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0198 777 COMPUTING SRSIC SOLAR AMD LUNAR DATA FROM THE AIR
11ALMANAC(IJ) NEATHER MING (5TN) LANGLEV AF8 VA
UNCLASSIFIE J SANDERS ET AL .DEC 87 5UN-TN-97-60 FG /1 U
I EhhEEEEE I
IEEE
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MICROCOPY RESOLUTION TEST CHARTNATIONA, BURErAU , TANDARDS-1963-A
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O-FC ILE GOPY5W/TN-87/001
* 0
5TH WEATHER WING TECHNICAL NOTE
COMPUTING BASIC SOLAR AND LUNAR DTIC
DATA FROM THE AIR ALMANAC AELECTa
December 1987 uJAIi98;D
5WA/DNC
Abstract: This Technical Note provides programmed instruction on theus of the Air Almanac to compute times of sunrise, suwset, moonrise,moonset, and duration of civil twilight for any location, betweenlatitudes 60S and 90'N. Appropriate basic astronomy is included.This Technical Note updates and supersedes 5W/TN-79/002.
Original Authors-Capt John Sanders and TSgt Charles R. ElliottUpdate by - MSgt George T. Gilligan Jr.
Distribution:AWS/DNT 1 4WW/DN 1 5WW FORECAST UNITS 11WW/DN 1 7WW/DN 1 3350TCHTG/TTW 12WW/DN I AFGWC/TS I OL-B HQ AWS I3WW/DN 1 USAFETAC/LDE 5
Distribution Unlimited; Approved for Public Release.
This publicationhas been reviewed and approved for public release.There is no objection to unlimited distribution of this report tothe public at large, or by the Defense Technical Information Center(DTIC) to the National Technical Information Service (NTIS).
RE NETH W. HERTZL , Lt ol, USAFChief, Climatology BranAerospace Sciences Division
FOR THE COMMANDER
S'ITEPH N J. AAVAG, LtCo , USAFChief, Aerospace Scienc6s Division
Accesion F .
NTIS CRA&Ip OTIC TAB 3~~~ur.+ ~: ced [
I AI
ED-
,.IC
REPORT DOCUMENTATION PAGE
,a. Reoort Security Classification: UNCLASSIFIED
3. Distribution/Availability of REPORT: APPROVED FOR PUBLIC RELEASE;
DISTRIBUTION UNLIMITED.
4. Performing Organization Report Number: 5WWA-TN-874001
6a. Name o: Performing Organization: 5WW
6b. Office Symbol: 5WW/DNC
6c. Address: Langley AFB VA 23665-5000
11. Title: Computing Basic Solar and Lunar Data from the Air Almanac
12. Personal Authors: Sanders, John K. , Capt; Elliott, Charles R.
Capt; Gilligan, George T. JR., MSgt.
13a. Type of Report: Technical Note (Final)
14. Date of Report: December 1987
15. Page Count: 56
16. Supplementary Notation: Technical Review completed by P. M.Janiczek, Head of the Ephemerides Division, Nautical Almanac Office.This Technical Note supersedes 5WW/TN-79/002.
18. Subject Terms: *Air Almanac , *Astronomical Data,•Sunrise/Sunset Time, * Moonrise/Moonset Time, * Beginning/EndingTwilight Time'
19. Abstract: This Technical Note provides programmed instruction onthe use opf the Air Almanac to compute times of sunrise, sunset,moonrise, moonset, and Duration of Civil Twilight for any locationbetween latitudes 601S and 90#N. Appropriate basic astronomy isincluded. This Technical Note updates and supersedes 5WW/TN-79/002.
20. Distribution/Availability of Abstract: SAME AS REPORT
21. Abstract Security Classification: UNCLASSIFIED
22a. Name of Responsible Individual: MSgt George T. Gilligan Jr.
22b. Telephone: 804 764-5901
22c. Office Symbol: DNC
DD FORM 1473
ii
'ON~
COMPUTING BASIC LIGHT DATA FROM THE AIR ALMANAC
INTRODUCTION
A pilot comes into your weather office and asks for the time of sunsetat his destination; or perhaps you're out in the field and have noaccess to a computer or some other means of computing astronomicaldata. How can you provide this information using the Air Almanac?
This Tech Note, which has been reviewed by the Nautical Almanac Office.U.S. Naval Observatory, describes the procedures for extracting thesedata from the Air Almanac. It will also describe basic theories andlaws governing these phenomena. A frame-by-frame programmed learningapproach is used.
The Air Almanac is published annually by the Naval Observatory, and isavailable from the Superintendent of Documents, U.S. GovernmentPrinting Office, Washington, DC 20402. Note: AWS units should obtainthe Almanac using procedures defined in AWSR 7-1.
The tables and graphs reproduced in this Tech Note are from the AirAlmanac 1987 edition; consequently the data, table numbers and page
"-. numbers will not necessarily agree with another edition. Theprocedures for extracting the data are the same, regardless of theedition used.
To complete some of the calculations you will need a few sheets ofscratch paper, both to cover the answers (which follow the questions)and to make calculations. A clear plastic straight edge, and in somecases either a pocket calculator or trigonometric tables will also beneeded
The following publications were used in preparing this Tech Note:a. AFM 51-40, 1983, Air Navigation , Chaps 9-10.b. The Air Almanac, U. S. Naval Observatory, U. S. Government PrintingOffice, Washington D.C., 1987.
Upon completion of the Program you should be able to extract the datanecessary to support your mission directly from the Air Almanac. Youcan use a worksheet similar to the one provided at the end of thistext, to make the extraction of data easier. ED.Note: The worksheet wasbased on an idea of SMSgt Depew of 25 Wea Sq. He had developed asimilar worksheet, which was distributed for use to his subordinateunits.
0.1 iii
LEARNING OBJECTIVES
1. State the main reason why sunrise, sunset and twilight times changefrom day-to-day.
2. Name two factors that cause moonrise/set times to change from dayto day.
3. Given a date and a position between 72 Deg. N. and 60 Deg. S,obtain the times of sunrise/set, moonrise/set, and morning and eveningcivil twilights in either Universal Time (Greenwich Mean Time), LocalMean Time, Local Standard and/or Daylight Savings Time, by using thetables in the Air Almanac.
4. Given a date and a position between 65 Deg. N. and 90 Deg. N,
obtain the times of sunrise/set, moonrise/set, and morning and eveningcivil twilights in either Universal Time (.Greenwich Mean Time), LocalMean Time, Local Standard and/or Daylight Savings Time, by using thetables in the Air Almanac.
5. Given a location, date and time, calculate the azimuth and altitude
of the sun.
ii
IIV
Iv%
% v . - -- -. - - -a -- - o% % % % %% '
PROGRAMMED LEARNING TEXT
4FRAME I
In order to utilize the Air Almanac to find Sunrise/set, and
twilight times for your given location you should have some
background as to why these times vary both on a daily basis and also
latitudinally. The main reason the sun does not rise at the same
time every day is the fact that the earth's axis is tilted with
respect to it's orbital plane. There are other factors such as, the
earth's elliptical orbit and it's wobble at the, poles but this only
tributes a few minutes to the annual variation. However, it is
the tilt of the axis that causes the seasons and the extremes in the
lengths of daylight and darkness.
In the illustration of the earth and its orbit (Figure 1) , the 21
December (winter solstice) and 21 June (summer solstice) earth
representations have been enlarged to show the extremes in length of
4 daylight caused by first one pole, then the other being tilted
toward the sun. Notice in the enlargements that the length of
daylight varies with latitude. On 21 June, for example, the length
of daylight becomes progressively shorter as you move from north to
south.
.* The axis remains tilted in the same direction as the earth moves in
its orbit around the sun. This causes the length of daylight at any
one location to vary from day to day. On 21 March (spring equinox)
and 21 September (autumnal equinox), the axis' tilt is in a plane
perpendicular to the sun's rays, and the durations of daylight and
darkness are about 12 hours each for all latitudes.
4%
Ip
'0
a ~~
21 SEP
N N ol
.. ..... ....... ....
0%~2 JUN0...21 DEC*"::::.... 21.MAR
Figur..1.. ILSRTINO.ATHSOBTAN.FETOF~~ TITE AXI UPO LEGH OF DA (DATES....
VARYto SLGTYFOkYAOYA)
21JU
OF TITE AXIS UPO LEGH O AYDAE
Using the illustration, (Figure 1) state the approximate duration of
daylight for the latitude 45' N. on the following dates:
A. 21 December
B. 21 March
C. 21 June
D. 21 September
ANSWER:
A. 9 hours
B. 12 hours
C. 15 hours
D. 12 hours
FRAME 2
The main reason that the times of sunrise/set, and the begin/end
times of the twilights vary is because:
A. of the obliquity of the ecliptic
B. the poles wobble.
C. the earth's orbit is an ellipse.
D. the earth's axis is tilted 23 1/2c with respect to the plane
of the earth's orbit.
ANSWER:
X D.
FRAME 3
The earth's axis tilt and other factors are taken into consideration,
by the Naval Observatory when they compute the times of sunrise/set
and twilights, which are published in the Air Almanac. The
published Almanac times are Greenwich Mean Time (GMT) or they are
also called Universal Time (UT) . "Mean time" is based on the
assumption that the earth rotates about its axis at a constant
velocity (actual changes from one day to the next are very slight)
Because of this assumption, it's possible to establish the
following relationship between time and the earth's rotation:
TIME ARC
24 hours 360-1 hour 15'4 minutes 1"
3
Thus in two hours the sun will appear to pass through an arc of 30'.
Greenwich Mean Time (GMT) is mean time measured with respect to the
Greenwich Meridian (See Figure 2.) At 0000 GMT, the sun (to be
correct we should say the "mean sun") is directly above the
ongitude opposite from Greenwich, i.e.; 180' from Greenwich, and
at 1200 GMT the mean sun is directly above the Greenwich longitude.
Local Mean Tf-nie is similar to GMT except it is measured with
respect to your local position. At 0000 LMT the mean sun is directly
above your longitude.
9W
5X
1%1
Figure 2. Measuring Greenwich Mean Time (GMT).
LMT is not useful to regulate our daily activities because it
varies continuously with longitude since it is based on the
", position of the observer. LMT is useful in solar calculations
because "for all places of the same latitude the corresponding
phenomena will occur at approximately the same Local Mean Time
(L.M.T.) and this will be approximately the same GMT. tabulated (Ed.
Note. in the Air Almanac) , since GMT. = L.M.T. at Greenwich.
The disadvantage of using LMT to regulate our daily activities was
overcome by the introduction of zone time. The world has been
divided :nto 24 zones, each zone being 15 (or one hour) wide. Each
zone uses the LMT of its central meridian as the standard time
(local standard time (LST)) for the zone.
4
li V
Below is a a replica of the list of contents (Figure 3) taken from
an Air Almanac. The tables and graphs used in this programmed text
have been underlined.
LIST OF CONTENTS
Pages Contents
Inside front cover Star list (57 stars) and G.H.A. interpolation tablesDaily pages Ephemerides of Sun, Moon, Aries and planets; moonrise and
moonsetFi-F2 (flap) tcF3 (flap) Star list (57 stars) and G.H.A. interpolation tablesF4 (flap) Interpolation of moonrise and moonset for longitude and star indexAI-A3 Title page, preface, etc.
I A4 -A i7 ExplanationAi8-Aig List'of symbols and abbreviationsAzo-A2 3 St
4 A2 4 -A 121 Sky diagramsA 122-AI 24 Planet location diagramA125 Moonlight interference diagram; planet/star confusion tableA i z6-A 129 Star recognition diagrams for periscopic sextantsA3o-Ai45 Sunrise, sunset and"civil twilightA 14 6-A 152 Rising, setting and depression graphsA153-AI56 Semi-duration graphs of sunlight, twilight and moonlight, in high
latitudesA157 Fraction of Moon illuminatedA]58-Ai63 Star list, 173 stars (accuracy o'. 1)A164-Ai65 Interpolation of G.H.A. Sun and G.H.A. Aries (accuracy o' i)A 166 Conversion of arc to timeA 167 Polaris tables IA168 Corrections for (total) refraction and Coriolis (Z) tableInside back cover Corrections to marine sextant observations and dome refraction
Figure 3. Air Almanac List of Contents
**NO RESPONSE NECESSARY**
FRAME 4
In the sunrise/set, and twilight tables the times are listed in
Local Mean Time (LMT) for every third day for the specific latitudes
shown at the side of the table. When there is less than a three
minute change between the days listed, simply use the time listed
for the nearest date. If the change is three minutes or more, you
must interpolate for the date required. You must also interpolate
between latitudes, if your latitude of interest is not listed.
Using the sample sunrise table in Figure 4, find the times (LMT) of
sunrise for the following dates and latitudes:
A. 3 December, 50' N.
B. 13 December, 20 ' S.
*," C. 29 November, 59' N.
D. 1 December, 23 ' N.
A144 SUNRISE
November December Jan.LAL
t9 22 25 28 1 4 7 0 6 19 2 25 28 31! 3
NI72 - m 1 m m - m 7 Wm m m70 1013 1038 1o5 M M M 41 " =68 0929 0943 0959 1015 10 32 3050 33612 111 411 M M 411 111 M
66 0900 09 i 09 22 0933 0944 09 55 1004 1 03 1021 102 1032 0 035 10 35 10 34 3030 10 2664 08 38 08 47 o856 0905 09 14 0922 0929 0936 0942 0946 09500 9 32 0953 0953 09531 094862 20 29 37 08 44 o851 08 58 0904 09 10 09 13 09 19 21 24 25 23 24 22
16o 0806 08 13 0820 0827 0833 0839 0845 0850 0834 0837 0900 0902 0903 0903 0903 090258 07 54 0800 0807 t3 38 24 29 33 37 40 0843 08 45 08 46 08 46 0846 084556 43 0749 07 55 o8o0 o8o6 o8.1 15 19 22 25 28 30 31 32 32 3154 34 39 44 0750 0754 0759 0803 0807 08 10 13 135 7 18 19 39 19
52 26 31 35 40 44 49 7 52 07 56 'o7 59 o8o2 0804 08o6 08 07 0808 o0o0 0808S50 07 18 07 23 07 27 07 32 0736 07 40 07 43 07 46 07 49 07 52 07 54 07 56 07 57 07 58 0758 07 5845 07 02 07 Oh 07 10 07 14 17 23 24 27 29 32 34 35 36 37 38 3840 0649 of 52 0656 0659 0702 0705 0708 07 30 07 12 135 17 18 20 23 22 22
3 38 40 43 46 0649 0651 0654 0656 0659 0701 0703 0704 07Oft 0707 0708 0708300 28 30 33 35 38 40 42 43 47 0648 0650 06 52 0653 0634 0655 0656
Nzo O6 o6 13 614 6t6 o6',8 o620 o622 0624 626 0627 629 631 0632 o633 o635 o636Nbo 055605570538 60 0601 0603 0604 0606 0607 0609 o6io o612 0613 0615 6t6 17
0 42 42 43 05 44 05 45 05 46 05 47 05 49 05 50 05 52 0 553 0555 05 56 05 58 05 59 06ooS to 28 28 28 28 29 30 31 32 33 34 35 37 38 40 42 05 43
S053 12 05 32 05 33 05 33 05 12 053 2 05 12 05 13 053 14 05 15 05 17 053 18 0520 05 21 23 25
S 30 04 54 04 53 04 52 04 52 04 51 04 531 04 51 04 52 04 52 04 53 04 54 04 56 0457 04 59 0503 0503
35 44 42 41 40 40 39 34 39 40 40 42 43 44 46 04 48 04 51
40 32 30 28 27 26 25 25 25 25 25 26 28 29 31 33 3645 18 04 135 04 13 04 1 0409 0408 0407 04 07 04 07 04 07 04 08 04 10 04 13 04 13 04 16 04 is50 04 03 03 57 03 54 03 52 03 49 0348 03 46 03 45 03 45 03 45 0346 03 47 03 49 03 51 03 54 03 57
S 52 03 52 03 49 03 45 03 42 03 40 0338 03 36 03 35 0334 03 34 03 35 03 36 03 38 03 40 03 43 03 46
54 43 39 35 32 29 a6 24 23 22 22 23 24 26 28 31 3456 33 38 24 20 0 03 13 03 03 03 30 0 3 (N) 0308 03 9 03 10 03 03 14 17 20So 21 16 03 30 0306 0302 025 02 6 02 54 02 52 01 52 02 52 02.53 02 55 02 57 0300 03046o 03 07 03 o 02 55 02 49 02 45 02 40 0137 02 34 02 32 02 31 02 31 02 32 02 34 02 37 02 40 02 45
FIGURE 4. SAMPLE SUNRISE TABLE
6
NOTE: For the r.ortherrimozt latitudezs on this and similar tables you
will see a number of symbols used. The symbols arid the~lr meanin8gs
are as follo'ws:
Sun conti-nuously above the hor'-zorn.
