69l-MO-#18c Orbital Venting Accelerations

Data Cards 9/8/69

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SECTION 1

SUMMARY AND INTRODUCTION

The Apollo/Saturn V AS-506 vehicle was launched from Launch

Complex 39, Pad A at the Kennedy Space Center on July 16, 1969,at 8:32:00 A.M. Eastern Standard Time (Range Time Zero) at anazimuth of 90 degrees east of north. Range time, which isreferenced to Range Time Zero, is used throughout this documentunless otherwise specified. Guidance reference release (GRR)was established to have occurred at -16.968 seconds. Firstmotion occurred at 0.3 second. At 13.2 seconds, a roll maneuverwas initiated, orienting the vehicle to a flight azimuth of72.058 degrees east of north. This flight azimuth, dependenton the launch time, launch day and month, is calculated usingpolynomial coefficients taken from the guidance presettings inorder to achieve the desired translunar targeting parameters.The translunar targeting parameters are functions of the moonposition, earth parking orbit inclination, earth-moon distance,and moon travel rate.

The vehicle performed with only minor deviations throughout theentire flight. The vehicle was inserted into a parking orbitat 709.33 seconds at an altitude of 191.1 km (103.2 n mi) and atotal space-fixed velocity of 7,793.1 m/s (25,567.9 ft/s). Thevehicle remained in orbit for approximately one and one-halfrevolutions. The S-IVB stage was restarted during the secondrevolution approximately midway between Australia and Hawaii,at 9,856.2 seconds.

At 10,213.03 seconds, the vehicle was injected onto a circum-lunar trajectory at an altitude of 334.4 km (180.6 n mi) and atotal space-fixed velocity of 10,834.3 m/s (35,545.6 ft/s). At11,723 seconds, the CSM separated from the launch vehicle at analtitude of 7,065.7 km (3,815.2 n mi) and a total space-fixedvelocity of 7,608.6 m/s (24,962.6 ft/s). Following LM extrac-tion, the launch vehicle maneuvered to a slingshot attitudefixed relative to local horizontal. The retrograde velocityto achieve S-IVB/IU lunar slingshot was accomplished by a LOX

dump, APS burn, and LH_ venting. The S-IVB/IU closest approachof 3,379 km (1,825 n ml) to the lunar surface occurred at78.70 hours into the mission.

The impact location of the expended S-IC stage was determinedto be 30.212 degrees north latitude and 74.038 degrees westlongitude at 543.7 seconds. The impact location of the ex-pended S-II stage was determined to be 31.535 degrees northlatitude and 34.844 degrees west longitude at 1,213.7 seconds.

Section 2 of this document defines the coordinate systems andlaunch parameters used for the postflight trajectory analysis.

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SECTION 1 (Continued)

The postflight mass point trajectory related parameters andanalytical procedures are presented in Sections 3 through 7.The trajectory is divided into six phases:

a

bC

de

f

Ascent PhaseOrbital PhaseSecond Burn PhasePost TLI Phase

Free Flight PhaseSlingshot Phase

The ascent phase, covering the portion of flight from guidancereference release to orbital insertion (709.33 seconds), isdiscussed in Section 3. This trajectory was established fromdata provided by external C-band radars and telemetered on-board data obtained from the ST-124M inertial platform.

The second burn phase, discussed in Section 3, covers theportion of flight from S-IVB restart preparations to trans-lunar injection (10,213.03 seconds). This trajectory wasestablished by integrating the ST-124M platform telemeteredguidance velocities between constraining state vectors ob-tained from the orbital and post TLI trajectory phases.

The orbital phase, discussed in Section 4, covers the portionof flight from orbital insertion to S-IVB restart preparations(9,278.2 seconds). The orbital trajectory was establishedfrom data provided by the C-band radars of the Manned SpaceFlight Network.

The post translunar injection (TLI) phase, discussed in Section4, covers the portion of flight from the translunar injectionto CSM separation (11,723 seconds). This trajectory wasestablished from data provided by the C-band radars of theManned Space Flight Network.

The error analysis of the reconstructed trajectory is discussedin Section 5. The criteria for error analysis are included andtrajectory uncertainty limits are assigned to the boost, parkingorbit, second burn, and post TLI phases.

The free flight phase, discussed in Section 6, covers thetrajectories of the expended S-IC and S-II stages. Thesetrajectories are based on initial conditions obtained from thepostflight trajectory at separation. The nominal separationimpulses for both stages were used in the simulation.

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SECTION 1 (Continued)

The slingshot phase, discussed in Section 7, covers the tra-jectory of the S-IVB/IU after it was separated from the CSM/LM.This trajectory was produced by integrating orbital modelequations forward from a state vector at 21.58 hours GMT,July 16, 1969, which was established by Goddard Space FlightCenter from Unified S-band (USB) tracking data.

Appendix A provides a detailed definition of the symbols,nomenclature, and coordinate systems used throughout thedocument.

Appendix B tabulates the time history of the trajectoryparameters in metric units.

Appendix C tabulates the time history of the trajectoryparameters in English units.

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SECTION 2

COORDINATESYSTEMSAND LAUNCHPARAMETERS

The time history of Observed Mass Point Trajectory parametersin both metric and English units is tabulated in Appendices Band C, respectively. These tabulations are in earth-fixedlaunch site, launch vehicle navigation, and geographic polarcoordinate systems. These coordinate systems are defined inReference I, "Project Apollo Coordinate System Standards,"(PACSS) and are designated PACSSIO, PACSSI, and PACSSI3, re-spectively. The trajectory symbols and terminology used inthis document are defined in Appendix A.

The Fischer Ellipsoid of 1960 (Reference 2) is used as therepresentative model for the earth and its gravitational field.All latitude and longitude coordinates are defined with respectto this ellipsoid.

The geographic coordinates for Launch Complex 39, Pad A, atthe Kennedy Space Center are as follows:

Geodetic LatitudeLongitude

28.608422 degrees north80.604133 degrees west

The height of the center of gravity of the launch vehicleabove the reference ellipsoid is 59.4 m (194.9 ft).

