TWO REFERENCE japollo LUNAR PARKING - ORBITS / T. P. TIMER. (NASA CR OR rmx OR AD NUMBER) OCTOBER 1965 GODDARD SPACE FLIGHT CENTER

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1 x * 1 TWO REFERENCE japollo LUNAR PARKING - ORBITS / I ! BY T. P. TIMER,< CFSTI PRICE(S) $ c 4 (PAGES1 (NASA CR OR rmx OR AD NUMBER) 277 I (CATEGORY) ff 653 July 65 OCTOBER 1965,r ; I '. GODDARD SPACE FLIGHT CENTER GREENBELT, MARYLAND 4 'I. 1, ' -- :P /,

2 X TWO REFERENCE APOLLO LUNAR PARKING ORBITS by T. P. Timr Octobr 1965 Goddard Spac Flight Cntr Grnblt, Maryland

3 I. TWO REFERENCE APOLLO LUNAR PARKING ORBITS by T. P. Timr Goddard Spac Flight Cntr SUMMARY This rport invstigats th variation of th orbital paramtrs for th forty hour priod aftr insrtion into two rfrnc Apollo Lunar Parking Orbitsl. It is found that whil th variation of most of th paramtrs undr th influnc of a triaxial Moon and othr prturbing forcs is small, th chang in pricynthion hight is significant. In Tabl 1 th amount of chang in th various lmnts during this tim is shown. Th most prtinnt pic of information drivd from this invstigation is with rgard to th choic of hypothticallunar landing sits on th surfac of th Moon (s Figur 1). Choosing a point on th arthward sid of th trac which satisfis th constraint that it has a longitud of btwn 315"and 45" and a latitud of +5" and -5" with rspct to a slnographic coordinat systm on has a hypothtical landing sit. It is found that any subsqunt trac of th sub-modul point at th sam longitud will always li within :5 in latitud of th initial landing sit chosn during th forty hours undr considration. Thrfor, landing sits chosn in th abov mannr mt th two rquirmnts as dscribd in Apollo Navigation Tchnical Rport' which stats that th two constraints on th lunar parking orbit mission ar as follows: (1) th plan of th trajctory must contain a landing sit vctor on th arth sid of th Moon which has a longitud of btwn 315" and 45" and a latitud of btwn +5" and -5" in slnographic coordinats. (2) th plan of th orbit must b orintd so that th lunar landing sit dosn't mov out of th orbital plan mor than :5 during th priod of 3 to 39 hours aftr lunar insrtion. 'pp. 3-1 Apollo Navigation Group Tchnical Rport 65-AN-1., Fbruary 5, $p. 3-6, 3-7. iii

4 TWO REFERENCE APOLLO LUNAR PARKING ORBITS T. P. Timr Goddard Spac Flight Cntr INTRODUCTION Th basic concpt bhind this rport was to s how th orbital paramtrs for th two rfrnc lunar parking orbits bhavd during th forty hour priod aftr lunar insrtion. To this nd two 79/794 computr programs wr usd to gnrat this information which is prsntd as two sris of graphs. Sris A graphs ar associatd with th 1968 rfrnc trajctory. Sris B graphs ar associatd with th 1969 rfrnc trajctory. It should b notd at th outst that svral coordinat systms ar in us throughout this rport. Th thr coordinat systms in us ar th following: cntr: slnocntric fundamntal plan: paralll to th arth's quatorial plan x-axis: man quinox of dat cntr: slnocntric fundamntal plan: lunar orbital plan x-axis: arth-moon lin of dat cntr: slnocntric fundamntal plan: tru quator of th moon x-axis: intrsction of th prim mridian and th quator of th moon. Th two computr programs usd as sourcs of data ar th Jt Propulsion Laboratory's Spac Trajctory program and th Goddard Intrplantary Trajctory Enck Mthod program. Both programs numrically intgrat th orbit by th Enck Mthod hnc on program srvs as an indpndnt chck of th validity of th data gnratd by th othr program.