Sun cc-ritinuousiy be.-ow, --he hoiIzon.
111/ Twilight lasts all night.
ANSWER:
A. 0739 LMIT
B. 0514 LMT
C. 0 8 23 LMT
D. 0624 LMIT
I.7
-'A -
'pj
Ai66 CONVERSION OF ARC TO TIMEo ko o w. ko 0 k:
0 0 400 20 8 o s; 00 240 j6 3001 0 04 62 4 04 12 8 04 191 12 04 a4i 16 04 301 20 04 2 0 042 o8 62 4o8 za 8 08 82 1o8 a4 - 6 3o2 20 2 00
3 0 12 63 412 123 8 1z 183 212 243 i612 303 20 12 3 0124 o16 64 4 16 124 8 16 84 tit6 244 166 3o4 2o 16 4 016
5 o20 65 4 20 125 820 8 5220 245 6 20 305 2020 5 0 20
6 0 24 66 4 24 2a6 8 24 z86 12 24 24616 24 3o6 224 6 0247 o 8 67 4 28 127 6 28 X87 12 28 247 16 28 307 202 8 7 02880 32 68 4 32 128 8 32 188 12 32 4 632 308 2032 8 329 0 36 69 4 36 129 8 36 189 12 36 29 16 36 309 20 36 9 036
10 0 40 70 4 40 130 8 40 190 12 40 250 40 30 20 40 0 0 40
01 0 44 71 4 44 131 8 44 191 12 44 252 16 44 312 20 44 1 04412 0 48 72 4 48 z32 8 48 192 12 48 252 1648 32 2o 48 12 048
13 0 52 73 4 52 133 8 52 193 12 52 253 16 z 313 20 52 13 05
14 o 56 74 4 56 x3 8 56 194 12 56 24 6 56 314 20 56 14 056
25 5 00 235 900 1951300 25 17 00 35 2100 25 100
-16 14 76 5 04 236 9 04 196 1304 17 04 36 21 04 16 04
17 8 77 5 08 137 9 o8 297 1308 257 17 08 317 2 08 27 1o8
18 1 12 78 5 12 138 9 12 198 13 12 258 17 12 328 21 12 iS 1 12
9 x 16 79 5 16 z39 9 16 199 13 16 259 17 6 319 21 16 29 16
20 520 So 5 2o 240 9o20 200 1330 26 1720 320 21 20 20 20
22 1 24 8 5 24 141 9 24 201 13 24 6 17 24 321 2 24 21 24
22 28 82 5 z8 242 9 28 202 13 28 262 17 28 322 2 28 22 5 28
23 1 32 83 5 32 243 9 32 203 1332 263 17 32 323 21 32 23 5 32
24 1 136 84 5 36 144 9 36 204 13 36 264 1736 34 21 36 24 1 36
25 1 40 85 5 40 145 9 40 20551340 26S 17 40 325 21540 2s 1 4026 144 86 544 246 944 206 1344 266 1744 326 2 44 a6 144
27 148 87 548 147 9 48 207 13 48 267 1748 327 21 48 27 14828 1 52 88 5 52 148 9S2 208 1352 a68 1752 38 2152 28 52
29 1 56 89 5 56 149 9 56 209 13 56 269 1756 329 2 56 29 I 56
30 200 90 6 oo O 10 00 10 14 00 270 1800 330 2200 30 200
31 2 04 9 6 04 152 10 04 211 14 04 271 1S 04 331 22 04 31 2 04
32: z08 92 6 o8 Sa Joo8 22 1408 272 180 332 22 08 32 20833 2 12 93 6 12 153 10-12 223 14 12 273 iS 12 333 22 52 33 2 52
34 2 16 94 6 16 zS4 to 36 214 14 16 274 11:6 334 2216 34 256
35J 2 95 6 20 55 10 20 225 14 20 275 18o 335 2220 35 220
361 224 96 6 24 IS6 102 4 2x6 14 24 276 1824 336 22 24 36 224
37 228 97 6 28 '57 to z8 217 14 28 277 1828 337 22 28 37 2 2838 2 32 98 6 32 2s8 0 32 218 14 32 278 1832 338 2232 38 2 3239 2 36 99 6 36 159 5 36 219 14 36 279 t836 339 22 36 39 2 36
40 2 40 200 6 40 26o o40 220 14 40 280 1840 340 22 40 40 2 40
41 2 44 lO 6 44 16 1044 22X 1444 281 844 342 22 44 42 2 44
42 248 202 648 162 1048 222 14 48 82 1848 342 2248 42 2 48
43 2 52 203 652 z63 10 52 23 14 52 283 52 343 22 52 43 2 52
44 2 56 o4 1 6 56 z64 o 56 224 14 56 284 Ii56 344 22 56 44 2 56
45 300 0 7 00 x6S i oo 25 1500 285 590 345 23 00 45 3 0046 3 04 zo6 7 04 z66 1104 226 15 042M519404 346 23 04 46 3 04
47 3 08 107 7 08 167 1 08 227 1508 287 1908 347 23 08 47 3 0848 3-:z o8 7 12 z68 5 12 228 15 12 288 19 52 348 23 12 48 3 12
49 3 s6 109 7 j6 z69 in x6 29 15 16 289 59 16 349 23 x6 49 3 16
50 3 1o0I 7 20 70 1120 230 550 1920 350 23 20 SO 3 20
52 3 24 112 7 24 271 11 24 231 15 24 292 19 24 351 23 24 52 3 24S2 3 28 112 7 28 172 it z8 232 15 z8 292 19 28 352 23 28 52 3 28
53 3 32 113 7 32 173 11 32 233 15 32 293 19 32 353 23 32 53 3 32
* 54 3 36 224 1 7 36 174 I1 36 234 15 36 294 19 36 354 23 36 54 3 36
55 3 40 225 7 40 175 It 40 23 15 40 295 19 40 35S 23 40 55 3 40
56 3 44 iz6 7 44 176 11 44 236 1544 2 9 44 356 23 44 56 3 44
57 3 48 .17 7 48 277 15 48 237 15 48 297 19 48 357 23 48 57 3 44s8 3 52 18 "7 52 178 11 52 238 15 52 29 19 52 358 23 52 S8 3 52
59 3 56 119 7 56- 179 15 5
6 239 15 56 29 1956 359 .23 s6 591 3 56
The above table Is for converting expressions in arc to their equivalent in time; its main use in this Almanac is
for the conversion of longitude for application to L.M.T. (added if w.est, subtracted if east) to give G.M.T., or vice v'ersa,particularly in the case of sunrise, aunset, etc.
Figure 9 Con' 'ersion o'f Arc To Time Table
-. '7"
0 .!&z I
FRAME 5
The sunset, and the morning and evening civil twilight tables are
read just like the sunrise table. Remember, these times are the
Local Mean Time (LMT) for the event, and can be converted to either
Local Standard Time or Universal Time (GMT) by using the Conversion
of Arc to Time table (Figure 5) of the Almanac. Notice that the
conversion factor in the Arc to Time Table is simply 1 of longitude
• 'equals 4 minutes time. The first six columns of the table are the
- "hours and minutes conversion, while the last column is the minutes
.. and seconds conversion. For example, (using Figure 5) we will find
the time difference corresponding to a longitude difference of 147-
37'. located 1471 in the third column. you will find that 1470
equals 9 hr 48 min and the 37' = 2 min 28 sec. add them together:
9 hr 48 min+ 2 min 28 sec
* 9 hr 50 min 28 sec
In computing these times, you can round off to the nearest minute.
1470 37' is 9 hr. 50 min.
Find the time difference corresponding to the following longitude
differences. Round off the time to the nearest minute.
A. 760 17'
B. 14" 55'
C. 1220 39'
D. 1200 16'
* ANSWER:
A. 5 hr 05 min
B. 1 hr 00 min
C. 8 hr 11 min
* D. 8 hr 01 ain
FRAME 6
Using the Conversion of Arc To Time Table to convert LMT to GMT is
fairly simple, since you are simply converting from your longitude
position to the 0' Meridian. First, convert your longitude to time;
then, add this conversion to LMT if your longitude is west, or
subtract it from LMT if your longitude is east.
For example, here is the conversion of 0630 LMT to GMT for Langley
AFB, Va, which is located at 76' 21' W.
760 = 5 hr 04 min+ 21'= 01 min 24 sec
t hr 05 mmn 24 sec = 5 hr 05min
6 hr 30 min LMT+ 5 hr 05 min(added; longitude is west")11 hr 35 min = 1135 GMT
Convert 0630 LMT on 18 May to GMT for the following stations:
A. Fulda, Germany 90 41' E.
B. Osan, Korea 1270 02' E.
C. Brasilia, Brazil 47- 56' W.
D. Amberley, Australia 152- 43' E.
ANSWER:
A. 0552 GMT, 18 May
B. 2202 GMT, 17 May
C. 0942 GMT, 18 May
D. 2019 GMT, 17 May
10
I,
0.
I ~ ~ ~ ~ ~ % % ~ V -' :-~*
a.- Frame 7
The easiest way to find LST using strictly the Air Almanac and
nothing else is to simply find GMT, as you did in Frame 6. and apply
the correction to standard time which is indicated in pages A20-A23
- of the Air Almanac. NOTE: Standard Time corrections are also located
in the Flight Information Publication (FLIP) pertaining to your Area
of interest. The Standard Time zones are based on specific Standard
Meridians which are normally spaced at 15' ' of longitude, either
east or west, beginning with the Prime Meridian (0,7 ; however,
either geographical considerations or local law can be used to
adjust Standard Time. Because the LST for your location must be
figured using The Standard Meridian for your time zone, which is not
necessarily the one closest to it. you must :nsure that the proper
correction is applied. e.g. In eastern and western Kentucky there
'as are 2 different time zones; Newfoundland has a Standard Time
correction of 43 hrs 30 Minutes etc.
if you do know the Standard Meridian that is used for your time zone
then you simply apply the correction as determined from the Arc to
Time Table to the Local Mean Time listed in the Sunrise/set tables.
Add the correction if you are west of the Standard Meridian and
subtract the correction if you are east. This correction will
p- normally be less than 1 hour, remember, because Standard Meridians
are normally 150 apart, and 10 of longitude = 4 minutes time. (See
the map on page 49)
P Let's use Langley AFB, VA as an example of this last case. Langley,
which is located at 37 ' 05' N., 76l 21' W. is :n the Eastern
Standard Time Zone which uses 75, West longitude as it's Standard
Meridian. The LMT for sunrise on the 18th of March is 0608 LMT. What
time does sunrise (LST) occur at Langley 9 Langley AFE, VA is
,- located 1' 21' West of the Standard Meridian and this equates to a
correction of 5 minutes (1'- 21' = 5 min 24 sec which rouunds off to 5
min). The correction added to the published LMT, ind:c Ates 3 sunrs=
time at Langley AFB on 18 March of 0613 LST.
'a
Find time of sunrise (LST) for the following stations using a time
of 0630 LMT:
Standard Meridian
A. Fulda, Germany (9-' 41' E.) 15*' E.
B. Osan, Korea (127" 02' E.) 135- E.
.. Brasliia. Brazil (47' 56 W.) 45 ° W.
D. Amberley, Australia (152"' 43' E.) 150' E.
ANSWER:
A. 0651 LST
B. 0702 LST
C. 0642 LST
D. 0619 LST
2
*1
9
o1pI12
d',!~
FRAME 8
Some locations use Daylight Savings Time (LDT). For an indication of
which countries use LDT see the Standard Time tables pp. A20-23 or
the applicable Flight information Publication for your area of
interest. To convert to Daylight Savings Time (LDT) you just add 1
hour to the LST.
7sing the following Figure (Figure 6) and the Conversion of Arc to
T:me Table (Figure 5) , find the LDT of sunset on 11 September for
the following stations:
Standard Meridian
A. Fulda, FRG. (50' 33' N. 9' 41' E.) 150 E.
B. Langley AFB, Va (37 ° 05' N. 76- 21' W.) 75- W.
C. Brasilia, Bra. (150 51' S. 47" 56' W.) 45 ° W.
* D. Amberley, Aus. (27c 39' S. 152- 43' E.) 150" E.
SUNSET
Lat. August September Oct.15 18 21 24 27 30.2 5 8 X 14 17 20 23 26 29 2
N72 21 45 21 27 2' 0 20 4o 20 2 0 1T, 1954 1938 19 22 1906 18 50 I834 18 19 1803 1748 1733 17 17
70 2 13 20 -57 -0 41 25 20 10 19 56 41 27 12 18 58 44 30 16 02 49 35 21
68 2'o io 31, 23 20 10 19 50 44 31 IS 1905 52 39 27 14 02 49 36 24
66 3- 20 0 u9 19 57 45 34 22 10 18 59 47 35 24 12 01 49 38 26
64 1 2007 1957 41 31, 25 15 1904 54 43 32 22 11 00 50 39 29
62 2' 19 54) 47 37 .8 8 09 18 59 49 39 29 19 10 18 00 50 40 30
N6o 1955 1947 1938 1029 1921 1912 1903 1854 1845 1836 1827 I817 18o8 1759 1750 1741 1732
58 V1 39 31 23 15 0( 18 58 50 41 33 24 16 07 59 50 42 34
56 3.. 1 24 17 0'9 Igo 54 46 38 30 22 14 06 58 51 43 35
S4 -' -, 5 i, 11 04 I87 50 43 35 28 21 13 06 58 51 43 30
52 25 2,) 23 07 190 53 47 40 33 26 19 12 05 58 51 44 37
N5 1921) 121)4 1go 1q02 I5t , IS.5 18 44 1837 1831 1824 1818 1811 1804 1758 1751 1745 1738
45 1) uM 1,903 I8 5S IS 53 48 42 37 31 26 20 14 09 03 57 52 46 40
40 I4 .5 K -5.1 52o 45 111 3i
) 31 26 22 17 12 07 02 57 52 47 42
35 4') 4' 42 38 34 32 26 22 18 14 10 05 01 57 52 48 4430 4- 39 31
' 33 29 20 22 19 15 11 08 04 18 00 56 53 49 45
N 20 S 1" I 2117 1825 1823 1820 2818 1815 1813 18I10 1807 1804 1802 1759 1756 1753 1751 1748
*w to IS127 2i 14 22 22 09 07 05 03 18 02 18 00 58 56 54 52 30
0 I1 08 1S107 1807 IS(10 ISo 1 28-4 1803 1802 1801 1800 1759 1758 57 5' 55 54 53S 10 175i 17 27517 258 17517 58 17 58 1757 1757 1757 57 56 56 56 56 56 5520 47 48 49 50 50 .51 52 52 53 54 54 55 55 56 57 17 57 17 58
S3o 1731 27.7 1739 1740 1742 1743 1745 1747 1748 1750 1751 1753 1755 1756 1758 1800 1801
35 211 3 33 35 37 39 41 44 4 48 50 52 54 57 17 59 01 04
40 20 z 3 29 32 34 37 40 43 46 48 51 54 57 18 00 03 0
s15 Is 2 1 S 2 L 2 "5 29 32 36 39 43 46 50 54 57 01 05 08
50 17 '1 0,5 0m) 13 I8 2 27 31 35 40 44 49 53 58 02 07 12
S 52 V- , -700 2705 1709 17 14 17 19 1724 17 29 1734 1738 1743 1748 1753 17 58 I8 03 18 o8 18 13
54 ',2 0, 55 17 00 05 1 20) 21 26 32 37 42 47 53 58 04 09 15
56 45 49 It,55 2702 n6 12 18 24 29 35 41 47 53 58 04 1o 16
58 37 43 49 22 55 1702 08 24 21 27 33 40 46 52 59 05 ,2 18
S 6o It' 29 It'36 Io42 1249 1656 2703 1710 1717 1724 1731 1738 1745 1752 1759 18o6 1813 1821
,-Figure 8. Sunset Table.
130"
.L ,r
ANSWER:
A. 1946 LDT
B. 1920 LDT
C. 1807 LST Why not LDT? Because it's not summer in the
,S D. 1740 LST southern hemisphere! Gotchal' i I
PROGRESS CHECK
FRAME 9:
Using the extracts from the four sun-event tables provided below and
the Conversion of Arc to Time table in figure 5, find the Local
Standard Times for the start of morning civil twilight, sunrise,
sunset, and the end of civil twilight on 1 January for the following
stations:
A. Langley AFB, Va (370 05' N. 76- 21' W.)
B. Amberley, Aus. (270 39' S. 152- 43' E.)
AM Twilight Sunrise Sunset PM Twilight
A. _ _ _ __ _ _ _ _ _ _ _
-J B.