The azimuth alignments are as follows:

Launch AzimuthFlight AzimuthST-124M Platform Azimuth

90.0 degrees east of north72.058 degrees east of north72.058 degrees east of north

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SECTION 3

POWEREDFLIGHT TRAJECTORYRECONSTRUCTION

3.1 POWEREDFLIGHT TRAJECTORY

3.1.1 Ascent Phase

A comparison of actual and nominal times for significant flightevents is presented in Table 3-I. The nominal times for theseevents are taken from Reference 3.

The tracking stations and the vehicle ground track for theascent phase are shown in Figure 3-I.

The actual altitude, surface range, and cross range are shownin Figures 3-2 through 3-4, respectively, for the entire ascenttrajectory. The magnitude of the total space-fixed velocityvector and the associated flight path angle are shown in Figure3-5. The magnitude of the total inertial acceleration vectoris shown in Figure 3-6. Mach number and dynamic pressure areshown during the S-IC phase of the ascent trajectory in Figure3-7.

Various trajectory parameters, such as altitude, velocity, andacceleration are given at some significant event times inTable 3-11.

Engine cutoff and stage separation conditions are given inTables 3-111 and 3-1V, respectively.

The ascent trajectory, from guidance reference release toparking orbit insertion, is tabulated in Tables B-I throughB-Ill in metric units, and in Tables C-I through C-Ill inEnglish units. These tables present the trajectory in theearth-fixed launch site (PACSSIO), launch vehicle navigation(PACSSI3), and geographic polar (PACSSl) coordinate systems.The definitions pertaining to the trajectory symbols and thecoordinate systems are given in Appendix A.

3.1.2 Second Burn Phase

A comparison of actual and nominal times for significant

flight events pertaining to the second burn phase is includedin Table 3-I.

The actual altitude is shown in Figure 3-8. The magnitude ofthe total space-fixed velocity vector and the associated flightpath angle are shown in Figure 3-9. The magnitude of the totalinertial acceleration vector is shown in Figure 3-10. Themaximum total inertial acceleration and earth-fixed velocityare shown in Table 3-11.

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3.1 .2 (Continued)

The second burn trajectory, from the time of S-IVB restartpreparations to CSM separation, is tabulated in Tables B-Vthrough B-VII in metric units, and in Tables C-V throughC-VII in English units. These tables present the trajectoryin the earth-fixed launch site (PACSSIO), launch vehiclenavigation (PACSSI3), and geographic polar (PACSSI) coordinatesystems. The definitions pertaining to the trajectory symbolsand the coordinate systems are given in Appendix A.

3.1.3 Targeting Parameters

The actual and nominal targeting parameters are given in Table3-V. These nominal parameters are used in the guidance com-puter as terminal conditions for the powered flight phases.The actual targeting parameters were close to nominal.

3.2 DATA SOURCES

3.2.1 Ascent Phase

Tracking data and telemetered guidance velocity data werereceived during the period from first motion through orbitalinsertion. The time periods for which tracking system coveragewas available are shown in Figure 3-11 and itemized in Table3-VI. The geographic locations of the tracking stations andthe ground track for the ascent trajectory are shown in Figure3-I. The antenna locations for the tracking system and thevehicle center of gravity are shown in Figure 3-12.

Considerable C-Band tracking data were furnished by the sta-tions located at Cape Kennedy, Patrick Air Force Base, MerrittIsland, Grand Turk Island, and Bermuda Island. These trackingdata were provided as measured parameters in azimuth angle,elevation angle, and slant range. These measurements aredefined in Reference 1 and designated as PACSS3a.

Comparisons between these data and the ascent trajectory werecalculated in PACSS3a. The position components of the ascenttrajectory in PACSSIO were corrected for the differences be-tween the center of gravity and the transponder location. Thecorrected position components were transformed into the meas-ured parameters of PACSS3a. Differences or deviations (track-ing data minus corresponding parameters derived from the ascenttrajectory) were calculated, smoothed, and plotted as functionsof time, and are shown in Figures 3-13 through 3-15.

Cape Kennedy (1.16) radar provided tracking data from 25 to400 seconds. The azimuth angle measurements were noisythroughout the time span of tracking, and oscillated about

D5-15560-6

3.2.1 (Continued)

the trajectory up to about 175 seconds. After 175 seconds,

the azimuth angle measurements agree favorably with the tra-

jectory with maximum deviation of 0.016 degree. The elevation

angle measurements were noisy throughout the tracking period

with maximum deviation of 0.037 degree from the trajectory.

The slant range measurements contained little noise throughout

the tracking period with maximum deviation of 48 m (157 ft)from the trajectory.

Patrick (0.18) radar provided tracking data from 25 to 500seconds. The azimuth angle measurements contained little noise

throughout the tracking period. They deviated considerably

from the trajectory up to about 225 seconds, but agree excel-

lently thereafter with maximum deviation of 0.008 degree. The

elevation angle measurements were noisy during the early por-tion (25 to 75 seconds) and the later portion (465 to 500

seconds) of tracking. The elevation angle measurements also

deviated considerably from the trajectory up to about lO0

seconds, and agree favorably with the trajectory in the timespan from lO0 to 465 seconds with maximum deviation of 0.028

degree. The slant range measurements contained little noise

throughout the tracking period with maximum deviation of 32 m(I05 ft) from the trajectory.

Merritt Island (19.18) radar furnished data from 80 to 425

seconds. The azimuth angle measurements were of good quality

except in the time spans of 80-120 and 165-200 seconds, where

the data were erratic. The azimuth angle measurements reached

a maximum deviation of 0.059 degree at ll5 seconds, and de-creased rapidly thereafter with near zero deviation after 300

seconds. The elevation angle measurements were of good quality

and deviated a maximum of 0.030 degree from the trajectory.The slant range measurements were of good quality except inthe time span of 170-200 seconds, where the data were erratic.