5 I. Gnral Dscription of th Rfrnc Trajctoris Th lunar parking orbit is constraind to b nar-circular with a smimajor axis of nautical mils (1886 km) with an altitud abov th lunar surfac of 8 nautical mils *5 nautical mils (148 9 km). Th duration of this trajctory is constraind to b btwn two to sixty hours3. In this study both cass mt ths rquirmnts. Th insrtion conditions for th two rfrnc' trajctoris undr considration (study) ar: Dat of Lunar Insrtion Rfrnc Trajctory #1 May 9, hrs/54. mins/56.61 scs. Dat of Lunar Insrtion Rfrnc Trajctory #2 Sptmbr 2, hrs/l mins/ scs. X = n.mi. Y = n.mi. Z = n.mi. X = Y = Z = n.mi. 95 n.mi. 51 n.mi. = ft/sc P = ft/sc Z = ft/sc It = ft/sc Y = ft/sc Z = ft/sc X = km Y = km Z = km X = Y = Z = km 111 km 517 km X = km/sc Y = km/sc Z = km/sc X = km/sc Y = km/sc z = km/sc convrsion factors: p 4-8 COORDINATE SYSTEM cntr: slnocntric fundamntal plan: plan paralll to arth's man quator of dat x-axis: man quinox of dat at insrtion. - 3p 3-7: 4p

6 In trms of orbital lmnts, th insrtion conditions, using th sam coordinat systm abov, ar: Rfrnc Trajctory #A 1968 a = km = i = 158' R = w = 357: m = : Rfrnc Trajctory #B 1969 a = km = i = R = 182t414 8 w = 262: m = OtOOl II. Discussion of th Graphical Rsults Th sris of graphs A-1 through A-6, and B-1 through B-6 ar rlatd to th rfrnc trajctoris A and B rspctivly and show similar trnds. Hnc only th first st of graphs will b discussd in dtail with much of th discussion bing applicabl to both sts. By inspcting graphs A-1 to A-4 th graphs of th smi-major axis, ccntricity, inclination, and longitud of th ascnding nod it can b sn that th orbit chosn is rlativly a vry stabl orbit. Th smi-major axis varis at most about.5 kilomtrs from its original lngth during th 4 hours of invstigation. Th inclination changs lss than.5 dgrs. Th ccntricity is plottd to a scal with a factor Its fluctuations during th forty hour priod ar of th ordr of magnitud of.3 X as a maximum. Th longitud of th ascnding nod for all practical purposs changs linarly with rspct to tim, varying lss than.5 dgrs during th tim intrval considrd. Th purpos of th prcding discussion was to show quantitativly how ths various lmnts varid with tim. Figur A-5 and Figur A-6, howvr, provid th most usful information dirctly affcting a lunar parking orbit. In Figur A-5, hight (radius vctor minus th man lunar radius) vrsus hours from poch, shows how th hight varis priodically with th priod bing th tim for on circumlunar orbit. This variation is lss than.15 kilomtrs. Figur A-6 shows th limiting cass, th first and th last orbit data, of th trac of th command modul on th lunar surfac or th lunar sub-modul point. It can b sn that for th worst cas by choosing a particular point on th trac of th first trajctory and thn choosing a point on th trac of th last trajctory at th sam longitud, th variation in latitud would b at worst Ot2. A considrabl portion of th tim, this variation is lss than Oz2. 3

7 I CONCLUSIONS (1) Basd on th graphical data prsntd, ithr th 1968 or 1969 rfrnc trajctory could provid an orbit stabl nough to mt th mission rquirmnts of having suitabl landing sits on th lunar surfac which do not vary mor than :5 in latitud from th original landing sit, This information is prsntd in graphs A-6 and B-6 rspctivly whr arbitrary hypothtical landing sits hav bn chosn. (2) Th us of two computr programs, on to srv as an indpndnt chck on th data gnratd by th othr, is justifid as th intr comparison of th data on th various graphs indicats. In Tabl 1 th maximum changs in th paramtrs for th two cass ar shown. Essntially, th rsults ar idntical. I Tabl 1 Maximum Changs in Orbital Paramtrs Cas # Data Cas # Data.5 km.3 X Ot5.45 km.3 X :5 -=i A Latitud 4

8 Srvic Modul) T c Figur 1 5

9 P P P \\\ E E E YYY.- L m E.- E h 6

10 Y Y P 3.2 ;. YYY... - I E E E YYY E, c Y a c 9 All 31111N

11 N W (saaj6ap) NOIlVNll3NI 8

12 " 22';. P P P L YYY W h( VI Z Q c n Z ou Z Q I- ki -I z

13 12 co ' *

14 9 s c w - L O -I 3 (Y (3 'l I a i c 11

15 I\ h m SI B OD ' 3. Eo

16 - a c " ; c 3 w E E E YYY I\ I\ m m 9 13

17 s ui 2 14

18 I= OD m c -.o E t 8 -!$ - bi? c. 3$! 9 m '9 N s N co N N 15

19 1% 9 w Y) 2 2

20 I - C / i / i / f LL