. 1 D. Dec.;
tat. D Lat.30 1 30 2 30 2 30 a
km% .JJ km b Inm k m ,, m I
S'-. 117; 1048 1040 N12 " "172 - - 172 13 0 2n% 70 095 09 48 70 - 70 -- 70 14 f3 14 .O4.68 09 I8 09 10) 63' 68 - - 68 14 47 14 51
66 08 54 08 52 66 to 3t toz6 64 13 34 13 4- 66 15 1! 15 M,64 35 34 64 oq 51 0949 64 14 14 14 10 64 30 3562 19 IS 62 24 2 6a 1441 1441 62 4t) 5 50
W60 @806 0805 N60 0903 0902 N6o 15o .of)60 1559 1603
- 58 07 54 0754 8. 08 46 845 58 20 23 58 lb 11-4 56 44 44 6 32 31 S6 34 37 26 , 4
36 35 54 19 19 54 46OiLj in 54 30 3352 2S 28 52 08 08 o8 Sa 5 5-3 to on 52 38 41
N 5 * 2 07 20 S~O 07358 0758 NSO rr 1)0, if)1 toN50 16 45 1) 4-1O 45 0704 0705 45 38 38 45 27 jo 45 17
o t 704
40- ° 51 0652 40 2a 14 40 44 10 41- 40 Ii 17
31 40 -,40 35 0708 0708 35 Iyb 5A700 35 V,) 2
30 29 30 O I6 55 o6 6 30 1710 1, 30 36 38
K 20 06 10 o611 26 1o2634 0633 N120 1731 1733 N 20 t755 1757
10 05 33 05 54 MiW 04,16 17 11101749 17 51 N 1O I 12 I 1r140 3 38 0 05 59 o600 0 So 1808 0 Z9 30S to 05 19 20 a t 42 05 43 S to 94 '5 S to TA 47 18 48
20 04 58 0500 23 25 20 1842 I843 20 1907 r o 8S 30 04 33 04 36 S4 $ '05o o o 3 3 10 1904 1905 S 30 Iqp~ 32 9 3
35 18 29 35 04 4Sq -4 50 .3$ 17 IS 3S 1,) 47 19 47
P"'404 o003410 33 31, 40 321 32 4 2o005 200o540 '' 4 0 0 4 03 z4S 04 15 04 18 45 19 50 19p jo 4S -10 17 17
. ,S 53 03 43 03 46 S 3J 1 -o ,42 lo , I 2 t
S54 i37 40 54 30 34 54 34 34 S4 Ad ,8 756 021 C5 o02 e9 56 t6 to 56 1o 49 20o 47 56S it 5o It 4S1
58' 09 46) 093' So 0300 03o04 58 It1 n5 -11 n3 So 1.1 is ,2 15S Go601 0o0 ofo08 S 60 o0 40 o-1 44, S 60 It ,$ It 43 S 6 "13o03 2, 57
Figure 7. Sun Events Tables1 14
'-4,
N 1%
"ANSWER;
A. 0650,0719,1659.1728
B. 0430,0457,1849,1915
(Answers within one minute of these can be considered correct
because of the interpolation involved.)
ONE FINAL NOTE: Nautical and Astronomical Twilight times are not
provided in the Air Almanac, but can be estimated by using the time
difference between sunrise and start of civil twilight, or sunset
and end of civil twilight. Add the difference to end of Civil
Twilight to get the end of nautical twilight; add the difference
again to get end of astronomical twilight. For corresponding start
of twilight times, subtract the difference from Starts of civil
twilight etc.
So far, you have learned how to find times of sunrise/set, and the
twilights between the latitudes of 72" North and 60' South. Although
* the Air Aimanac does not cover the area south of 60 ° South latitude,
it does cover the area north of 72' North. The next few frames
will explain these graphs.
**NO RESPONSE NECESSARY**
15
FRAME 0:
An example of a Semiduration of Sunlight Graph is shown below.]
SUNLIGHT AND TWILIGHT A153
12 10 00 12500-J NRS - 12'141 121141 __II_ _ _ _ _11 _ _ _ _ N85
• 4,. ,EMIOURRTION OF SUNLIGHT
NO NSOSUN BELOW SUN ABOVEHORIZON HORIZON
N75 -N75
0 212- 6N
1 16 1 16 1 1 ' 11 I 1 1 16
J:NUART FEBRUARY MARCH APRIL MAT JUNE
Figure 8. Semiduration of Sunlight
The graph covers a six-month period; the months are indicated across
the bottom. Every fifth day there are tick marks; they are depicted
along the top and bottom of each chart. The sides of the graph
, indicate latitudes from 65' North to 9O0 North. Across the top you
+.'so see time in hours and minutes. e.g. 12H 14m .... etc. These
imes are the times of meridian passage which can be read to the"I
nearest minute for each day. Meridian passage is the time that the
sun passes your iong.tude; i.e. the time of apparent noon during
each 24-hour period. The skewed lines on the graph are the
semiduration lines. They show the number of hours of sunlight that
will occur before ar.J after the meridian passage--hence the term
s-mid'.iraton". "Sun below horizon" and "Sun above horizon" are
self-explanatory. in the regions of the graph that you find
dlicfiult to interpret, the phenomena themselves are generally
speaklnrg. uncertain.
16
'S " , 5 , . .,,. ,- ,.-,.- .. '", ,"" ",.", ., . , .,", .. , .. - - -
*FRAME 10 (contd)
Here's an example of how to read the graph to find the sunrise/set
times on I March at S0 North (using figure 8): first, follow the
I March" line to the top of meridian passage. An "x" has been
placed there, between 12h 14m and 12h 10 m, or approximately 12h
12m. Thus, the meridian passage time on I March for any meridian
is 12h 12m LMT. Next proceed along the line to your latitude of
interest (80" N.). An "x" has also been placed at that point. This
point lies approximately on the skewed line labelled "3h.
Therefore, the semiduration of sunlight on 1 March at 80' North
latitude is 3 hours. With 3 hours sunlight before and after the
meridian passage time you can now compute the sunrise to be 0912 LMT
- ,2 - 3h = 0912) and he sunset to be 1512 LMT (12h 12.m + 3h = 1512)
Ncw it's your turn' Use figure 8 and find local mean times of
* sunriseiset for the following dates and latitudes. (A clear straight
edge will be useful here.)
Sunrise Sunset
A. 16 April, 80', N.
B. 10 February, 70- N.
C. 15 March, 78" N.
D. 1 April, 73" N.
ANSWER:
A. Sun continuously above horizon.
S0854 MT 1534 LMT0639 LMT 1739 LMT
. 0449 LMT 1919 LMT
17
% 0 %
4P 4
FRAME 1 1
N80 08
N85CONTINUOUSLTWILIGHT
N75 OR SUNLIGHT N75
N70 *2 4 8 N70
1-- 16 1 16 1 16 1 16 1 16 1 16 1JANUARY FEBRUARY MARCtH APRIL MAT JUNE
Figure 9. Duration of Twilight Graph
The Duration of Twilight graph (Figure 9) is similar to the
Semiduration of Sunlight graph; but notice that the skewed
hour lines are not smoothly curved as ,,hey are on the sunlight
graph. They are kinked in places. These kinks, if superimposed onto
- the corresponding sunlight graph, would fall on the "Oh" line, and
along this line the sunrise may or may not occur. We have drawn a
dashed line in the example which enables us to define the four areas
* in the chart as follows;
Area A - No Twilight or sunlight. In this area the sun never gets
within 6" of the horizon.
Area B - This is the area where the sun is continuously below the
horizon but does get near enough (within 61) to the horizon during a
portion of the day that there is twilight. The value determined in
this region of the graph is actually the interval between the
beginning of twilight and the time of meridian passage.
Area C - This value when applied to the time of sunrise (-) or
sunset (+) gives you the amount of available twilight
Area D - Continuous Twilight or Sunlight - self-explanatory.f
18
I ,
FRAME 11 (contd)
Let's work an example to show 3ust how this graph works (see figure
8) on a worst case scenario. We want to find out the amount of
twilight available on 11 February at 77: North (Point x' , As you
S.can see it sits in the he-Lrt of the t-ansition zone between sunr-se
and no suinrise. The first thing we do ;s draw a jotted line
connecting the kinks in the hour lines. Point x" is located between
the -3h" lines, so we must interpolate between the 3h and 4h lines
* to get a usable value to work w-th. It is located about 2/3 of the
way (2/3 of 60 min = 40 minutes) , so the correct value of twilight
is 3h 40 rin. The sun may or may not rise completely above the
horizon on this date at this position. A good ii1ht forecast for
this date would be 7 hrs 20 minutes of twilight, with the
possibility of the sun actually being visible for a few minutes
around the time of meridian passage.
Now, you work a few examples. Find the total duration of twilight
(using figure 9) for the following dates:
A. 16 January, 78' N.
. B. 1 February, 731 N.
C. 31 March 80" N.
- D. 16 February, 80' N.
ANSWER:
A. No Twilight or sunlight.
B. 6 hr 00 min.
C. Continuous twilight or sunlight.
D. 6 hr 40 min.
FRAME 12
The Duration of Twilight (Figure II) graph is read in conjunctcon
with the Semiduratiorn of Sunlight graph (Figure 10). Notice that the
twilight graph does not have the times for meridian pascag on it.
However, since the twilight graph is always placed directly
underneath the sunlight graph in the Air Almanac, the merldian
-: passage time can be obtained with a straightedge, if necessary.
,*
• 19
. , .. ." .. . 'r " e.. ...-.'. ' v .. '..,. . .
- - ---- --- - -- uwr---w W7-~ ' -~t'- - WV WV WT 4 V~W U.UnR 70a~u 1x',-', v 1w- -VV-.r
* 2'V 12 Nr 12'14' 12,14 11 12'05' 12'00"
MI SU ABOVE
11 'i, O IO
N71)
JANI'AIY FEBIRUARY MARCH APRIL
Figure 10. Semiduration of Sunlight
CONT N~OW., TWII.AGH'fN, stNI. ; I'' (1R SUINLIGHT
Nso
N75 ____
N~u
1 1;1 16 1 16 1 161JA%1 AHN K I<t ItVA RY MARC H APRIL
Figure ii. Duration of Twilight
20
0
,nh.
FRAME 12 (contd)Let's recap the steps for findin8 the times of sunrise/set, and
twilight times in the 5 to 90' North latitude region.
F .r. id the timp of meridian passage.
2 .Find the Semiduration cf Sunlight.
-. . -7v the value to the meridian passage time for sunrise
{subtract) and sunset (add).
4. F:nd. the duration of twilight.
Apply the value to the sunrise time (subtract) for begin time of
morning twilight and to the sunset (add) to obtain the end of
evening twilight.
6. Remcaember, even if there is no sunrise or sunset there can still
be ;w-l1:ht. Subtract the value from the meridian passage time for
beginning time; add the value to the meridian time to compute the
*end time of twilight.
Now let's find the local mean times (using Figures 9 and 10) for all
of the events listed below:
BEGIN TWI SUNRISE SUNSET END TWI
A. 18 February, 75'' N.
B. 16 April , 78 N.
C. 1 March , 84. N.
D. 1 April , 75- N.
ANSWER:
A. 0744, 0924, 1504, 1644
B. Continuous, 0200, 2200, Continuous
SC. 0722, None, None, 1702
D. 0304. 0444, 1924, 2104
N. (Twilight times within 15 minutes of our answers may be considered
N"- as correct)
S
21
0v J 2
FRAME 13
To compute the sun's azimuth and elevation at a specific time and
place, you must use the daily pages and Interpolation of GHA Tabie
- in the Air Almanac.-A
o You will need a hand-held calculator; there are numerous p o.r-ms
available for both the TI-59, and HP 41 calculators. Prcgrams are
also being developed for microcomputers. See AWS TC 8X/001 for a
,*~listing of available programs. They are simple to use; just fill in
the values from the Air Almanac, as directed.
NOTE: The time of sunrise/set is given as the time the observer on
earth would first see the upper edge of the sun along the horizon.
However, solar altitude is determined by the position of the sun's
center not it's edge. Consequently, the time that the solar altitude
equals 0' may not exactly match the time of sunrise/set.
***NO RESPONSE NECESSARY***
- FRAME 14
You should now be able to calculate sunrise/set, and twilight times
for any point North of 60 ° S. The next few frames will teach you how
to find moonrise and moonset times for the same area. Their-"
*- organization in the Air Almanac is the same as for sun times; there
are tables for latitudes between 72 N. and 60" S. , and graphs for
latitudes between 65" and 90" N. Before discussing how to read these
tables and graphs, let's look at some of the reasons that make them
necessary.
**NO RESPONSE NECESSARY**
FRAME 15
The moon revolves around the earth once every 28 days or so. The
phases of the moon are caused by its position in its orbit. Using
figure 12 you can see how the moon is viewed from earth, by looking
at the outer figures at each position. From space the moon can be
22
%
-~ I I ia...................i i-- I I 3 ~~.......ur ......
ow 01,, -
L4.1:::,,"
I I
...... .....
16-z M
:J' Is.... .... ....
%0% S
....-... .. ..
FRAME 15 (contd)
seen as half-illuminated at all times (the inner figures).
The 24 hour clock face around the earth illustrates to you how you
can obtain a rough estimate of the times of moonrise and moonset by
the phase of the moon. Look at the full moon portion of the diagram.
which is adjacent to 0000 time on the clock face. The full moon
crosses the meridian around midnight. Imagine that you are at a
* point on the right edge of the clock-face earth. As this point turns
counter-clockwise (direction of the arrow), the full moon becomes
visible as you approach the 1800 position. Moonrise occurs at about
1800 for a full moon. Continuing around the clock face, the moon
would recede from your view at about 0600. Moonset occurs around
0600 for a full moon.
In other words, the moon is *full* because it is located on the side
• of the.earth opposite the sun. We tell time on earth by our position
in the daily rotation of the earth with respect to the sun. A full
.' moon can only be seen from earth from about 1800 to 0600 because of
the mechanics of the situation.
EXCEPTION: In extremely high latitudes, the mechanics get more
complicated due to the axis tilt and other irregularities that will
be dealt with in succeeding frames.
The other phases of the moon are only visible between certain hours
for the same reasons.
.5, Using Figure 12, state the approximate times of moonrise and moonset
5-. for:
MOONRISE MOONSET
A. Third Quarter Moon
B. Full Moon
C. First Quarter Moon
*suesime24
0-
'. .5. 5... -.. 5- * -K.-55.S. Y-U*Il -, S
zz005
o 0P 0
0 0
zFr 0w
a
.... .... ... Co
0-...... ..-.. .. .. .. .... .. .... .............. ..... .... ..
0.0L.......-. ............. .. .. .. .. .. ..... ..
.......... . ... 4
. . . . . .. . .-..... ..... . ...
-J 7
. .... .... ...
....5 .
.... .. .... on " q~
* ANSWER:
A. ;-000 12C00
B I 3 I 0 C) If0 9'0p)
"wo -artcr c.]. .- nrlse -ncf moor, et times to change frrm
z:a'.'. ...." , r the moon orbital speed and its orbital angle.
t . see if we car exr-. aln that more fully. Assume that both the
- moo. s orbttal spe -d .ind angle are constant. This would result from
the :ieaiizei slt:.:ation of the moon being -n a circular orbit
d:rectiy above the equator. The moon orbits the earth once every 2.
d.'.s- th:s equates to 1/29: f its orbit being completed every 24
. ours. 1/28 of 24 ho.urs equals approximately 51 minutes. Now, with
• he mon making a circular orbit in the same direction that the
earth turns this would mean that the moonrise/set would occur about,
151 minutes later each day (See Figure 13).
Th.: exaggerated illustration in Figure 12 looks down -)n the earth at
* rh. North Pole with the equator the edge of the circle. The earth is
rotatirng clockwise and the moon is orbiting in the same direction.
Therefore, each day (24 hours) when a standard meridian on earth
makes a complete revolution, it must continue on for 51 more minutez
- for the moon to come in view. Consequently, moonrive occurs 51
minutes later each day.
Beause of it's orbital speed, the moon would rise about 51 minutes
later each day if the mccri's orbit was:
A. Fipti:al and inclined to the eqiatcr.
B. -ir:ular, arid directly above the equator.
I
S,,
,S.
-S.