The slant range measurements had a discontinuity at about 390

seconds, indicating a switch from beacon to skin tracking. Themaximum deviation of slant range measurements from the trajec-

tory amounted to 35 m (ll5 ft).

Grand Turk (7.18) radar supplied data from 230 to 520 seconds.

The azimuth and elevation angle measurements were noisy and

erratic throughout the tracking period. Although the slantrange measurements contained little noise and deviated reason-

ably from the ascent trajectory, the data were considered as

invalid and were not used in the trajectory reconstruction.

Bermuda (67.16) radar provided data from 275 to 710 seconds.The azimuth angle measurements contained little noise through-

3-3

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3.2.1 (Continued)

out the tracking period. Except for a characteristic deviationfrom 500 to 600 seconds, the azimuth angle measurements werein good agreement with the trajectory with maximum deviationof 0.012 degree. The elevation angle measurements were noisyat the beginning (275 to 330 seconds) of tracking. A char-acteristic deviation occurred from 500 to 625 seconds. Theelevation angle measurements were in good agreement with thetrajectory near the end of trackina with a deviation of 0.022degree at parking orbit insertion (709.33 seconds). The slantrange measurements contained little noise throughout thetracking period; however, a large deviation occurred in theinterval 375 to 575 seconds. Approaching the end of thetracking period, the deviation in the slant ranae measurementsdecreased rapidly with a deviation of 48 m (157 ft) at parkingorbit insertion.

Bermuda (67.18) radar provided data from 250 to 710 seconds.The azimuth angle measurements contained little noise throughoutthe tracking period. As with the 67.16 radar, a characteristicdeviation was evident from 500 to 600 seconds. Otherwise, theazimuth angle measurements were in good agreement with the tra-jectory with maximum deviation of 0.024 degree. The elevationangle measurements were noisy at the beginning (250 to 330seconds) of tracking. A characteristic deviation occurred from500 to 625 seconds. The elevation angle measurements were ingood agreement with the trajectory near the end of trackingwith a deviation of 0.030 degree at parking orbit insertion.The slant range measurements contained little noise throughoutthe tracking period; however, a large deviation occurred from400 to 575 seconds. Approaching the end of the tracking period,the deviation in the slant range measurements decreased rapidlywith a deviation of 20 m (66 ft) at parking orbit insertion.


Telemetered guidance velocity data during the S-IVB second burnperiod were received. Also, C-band radar tracking data wereobtained from the Redstone Ship from 9,726 to 10,098 seconds.These tracking data were found to be invalid and were not usedin the trajectory reconstruction.

3.3 TRAJECTORY RECONSTRUCTION

3.3.1 Ascent Phase

The ascent trajectory from guidance reference release to orbitalinsertion was established by a composite solution of availabletracking data and telemetered onboard guidance velocity data.

3-4

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3.3.1 (Continued)

Before the data were used in the trajectory solution, one ormore of the following processing steps was performed:

a .

b.C.

d.eo

f.

Inspecting for format and parity errorsTime editingData editing and filteringRefraction correction

ReformattingCoordinate transformation

The position components of the tracking point of the vehiclein PACSSIO were established by merging the launch phase andascent phase trajectory segments.

The launch phase (from first motion to 20 seconds) was estab-lished by integrating the telemetered guidance accelerometerdata and by constraining it to the early portion of the ascentphase trajectory. The ascent phase (from 20 seconds to orbitalinsertion at 709.33 seconds) was based on a composite fit ofexternal tracking data and telemetered onboard guidance velocitydata. The ascent phase was constrained to the insertion vectorobtained from the orbital analysis of Section 4. The outputdata were transformed to the vehicle center of gravity.

A computer program (GATE), which uses a guidance error model,was utilized. The telemetered guidance velocity data wereused as the generating paramete_ and error coefficients wereestimated to best fit the tracking observations. The Kalmanrecursive method was used for the estimation. Reference 4gives a theoretical discussion of the GATE program.

The position components, in PACSSIO, were filtered and differ-entiated to obtain vehicle velocity and acceleration components.Since numerical differentiators tend to distort the datathrough the transient areas (engine cutoffs), the guidancevelocity data were integrated and used to fill in these areas.

The trajectory data in PACSSIO were then transformed to severalcoordinate systems. Various trajectory parameters were alsocalculated and are presented in Appendices B and C. In cal-culating the Mach number and dynamic pressure, measured meteoro-logical data were used up to an altitude of 56.0 km (30.2 n mi).Above this altitude the measured data were merged into the U.S.Standard Reference Atmosphere.

3-5

D5-15560-6


The second burn trajectory was established by combining anorbital trajectory segment and a powered flight trajectorysegment.

The orbital trajectory segment covers the 9ortion of flightfrom the beginning of S-IVB restart preparations (9,278.2seconds) to 9,715 seconds. This trajectory segment was ob-tained from the orbital solution as described in Section 4.

The powered flight trajectory segment covers the time spanfrom 9,715 seconds to translunar injection (10,213.03 seconds).This trajectory segment was established by integrating thetelemetered guidance velocity data forward from the statevector at 9,715 seconds and constraining the end point to thetranslunar injection vector (obtained from the post TLI tra-jectory of Section 4). The GATE program was utilized forthe solution.

The Redstone Ship tracking data during the second burn phasewere noisy and erratic. These tracking data were not utilizedin the trajectory reconstruction.

The position components, in PACSSIO, were filtered, differen-tiated, shaped, and transformed in the same manner as describedin Paragraph 3.3.1.

