NASA Technical Paper 3394 Lifetimes of Lunar Satellite Orbits Kurt W. Meyer The George Washington University/JIAFS • Washington, D.C. James J. Buglia Flight Mechanics & Control, Inc. • Hampton, Virginia Prasun N. Desai Langley Research Center • Hampton, Virginia National Aeronautics and Space Administration Langley Research Center • Hampton, Virginia 23681-0001 March 1994 Acknowledgments This technical report is the cuhninat ion of research in the Vehicle Analysis Branch of the Space Systellls Division at Langley Research relater, during which time the authors received technical guidance from numerous sources. \Vc particularly wish to express appreciation to Dr. Gerald \Vatberg of North Carolina State University at Raleigh for providing vahmble _ussistanee in developing a plan of aetion for addressing lunar parking orbit issues. Additionally, we would also like to thank Robert Tolson of Tile George Washingt(m University for sharing his insight on modeling the Moon's gravitational field, and \_5_yne MeClain of I)rat)er l.aboralories and Richard Cook of lhe .let Propulsion La|)()ratory for their comm_,nls and sug,e, est ions. Summary satellite tracking data from the far side of the Moon, arc inherent in all existing hmar gravity models. The Lifetimes of low-altitude lunar orbits are studied uncertainty in orbital lifetime predictions due t.o er- in this report to identify feasible parking orbits for rors it( the hmar gravity model is addressed through fllture lunar missions. The hmar missions currently tile use of sensitivity eoefficients. The uncertainty ill under stud,,', unlike tile Apollo missions, involve long the rate of perihlne altitude deeay that corresponds stay times. To determine orbital lifetimes of hmar to the uncertainty in the values of the coefficients parking orbits, a model to describe the nonspherical for the gravity model adopted in this analysis is pre- mass distribution of tile Moon must be adopted. A sented. Also, plots of the values of the sensitivity short discussion of previous attempts to describe the coefficients, which can be used to evaluate the uncer- Moon's gravitational field is included, and emphasis tainty ill perihme-altitude decay rates of each grav- is placed on spherical harmonic-gravity models. A itational coefficient for any hmar gravity model, are subset of the fifth-order and fifth-degree hmar gravity presented. model was adopted in this investigation to generate orbital li%time predictions. This simplified inodel Introduction consists of the five gravitational coefficients J2, J3, ,15, C22, and Cal. President Bush's proposal of a Space Exploration Initiative ill 1989 sparked a renewed interest in hmar The primary perturlmtion on a low-altitude mission planning. The objectives outlined in this ini- (100 km or 300 kin) hmar parking orbit is tile Moon's tiative include the establishnlent of a permanent hl- nonspherical gravity field. In this analysis, all other nar outpost. (See refs. 1 and 2.) Lunar stay times on tlerturl)ations (third body perturtmtions, solar radi- the order of 30 to 180 days will be required for initial ation pressure, etc.) are neglected. Although per- det)loynlent and ongoing support of tile outpost. In turbations due to the Earth and tile Sun are not some analyses, preliminary nfissions will involve the negligible for hmar orbits, these effects are small com- insertion of a satellite into a low-altitude hmar orbit pared with the Moon's nonspherical potential for all to inap the Moon's surface. Also in these analyses, tile orbits considered in this analysis. By investi- initial manned lnissions will require tim l)lacement gating the effects that initial conditions have on the of a hmar transfer vehicle in a low-altitude parking subsequent lifetime of an orbit, a technique is intro- orbit. Ongoing support of an outpost nlight include duced t.o aid mission planners in the selection of hmar tile t)lacement of a st)ace station in low lunar ort)it. parking orbits. In this investigation, tile lifetimes of Any of these nfissions will require spacecraft, to be in near-circular parking orbits, with various initial or- lunar parking orbits for long periods of time. Pre- bital elemenls and either lO0-km or 300-kin perihme vious orbital determination studies for hmar satel- altitude, are analyzed for mission phmning purposes. lites have indicated that the Moon's nonspherical Orbital lifetilnes are heavily dependent on the gravity field will have a great effect on the sul)- initial conditions of the orbit, particularly tile ini- sequent lifetime of the ort)it. (See refs. 3 to 5.) In tial inclination and argument of l)erilune. The lu- fact, a hmar-orbit space stati(m Ilropose(t by NASA nar gravity model ulilized in this analysis for the to be in a 60-n.mi. (111 