26
NN
UL
N
S5
Figure 14%. ECLIPTIC AND ORBITAL PATH OF MOON RELATIVE
TO EQUATORIAL PLANE OF EARTH
2.7
A. Circular and directly above the equator.
FRAME 17
With the moon in a circular orbit above the equator, moonrise would
occur about 51 minutes later each day for all positions or the earth
-except the poles). However, the moon is, in fact, neither in A
circular orbit, nor does it orbit directly over the equator. What
does this mean' Well, for any one position in the low and mid
latitudes the moon does rise about 51 minutes later each day, but
the difference along a single meridian longitude can vary more than
6 hours between 60 S. and 72 ' N. This is mainly because of the
moon's orbital angle. Rather than orbitting directly above the,
equator the moon moves both north and south oe the equator dur~ng
each orbit. When the moon is in the northern part of its orbit, it
can be seen earlier by northern observers than by those to the
south, and vice versa.
Earlier, you learned that the sun moves 23 1/2' north and south of
the equator during the course of a year because of the earth's axis
tilt. The apparent path of the sun across the sky is called the
ecliptic. The ecliptic crosses the equator at an angle of 23 1/2 .
The moon's path crosses the ecliptic at an angle of 5" . The point
where they intersect moves around the ecliptic in a little more than
18 years, causing the angle at which the moon crosses the equator to
vary between 18 I/2' and 28 1/2 . These apparent paths are
illustrated in Figure 14.
*Moonrise varies by latitude along a particular meridian of longitude
mainly because of the moon's:
A. orbital speed.
B. orbital angle.
* C. elliptical orbit
D. circular orbit.
L 28_~ %"
2 IN
ada
S.02
a.,a
a. a
0 w a
mco-
MAU
.... ... ..... .
....... . C
r :4. e.- f -. ht
5A-
w r, -i .w ':' tZS r ' e hZ :A jty' . a:.
r - - . - Jr ~ i P5 I c :-v rm A' Frer :'
r!ar- -T -
4
3 ~ ~ ~ O U1W LPtt'. .. a .,.4:1U. 14 Ac u .L
ANSWER :
Spe ,: Ar.lIe either ,_:d._r
* The azi. ew faneE h.&,,e --w% - t:.at a t ihough you ca:, 4et .i rouu ,
a .- f -hm ,
A a
v. r a. 1 7 , " ' - : . , t A L M -t [.AI i1.,L;.'!, n,: L~ he : / 2 ,r : -A r ' +,:-- A.' ,:,r t ! r.s + Ix e
- a. - J. n-. . - w I - p s.r
w -: --over ap .n "-.-, r: p ,r . - ', 7r f e A.
" " • ::' . .. : .. : t. _ .. i -. : ..he Almanac seemrs . I :ttle
S I-e , . ;'T u .hc,." d n-w Y av. sr.)e a r ecu 1 at, c f r the
" ": ca .,.5 .:-'I .v d N:E Although t r q i esp:.lu t n
', t s prv:ded ri th1e A r AI -. an- . Se,
. *- the F:-:.t + a e nurnber
*-' NC RESPONSE NECESSARY****
:e1ween 60 S. and 7 I N fro the Ar
Am.Rngc ".'.u must use -hree different sets of tables. They are:
. M..nr.:se, onset data (Daily Pages).
* ... erp,-at:cn of V-Drize, Moonset for Longitude.
: . "wv ~~rv r i of Ar. -,,- Time Table.
-... ons--t anrd rno-nrise tables are found -,n the upper right hand
-r:.er of each da:iv p-.e. They alternate, w:th moonset on the left
and mDonrlse or, the ', ght page of each opening. The next two
er' (F:-ures 16 nrid 17) are excerpts of complete daily pages with
s-? e ind ,cr el ta :!es circled.
**NO RESFONSE NECESSARY**
31
0
A%4.~~ %% .%. N N ~
%".
(DAY 325) GREENWICH A. M. 1987 NOVEMBER 21 (SATURDAY) 649
GMT1 0 SUN ARIES VENUS-3.9 MARS 1.7 JUPITER-2.8 0 MOON Iat Moon. Dif(U T) GHA Dc GHA Y' GHA De. GHA Dec GHA Dec GHA Dec fse
00 00 183 35 4 S19 448 59 27;8 159 07 S24 0' 213 13 $I0 01 39 42 N 6 44 188 19 S22 54 ,, ,10 IH6 054 449 61 582 161 37 215 43 42 12 190 43 56 72 m20 188 354 450 64 286 164 0b 218 13 44 43 191 08 58 7030 191 05 4 45.1 66 590 16b 36 220 44 47 13 195 32 22 59 b0 mm40 193 353 45.2 69 295 16
9 06 223 14 49 44 197 57 23 016 i
50 19b 053 452 71 59.9 171 34b 225 44 52 14 200 21 03 66 13b4 10 35 '
01 00 198 35 3 519 45 3 74 30 3 174 Oh S24 08 2?8 14 S10 01 54 44 N 6 44 202 45 S23 04 62 09 48 b910 201 053 454 77 00.7 176 36 230 44 57 15 205 13 0620 203 35.2 45.5 79 31 1 179 05 233 14 59 45 207 34 08 60 0917 5630 206 05.2 456 82 01.5 181 35 235 45 62 lb 20q58 I 0 08 54 51
40 208 35.2 457 84 31.9 184 05 238 15 64 4b 212 23 11 56 08 36 4650 211 052 458 87 02,3 186 35 240 45 67 17 214 47 13 52 08 07 44
0200 213 35.1 519 45.9 8932.7 18905 52408 243 15 SI002 6947 N 644 21712 S23 15 50 0755 4210 216 051 460 92 032 191 35 245 45 7? 18 219 36 lb 45 07 31 4020 218 35.1 46.1 94 33.6 194 04 248 15 74 48 222 00 18 40 07 2 330 221 051 4b.2 97 040 lqb 34 25045 77 19 224 25 20 3 06 56 3640 723 35.0 4,.3 99 344 199 04 253 16 79 49 226 49 2230 06 42 3450 2.6 05.0 4b4 102 048 201 34 255 46 82 19 229 13 23
03 O228 35.0519465 104352 20404 52408 25816 51002 8450 N 6 44 231385232520 Ob 19 32
10 231 05.0 466 107 05.6 206 34 260 46 87 20 234 02 27 10 0559 3020 233 349 46.7 109 36.0 209 04 263 16 89 51 236 26 28 0 05 40 2830235b04 9 -4b,7 112 064 211 33 2b5 46 92 21 238 50 .3Q
0 O22 7
40 2'8 34) 4b.8 114 3b.8 214 03 2b8 lb 94 52 241 15 32 20 05 02 25
50 241 049 469 117 07.3 216 33 270 47 97 22 243 39 33 30 04 39 2335 04 26 21
0400 243 348 519 470 119 37.7 219 03 S24 09 273 17 S10 03 99 53 N 6 44 246 03 523 35 40 04 11 20
10 246 04 8 47 1 122 08.1 221 33 275 47 102 23 248 28 3720 248 34 8 47.2 124 38.5 224 03 278 17 104 53 250 52 38 45 03 53 1830 251 048 473 127 08.9 226 33 28047 107 24 253 16 4050 0331 15
*40 253 34.7 47.4 129 39.3 22902 283 17 109 54 255 41 42 52 03 20 1350 25b 047 47.5 132 09.7 231 32 285 48 112 25 258 05 43 54 03 09 12
0500 258 347 S19 47 b 134 401 234 02 524 09 288 18 SO 04 114 55 Nb 44 260 29 523 45 56 02 55 10
10 261 04 7 47.7 137 10.5 236 32 290 48 117 26 262 53 46 S8 07 40 0620 263 346 478 139 410 239 02 293 18 119 56 265 18 48 60 02 21 03
30. 2t 046 479 142 11.4 241 32 295 48 122 26 267 42 5040 2(,8 346 480 144 418 244 01 298 18 124 57 270 06 51
50 271 045 481 147 122 246 31 300 49 127 27 272 31 53
06 00 273 34.5 S1948 1 149 42,6 249 01 524 09 303 19 510 04 129 58 N 6 44 274 55 S23 55 mon-s P. . A
10 276 045 48.2 152 13.0 251 31 305 49 132 28 277 19 56 A C A CSI o t20 278 345 48 3 154 43.4 254 01 308 19 134 59 27943 58 0 ,30 281 044 484 157 138 256 31 310 49 137 29 282 08 23 5940 283 344 485 159 44.2 259 00 313 19 140 00 284 32 24 0150286044 486 16214.7 26130 31549 142 30 28656 03 0 54
59 3407 00 288 144 519 48 7 164 45.1 264 00 524 09 318 20 510 05 145 00 N 6 43 289 20 S24 04 58 33
10 28104 3 488 167 15.5 266 30 320 50 147 31 291 45 06 12 5 3220 724 14 1 489 169 459 269 00 323 20 15001 29409 07 16 57330 ,"' 04 3 490 172 lt.3 271 30 325 50 152 32 296 33 09 19 5840 298 34 3 49 1 174 46.7 274 00 328 20 155 02 298 57 10 22 3050 301 04. 492 177 17.1 276 29 330 50 157 33 301 22 12 2 4 6 29
08 00 1 03 147 519 49 3 179 47.5 278 59 524 10 333 20 510 06 160 03 N 6 43 303 46 524 14 26 6 28
10 10 6 042 494 182 179 281 29 335 51 162 34 306 10 15 28 63? 04, Jh 34? 495 184 483 283 59 338 21 165 04 308 34. 17 30 2630" 311 14 1 49 ' 187 188 28629 34051 167 34 310 58 18 32 5 6 25401 1j 4 1 49 6 189 492 288 59 343 21 170 05 313 23 20 34 9 2450i 316 041 49 7 192 196 291 28 34551 172 35 315 47 21 36 23
36 47 22Oq 00 4!H 14 S19 498 194 50.0 293 58 524 10 348 21 510 06 175 06 N 6 43 318 11 524 23 37 6B', . 49" I37 204 29b 28 350 52 17736 32035 25 4b 21
'),i 4., 40 500 199 508 298 58 353 22 180 07 322 59 2f 40 45 70 2031 '. 04 SO 1 202 21 2 301 28 355 52 82 37 325 24 28 42 4 19401' .4 4 5021 204 516 303 58 358 22 185 07 327 48 29 43 72 8547. 4 50 1 207 220 30628 0 52 187 38 310 12 31 42 7 1II ~45 7
0'2 ( 4' 44\ 119 504 709 52S 308 57 524 10 3 22 sic 07 190 08 N b 43 332 36 524 32 46 4 1I' 14 * 50', 212 229 311 27 5 53 112 39 335 00 34 47 75
. l I , ')1) 214 533 313 57 8 23 lq5 09 337 25 35 49 141 1 . H. , 7i . 'i7 , 316 ,7 10 53 - . 197 40 339 49 37 38 13
,i '4. 1, ;i lq ' 41 318 57 13 , 3 200 10 342 13 38 5 12S0- 14- t.' SO' H.4 2 27?45 321 2 7 15 53 702 41 344 37 40 51 36 78 11
.I . 44 513 504 1 -4 549 323 56 54 11 18 23 510 07 205 11 N 6 43 347 01 524 41 52 0 1051 77 25 3 424 26 20 53 207 42 349 25 41 34
14 4 51 21,14 55 7 128 5, 23 24 210 12 351 50 443 4;, , 517 2312 '62 331 6 '554 21242 354 14 4, S212 42 3414"4 Sun SD 16'2
I' 4', k4 1 74 544 11 , .'8 14 215 13 35t, 18 4)I k 51 4 2 270 437 24 40I t4 217 43 359 07 49 Moon SD 16
1., ' ,4' 7 0"3 44584 50003 15009 50006 1502 S0004 14756 s009 P Age Od
4 3 F, U v- r *srpLF_ TFIGLK
.3
%650 (DAY 325) GREENWICH P. M. 1987 NOVEMBER 21 (SATURDAY)GMT - SUN ARIES VENUS-3.9 MARS 1.7 JUPITER-? 8 0 MOON Ldt 13- 1
(I D , GHA De, UNA" GNA U., HA D. GHA D. C.,IA b.s
1?20 3 33 tS19 51 s239 57 4 338 55 S24 11 33 24 SIO U8 22U 14 N b 43 1 26 S24 5010: o Ojt 51o 242 278 341 25 35 54 222 44 3 50 51 7.( 8 j35 517 244 582 343 55 38 24 225 15 , 14 53 70 i3 1 11 035 5/e 247 2db 346 "5 40 55 227 45 8 9 - 54 a-;( 13 33 5 5 10 249 59 0 348 55 43% 25 2J0 15 11 03 5b bb,
.0 35 W 20 252 29.4 351 25 45 55 232 4b 1U 27 57 64 13 01 1)I~~5 13 52 1 45.8335
13 00 18 33 4 519 521 254 59.8 353 55 524 11 48 25 S10 0 235 io N b 43 15 51 524 59 o2 13 49 -0810 21 034 52 1 257 303 35b 24 50 55 237 47 18 15 25 00 bO 14 20 t04. 235 3 4 522 2bU 00.7 358 54 53 25 .40 17 20 39 02 58 14 43 09
3U 2t 034 52 1 2t2 311 1 24 55 55 241 48 23 03 03 Sb 1502 1240 2 3 3 524 25 01 5 3 54 58 2b 245 18 25 27 04 54 15 18 14
! 3/ 633 5252b7 319 b 24 O 5b 247 49 27 52 Ob 52 15 32 lb14 00, 33 333 51 52t 2'0 02.3 8 54 S24 11 b3 2b 510 09 250 19 N b 43 30 lb 525 07 5 15 44 18
"" U 10 3 ".2 1 272 32.7 11 24 05 5o 252 50 32 40 09 45 16 og 20VI', 3 2 2 275 03 1 13 53 b8 2b 255 20 35 04 10 40 16 30 22
301, 4. 02 529 277 33 5 It 23 70 56 257 50 37 28 . 12 35 16 47 224 4 332 U !3.0 04.0 18 53 73 27 2t0 21 J9 52 13 30 17 01 25
Q 4t. 531 262 344 2i 23 75 57 2b2 51 421b 14
15 00 i 4d 1 5, 3 2 1 5 0433 23 53 524 12 78 27 5I0 10 265 22 Nb 43 4440 525 0 10 17 2 26
IQ U3 5I 2O7 35.2 2t 23 80 57 20 52 47 04 17 0 18 08 3001 53 433 53 3 290 05.b 28 52 83 27 270 23 49 28 19 10 18 28 30
."44530 312' 8557 272 53 51 52 20 20 18 50 33d" , 10 535 245 054 33 52 88 28 275 23 54 17 21
U,. So:' J ib 497 3b.d 3b 22 90 5 277 54 5b 41 23 30 19 15 3535 19 30 361b 00 0 33 0 51 53 7 300 07.2 38 52 524 12 93 28 Sl0 I0 280 24 N b 43 59 05 525 24 40 19 48 37
t ' 2 4 0 b 302 37 7 41 22 95 58 282 55 bl 29 25 45 2009 39t, 2'6: 324 534L 305 081 43 51 98 28 285 25 63 53 27
O 4 0,''71 * 02 54 .U3U/ 3 5 4 b21 100 58 207 56 bb 17 28 50 20 35 414U, 7 3 12. 54 1 310 089 48 51 103 28 290 2b b8 41. 29 52 20 48 42..o1 7b 02 '42 31, 393 51 21 105 59 292 57 71 05 31 54 21 03 44
1 u 'd32 Z b±9 547 315 09.,7 53 51 Se24 12 108 29 510 11 295 27 N b 43 73 29 525 32 5b 21 21 4b
11j 81 02o 544 317 401 5b 21 110 59 297 57 75 53 34 b 22 09 4
".20' 3 21 545 320 105 58 51 113 29 300 28 78 17 353io 6t U 7 545 )2 409 b o 115 559 302 5a 80 41 3 3b s4u ,I d 3 27 54 t 325 11 3 63 50 118 29 3U5 29 83 05 385, I 09 Ol 7 54 3' 27 41 8 bb 20 121 00 307 59 85 29 39
4 43 . 7 519 54.8 330 122 68 50 S24 13 123 30 510 11 310 30 N b 43 87 53 S25 4010: 'o 02 b 4 4 332 42.b 71 20 126 00 313 00 90 17 41 A C A CI 0 0
l01 '8 ', 550 335 13.0 73 50 128 30 315 31 92 41 43 L 0 I 1030 101 02b 55 1 337 43 4 7b 19 131 00 318 01 95 05 • 444U 1.3 55 2 340 13.8 78 49 133 30 320 31 97 29 45- 0l10b 02 5 55 3 342 44.2 81 19 13b 00 323 02 99 53 47 055 4 '
7 5 349 00 108 32 5 519 5s 4 345 14.b 83 49 524 13 138 31 510 12 325 32 N b 43 102 17 525 48 58 33' 1h 111L2 555 347 45.0 80 19 141 Oi 328 03 104 41 4 12 563•57 .. 32
20 113 324 55o 350 155 88 49 143 31 330 33 107 05 50 16 5730 1 t024 • 55.b 352 459 91 18 146 01' 333 04 109 29 - 5219 5840 1'8 324 557 355 Ib3 93 48 148 31 335 34 il 53 53 22 55 .9 30
. 501 121 024 558 357 4b.7 96 18 151 01 338 05 114 17 54 54 2253 6128,,20 00 123 32 3 S10 555 0 17 1 98 48 524 13 153 32 510 13 340 35 N 6 43 lib 41 25 5b 27 52 62 271^ 22 47. 10 1
01 1 2b 02 3 50 2 47.5 101 18 156 02 343 05 119 05 57 29 63• ,3"51 64 2b0 20 18 323 5t,1 5 17.9 103 48 158 32 345 36 121 29 58 31 6 25
30 131 02 3 . 5b2 7 48.3 10b 18 1b1 02 348 Ob 123 53 25 59 32 65 240 133 32 2 55 b 10 lb7 108 47 10 32 350 3? 12b 17 2t 01 3 49 2450 lib U22 54 12 492 111 17 Ibb 02 353 07 128 41 02 3 48s 67 23
21 00 138 32? 519 5t5 15 19.6 113 47 524 13 108 32 510 13 355 J8 N b 43 131 05 S26 03 37 4 b 210 , 141 022 5b b 17 500 l1.b 17 171 03 358 08 133 29 04 39 46 39 220' 141 321 5t,7 20 204 118 47 173 33 0 38 135 53 05 -, 45 70 20303' 146 021 -50d 22 5U 8 121 17 - - 170 03 3 09 138 17 • 42 44 1
42 714,1 148 32 1 5b8 25 21.2 123 4b 178 33 5 39 140 41 08 43 2 18p50151 02 1 564 27 51.b 12b lb 181 03 8 10 143 05 09 45421 ' 1745 7
22 0 53 3, 0 S19 57 0 30 22.0 128 4b S24 14 183 33 510 14 10 40 N b 42 145 29 520 10 46 74 b10! I 5b 02 0 57 1 32 52.4 131 1b 18b 04 13 11 147 53 12 40 75
15. 30 o 5712 05 2218 133 46 8k 34 1, 41 150 17 1 49 39 7730 it, 1O0 9 '51,3 37 53.3 .1 b lb • • 191 04 18 12 • 152 41 • 14 38 1340 1b3 31 9 57 4 40 23 7 138 46 193 34 20 42 155 05 15 50 77
, 50 lbb 0 9 575 42 541 141 15 19604 23 12 157 29 lb 51 78153 79
23 00 Ib8 319 S19 57b 45 24.5 143 45 S24 14 198 34 510 14 25 43 N b 42 159 53 526 17 35 1a10 17 1.7 7 54. 146 15 201 04 28 13 16.2 17 19 5434 820 17 3 31 578 50 253 148 45 203 35 30 44 Ib4 41 2030176 l018 - 57 8 52 55.7 151 15 20b 05 33 14 167 05 - 21 Sun SD 16'240 178 318 579 55 2b.1 153 45 208 35 35 45 1b9 29 22
181 01 7 58.0 57 5.5 15b 15 211 05 38 15 171 52 23 Moon SD 16lat 14 598 0 06 1459| ,00 33009 50006 53026 5000 | 1 4 242 ,0 ?9- Ag. Gd
U y-- p
ii or c I&
'"i ', ;*
: 7.2 : ? :.-; •' ' - '.-- '- .?. - ' wh w.h w.Pe t.- ufl : .'an
t- -.. --"'n <; . ': , .- i: rd :mr, i'Hc *h t. mc i , mo- ':2: , ~-: . -. , .. .~: :, .- c:r i :: f r thos,.q latituder . N,-,t '- th- t,
-- , .. , : . , 5 f rence be ween the ror thor - " . ;. •• - .. : " . .,* .. 1o Th i- i
d T'. is becaus e of the n 's r
IL.. 4w-. -, - b : l t, c-_ t e moo n' , rb ta. speed , th er _ a
,. , a 'ou t f, r this di ff rernce label ed Diff. DIt f " ..e
h I IJi y feren.c - :;nies i .OC-a. mean time for the
c -. rct-,P when applid to th
-- j moonrise o,.r e st viales wil give you the LMT time ,ia.t
<-," --L., , ts wl occr 1 1 1 G 0 n i n t u OTE An As ter s, *) ers
the Df f Colmn under e-tre, conditions where an
a i rT cannnot be made.