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First Motion

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Mach l

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S-IC Center Engine Cutoff

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S-IG/S-II Separation Command

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OF SIGNIFICANT EVENTS

RANGE TIME, SEC

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D5-15660-6

TABLE 3-11. SIGNIFICANT TRAJECTORY PARAMETERS

EVENT

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Math 1

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S-II

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S-IVB 2nd Burn

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Dynamic Pressured N/cm 2

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D5-15560-6

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Surface Range kmIn mi)

Space-Fixed Velocity,

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m/s(ft/s)

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3-28

D5-15560-6

SECTION 4

ORBITAL TRAJECTORYRECONSTRUCTION

4.1 ORBITAL TRAJECTORIES

The S-IVB/LM/CSM was inserted into a circular parking orbit at709.33 seconds. While in parking orbit, vehicle subsystemcheckout was carried out from the tracking stations and MissionControl Center at Houston. During the second revolution,approximately midway between Australia and Hawaii, the S-IVBstage was restarted and the vehicle was placed onto a circum-lunar trajectory.

The parking orbit insertion conditions were close to nominal.The space-fixed velocity at insertion was equal to nominal, andthe flight path angle was 0.013 degree greater than nominal.The eccentricity was 0.00001 less than nominal. The apogeeand perigee were 0.5 km (0.3 n mi) and 0.6 km (0.3 n mi) lessthan nominal, respectively.

The translunar injection (TLI) conditions were also close tonominal. The eccentricity was 0.00029 greater than nominal,the inclination was 0.004 degree greater than nominal, thenode was 0.019 deqree lower than nominal, and C3 was 16,877m2/s2 (181,663 ft2/s 2) greater than nominal. The space-fixedvelocity was 3.2 m/s (10.5 ft/s) greater than nominal, and thealtitude was 3.1 km (I.6 n mi) less than nominal.

The parking orbit trajectory spans the interval from insertionto begin S-IVB restart preparations (9,278.2 seconds). Thepost TLI trajectory covers the period from translunar injection(10,213.03 seconds) to CSM separation (11,723 seconds). Thesetwo orbital trajectories were established by the integrationof the orbital model equations using the insertion/injectionvector as the initial conditions.

The insertion/injection conditions, as determined by theOrbital Correction Program (OCP), were obtained by a differ-ential correction procedure which adjusted the estimatedinsertion/injection conditions to fit the C-band radar trackingdata in accordance with the weights assigned to the data.After all available C-band radar tracking data were analyzed,the stations and passes providing the better quality data wereused in the determination of the insertion/injection conditions.

4-1 PRECEDING PAGE BLANK NOT FILMED

D5-15560-6

4.2 ORBITAL DATA SOURCES

4.2.1 Orbital Tracking Data

Orbital tracking was conducted by the NASA Manned Space FlightNetwork (MSFN). A summary of the C-band tracking data isgiven in Table 4-I. There were also considerable UnifiedS-band (USB) tracking data available during these periods offlight which were not used due to the abundance of C-bandradar data.

4.2.2 Orbital Venting Acceleration Data

During the orbit, no major thrusting occurred; however, theorbit was continuously perturbed by low-level LH2 ventingthrust. To accurately model the orbit of the vehicle, thisperturbation was taken into account. The venting model wasderived from telemetered guidance velocity data from theST-124M guidance platform. The guidance velocity data werefitted in segments by polynomials in time. These polynomialswere analytically differentiated to obtain the accelerationcomponents measured by the guidance platform. Table 4-11lists the acceleration polynomials derived by this method.Figure 4-I reflects the best estimate of the total ventingacceleration (RSS of components) after atmospheric effectsand biases have been removed.

4.3 TRAJECTORY RECONSTRUCTION

4.3.1 Parking Orbit Insertion Conditions

The Orbital Correction Program (OCP) was used to solve for theparking orbit insertion conditions utilizing C-band trackingdata and the above-mentioned vent model. The insertion condi-tions are given in Table 4-111. The parking orbit solutionwas based on a composite fit of the two Bermuda stations atinsertion, pass one of Carnarvon, pass two of Patrick, andpass two of Carnarvon. This combination of trackers is geo-metrically spaced to insure adequate coverage of the parkingorbit. The Bermuda data at insertion were also used in thetrajectory reconstruction of the ascent phase. The use ofBermuda data in the ascent phase solution and also in theorbital phase solution aids in assuring the continuity of thetrajectory. The orbital solution, with the exception of theFPS-16M Bermuda radar, is based on the higher quality FPO-6radars. The ground track from parking orbit insertion to CSMseparation is given in Figure 4-2. The parking orbit trajec-tory in PACSSI is given in Tables B-IV and C-IV.

4-2

D5-15560-6

4.3.2 Translunar Injection Conditions

The translunar injection (TLI) conditions were determined bythe Orbital Correction Program (OCP) utilizing the post injec-tion C-band tracking data. The TLI conditions are given inTable 4-1V. The TLI state vector obtained by the GATE programfrom the integration of guidance velocity data agreed favorablywith the OCP determined TLI vector. The post TLI trajectoryis included in Tables B-V through B-Vll in metric units andTables C-V through C-VII in English units. The CSM separationconditions are given in Table 4-V.

4.4 ORBITAL TRACKING ANALYSIS

The stations used to obtain the parking orbit insertion condi-tions and translunar injection conditions are given by Tables4-VI and 4-VII, respectively. These two tables also includethe number of data points and the Root-Mean-Square (RMS)errors of the residuals for each data type. These RMS errorsrepresent the difference between the actual radar observationsand the calculated observations based on the orbital ephemerisdefined by the initial conditions. The RMS residual errors include high frequency errors (assumed Gaussian), systematicerrors due to instrumentation biases, mathematical model error,and errors in the correction for atmospheric refraction.

The maximum RMS error of the radar residuals for the parkingorbit was 18 m (59 ft) in slant range, 0.030 degree in elevationangle, and 0.015 degree in azimuth angle. The maximum RMS errorof the radar residuals for the post TLI trajectory was 18 m(59 ft) in slant range, 0.025 degree in elevation angle, and0.020 in azimuth angle. The magnitudes of these RMS errors arereasonable and indicate the validity of the parking orbit andpost TLI trajectory.