kin) circular polar orbit 100-kin initial perihme altitude case yields lifetime al)out tile Moon wa_s foun(t to impact the hmar sin'- predictions of less than 40 days for some orbits, and face in 140 days if no station-keeping altitude boost more than a year for others. Five distinct bands of maneuvers were performed. (See ref. 6.) short-lifetime orbits appear a.s a function of the ini- An important element involved ill establishing a tial inclination: these bands are separated by bands base on the Moon is the initial manned mission t.o of long-lifetime orbits. Of particular interest is a set the hmar surface. As with the Apollo missions, the of orbits with an inclination of approximately 70°; hmar transfer vehicle (LTV) will be inserted into a this set of orbits yields hmg lifetimes and provides parking orbit about the Moon at arrival. Apollo mis- the high latitude coverage that is desirable for vari- sions restricted these parking orbits to circular, near- ous nfissions. Thv .15 coefficient contributes the dom- equatorial orbits. However, the utilization of park- inant efl'eet ill perilune altitude decay and, therefore, ing orbits at all inclinations must be addressed to orbital lifetimes. a(:commodate tile vast array of hmar missions cur- The methods presentetl in this report are suit- rently being proposed. Tile LTV will remain in this able for incorporating the Moon's nonspherical grav- parking orbit until a departure burn for return to itational effects into the preliminary design level for Earth is initiated. The transfer of cargo and person- fllture hmar mission planning. However, inconsisten- nel to tile hmar surface is accomplished by the de- cies and limitations, caused primarily by a lack of scent of a lunar lander from the parking orbit. Ascent @Trans-lunar Nomenclature ® Trans-Earth injection AHlrL_J_TlTrl Fourier coefficients a senfimajor axis, km LandingAscent(__ Cnm , _nm gravitational coefficients Deorbil@\_ (_Lunarorbit insertion (_Earthorbit dm infinitesinml nlass ckunent, kg insertion e eccentricity Figure1.Earth-hnmrmissionsequence.(Fromref.1.) eccentricity averaged over period of third body about central body and rendezvousof the landerwith tile LTV in the (_IIOW new vahle of eccentricity (after parkingorbit initiatestheEarth-returnsequenceof integration) the mission.(Seefig. 1.) Therefore,longstaytimes onthehnmrsurfacewill requirethat theLTV remain Cold old vahle of eccentricity (before in a parkingorbit for a longperiod. Tile mission integration) designermustaddressthevariationsill theorienta- tion of theparkingorbit for thedurationof themis- G gravitational constant, sionto establishthenecessaryAV requirelnents for 6.67 x 10 11 ma_kg l_s-2 performing the rendezvous and trans-Earth injection h altitude, km nmneuvers. i inclination, deg Since the Apollo nfissions involved only short stay times at the Moon (on tile order of 1 to 3 clays), little 7 inclination averaged over period of work was performed on predicting long term changes third body about central body, (leg ill the parking orbits of hmar modules. However, for JTi zonal gravitational coefficient, -C,,0 longer stay times (30 to 180 days), an accurate model LTV lunar transfer vehicle of the Moon's gravity field is required for preliminary mission planning, especially with low-altitude park- M inean anomaly, (leg ing orbits. The need for long orbital lifetimes is a key criterion in the process of selecting tk'asible parking 34 mass of Moon, 7.35 x 1022 kg orbits. By investigating the effects that initial con- 7_ mean angular motion, tad/day ditions have on the subsequent lifetinte of an orbit, a technique is introduced that will aid mission planners mean angular motion averaged over ill the selection of humr parking orbits. period of third body about central body, rad/day Because of the Moon's irregular internal structure and surface shape, the lifetime of a hmar satellite or- n3 mean angular inotion of third body bit is constrained by the nonspherical nature of tile about, central body, rad/day Moon's gravity field. Ill tile present analysis, a sim- PItIH associated Legendre polynonfial plified gravitational model of tile Moon is introduced that will enable mission planners to easily predict P position vector long-term changes in lunar parking orbits at the pre- R radius of Moon, 1739 km liminary design lewq. The development of a simpli- fied gravitational model with sufficient accuracy is 7-¢ distance betwecn mass element and necessary to investigate orbital lifetimes for the large exterior point, kin number of initial orbital parameters possible. Uti- r radius, km lization of a simplified model will significantly reduce the required comtmtational time needed to perform rate of altitude decay, kin/day this analysis. The effect of