Lol Moon, Moon , 0.
N N
72 72 10 4170 .10 10 32 70 12 29 1568 09 23 32 68 13 10 2066 08 52 32 66 13 38 2264 08 29 32 64 13 59 2362 08 11 32 62 14 16 24
60 07 55 32 60 14 31 25' 58 07 43 32 58 14 43 25
56 07 31 31 56 14 54 2654 07 22 32 54 15 03 2652 07 13 32 52 15 11 27
50 07 05 31 50 15 19 2745 06 48 31 45 15 35 2840 06 35 31 40 15 48 2835 06 23 31 35 15 59 28
-*30 0613 31 30 16 09 2920 05 56 31 20 16 26 29
* 10 05 41 31 10 16 41 300 05 27. 31 0 16 55 30
10los 13 31 10 17 08 31201 04 58 30 20 17 23 31
30 04 41! 30 30 17 40 3135 04.31 30 35 1750 3240 04 19 30 40 18 01 3245 04 06 30 45 18 14 33
S50 0350 29 50 18 30 3352 0342 29 52 18 38 335C'4 03 33 29 54 18 46 3356 03 24 29 56 18 56 34%8 03 13 29 58 19 06 3460 0301 29 60 19 18 34
n, S_: r S . 7 Y' / . :' ':E A L -
s'p
' .. .
0-' %%%
F 7'AMVE Z.I (con t
F r- n the moonr:se table (figure IS) list the ILMT of mrionr'is-e at C
and 18lor;gi tude foi- the followin,~ latitudes;
A. 7,N•
. C. 3 CV N__ __ _
ANSWER:
A. lI C, 10 42
% B2. 0342, 041 1
C. 0513, 0644
D . 0633, 0704
FRAME 22
Ncw you know how to find the LMT of Moonrise/set at 0" arnd .80lon8itude. What happens if you are latedewe
-an either divide the Diff. by 180 to find the correction for each
or~ just use the table that's provided. That's right' There 15 a
table rovided in the Air Almanac to assist you in interpola->ting for
longitudes other then 0' and 180". An example of this table,
-ntitled Inte-rpolation of Moonrise, Moonset for Longitudes is
44% repro duced in Figure 19.
Xc'-t~ce that the table actually consists of 3 vertically stacked
Sectio-n&. The top table lists Diff. values from 5-30, the mid level
* M- .0. and fially values from 65-90. The longitudes are listed
I the 'ef. side. The 0" longitude value will always be zero and
!-he value atiS will always be the same as the value at the head
+5 ,:". 342, 04.
.35
-0
4",
,I . ,
FRAME 722 cntd.
To obtain the t-we difference for your location, u e the Diff. ia
you derived :'rom the m ronrise/set. tables and the lonitude valueo
* nearest your loc-ation the correction amount is accurab eni,'._ h
that further interpolation is not necessary.
For example, if your Diff. value :r.rn
*, the daily pages was 37 and your
F4 LNTERPOLATIONOF longitude was 87" West, you would -uzeMOONRISE, MOONSET ,
FOR lWNGUDE a Diff. value of 35 and enter theAdd d i-4-& ."
d.W.Swd,. .w table at 90" longitude to get a
0. 6 15 0 U 30 correction of + 18 minutes. It ;s
o" o o o I because you're at West Longitude.
""I 11 t Select the correction factor from th,-
6 03 0"0 i 11 2 interpolation table for the following1" 04 08 02 194 2
1" , 04 09 1,, , 2 Diff. values and longitudes. When the160 06_L 10 15 2 5 30
-. 36 0 45 so Sdaily tables indicate a 'POSITIVE00 - Diff. value indicate + if the
II 0304 04 0R 00 0 7 1 6 010 , correction is West/ - if the
" 1 t1 2 13 I i1 ,0
-. 17 19 21 n Z5 correction is East." 0 ; 0s 0 2 00 2 30
"0 2 3 1 r, 1 0 EXCEPTION: If the Diff. value in th00 36 _______41_ ,
100.26 00 40 3bW 29 33 U 2 , daily tables is negative '- then you
1" 35 4 45 0 '. ItD. -40I. subtract the correction from the LMT
40 7 1 5 so U g-,. I . when you are at West longitude and add
0 00 @ 0 00 @0 .0,. 0 04 it if you are East.U 0 07 0 0 9 00 s0 10N 11 12 13 14 150 16 4 7 111 19 2D DIFF. LONG. CORR.
18 1: 21 22 U 24 6
74 Z . 2 13 06 A. 2 5 100 W.2 a . 42 46 B. -7 68 W.UN a0 a0 4 47 0
6 43 41 62 643 V . " 1 87 go C. 42 122 E.
I" f 6 4 18 2 66 70 D. -16 15 E.10 7 6 I 76 20 V 71
"to. _ '6 7 71- " ANSWER:
A. +14 C. -27
B. -2 D. +2
F' {u - r' . teoroat~con of, . crset for Lonit ode.
4P..£ h . e e"" - z".""" "."""--' . ,""-".". 36"q~L. .'"V . ..
- FRAME 23o- complete the process of ufbtair;._ moerrse./set t use the
Conversl,-n -f Arc to Time Table frorm the A manac (hr 4:-r'C 5) t_
convert ti I at y.:,ur :c1s, tl r:i;u did fc-, .- ,r.
NOTE: Each month there is one day near r h f rst Z qar ter ,vi',h,- u.
.r*oon-et and one tav near t ',rter w ". ;- . . .
tabu' a e4 mes may :ndlc-ate 4 4 h1:%'s ' I.
o r er r- vers icn the LST 'ia : e Dve- itc urs "
N E F Y,. E "N E .
FRAME 24
'-,_,Us:n.5 trhe r,,-nr.-se .ar,,,c mooncc e t7L7',?- . >........f,' .. ,...*-., sho:, II
o , t d I (Fi,:.,re _9) ,th ,- , - e r s i c, ir . Arc to : no Tab
9 (F1:ure 5n,and r.h o :vrs:icn tabli f-rr rdarJ1 time 'A:re." Almanac) f ni r.1onr~se.'s.< .... ,e.-. . ,-r bh f.. ,icow..n, stat ,cu. .n LST.
M ono-rse/ Set
A. Lan ev AFB, Va (7' 05' N. '7F," 21' W. /
B. Fulda, FRG (50' 33' N. 9- 41' E.) /
C. Osan, Korea (,37' 06' N. 127 ' 02' E. /
ANSWER:
A. 0724/1655
B. 0818/1601
-C. 0709/1657
FRAME 25
, Moon phase data are shown at the top of the daily pages in the
Almanac. The symbols are related to the phase symbols in F gure 12
At the bottom right of each dally page, the number of days since the
last New Moon are given as "Age(#,d. Finally, FractCInai
Illumination data are also provided in the Air Almanac (tee T:-t
Contents).
**NO RESPONSE NECESSARY**
FRAME 26
For latitudes between 65: and 90' North. emi ,urat of ,orI ght
[ • graphs are provided in th Almana_. Tne-se . ar' ver' srmi ar to
the Semiduration of Sunli.ght egraphs. Each -'-n has -:, own Sr-plh,
-7
" "- -. 7 'e
~FRAME .'S <CONTD'
A 7,e-'erber " 9J<,' Ir-ph is hown i.' Fi ure 20. Dates are shown across
, -, , -;f me'iDdaa o, ass-4,e times are indicated near the
r V o 'c t -t rnie hour anerv.l.s . The skewed
, --. , r -es ar1e s:.mii.- tr-, thDse ir. the sunlight _r-tph, as
. -- D .Z -o.. ) ,t''e n moon t elow horizon portions cf the graph.
r nd1 cated con ther date of occurrence. Vote that the
.... " :' e . ~ t.,- mr lan pa3sai5e times (6 hours apart) and are
tne sam-,e as [i~ustrated n Uure 12.. You'll need to keep Figure 12
n m- n- to ensure the rise/ret times are figured for the 'correct
day. :cr example, on 6 December there is a full moon. As depicted
S1. 12 a, fulI moon rasses the meridian near midnight. At 70"
*:,rth on 5 December, F Ig. 20 shows that the moon is (continuously)
above the horizon. There is. therefore, neither rise nor set on 6
Lecember, but there :s continuous moonlight. On 130 December the
moor :s near third quarter (figs. 12 and 20) and so it passes the
meridlan near 0500. From Fig. 20, the semiduration of moonlight for
latitude 75" North on 13 December is approximately 8 hours. Thus,
moonrise is on December 12 at approximately 2200 and moonset on 13
December is approximately at 1400 for latitude 75'".
tiN . ..... . NtisSS * . . . . . .
--- ___ L~ - -NUS
0 -
MOON-- UUVL MOON 8[LOW N80HUH I LUN HOHHUN
D- - N75
Jt CtMti 5 I Is 20 25 30 1
P
F i ure 20. Semiduration of Moonlight
38
%
FRAME 26 (CONTD)
Find the LMT of moonrise and moonset for the following date., a:;d
latitudes:
,MOONRISE/MOONSET
- A. 10 Dec, 74:' N. _
B. *25 Dec. S 0' N. /
... . -7 " e c 70' N /
D . 17 Dec, 69: N. /9
e, ANSWER:
A. moon above the horizon.
B. moon below the horizon.
C. 1130, 2330
D. 0559, 1159
I
5.
-4.
* 39
%
-% * . - A kP . S . p~N.P, ,. *~,~ p- , N '~" P-. '[!i A ~ , ~ ~ a
A . .L
"'%S
TEST QUESTIONSThe fol.wln test is pr-,vided so you can determln-? wh,-.the..you reached the objective- stated in the beginning of this TchNote. Tables and graphs to be used for this test are located ,;i -h-f -, I Iowirg pages.
State the main reason that sunrise, surset, and tw-li41 *1-t --e7.-hange from day-to-day.
2. Langley AFB, VA is located at 37' 05' N, 76 21' N. List theLocal Standard Time on 15 April that the following events willoccu-r:
AM Civ Twilight Sunrise Sunset PM Civ Twilight
3. State the Local Mean Time of occurrence at 75' N. on 1 AprilS for the following events:
AM Civ Twil2ght Sunrise Sunset PM Civ Twilight
4. Name two factors that cause moonrise/set times to change fromda, .o day.
*~ A.
S..
%. F':lX (lap, FR<l is located at 50" 33' N, 9- 41' E. Figure the1 ..... f o.--currence of the following events on 15 Apr 87.
, c~rrse Moonset__ GMT GMT
LST LST,-
S tr. .Local Mean Time of moonrise and set at 75. N. on 7 May
O. ~ ~ ~ ~ ~ ~ n : , ' -M,,ns e.1
O'.,
04
& 40
L ' p ~~*
ens-a-~.S.. J..r ~' . UT. r ru rj IOU4 r O r4. v-wVw. -n 4_ - rrr , ~--r
SUNLIGHT AND TWILIGHT A153
12 *10 12?1 12008 12100'N 1214 1214' I t
' 1 S N5
SEMIOURTION OF SUNLIGHT
NBO - NBOSUN BELOW SUN BOVEHORIZON HORIZON
N75- N75.-- - - .--- -_
N70 / 4m- _6 8. N7O
1 16 16 1 16 I 16 I 16 I 16 1JANUARY FEBRURRY MARCH APRIL MAY JUNE
S...................... I ..........
12 105 I2.0 . 12'00 11'50. 11 45 11'45' 11 °50' 1? 0012106' 12'061 11'44' 11*44'
SEMIDLIRATION OF SUNLIGHT
N8O NBO
SUN ABOVESUBEOHORIZOHORIZON
N75 ------- N75
120
N ____ 6'/---- 4 N70
1 16 1 16 1 16 1 16 1 16 1 16 1
JULY AUGUST SEPTEMBER OCTOBER NOVEMBER OECEMBER
N85 - NO TWILIGHT _________ ________-- "
OR SUNIG~rDURATION OF TW4ILIGHTNBO " -o- N --/ 1" -'/ .. . . . . . . ... . . . . . . .-- NBO
CONTINUOUS TWILIGHT
N75 I I -. OR SUNLIGHT
2F 16 1205 1 N75
is 1 16 1 16 1 16 16 1 16 1jlPN(JPRT FEBRURY MRRCH PPRIL MAY JUNE.