4-3

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4-5

D5-15560-6

TABLE 4-I. SUMMARYOF ORBITAL C-BAND TRACKING DATA AVAILABLE

STATIONi l

Bermuda

Bermuda

Tananarive

Carnarvon

California

Patrick

Grand Turk

Redstone Ship

Hawaii

Antigua

Ascension

TYPE OF RADARS

71r

FPS-16M

FPQ -6

FPS-16M

FPQ-6

TPQ-18

FPQ-6

TPQ-18

FPS-16M

FPS-16M

FPQ-6

TPQ-18

REV 1

X

X

X

X

X

REV 2

X

X

X

POST TL I

X

4-6

D5-15560-6

TABLE 4-11. ORBITAL VENTING ACCELERATIONPOLYNOMIALS*

X**

Tb 710 1 ,483 9,535Te 1 ,483 9,535 9,840CO -0.29883288xi0 -5 -0.12140570xi0 -5 -0.61607689xi0 -6

C1 0.19159214xi0 -7 -0.25510786xi0 "9 0.49930034xi0 -7

C2 -0.46780418xi0 "I0 0.13961048xi0 -II -0.39763102xi0 -9

C3 0.34343775xi0 -13 -0.59877535xi0 -15 0.86249576xi0 -12

C4 0 0.89589398xi0 -19 0

C5 0 -0.44624259xi 0-23 0

Tb 710Te 9,840

CO 0.13272155xi0 -7

C1 0.601 77901xi0 -II

C2 0C3 0

C4 0

C5 0°,

ZT b 710 1 ,483 9,535

T e 1 ,483 9,535 9,840

CO 0.54491435xi0 -5 0.39339382xi0 -6 -0.26517094xi0

C 1 -0.37627287xi0 °7 -0.24289009xi0 -8 0.I0419636xi0

C2 0.86370452xi0 "I0 0.15008060xi0 -II -0.92767644xi0

C3 -0.61633706xi0 -13 -0.30356055xi0 -15 0.22408258xi0

C4 0 0.20894634xi0 -19 0

C5 0 -0.21112472xi0 -24 0

-6

-7

-I0

-12

t3+C4t4+C t 5* Polynomials are of the form a=Co+Clt+C2t2+C 3 5

where a is the acceleration component (km/s2) and t = T-T bwhere TbST<T e. The begin time (Tb) and the end time (Te)for the polynomial segments are expressed in seconds.

** The acceleration components are expressed in the launchvehicle platform-accelerometer system (PACSSI2).

4-7

D5-15560-6

TABLE 4-111. PARKING ORBIT INSERTION CONDITIONS

PARAMETER

Range Time, sec

Altitude, km(n mi)

Space-Fixed Velocity, m/s(ft/s)

VALUE

709.33

191 .I(103.2)

7,793.1(25,567.9)

Flight Path Angle, deg

Heading Angle, deg

Inclination, deg

Descending Node, deg

Eccentricity

Apogee*, km(n mi)

Perigee*, km(n mi)

Period, min


Longitude, deg E

0.012

88.848

32.521

123.088

0.00021

186.0(100.4)

183.2(98.9)

88.18

32.672

-52.694

*Based on a spherical earth of radius 6,378.165 km(3,443.934 n mi)

4-8

D5-15560-6

TABLE 4-1V. TRANSLUNARINJECTION CONDITIONS

PARAMETER VALUE

Range Time, sec

Altitude, km

(n mi)

Space-Fixed Velocity, m/s(ft/s)


10,213.03

334.4(180.6)

10,834.3(35,545.6)

7.367

Heading Angle, deg

Inclination, deg

Descending Node, deg

Eccentricity

C3", m2/s 2

(ft2/s 2 )


Longitude, deg E

60.073

31 .383

121 .847

0.97696

-1,391,607

(-14,979,133)

9.983

-164.837

* Twice the specific energy of orbit

C3 = V2 _

where V = Inertial Velocity

!J : Gravitational ConstantR = Radius vector from center of earth

4-9

D5-15560-6

TABLE 4-V. CSM SEPARATION CONDITIONS

PARAMETER VALUE,,

Range Time, sec

Altitude, km(n mi)

Space-Fixed Velocity, m/s(ftls)

11 ,723

7,065.7(3,815.2)

7,608.6(24,962.6)


Heading Angle, deg


Longitude, deg E

45.148

93.758

31.246

-90.622

4-10

D5-15560-6

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4-12

D5-15560-6

SECTION 5

TRAJECTORYERRORANALYSIS

5.1 ERRORANALYSIS

The confidence level or uncertainty one may assign to a recon-structed trajectory depends on the degree of fulfillment of thefollowing criteria:

a. Quantity of Tracking Datab. Quality of Tracking Datac. Consistency between Tracking and Guidance Velocity Datad. Continuity between Trajectory Segments

These criteria vary from flight to flight. Therefore, a rig-orous statistical error analysis of the reconstructed trajec-tory is difficult to obtain. The following paragraphs summarizethe results for this flight, and lead to the position and ve-locity uncertainties for the reconstructed trajectory.

5.1.1 Quantity of Tracking Data

The available tracking data for the powered flight phases aregiven in Figure 3-11 and Table 3-VI. The tracking coveragesfor the parking orbit and post TLI phases are given in Table4-I.

The tracking stations for the ascent and post TLI phases pro-vided extensive redundant coverages. The available trackingdata during parking orbit provided adequate coverage. TheRedstone Ship C-band tracking data were available for a portionof the second burn phase.

5.1.2 Quality of Tracking Data

The tracking data were generally of good quality. The Grand

Turk (7.18) radar data for the ascent phase and the Redstone

Ship radar data for the second burn phase were found to be

invalid. However, the tracking data furnished before and

after the second burn phase were of good quality.

Comparisons of the tracking data in measured parameters (PACSS3a)

with the ascent trajectory are shown in Figures 3-13 throuQh

3-15. These plots indicated that the tracking data from the

different stations were mutually consistent. Except for thecharacteristic data deviations from the Bermuda stations occur-

ring approximately in the time span 400-600 seconds, the track-

ing data deviations were of acceptable magnitude. The tracking

data obtained during the parking orbit and post TLI phases were

5-I

D5-15560-6

5.1.2 (Continued)

of good quality. The RMS errors of residuals for each data

type are given in Tables 4-Vl and 4-VII, respectively.

The tracking data were transformed into the earth-fixed launchsite coordinate system (PACSSIO) and differenced with the re-constructed trajectory to provide a more direct indication ofthe spread of the tracking data. The tracking data spreadsfor the ascent, parking orbit, and post TLI phases are givenin Tables 5-I through 5-111, respectively.

5.1.3 Consistency Between Tracking and Guidance Velocity Data

The consistency between tracking and guidance velocity datacan be obtained by examining the guidance velocity error plotsduring powered flight trajectory segments. These error plotsgive the differences between the guidance velocities from theST-124M platform and those derived from the reconstructed tra-jectory.

The guidance velocity error plots for the ascent phase hadreasonable shapes and magnitudes. The maximum error amountedto 1.5 m/s (4.9 ft/s) in the X-direction, 2.8 m/s (9.2 ft/s)in the Y-direction, and 0.7 m/s (2.3 ft/s) in the Z-direction,referenced to launch vehicle platform-accelerometer coordinatesystem (PACSSI2).

The guidance velocity error plots for the second burn phase

had reasonable shapes and magnitudes. The maximum error

amounted to 1.2 m/s (3.9 ft/s) in the X-direction, 1.7 m/s

(5.6 ft/s) in the Y-direction, and 0.9 m/s (3.0 ft/s) in the

Z-direction, referenced to PACSSI2.

5.1.4 Continuity Between Trajectory Segments

The continuity between trajectory segments can be obtained byexamining the spread of solutions at parking orbit insertionand translunar injection before the trajectory segments weremerged together.

Comparisons of the spread of solutions at the parking orbitinsertion obtained independently by the powered flight andorbital analyses yielded good agreement. The position andvelocity components of the solutions had a spread of 70 m(230 ft) and 0.3 m/s (I.0 ft/s) in the downrange direction,170 m (558 ft) and 0.8 m/s (2.6 ft/s) in the vertical direction,and 130 m (427 ft) and 1.7 m/s (5.6 ft/s) in the crossrangedirection, referenced to the earth-fixed launch site coordinatesystem (PACSSlO).

5-2

D5-15560-6

5.1.4 (Continued)

Comparisons of the TLI vectors determined independently fromthe powered flight and orbital analyses yielded good agreement.The TLI vector from the powered flight analysis was obtained bypropagating forward the state vector at 9,715 seconds (fromparking orbit analysis) to 10,213.03 seconds. The TLI vectorfrom the orbital analysis was determined separately by usingthe post TLI tracking data. The position and velocity compon-ents of the two solutions had respectively a spread of 90 m(295 ft) and 0.3 m/s (I.0 ft/s) in the X-direction, 80 m(262 ft) and 1.2 m/s (3.9 ft/s) in the Y-direction, and 430 m(1,411 ft) and 1.4 m/s (4.6 ft/s) in the Z-direction, refer-enced to the earth-fixed launch site coordinate system (PAC_SIO).

A dispersion analysis was performed for the parking orbit tra-jectory. Three solutions were obtained by judiciouslyselecting various tracking data combinations. The parking orbitinsertion vectors had a spread in position and velocity compon-ents respectively of 60 m (197 ft) and 0.3 m/s (I.0 ft/s) indownrange (Z), 275 m (902 ft) and 0.I m/s (0.3 ft/s) in vertical(X), and 80 m (262 ft) and 0.2 m/s (0.7 ft/s) in crossrange(Y), referenced to the earth-fixed launch site coordinatesystem (PACSSIO).

5.2 TRAJECTORY UNCERTAINTIES

Based on the information of Paragraph 5.1, past experience, andengineering judgment, the trajectory uncertainties were esti-mated.

The trajectory uncertainties for the ascent phase are shown inFigure 5-I. At S-IC OECO, the uncertainties in position andvelocity components in PACSSIO are ±60 m (±197 ft) and ±0.4 m/s(±1.3 ft/s), respectively. At S-II OECO, the uncertainties inposition and velocity components in PACSSIO are ±350 m (±1,148ft) and ±0.7 m/s (±2.3 ft/s), respectively. At insertion andthroughout the parking orbit, the uncertainties in positionand velocity components in PACSSIO are ±500 m (±1,640 ft) and±I.0 m/s (±3.3 ft/s), respectively. The trajectory uncertain-ties increased to ±750 m (±2,461 ft) in position componentsand ±1.5 m/s (±4.9 ft/s) in velocity components at TLI. Thetrajectory uncertainties at CSM separation are ±1,500 m(±4,921 ft) in position components and ±2.0 m/s (±6.6 ft/s)in velocity components.

5-3

D5-15560-6

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D5-1 5560-6


5-8

D5-15560-6

SECTION 6

SPENT STAGE TRAJECTORIES

6.1 S-IC SPENT STAGE TRAJECTORY

Postflight predictions of earth surface impact parameters forthe spent S-IC stage were computed using a mass point trajec-tory simulation computer program. S-IC postflight burnoutposition and velocity data were combined with nominal mainpropulsion system decay performance and nominal retro rocketperformance to initialize the simulation program.

Three separate theoretical trajectories were computed for the

spent S-IC stage. These three trajectories represent the fol-

lowing booster atmospheric entry conditions:

a. Zero-degree angle-of-attack entryb. Ninety-degree angle-of-attack entryc. Tumbling entry

The tumbling booster case is considered to define actual caseimpact conditions although no tracking coverage was availablefor confirmation.

Results of the three computed S-IC spent stage trajectories

are summarized in Table 6-I. The ground track is shown in

Figure 6-I.

6,2 S-II SPENT STAGE TRAJECTORY

Three separate theoretical trajectories, corresponding to thezero-degree, ninety-degree, and tumbling case trajectoriescomputed for the S-IC stage, were computed for the spent S-IIstage.