611,/ 5M -~---.NO TWILIGHT -- - -
D U R A T I O N f T -[ .. . . . . ..O R S U N ..G.
NBC--- ------- NBO
CrINTN'!OUS TWILICHT >
_ 1 n- - N -c H -- "- 1" "N "i'.. - -o- 1 ,_47
/ n I N I-- "
I 6 1 16 I 16 1 16 1 16 1 16 lI T fAIGIST 'f PTFMRFR OCTORFR NOVFMBFR 1fEF;EFR
41
A. I\ Oh coNVERSION OF ARC TO THIME
" b h 1. h h o h b
0" 0 00o 6o 4 oo 120 h 00 IS 18o 00 240q 16 00 300 20 00 o ooo0
1 0 04 6101 4 4 21 8 04 181 12 04 z4x 16 04 3o004o1 0 42 0 ON 62 4 08 122 8 ON x82 12 O 242 16 o8 302 20 08 2 0 08
3 1 2 6 4 1z 2 23 z 183 12, 12 243 :6 12. 303 20 12 3 0 12%4 0 Ib 64 4 16 124 S it) 184 12 16 244 6 16 304 120o 16 4 o 16
5 o2 65 4 zo 1215 8 20 185 12 20 24 12 305 20 20 o 0 2
6 4 66 4 24 126 S 24 x86 kz 2 4 z46 16 24 3o6 20 24 6 0 4.,7 0 -S 67 4 "1 127 h 28 187 12 2H 247 16 28 307 20 28 7 o 28
S" 0 32 6,8 4 32 !128 8 32 I8N 12 32Z 48 16 32 3o8 20 32 8 0 329 0 30 60 4 36 x29 H 36 189 123 zg 1 36 309 20 36 9 036
19°
0 0 7 0 1 3 0 Io 1 40 250 16 40 310 2. 40 10 0 40
1. i 0 44 71 4 44 .1 X 44 19 1 44 251 16 44 311 20 44 11 0 44I. 1z 0 4 72 4 4h 13A X 48 192 12 4h 252 16) 49 312 20 48 12 0 48
, 13 0 52 73 4 SA 133 K 52 193 12 52 253 16 52 313 20 52 13 0 521" 4 o i6 74 4 0O 134 8 5b 194 12 56 254 1 6 56 314 z0 q6 14 0 56
1. 5 1 00 75 5 o0 135 9 00 195 13 00 255 17 00 315 2 1o 00 1 oo 0i 16 1 o4 76 q o14 136 9 04 x96 13 04 zS6 17 04 3z6 21. 04 .6 1 04
17 1 UN 77 5 ON 137 y 08 t97 13 08 257 17 08 317 21 08 17 , 08IS 1 [2 78 5 12 138 Y 12 x98 13 12 258 17 12 318 21 12 18 1 12
4. 19 1 to 79 5 16 X39 Y 16 199 13 16 259 17 16 319 2 1 6 x9 I I 6
0 1o 20 90 8 5 20 140 9 20 20o0 13 20 260 17 20 320 21 20 20 1 20% 1i 1 24 81 5 24 141 9 24 201 13 a 6z 17 24 321 21 2 4 21 Z 4
22 1a 26 82 8 5 28 142 t) 28 2o 3 zh 262 17 28 322 21 28 22 28
%" 43 1 32 83 5 32 143 9 32 20o3 13 32 263 17 32 323 21 32 23 1 32S24 1 30 H4 5 36 144 9 36 204 13 36 264 17 36 324 21 36 24 1 36
25 1 40 85 5 40 145 9 40 20o5 13 40 265 17 40 32S 21 40 25 1 40
a~ao6
'2, 6 1 44 867 5 44 146 1044 -13 44 26 17 44 326 21 44 a6 1 44P'. 27 1 498 7 5 4h 147 9 48 207 3 49 26 I7 48 327 21 48 27 1 48
,8 1 Sa 98 S S 148 , 5z a 3 52 268 17 52 328 21 52 28 1 52
2? 9 1 jh 89 5 56 IL49 9 56 209 13 56 269 17 56 329 21 56 29 5630 2 0o 90 6 oo ISO 10 00 21o 14oo o 8 330 22 00 30 2 0031 o4 91 6 04 121 1o04 21i 14 04 271 18 04 33 22 04 3 0 2 04
32 Ox 92 08 122 8o o8 a 2 14 O8 272 6 08 332 20 08 32 2 oN
33 2 12 93 6 1z S3 10 12 213 14 12 273 :8 12 333 22 12 33 0 12
34 0 16 94 6 6 1 54 o 16 214 14 16 274 18 16 334 22 o 6 34 0 11
- 5 2 O0 95 6 20 155 1O20 15 14 24 275 I Mzo 335 22 20 35 0 20
36 z4 96 6 24 x56 10 24 216 14 24 276 18 24 336 20 24 36 0 24
37 0 28 97 4 z8 157 o 28 217 14 28 277 8 28 337 20 z8 37 2 2838 0 32 98 6 32 158 80 32 218 14 32 278 16 32 338 20 32 38 0 32
39 0 36 99 6 36 S9 o 36 219 14 36 279 1 36 339 22 3()
39 2 36
40 2 40 oo 6 40 16o 10 40 22 14 40 280 16 40 340 22 40 40 0 40
41 0 44 701 4 44 11 44 221 14 44 281 I6 44 341 22 44 41 0 44
42 48 172 4 48 z62 o 148 22 4 4M 252 IN 48 34 20 4h 42' 0443 2 52 3 4 52 133 10 52 223 1 52 283 18 52 343 20 52 43 0 S244 0 56 104 b 5b r64 80 56 2214 256 284 !8 56 344 20 56 44 0 it)
"45 3 00 105 7 00 x6s A oo 225 005 00 285 19 0 345 03 00 4 3 o46 3 04 xo6 7 04 166 1 04 226 15 04 256 7) 04 346 2 1 04 46 1 04
47 1 oN 17 7 8 167 11 1O 287 19 oN 347 21 o 47 3 O48 3 12 708 7 12 168 1 : 12 198 13 12 25 1) :2 318 23 12 48 3 12
4o9 3 1 7 16 i69 I 16 299 I 6 259 17 t6 349 23 1) 49 3 16
so 3 2 0 10 7 20 170 9 o20 230 5 10 290 9 20 350 23 20 2O 3 20
51 3 24 811 7 24 171 1 124 231 15 24 191 19 24 35 23 24 21 3 2452 3 28 812 7 28 172 9 2 8 232 13 28 a9 19 z8 352 23 28 2 3 2853 3 32 813 7 32 173 91 32 233 13 32 263 :7. 32 353 23 32 23 1 3224 I 36 814 7 36 174 19 36 234 I3 36 294 1:) 36 354 23 36 54 3 3625 3 40 tS 7 40 175 9 40 235 13 40 295 19 40 355 23 40 55 1 40
56 3 44 116 7 44 176 19 44 236 15 44 26 17 44 36 23 44 56 ; 44
57 3 4) 817 .7 48 177 1 48 237 15 48 297 :7 48 357 23 4H 27 3 48% 58 3 52 x8 7 52 178 19 52 238 15 52 298 19 52 358 23 52 28 3 52
59 3 56 S9 7 56 179 1 56 239 15 56 299 17 56 359 23 $6 29 3 56
I.The above table is for converting exprLssions in arc to their eqjuivalent in time; its main use in this Almanac is
for the conversion of longitude for application to IL.M.T. (added if west, subtracted it east) to give G~m.T., or %ace %ersa,particularly in the case ot sunrise, sunset, etc.
30 20 90 60 10 100 21 1400 20 80 30 220 30'20
ow vv, - qw of C - - v -. r'wr1 VM -- -.n~
.5"
\134 SUNRISE
Lat. April May8 1 14 17 20 23 26 29 2 5 8 11 14 17
N72 4.... 5- , I4: . 4 13 3 (0 3 1 4 35 2 350 . 14 I 5t,
o2 (4470 0' 3: 1' 13 h, 1 11 5 13 ,) 35 11
3 11) u3 03 o: 47 02 1 t - 1 I 0 1 1l "1) 51 111( 1
4 1'
4 ,
3, 17 04 €14 "3 .51 37 0 3
111 " 2 Y 4 -1 I42-' 2' 7 1
6t) 4
,9 415 114 IN ol 2 I S 03 17
3 4 37-2 i3 3" .1 02
4 'It 4''
J 25 14 040 t45053 - 3 33 - 3 11 03 1 12 0 114 33 4I
42 62 4 - - 33 214 4 0 5 13 25 i "7 7 S 2 1 0 1 (
3 013
N 6o ( s1i 0 7 1)4 Vo 4 ' 1 04 0 4 i 4 I3. 0 534 t-, 1 2. 5 " 1 3 7 03 0)
3 4 0 53 "3 0 2h 0 )58 'I ,s 4 - 54 11, JS 3" 1- I2 1. 4 7 (14 o 1 43" .o ')5 1'4 -4 59 51 14 37 0 59 1 .1 11. oOf 04 40 03 5 3 50 5354 .1 t
3 0 4 50 42 13 31 z) . I 4 t 8 (9 4
21 03
5 17 .0 1 0''" 03 o I 0 Ii4 0 4 42 t, 3- 4 103 4, 0 1 9 0 4-1N So , t, , , ,
5 2 5 - ( 5 I li 1 ' 1 , 11 1d 4 5 3 04 47 1)4 11 1 4 3e 4.) 31 "
4 I ' " o(
4 ='n 1 '4 1 7 0
4
45 4 1 4 -0 ) 13 5 , 8 05 03
04 YS 3 4 5 3 - 49 45 41 37 33
40 14 31 34 34 27 30 13, 12 5
4 4 5 ) 4 5" 114 3 04( 4 41, 1.5 0 43 5 1 13 30 3I 40 7 '3 5 I 0702 0707 05 ( 4 .5 03 0 () 4 0 43(, i.l 4"
' 4"-- ill 35i 32 1 t _) 11 23 -11 I 7 1 ; I - I 1 0u5 OS o, o1
N 2o I i Ili I,1 °. i' I 3 00 4'
03 43 0) 11 4 5 3) o5 3 u53 )5 3805 31 05 29) 517 2 721 05 -3 07 23N o j " 3I 1 4 1 50 4 7 7 402 .5 43 43 42 41 3 ' 44
0 ,, l ( 38, 11 j 5 ) .4 i 5 -", U 51, 111 51, 0i 15 ' 113 0 u 05 54 05 54 05 53 05 5 3 (15 i)3 05 3 (-, " 3
58 2o 34 4", 1) 4 04 01 04 0( 0 ) 0 " ( 44 "'4 o 04 Of( 1 14 0 3.411 4 0 0 7 52 I *1 1 'It, Of 0
720 IN7 Off A )) 10 1 1 1 2 13
14 1i)
It)I 17 isIN 1(I -14 21
30 O t' 1,* I l 14 1( "4
"I, I I) '1(' 2V0 % u 2 2 01' -3 It' 25 Off -7 06) 21) 1)4 31 06) 33 Vf, 3 5 04) 37 00 Y5'
S35 % I S '.0 .1 -1 22 5 27 N) 32 34 37 30 41 44 46 4M
4 2 1 S I 8 1 -4 7 2 0 33 31, 3( 4- 45 48 i t ) 54 O 1 57 V(1 5()40 . 2 33 1 25 2 00 33 37 4 0 44 48 Of 51 Of, 55 O 59 7 02 0 7 0(1 07 0 0
7 1 2
50 1 Zi, 30 3i 40 4 V 53 0() 58 07 02 07 47
07 1 4 13( 2 V14 24 2 I
652 2S (. 33 00 3S7 o7, 43 094 "(.53 0(U5 0 3 07 4,I 0712 0717 u722 07 17 7 3 2 7 3',
5 43 0 3541 , 411 51 1, 57 07 021 O ( 3 14 3 204 - 4 24 446o , . 8. J I .) 4') I)t 4934. I I )" 0) 2t", Wl O 1 ,2 J7 1 2( 0 558 44 4t 7 54 07 00 0
7 144 2 -() 34 33 3 ) 4 7 i 2 1 0 8 24
S 60 1' 1', 54 ( i I I I' 1 (70 0 7 13 ( 2 28 74 0 .4 _ 41. 47 44)8 ((
SUNSET;':Lat. April May
4 2 8 1 44 17 20 23 2 27 a 5 8 it 14 5 7N 7 , ,, . , . , . f} , hh , h . h I t1 h . h . h h
52 I1 9 4 1 4 5 0 5 (1 (4 2If: 2 1 4 2 4-' 35 40 4I 4-_
No 3 87 (42 4..(4 84 (r4 oS 4_(45 444 .2 )8 493 447 44
7 101 2 1 33 4.1, 0O IQ 1 27 20 4 1 2057 1 1 1 ( 212 4 9 2147 2207 1 .41 21 2
08 1 2 28 34 35 1')47 1il 30 4 1 -3 , i 4 8 1 0 51 2 41 4 441 3 41 01 l .466 J" ' t* , 37 -47 110 -57 2" A) N 2 20 41) -0 52 21 (13 1 21 I 1 2 J, 3:
464 22 4 2 4 3 4" 11 55 , 115 14 z4 31 20 4 1 0 - J 41 01 21 1-86 4 I ll 0 2
4 1 2 1 - 2 4 3 3 0 2 Il I 47 3i 20 43 ) 51
N(o I 4 8 I84 0l 1'I (I7 is 1-4 1() - 2 II 824 49 221 4 4 4 51 l 1(21 4 827 4 28 4129t 58 11i i
' I5 1(I(I t. j "S 63 2 -, 35i 2 "1 % 14 S5$ 1) - 21) 0 S 1 21
5N Ill a 51 57 40) -3
44) 10 44 2 4 , 34 .2 42, 43 1 i I4 4 0 1
54 30 ' 47 53 1 il, 14 1o 1 -( - I 4 , is 8 4. 4S l 53 1) is
52 4 '2 4, ) 017 i,'' ) , (53 1 5 47 -' 4 74 4 41 4N so0 I' 12 3' .7 1 12 -' .1
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I - :,0 -,% lh 1 3 1,) 37 Ill 41
S45 0 i i2 (4 l(l 4 1 47 1,' l I 4 , S 33 1 0 1) 472 4) 4 7' III ) _, 17 _ , 7 -- I
40 4 ,( ' 2 34 3 3 2 3 24 7 4 4, 47, 1') 07.4 7 1
m4 4 2 3 4 31 4 4 4(1 (I. 12 37o. 470 4 70 42 49 (1 4 1( 9 07 Il
35 22 ' 44 -1 24 1 j1 3 47 (2 407 4703 46)
44' 5 ,I I "t4 I 4 4i is 4i
50 It' Z2 4'4 ' 2 2 ' J 1 3( 1 34 1, 37 7 ) 41 43 4 17
S 2 , 4 2 1 7 , ( I 4 1 I( I 5 I 4 8 I I 1 2 4 44.4-' I 2 4 18 ,2 4 4 4.2 5 I I S 2 4 -, I I O , ' )N 10t I( Ill IO u II II I I I I I I I I I I 1 2 1 2 13 Ij 1I4 14
54 4 ,. 172' 4 177 - 1 17 21 2 17 51 1 54 4 71 41 174N 1747 127 4 3 174120 44 4.4 5 51 4713 4 11, 1 4 4 1 35 x 2, 45 31 4 14 J
S30 1- )) 7 "i 5 17 4') 1 7 4 17 43 17 31 ) 7 11 1 733 17 30 1 72 7 17 25 17 2. 17 o 1" 17 1,1 1 7 It,1 171.4
3t 5 41 A( t '
t J q 34 31 - 1 3 Ill I7 14 1 1 17o(10 17 Off 17o(
4
4u
- 40 22 4" 34 P5 50 "1) 3u 2 24 43 1 7 44. 0h s)0 If5, i 4 345 -'1 -1 1 .4 7 2
7 n: i o 3 1 4 5 e 4 x6 ,,o 47 43) 40'
51, 0 )
' $ 2) 14
-j 1I7
03 111 57 It, 51 47, 42 37 P2 28 24
F S 52 17 1 7 1,- 15 3 1 1 24 1U7 1 7 17 1 1 17 Il If- 514 If' 52 Ill 47 Ill 41 It, 35 16 310 , i s It I, 1 I hit, i
5 t,1 €,13 -5 1,' "1 17 03 lit i, 4,% 41 35 is 22 I5 l i 1) Il() N
5 59
se ill 1, J . It 1 ¢ II, it is y i " I I8 - I o 13, 160 7 I1',(m) 1,15.5 4K
S 6o 17 47 47 7 ) 7 4 17 Of 10,13 ,4,44 ', Ill 28 1(' ") ,12 14104 15V)15 4) 5 4 3134 ,
44
MORNING CIVIL TWILIGIIT A135
Lat. April May
2 5 8 1 14 7 20 Z3 z6 29 2 5 1 1 14 17
7o7" 5 t 4 . ¢' " ft f - ' I " I ' t *' ' ft .'f, ft 1f 1 ft " I '' " 2 ft ' -' ft
68 V'4' I. 1 4 M' "I'' 2. I3 Of 3044 '
5 . 1ii 1 4' " 2 '| 1" 5 4 ' ''2 17 s 4 21) 12 )1 5 312-
64. . - , " ' 2-'2 4'52 k 4 4 11 '1
2 s I "2 0] 1 27 1 3 ,
62 .1 (- -1 " ,5", 11 4 4 31 "'' 4'' 4'4 .2 j ('4 33 '' 47
N6o A 2 I I i I 'i 11 '3 3 44 ,33 31 924 '1 ' 1 14 03 0.4 112 ' ' 4 02 " 'Z 3 2 ''2
58 .4' 2 ' .' 24 1, 11 ( ' ; 0 5 , 2 ' 11 1 10 (5 11 0 2 3 ' i 1
56 , 4 IO j
' | ' Y) ' 4', 3 2. 39 34 23 If-I
54 ''1-'' 4S .1 2', ; 3 ' 14 1 3h .1 0 .32 35 2, 2. .,, . ,
52 3 40 -, 4 1 2 f 1 t2 -13 5 4 43 3-1, 33 |
30 -1 ! 51 o -4 , O494 115 3 5 1)4 "3 4 0 5.1 ') , 4 1Is 2 'A ,I
N~ . 5 | ''.''' .1 ' .'. .) o7 l) 5 4 ~,'.l 1544 '19 42-I' 40 1211 (11. 5 17 5 tII 110
4N 0 4 34 43 1 11 12 7'3
25 Z3 02 1 1 7 20 2 'f , 47 j ''
40 4' -1 4' 3" 3'' 35 35 3.4 .3.) 35 32 24 3 1 31 3 11
3510 4 1 57 43 42 4 i . 4 2 2 4 43 3 .4 4; -443 I
30 45 4' I 4 4I 4l .I I' I -'; I " I 1 S I 19 452 0 4 V 0 1 5 4 1 1 4 44 1 15 4
N 30 ''5.11 ''5 I ;4 1' SI 0" 92 4 11 ' '19 " 5 ' i I1 I1 1004 I ' 03 0 11)1 () O 103,C'0 1)0 1 1,0 i 1 44 "I ' 3
40 4" 54 i4 3'57 .~'1'''l 3 3 01 33 44 37 2 0 3 2 3 9 27 331 3
4 to 4 2 1 4 " -O 11 1 07 41 2 17 3 4 3 4 3 4 .1 1 1 4' '
50 4') 53 4- 412 (2 ' 51 " 210 3.1 2 4 4 0 52 3 .4 49 i i 1' 14 52
-~S 30 115 4' P) 94 0 i ' "'4 ' 4 ( '1 5" 4 " 114 4 5 1. 23 1 1.2 0'' 32 04 00.1 It4' 'IllI 5 0 'll1 01I.9l $ I
5 .44 4S s oI 0 I1 " 21 S27 34 3"' 44 13 06 0 94 12 I ' Iso ' VI ~ 0 424 CII 5 IT ".1 1~ 1 117 1 4 zS 3 7 4 s piii s ~~60 4, ) 55 I'll Of .. . .. .... .. ....- 1....E E IG"13 is: 2o 3 2 431, 40 4%, 5, 17 01- 517 "7 0CVI .... TW LI7t 4 " M "..