The computed results, assuming a tumbling stage, were consideredto define stage impact conditions since no tracking coverageof the spent S-II stage was available.

Results of the three computed S-II spent stage trajectoriesare summarized in Table 6-11. The ground track is shown inFigure 6-I.

PRECEDING PAGE BLANK NOT FILMED6-1

D5-15560-6

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6-2

D5-15560-6

TABLE 6-1. S-IC SPENT STAGE TRAJECTORY PARAMETERS

EVENT

Impact: Tumbling Case

Impact: 0 ° Angle-of-Attack


Apex: Tumbling Case

PARAMETER

Range Time, sec

Latitude, deg N

Longitude, deg E

Surface Range, km(n mi)

Range Time, sec

Latitude, deg N

Longitude, deg E


Range Time, sec

Latitude, deg N

Longitude, deg E


Range Time, sec

Altitude, km(n mi)


VALUE

543.7

30.212

-74.038

661.4(357.1)

503.5

30.231

-73.942

671.0(362.3)

577.8

30.198

-74.105

554.9(353.6)

269.1

115.0(62.1)

327.4(176.8)

6-3

D5-15560-6

TABLE 6-11. S-II SPENT STAGE TRAJECTORY PARAMETERS

EVENT

Impact: Tumbling Case



Apex: Tumbling Case

PARAMETER

Range Time, sec

Latitude, deg N

Longitude, deg E


Range Time, sec

Latitude, deg N

Longitude, deg E


Range Time, sec

Latitude, deg N

Longitude, deg E


Range Time, sec

Altitude, km(n mi)


VALUE

1,213.7

31.535

-34.844

4,392.5(2,371.8)

1,179.9

31.497

-34.582

4,417.8(2,385.4)

1,252.7

31.573

35.113

4,366.7(2,357.8)

587.0

188.8(I01 .9)

l ,862.9(l,OO5.9)

6-4

D5-15560-6

SECTION 7

S-IVB/IU SLINGSHOT TRAJECTORY

Following LM extraction, the S-IVB/IU was placed on a lunarslingshot trajectory. This was accomplished by slowino downthe S-IVB/IU to make it pass by the trailino edge of the moonand obtain sufficient energy to continue to a solar orbit.The velocity increase was achieved by a combination of 108-second LOX dump, 280-second APS burn, and LH 2 vent. A timehistory of the vehicle longitudinal velocity increase for theslingshot maneuver is presented in Figure 7-I. Table 7-Ipresents a comparison of the actual and nominal velocityincrease due to the various phases of the maneuver. The majorerror contribution in total velocity increase is the resulting7.3 m/s (24.0 ft/s) from the continuous venting system (CVS)as compared to 3.5 m/s (11.5 ft/s) for the predicted value.Figure 7-2 presents the resultant conditions for variousvelocity increases at the given attitude of the vehicle forthe maneuver.

The S-IVB/IU closest approach of 3,379 kilometers (1,825 n mi)above the lunar surface occurred at 78.70 hours into the mis-

sion. The trajectory parameters were obtained by integratingforward a vector furnished by Goddard Space Flight Center(GSFC) which was obtained from USB tracking data during theactive lifetime of the S-IVB/IU. The actual and nominalconditions at closest approach are presented in Table 7-11.Figure 7-3 illustrates the influence of the moon on the S-IVB/IUenergy (velocity) relative to the earth and shows that theS-IVB/IU escaped as a result of the lunar encounter. Figure7-4 illustrates the relationship between the S-IVB/IU and thespacecraft in the lunar vicinity, with all paths shown in thespacecraft's orbital plane. The spacecraft had completed onelunar revolution prior to S-IVB/spacecraft close approach, atwhich time the two vehicles were approximately 3,500 km (1,890n mi) apart. Some of the heliocentric orbit parameters of theS-IVB/IU are presented in Table 7-111. The same parametersfor the orbit of the earth are also presented for comparison.

7-I

D5-15560-6

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TABLE 7-I. COMPARISON OF SLINGSHOT MANEUVER VELOCITYINCREMENT

PARAMETER ACTUAL NOMINAL

Longitudinal Velocity Increase, m/s(ft/s)

LOX Dump_ mls(ft/s)

APS Burn, m/s

(ft/s)

Continuous Vent System*, m/s(ftls)

36.3(I19.1)

17.0(55.8)

12.0(39.4)

7.3(24.0)

31 .5(103.3)

16.0(52.5)

12.0(39.4)

3.5(II .5)

* Latched open at 17,468 seconds

7-6z

D5-15560-6

TABLE 7-II. COMPARISON OF LUNAR CLOSEST APPROACHPARAMETERS

PARAMETER ACTUAL NOMINAL

Selenocentric DistanCelnkm mi)

Altitude Above Lunar Surface, km(n mi)

Time from Launch, hr

Velocity Increase Relative toEarth from Lunar Encounter, km/s

(n mi/s)

5,117(2,763)

3,379

(l ,825)

78.7

0.680(0.367)

3,700(I ,998)

1 ,962(I ,059)

78.4

0.860(0.464)

7-7

D5-15560-6

TABLE 7-111. HELIOCENTRIC ORBIT PARAMETERS

PARAMETER

Semimajor Axis, 106 km

(106 n mi)

Aphelion, 106 km

(106 n mi)

Perihelion, 106 km

(106 n mi)

Inclination,* deg

Period, days

S-IVB/IU

143.08

(77.26)

151.86

(82.OO)

134.30

(72.52)

0.3836

342

EARTH

149.00

(80.45)

151 .15

(81 .61)

146.84

(79.29)

0.0000

365

* Measured with respect to the ecliptic plane

7-8

D5-15560-6

APPENDIX A

DEFINITIONS OF TRAJECTORY SYMBOLS AND COORDINATE SYSTEMS

SYMBOL

XE, YE, ZEDXE, DYE, DZEDDXE, DDYE, DDZE

XS, YS, ZSDXS, DYS, DZSDDXS, DDYS, DDZS

GC DISTGC LATGD LATLONG

DEFINITION

Position, velocity, and acceleration compo-nents of _tehicle center of gravity in Earth-Fixed Launch Site Coordinate System. Theorigin of this system is at the intersectionof Fischer Ellipsoid (1960) and the normalto it which passes through the launch site.The X axis coincides with the ellipsoidnormal passing through the site, positiveupward. The Z axis is parallel to theearth-fixed flight azimuth, defined atguidance reference release time, and ispositive down range. The Y axis completesa right-handed system. This coordinatesystem is identical to Standard CoordinateSystem I0 of Project Apollo Coordinate SystemStandards, abbreviated as PACSSIO.

Position, velocity, and acceleration compo-nents of vehicle center of gravity in LaunchVehicle Navigation Coordinate System. Theorigin of this system is at the center ofthe earth. The X axis is parallel to FischerEllipsoid normal through the launch site,positive upward. The Z axis is parallel tothe flight azimuth, positive downrange.The Y axis completes a right-handed system.The direction of the coordinate axes remainsfixed in space at guidance reference release.This coordinate system is identical toStandard Coordinate System 13 of ProjectApollo Coordinate System Standards, abbrevi-ated as PACSSI3.

Position components of vehicle center ofgravity in Geographic Polar CoordinateSystem. Position in this system is definedby the geocentric distance (GC DIST), geo-centric latitude (GC LAT), geodetic latitude(GD LAT), and longitude (LONG). Geocentricdistance is the distance from the geocenterto vehicle center of gravity. Geocentriclatitude is the angle between the radiusvector of the subvehicle point and the equa-torial plane, positive north of the equa-torial plane. Geodetic latitude is the

A-I

D5-15560-6

SYMBOL

EF VELVEL-AZVEL-EL

SF VEL

FLT-PATH

HEAD

APPENDIX A (Continued)

DEFINITION

angle between the normal to the Fischer

Ellipsoid through the subvehicle point and

the equatorial plane, positive north of theequatorial plane. Longitude is the angle

between the projection of the radius vector

into the equatorial plane and the Greenwichmeridian, positive east of the Greenwich

meridian. This coordinate system is iden-

tical to Standard Coordinate System l of

Project Apollo Coordinate System Standards,abbreviated as PACSSI.

Earth-fixed velocity of vehicle center of

gravity in Geographic Polar Coordinate

System. Velocity in this system is givenin terms of azimuth (VEL-AZ), elevation

(VEL-EL), and magnitude of the velocity

vector (EF VEL). Azimuth is the angle be-

tween the projection of the velocity vector

into the local horizontal plane and the

north direction in this plane, positive

east of north. Elevation is the angle be-

tween the velocity vector and the local

horizontal plane, positive above the hori-

zontal plane. This coordinate system isidentical to Standard Coordinate System l

of Project Apollo Coordinate System Stand-

ards, abbreviated as PACSSI.

Space-fixed velocity of vehicle center of

gravity in Geographic Polar Coordinate

System. Velocity in this system is givenin terms of heading angle (HEAD), flight

path angle (FLT-PATH), and magnitude of

velocity vector (SF VEL). Heading angle is

the angle between the projection of thevelocity vector into the local horizontal

plane and the north direction in this plane,

positive east of north. Flight path angle

is the angle between the velocity vector

and the local horizontal.plane, positiveabove the horizontal plane. This coordi-

nate system is identical to Standard Co-

ordinate System l of Project Apollo

Coordinate System Standards, abbreviatedas PACSSIo

A-2

D5-15560-6

SYMBOL

ALTITUDE

RANGE

TIME

APPENDIX A (Continued)

DEFINITION

Perpendicular distance from vehicle __nterof gravity to Fischer Ellipsoid, positiveabove Fischer Ellipsoid.

Surface range, measured along Fischer Ellip-soid from the launch site to the subvehiclepoint.

Range time, referenced to nearest integersecond before IU umbilical disconnect.

A-3

D5-15560-6

THIS PAGE INTENTIONALLY LEFT BLANK,

A-4

D5-15560-6

APPENDIX B

TIME HISTORY OF TRAJECTORYPARAMETERS- METRIC UNITS

The postflight trajectory, from guidance reference release toCSM separation,is tabulated in metric units in Tables B-Ithrough B-VII.

Table B-I gives the earth-fixed launch site position, velocity,and acceleration components for the ascent phase of the flight.

Table B-II gives the launch vehicle navigation position,velocity, and acceleration components for the ascent phase ofthe flight.

Table B-Ill gives the geographic polar coordinates for theascent phase of flight.

Table B-IV gives the geographic polar coordinates for theparking orbit phase of flight.

Table B-V gives the earth-fixed launch site position, velocity,and acceleration components for the second burn phase of theflight.

Table B-VI gives the launch vehicle navigation position,velocity, and acceleration components for the second burnphase of flight.

Table B-VII gives the geographic polar coordinates for thesecond burn phase of flight.

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APPENDIX C

TIME HISTORY OF TRAJECTORYPARAMETERS- ENGLISH UNITS

The postflight trajectory, from guidance reference release toCSM separation,is tabulated in English units in Tables C-I

through C-VII.

Table C-I gives the earth-fixed launch site position, velocity,and acceleration components for the ascent phase of flight.

Table C-II gives the launch vehicle navigation position,

velocity, and acceleration components for the ascent phase of

flight.

Table C-Ill gives the geographic polar coordinates for the

ascent phase of flight.

Table C-IV gives the geographic polar coordinates for the

parking orbit phase of flight.

Table C-V gives the earth-fixed launch site position, velocity,

and acceleration components for the second burn phase of

flight.

Table C-Vl gives the launch vehicle navigation position,velocity, and acceleration components for the second burnphase of flight.

Table C-Vll gives the geographic polar coordinates for the

second burn phase of flight.

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DOCUMENTNO. TITLE APOLLO/SATURN V POSTFLIGHT …