EVEIN CIILTWILIGHT
Lat. April May2 5 8 1I 14 17 20 23 26 29 2 5 8 II 14 17
ht . hr t, h Ill h I, h h n h m ft ft f m h m m h h h
72 . 32 20 SO 21 1 1 1 31 21 2 55 2-24 230",
;1, 111/ ,'llI "M '; I . ' 1 , • I70 45 31 20 45 21 '2 21 21( 21 3'0 22 02 22 2" 23 07 Q/: /I M ( I HI !1 If/! I I'
68 2. 2 14 25 2041 2" 51, 24 It 21 27 21 1.5 2205 22.2' 2304 Of 10 1/ 1i , '
66 1) 51 20 02 t 25 37 21.1 5 24 03 21 17 24 32 21 4, zz 06 22 2h 22 51 23 33 '.';'' ,
64 42 I 52 2002 42 22 33 2044 2054, 21 oS 2 21 34 21 48 22 03 22 20 22 39 23 02
62 34 43 1') Is2 211 01 In 21 21 (1 . 110 .9 21 'In 204-1 22 21 33 21 45 21 58 22 11
N6o 1 2S 4 ') I41444 1'32 201 1 , 20 17 202 5 213-4 211.3 2053 21 02 21 4 21 21 21 30 21 40
58 22 2') 34. 4.4 I'Q 9 I' 59 21) "1, 14 22 30 38 20 45 2O 54 2l 02 2 I0 18
4756 17 23 30 37 .43 W1 Vt) S7 20'"1 11 45 25 32 30 20 40 205 3 21 00
54 14 45 24 30 31. 43 1) 14 955 201 Of20 o9 44 20 21, 33 310 20 45
52 o1 44 21 25 31 31, 42 47 11) 53 41) 5) 20 04 40 1, 21 27 32
N 50 1 4 )1 I9 49 I () 15 10 20) 02 ' ) I 3 1435 14 411 I 4(' 1 51 19 1) ! .of 20 0( 20 1 1 2( 1t 20 24
45 Is 5 5 1 9111 ., 0 I .1 4. '4 3 34 3S 19 42 4 4) 46 50 1 1) 54 1q ,
40 52 1,) 55 Iq 5S III I (4051.19 44 44 I, 24 24 5 34 34 37 40
35 47 4'0 92 45. i- q~ 47 1'1 'll I1) 41 4 115 11) 117 4 1 3 49 45 241 251 i4,
30 43 45 47 .41 11 Is4 53 I 55 S 97 IS 11101 1)03 49115 4907 19O O 9 I I 14 3
N 20 1~ 37 4s537 413 "'~ 3S I )S .40 184 41IS42 45S.43 45.14 4 V 41 44 48 48 48 414 4N550 IS5 1 A4531
N to 12 32 32 32 32 42 32 32 1 3.3 33 34 34 35 .'' 3'2 27 ' '5 25 2.1 23 23 23 22 22 2Z 22 2 22 22
S 1o 22 20 t23 47 I 4.4 43 12 44 1 41 18 01 I50w) I oS I545
20 22 . 15 13 "1t
411 r 11; 1X 12 48 O4 17 5 1 1 4
17 5- 1 9 51 47 54
S 30 14 ll I0 4 t' :I IIl1 I 1 S7 4 14 1 1', 1 7 SS I 5s 1 97 2 1749 17 47 174 1743 174 11 I7 39135 1') 1- i t 1 17 "1 1 I
'll 1 7 i'l I,1 -' Tel 43 41 0;
g ' 1 31
40 1'4 14 o5, 15 ', 17 i,'' 52 45 44 .41" 37 34 30 27 25 12
* 45 14 1. j I7 1 112 7 92 47 42 35 i4A 2n 2 22 I 49 s 250 4 14 2 "' 1 4 -, 53 17 .12 ', 31 21, 21 11, 142 o7 41.5 41o
S 52 .1 4 1 .1 1 17 5 ,f 1 52 17 47 3l 17 11 17 17 22 ' 17 1 I 1472 1 7 1-, 7 '2 It, 1S If1'9
54 1 4141 44 17 3'' 2i 1 143 (7 17 ll 1 1,7 ;2 .44
56 14 o -37 .42' 44 08 4702 44, 51 i 44, 42
58 it 40 '2 34 44 3'
31 24 4'' t,' 1703 If,57 31 45 31 34
S 60 "I5 "I 1"4IS- I 'It 1752 17 14 1 7 2- 1 7 1' 17 42 1719 1( 7 V'5O Ih .4 If44 , 3R 41f, 2 I6 PI'
4,1
-I- -- w-1(DAY 105) GREENWICH A. M. 1987 APRIL 15 (WEDNESDAY) 209
(UT r, GV VA Ct4IA V-)e C.HA V., CGHA D-( G, A De-rJf
00 00'. -q 55 7 h ) 2q ' 202 7 2210 15 S 4 52 138 2b N?2 14 192 38 N 3 07 349044515 35 b .
10 30 0 5 00, , C, 7 b 2 3 05 140 5 i95 09 lll,209 72 m20 04 1,' 2: 20738 0 2 1' 5 1 432 19: 39 154 34 40 7.[3 0 3m 5 0 A 2 1 0 0 8 5 2 8 0 5 " " 1 4 5 5 7 • ' 2 0 0 0 9 •1 5 6 5 9 4 2 2 =4 9
i 4 0 .1 [' 5 8 (4 2 12 8 9 2 ?I
3 5 14 8 2 7 2 0 2 4 0 3 5 9 2 4 4 4 b b 3 290 l< q 30 6 2 5 0 9 2 2
0 5 150 5 7 2 0 5 0 1 4 8 4 7 64 2 2 54 7 4
010... .8.0"?73 7253 1 5 7N214274 0 3S54 62 22 30 627"-0 :,4, 9 30 9220 0 1 229 05 155 57 210 11 b68 52 60? 11 5" -"20 ;~ 1,, I0 222 40 5 210 35 158 2 7 212 41 9 03 54 50 22 55 5 2.e.30 i
215. 21225 10.1) 2330(4 - b0 58 215 1 1 28 - 5t, 56 2 45 494011 4 55 9 3 3 227 41.3 235 14 163 28 21, 4 1 1 13 15 5 '54 21431 47
0 50 2b2 0 rqQ315 230 11.7 238 04 165 58 220 12 10)18 1 52 21 20 4502 01,3 50 b 0 3 6J 232 42.1 240 34 S 4 50 16828 N22 15 222 42 N 3 07 18 43516b0350 21 11 44
1, C-:j 212 26 0 31 8 1 5 12.b6 243 04 170 58 225 13 21 08 06 45 20 5 3 4 0"-201 -4 56 0 31.9 237 43,0245 34 173 28 227 43 23 32 08402 37 8
X, ~ ~ ~ ~ ~ ~ ~ ~ ~ 4 20 37 1 21201 280 823 32 7 . 1,,,. 1 19; 56 1 32 2 242 43.8 250 34 178 28 2"12 43 28 22 131 35 20 24 36:" 5c'? , 32.4 245 14.2 253 04 180 58 235 14 30 47 15 30 20 13 34
Jl0300! 2 24 5,1 N 932 5 47 44.6 255 34 S54 49 8 29 N22 15 237 44 N 3O0 33 12 S16z 18 0 19 5 38 2",0 2 2 ,' 2 62 32 7 2 5 0 5 0 58 0 4 1 5 5 9 24 0 4 3 5 3 7 2 0 0 19 2 2 2 7
20 20 1 , 8 2 252 45.4 260 34 188 29 242 45 8 02 . 22 0 19 07 25L ' 12 ?2 .33 0 255 15.8 263 04 9 025 54 7 2t,-40 24 5f- 9331 257 4b.3 265 34 193 2 247 45 4251. 27'2 8 1 2
50*-"uS2 137 263 33.3 260 16.7 268 04 195 59 250 16 45 16 29 530 18 3 3 2(0
04%,, { 0 3 . 2 2 71 7 3 S 4 4 198 29 N22 15 252 46 N 3 08 47 41 S16 3 0 1 0 110123 563N93.26 712734842b6 3 33 6 265 17.5 273 04 200 59 255 16 50 06 34 45 17 56 142024 5 4 337 267 479 275 34 203 2o 257 47 2 1 365 7 9 13L• 247 2b4 . 13 270 18 3278 03 20b 00 260 17 54 56 - 395 731 ]402q564 34 0272 48 7280 33 208 30 262 47 5721 4152 17 31 10(50 252 26A 34 2275 Iq 1 283 03 211 o 265 18 5q 45 43 54 17 22 08
56 1712 06050 254565 N 9 34 3 277 49 5285 31 S 4 47 213 30 N2216 267 48 N 3 08 62 10516b465 7 0
"10] 257 26 5 34 5 280 20.0 288 03% 216 00 270 18 64 35 4858101 4o 5 05 .6 282 50.4 290 33 218 30 272 48 b7 00 50 0148 0
30262 26.5 - 34.8 285 20.8 293 03 221 00 275 1,9 69 25 - 53 S,#[ 40] 264 5b6 b 4 9 287 51.2 295 33 223 30 277 49 71 50 5550] 21,7 2b6 35 1290 21.6 298 03 226 01 280 19 74 14 16 57
060 ,9566 N q 35 2 2q2 52 0 300 35 S 4 4b 228 31 N22 16 282 50 N 30C8 76 3qS170o M"".', P A
10 17226,6 35 4295 22 4 303 03 231 01 285 20 79 04 02 A I A -C20] 274 56 7 35 5207 52.8 305 33 233 31 287 50 81 29 04 11 0, 1030] ?77 267 - 5 7 300 23.2 308 03 236 01 290 21 83 54 - 0740 279 5b7 35.8 302 51.6 310 33 238 31 292 51 86 18 09 .. .50. 282 26 7 36.0 305 241313 03 241 01 295 21 88 43 11 0 ' 54 '
4 59 55 3407'. 00] 294 5bg N 9 3b6 307 54.535 13 S 4 44 243 31 N22 lb297 52 N 3 08 91. 08 Sv 13 158 33
10 _ ( 287 26 8 3b A 310 24 9 318 03 246 01, 300 22 q3 33 16 11 57 %3 3220 289 568 36.4 312 55 3320 33 248 32 302 52 95 58 IS 15 5 73
1 -'30 29'2b 28 - 366 315 25.7 323 03 251 02 305 23 98 22 - 20 19 5.5/340, . 4 2 569 3b 7317 5&1 325 32 253 32 307 53 100 47 23 21 5950. ' 2726° q l.9 320 26.5 328 02 256 02 310 23 103 12 25 245_02
,-.08 00 2990569 N 9 37 0 322 56.9 330 32 S 4 43 258 32 N22 16 312 54 N 3 09 105375S17 27 26o53 2 28.10"I 302 260q 37 1325 27.3 333 02 2bl102 315 24 108 02 29 28 6320" 1 04 57 0 37 3 327 57.8 335 32 263 32 317 54 110 26 32 30 51 64 2630" in7 2 . 0 . ,7 4 330 28 2 33B 02 2bb 02 320 25 112 51 - 34 3"50 .. 5
'"40 10O? 57 0 37 b 332 586 340 32 26833 322 55 115 16 36 34 4q 66 24.50; 1227 0 37 7 "335 290 343 02 2/1 03 325 25 117 41 3"4 35 6
,09, 0 0 314 57 1 N 9 37 9 337 59.4 345 32 S 4 42 273 33 N22 1 7 327 56 N 3 09 120 05 517 41 37 47 8 21 0 31 727 1 380340 298348 02 276 03 330 26 1,22 10 43 39 46 69 2120• 10 t 5 57 1 38 2 343 002 350 32 278 31 332 56 124 55 45 40 45 70 20
,#.30 32,127 1 - 38 A 345 30,6 353 02 281 03 335 27 127 20 -4 8 42 44 71 lc),t.40 124 57 2 3R 5 148 01 0 355 32 283 33 337 57 129 44 50 .. 43 18 l
50 27727 2 38 6 350 31A 358 02 286 03 340 ?7 132 09 52 44 2 17
10 00 312157 2 N 9 38 8353 01 9 0 32 S 4 41 288 33 N22 1.7 342 57 N 3 09 134145S17 54 Q, 4 1
4 ,
10 332 27 3 I89 355 12 3 3 02 291 04 345 78 ]16 59 514 40 7 1 .'.'20 134 57 3 39 1 5802 7 5 32 2q3 34 347 58 139 23 17 54 47 19 75 '4
I 30 337 '73 39 2 0 33 1 8 02 296 04 350 28 141. 48 1,801 49038 76 13
,t,40 3 V) 57 3 394 3 03 5 10 31 298 34 352 5q 144 1,3 03 50 A 7 77 1
"'p, 50 142 2 74 39 5 5 33.9 13 01 301 04 355 2q 146 38 at, 51 78 12I" 11 00 144 57 4 N 9 3497 8 04 3 15 31 S 4 40 303 34 N22 1.7 357 59 N 30Oq 140 02 SIR 08 35 ^ (
1 0 347 27 4 398 10 34 7 18 01 306 04 0 30 151 27 l 0 54 34 8F,'20 349) 57 4 40 0 13 05.1 20 31 308 34 3 00 1 53 52 12 5 45
30 . 352 27 5 40 1 15 356' 23 0 1. 311 05 5 30 115 1 17 15 u D 1 ,40354 57,5 40 3 1,806.0 25 31 313 35 8 01 158 41 S.SO 1050 57 27 5 404 20 364 29R 01 l1b 0s 10 31 ibi Of" iq Moon SO 16'
ato 13 002 NO0DO91 14 5971 NO0 11 15 n,)7 NO00) 3 115 0 19 No00 2 114 78 9 50 13 9 Age 17d
{40
210 (DAY 105) GREENWICH P. M. 1987 APRIL 15 (WEDNESDAY)GMT SUN ARIES VENUS-4.0 MARS 15 JUPITER-2.0 r MOON Lat Moon- Dff
L, T :-A .J, -H; - tIA D- C, hA D c , OHA Dc GHA Dec wt
12 00 %x' 4 3, 1 4 14 31n 3, N22 18 1i 01 N 3 10 t,3 51 S18 21 ht,,2i 2" 15 Ill 10 55 23
3'3013 5180 72 02 302c 7 0 3' 3, 3' 351602 t6 20 2t 70 03 104 ic 3 ib i" 1.1 02(5 20 32 170 45 28 68 03 39 .2b
4 - 3 )b 4
4o 3. 1.7 .b 23 03 173 1 60 04 00 145. 3 3 3- It O: J3l 05 25 33 175 34 32 64 04 1 -08
13 0ji 4 0 i 4. o 3 45 3'I S 4 381 113 3o N22 18 28 03 N 3 10 177 58 S18 35 62 04 32 03- 4 7 46 . 33t, 0 30 34 180 24 37 60 04 44 00
,20j' ' - 51 31 3A8 1, 33 04 182 48 39 58 04 55 .033oJl 2 - 4 C 0 341 Oc 35 34 185 13 41 5t 05 04 0521- 4-, 1 '0 9 5 3 IV 143 l 38 04 187 38 43jI54 05 12 07501 2 4 4A 58b 00 34t 0 40 35 190 02 4 52 05 20 08
14 001 2- N 4 4 53 1- 0 30 5 4 37 346 36 N2Z 18 43 05 N 3 10 192 2; 518 48 50 05 27 1010! j 42 55 42 o3 00 351 3t 45 35 194 52 50 4 05 41 1220 34 , 4j 5P 12 5 o 30 353 3t 48 O 19? Io 52 40 05 53 15301 1 ' 2 k no 42 4 b8 00 - 35t 0' 50 36 194 4! 4 35 0 03 t40- iq 4 43J b3 11 4 70 30 358 37 53 0b 202 0b 5t, 35 0b 03 b
50 42 j 431 65 438 3 00 1 07 55 37 204 30 18 59 0612 182006 28 21
15 00 44518U N 9 433 b8 14? -530 S 4 3 3 37 2219 58 07 N3 10 20t>55S19 01 10 06 42 2410 47 28 0 434 70 44 o 78 00 b 07 b0 37 209 20 03 0 Ob 5 2620 49 580 43 b 73 15 0 80 30 8 37 t3 08 211 44 05 10 07 05 2830 52 281 43.7 75 454 83 00 11 07 65 38 214 09 07
40 54 581 439 78 158 85 30 13 37 b8 08 21b 34 09, 50 57 281 440 80 462 88 00 I6 07 70 39 218 58 12 30 07 36 34
35 07 47 3516 00 59 58 1 N 9 44 2 83 10 b 9Q 30 S 4 34 18 38 N2? 19 73 09 N 3 11 221 23 S19 14 40 07 58 3710 62 282 443 85 471 9$00 21 08 75 39 223 48 16 45 08 10 4020 64 582 445 88 175 95 30 23 38 78 10 226 12 18 50 0826 4330 67 28 2 -44 b 90 479 97 59 2 08 80 40 228 37 2040 69 58 3 448 93 183 100 29 28 38 83 10 231 01 22 52 08 33 4450 72 283 44 9 95 48 7 102 59 31 08 85 41 233 26 25 54 08 41 46
56 08 50 4817 00 74 58 3 N 9 45 1 98 19.1 105 29 S 4 33 33 38 N22 19 88 11 N 3 11 235 51 519 27 58 09 01 405,0 77 283 42 100 49 5 107 59 36 08 90 41 238 15 29 60 09 13 54
20 79 584 454 103 199 110 29 38 38 93 11 240 40 3130 82 28 4 45 5 105 50 3 112 59 41 09 95 42 243 05 - 3340 84 584 45.t 108 208 115 29 43 39 98 12 245 29 35
50 87 284 458 110 51.2 117 59 46 09 100 42 247 54 37
18 00 89 58 5 N 9 45.9 113 21 6 120 29 5 4 32 48 39 N22 19 103 13 N 3 11 250 18 S19 39 Moon's P ,n A
10 92 285 4b1 115 52,0 122 59 51 09 105 43 252 43 42 A C A C3 I o
20 94 585 4o2 118 224 125 2q 53 39 108 13 255 08 4430 97 285 • 4b4 120 52 8 127 59 - - 5b 09 110 44 257 32 - 4640 99 5 6 40 5 123 23.2 130 29 58 39 113 14 259 57 4850 102 28b 4b " 125 53 132 59 61 10 115 44 262 21 50 0 54
19 00 10458b N 94.8 128240 13529 S 431 6340 N2220 11815 N 3 12644b S1952 6 58 55 35 5 33
10 1? 2h o 4'? 130 54 4 137 59 bb 10 120 45 267 11 54 6. 5 32201 109 58.7 4 1 33 249 140 29 b8 40 123 15 269 35 5b 16 b57.^ S 31I )30 112 28' 473 135 553 142 58 71 10 125 46 272 00 19 58 19 5840 114 j 7 47.4 138 25 7 145 28 73 40 128 16 274 24 20 01 22 55 5930
50"1 1 26 7 47't)0 56 1 147 58 7b 10 130 46 276 49 03 24 54 61 2
20 00 1.1 58b N 47 7 143 2,.5 150 28 S 4 30 78 40 N22 20 133 17 N 3 11 279 13 S20 05 26 52 b2 27
10 '22 2d, 479 145 5b9 152 58 81 10 135 47 281 38 07 29 52 63 2720 174 588 48 21 148 27 3 155 28 83 41 138 17 284 03 09 3051 645 26
30 12 2 6 - 482 150 57.7 157 58 86 11 140 47 6528b 27 • 11 32 5 640 1 4 S 1513 281 1100 28 88 41 143 18 288 52 13 24 48 6 23
12 53,9 4o ' ;55 586 b2 58 91 11 145 48 291 16 15 36 b7 23
21 00 134 5,1 N 48t, 158 290 Ib5 26 S4 19 93 41 N22 20 148 18 N 3 12 293 41 520 17 374 68 220 3 Z 4?j i 6 594 Ib7 58 96 1 150 49 29b 05 19 39 46b 9 21
20 139 7240 4r 163 298 170 26 98 41 153 19 2S8 30 21 40 4S 7030 i4- 2,'o 4,41 1h6 002 17? 58 01 11 1" 55 49 300 54 23 42 71 1940 144 5, 432 168 30b 175 28 103 42 158 20 303 19 26 4 72 1850 142/90 494 171 010 177 58 10b 12 160 50 305 43 28 45 42 73
2200.44 4,, N9 4. .*3 3 14 1d0 2 b 4 28 108 42 N22 21 163 20 N 3 12 308 08 S20 30 46 41 74 1610 1 2 24 1 49" 17o U 18 182 58 111 12 165 51 310 33 32 47 0 75 1520 154 54. 4;l, . 8 32.3 1d5 27 113 42 168 21 312 51 34 9 76 14
I 15" 21i 500 161 02 7 18757 116 12 170 51 " " 315 22 - 3b 49 38 76 13401 i, 53 2 50 1e3 331 1 90 2' 118 42 173 22 317 46 38 50 7 1
1 11 3 186 035 192 57 121 12 175 52 320 11 40 52 37 79 12
23 00 ,t,4 5'I ' N , 4 lob 334 195 2 S 14 27 123 42 N22 21 17b 22 N 3 12 322 V) 520 42 52 ') 79 101 b292 50., 141 043 197 57 126 13 180 53 325 00 44 54 34 8
2 , 59 3 5 u' 191 34 7 20 27 128 43 183 23 327 24 4b 55301 23 3 504 196 05i 202 57 131 13 185 53 329 41? . 4m Sun SD 16'040 i4 5"3 510 198 355 205 27 133 43 188 24 332 13 50s50 1"7 24 3 51 2 201 059 20/ 57 13t 13 190 54 334 39 52 Moon SD 16'
15 (A, I N U() 3914 597 No U II ;5001 NO OC 0 35019 NO 002 14278 0 127 Age l7d
-- 4'i1-F~' ~ jr.
A154 SEMIDURATION OF MOONLIGHT
3N PBO VE ,, I N b
- , ',, MOON 8ELCW ,4
I'K - -r . .. .. . __, _ T-" - __'_'_-_- -- N7
2 I I '1S
-I ' / ,j,\ / 1
N!'' S 10 15 20 25 30
............... r.........................- B
S.-ON B-CWj N80
' "\rI H IiON , r ] HORIIONNijS - - - -7 / \ N75
, 0 /
-10.. ' S! 15 20 25 30 I O ?
II
NbL '. " . ". - - . .
' VE MOON BELOW N60
SHOI 1ZON
I' i ,: - ,"{ - N 75'
j N V' L4 4'-____._,, N,
0 1.5 20 25 30 N80
b t I MOON I IN
aU I L 5 0 15 2 0 25 30
4 7
SW
F4 INTERPOLATION OF' MOONRISE, MOONSET
FOR LONGITUDE
Add if longitude westSubtract if longitude east
Longi- Diff.*"- tude 05 10 15 20 25 30
m m m m m m
0 00 00 00 00 00 0020 01 01 02 02 03 0340 01 02 03 04 06 0760 02 03 05 07 08 10
' 80 02 04 07 09 11 13
100 03 06 08 11 14 17120 03 07 10 13 17 20140 04 08 12 16 19 23160 04 09 13 18 22 27
180 05 10 15 20 25 30
' Ln--DiIT.*gtude 35 40 45 50 55 60
tud ID i n i• m va m m m m
0 0000 00 00 00 0015 03 03 04 04 05 05
30 06 07 08 08 09 1045 09 10 11 12 14 15
60 12 13 15 17 18 2075 15 17 19 21 23 2590 18 20 22 25 28 30
105 20 23 26 29 32 35
120 23 27 30 33 37 40
135 26 30 34 88 41 45150 29 33 38 42 46 50
165 32 37 41 46 50 55180 35 40 45 50 55 60r ,- Diff.*
tude 65 70 75 80 85 90
m o ni ID m m
0 00 00 00 00 00 001 10 04 04 04 04 05 0520 07 08 08 09 09 10
30 11 12 12 13 14 1540 14 16 17 18 19 20
50 18 19 21 22 24 2560 22 23 25 27 28 30
70 25 27 29 31 3 3580 29 31 33 36 38 4090 32 35 38 40 42 45
100 36 39 42 44 47 50110 40 43 46 49 52 5120 43 47 50 53 57 60130 47 51 54 58 61 65
a- 140 51 54 58 62 66 70
1S0 54 68 62 67 71 75160 58 62 67 71 76 80170 61 66 71 76 80 85
18 65 70 75 80 85 90
When negativo subtract corre&tio if longitudewmt a add if eas
48
aa%
I at
, ..... . ., : t. P . A t - .t,- . ,oe,] ::P :
.. * - - *:, ' " -, e t -, d * :-Z.\ t ' , i f
.- ,.. A w-_1. , f
::: : ... . i 'h-:rt a2".1 th m~-''ite ' of "o' :t. Lde t - L
:,-- - a".: a:e 'nn .:d..Je.-: fco' /ev. - Lo '_;t e) *o th MT obta'nede ,. resulr n h' _ t o_ event an ,
... *':-rt G,4T tc LST usirg starnda-rd cor're.ction obtained from
S . ..... . A2 - A________
,.3 .: tude: _______ :)_______ ______ '4. ' .d Tirmle Cor rection r- hrs n
,-:. .cr'oprz,-Ate page from A'30 -Al4 = , At the :ntersectzon of iters- the Local Mean Time and enter below:
:-=.:. .... TW:LIGHT SUNRISE SUNSET End Civil Twilight
_ tMT _ _ M _ _LMT _weLMT
e,,:: 1
-. h Arc to Time Tabi-, on mae A16: Determine the GMTv rvrj MT hLs T mu n based on whole (U') lonitude. La t
• -__._ ml-__._,___ sec based ,on rrinutes and seconds of
t ,I,'
Cbining the two and rounding m off second to minutesge foro A13 .- ' t _
r :; fo' West Longc M uee / - Correction for East Lon-i':,fi
V I... w C .ht) "-, (5) Hr s Mi nT 7) +/ - HTMrs M T
--- '- irs Mmn o
:1se ..... n min standard (8) Hrs Manmb - r. (4) to n) (4) o/- Hrs Min
Hrs Mirg LT
-. " Twi' @t 0/:T be computed in steps 8 and 9 using data from.. ,: .t t~os.' Mf,.,,E. Nautical Twilight Time can be estimated
|'............. .... : t¢:co *; dfforence between civil twilight timeh ands' -~ "ixf Twcht. and adding the difference between
S.h time and sunset to the end civil twilight time.
t 50
Hr s- W' n
.ONR - SE.~M0ONSET CALCULATIONC W(-.KE' T
e and the -ati.tude/longltude cf thi- l, 'awrz'heet below.
-.. ., 'n:crmation, from step I determine the Moon-ise'setf : a propr, r -te Air Almanac table (pp 1 -732) fc r, t h-e a-
. i:-. po ation will be required. This is e is c*L.: - ven 1 . ) Lono - tude. At the same tme, c.y -,w!-,
-f c-m the i~iuecloses,;t to youLr locatitrn.
'rt t, local mean tlm,. -for your location, Enter page F4,vsre-. *ide and the Diff from step II to determine the
-:rre-.ti~r, te appled to LMT. After applying the correction andi_ : i 7.have the local mean time of the event for your location.
. ,. - it:-lng the procedures below in para 9.
"".* V. Convert :, LT using the procdeures in para 10 (The Standard"C'rrect:on (51 obtained from pages A20-A23 of the Air Almanac.
% 3. Lor 5 ude: (':) ( ) _ _ _ _
- . Diff value(s) / minutes
5. Standard Time Correction +1- hrs
S. Using 1 and 2 determine moonr.se/set times at 0 - Longitude frompp 1 -7.32. MR: /MS:
Using 3 and 4 determine the correction for your longitude andapply to the time arrived at in 6. MR /MS
From The Arc to Time Table, on page A166: Determine the GMT-Cnverslon on the left side of the chart hrs min based
-"r. whole (') longitude. From the last column determine the minsec based on minutes and seconds of longitude. Combining the
"wO atnd rr;unding off seconds to minutes will giv you the Total (MT:orvers:on (8.
ee! -otal GMT conversion +/- Hrs Mie,'U=e<*correct~cn for West Longitude a - Correction for East
'; "V,< UMI ?4'Iadd 7 and 9isM(7) Hrs M In
. g +/- Hrs Min-Hrs Mmn
.. :1 -appLy standard (10) Hrs Mincor. to ( 0) (5) +/- irs Min
Hrs Min
51
S%
IL LP.
___ ( F ASTRONOMICAL DATA -TEST ANSWERhJ
s AXiSs not perpendicular to the plane of it's orbit.~. :d .3 >2~.(o-r words to that effect.)
AN:, >. Tw:,Ojh Sunrise Sunset PM Civ Twilight0 2 1840 1907
*AM II W±>Iiht, Sunrise Sunset PM Civ Twilight.73 4 0444 1924 2104
-.A. mo no s orbital speed(in either order)
ii 'h e moo:)n's orbital angle
5. Mconrise Moonset.2035 GMT 0449 GMT2>35 LST 0549 LST
!5. Moonrise Moonset7 May '0645 8 May /0645
you missed any of these questions, go back and reread theappropriate sections of this Tech Note.
52
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I4
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S.l
4,,. I_4
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