JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 102, NO. E7, PAGES 16,339-16,359, JULY 25, 1997 A 70th degree lunar gravity model (GLGM-2) from Clementine and other tracking data FrankG. R. Lemoine,David E. Smith,Maria T. Zuber,• Gregory A. Neumann,• and David D. Rowlands Laboratoryfor Terrestrial Physics, NASA Goddard Space Flight Center, Greenbelt, Maryland Abstract. A spherical harmonic model of the lunar gravity field complete to degreeand order 70 has been developedfrom S band Doppler tracking data from the C]ementine mission,as well as historical tracking data from Lunar Orbiters 1-5 and the Apollo 15 and 16 subsate]lites. The mode] combines361,000 Doppler observationsfrom Clementine with 347,000 historical observations. The historical data consistof mostly 60-s Doppler with a noiseof 0.25 to severalmm/s. The C]ementine data consist of mostly 10-s Doppler data, with a data noise of 0.25 mm/s for the observationsfrom the Deep SpaceNetwork, and 2.5 mm/s for the data from a naval tracking station at Pomonkey,Maryland. Observationsprovided C]ementine, provide the strongest satellite constraint on the Moon's low-degree field. In contrast the historical data, collectedby spacecraftthat had lower periapsis altitudes, provide distributed regionsof high-resolutioncoverage within +29 ø of the nearsidelunar equator. To obtain the solution for a high-degreefield in the absenceof a uniform distribution of observations,we applied an a priori power law constraintof theform 15 x 10-5//2 whichhad the effectof limitingthe gravitational power and noiseat short wavelengths.Coefficients through degree and order 18 are not significantlyaffected by the constraint, and so the model permits geophysical analysis of effects of the major basins at degrees 10-12. The GLGM-2 model confirmsmajor featuresof the lunar gravity field shown in previousgravitational field models but also revealssignificantly more detail, particularly at intermediate wavelengths(103 km). Free-airgravity anomaly maps derived from the newmodel show the nearsideand farside highlandsto be gravitationally smooth, reflectinga state of isostaticcompensation. Mascon basins (including Imbrium, Serenitatis, Crisium, Smythii, and Humorurn)are denotedby gravity highsfirst recognized from Lunar Orbiter tracking. A]] of the major masconsare bounded by annuli of negative anomaliesrepresenting significant subsurfacemass deficiencies.Mare OrientMe appears as a minor masconsurrounded by a horseshoe-shapedgravity low centered on the Inner and Outer Rook rings that is evidence of significant subsurfacestructural heterogeneity.Although direct tracking is not available over a significantpart of the lunar farside, GLGM-2 resolvesnegative anomaliesthat correlate with many farside basins, including South Pole-Aitken, Hertzsprung, Koro]ev, Moscoviense,Tsio]kovsky, and Freund]ich-Sharonov. Introduction setted into elliptical orbits with periapses of 50 to 100 km above the lunar surface. The Apollo spacecraftwere Until the launch of Clementine, on January 24, 1994, placed in near circular orbits at low inclinations with a the sourcesof tracking data for gravity models derived mean altitude of 100 km, although sometracking was by U.S. investigatorshave been the Lunar Orbiters and acquired from altitudes as low as 10 to 20 km. The the Apollo spacecraft. The Lunar Orbiters were in- tracking data sampled the gravity field of the Moon at a resolutionunprecedented for orbiting spacecraft, at • Also at Department of Earth, Atmospheric,and Plane- either the Earth, Venus, or Mars. However,the spatial tary Sciences,Massachusetts Institute of Technology,Cam- coverageof the tracking was incomplete, with no direct bridge. tracking data availableover large portions of the lunar farside. During the initial investigations,in the 1960s Copyfight 1997 by the American GeophysicalUnion. and 1970s, researchers were limited in the size of the Paper number 97JE01418. spherical harmonic solutions that could be developed 0148-0227/97/97JE-01418509.00 by the computersthen available. Becauseof the power 16,339 16,340 LEMOINE ET AL.: A 70TH DEGREE LUNAR GRAVITY MODEL (GLGM2) of the higher degreeharmonics in the tracking data, the the Apollo spacecraftwere also located in low-altitude, early solutions encountered severe difficulties with the near-circular orbits. In some cases, these spacecraft aliasing of the high-degreesignal into the lower degree came as low as 12 to 20 km from the lunar surface;how- terms. In an effort to exhaustthe availablesignal in the ever, these data were limited spatially and temporally. tracking data, other methodswere employedto map the The data from Apollo missions8 and 12, in combination lunar gravity field. These alternate methods included with the Lunar Orbiter data, were used by Won# et al. the estimation of discrete massesover the lunar surface, [1971]to solvefor 600 discretemasses over the nearside or the mapping of the accelerationsexperienced by or- (4-600in latitudeand 4-95o in longitude).Data from biting spacecraftin the line of sight(LOS) betweenthe Apollo missions14, 15, 16, 17, were used by Muller et spacecraftand tracking station. al. [1974],and $jogrenet al. [1972a,b;1974b,c] to map A selectionof the solutionsfor the lunar gravity field the LOS accelerations. that have been developed since the 1960s is summa- Ferrari [1977]derived mean elements from short-arc rized in Table 1. The landmark solutions include those fits to the tracking data. Ferrari [1977] developeda of Muller and Sjogren[1968], Williams et al. [19731, 16th degreespherical harmonic solution that wasamong Sjogrenet al. [1974a],Ferrari [1977],Bills and Ferrari the first to show plausiblecorrelations between a map [1980],and Konop!ivet al. [1993]. The analysisof the of surface gravity anomaliesand farside lunar features, Lunar Orbiter data by Muller and Sjogren[1968] led to such as Mendeelev, Korolev, and Moscoviense. Bills the discoveryof the massconcentrations ("mascons") and Ferrari [1980]combined much of the data usedby under the ringed lunar maria. Williams et al. [1973] previousinvestigators, such as the Lunar Orbiter data, employedlaser ranging to retrofiectorsleft on the lunar the Apollodata from Wonget al. [1971],the trackingof surfacein combination with lunar gravity solutionsde- the Apollo 15 and 16 subsatellites,and lunar laserrang- rived from radiometric tracking. The lunar laser rang- ing. They developeda 16th degreespherical harmonic ing data are sensitive to the second-degreeand third- solutionthat remainedthe best lunar gravity model for degree gravity field harmonics, through their influence the next 13 years. on the lunar physicallibrations [Dickey et al., 1994]. Konoplivet al. [1993]developed a 60th degreemodel Sjogrenet al. [1974a]used data from the Apollo 15 and from the tracking of the Lunar Orbiters and the Apollo 16 subsatellites to map the nearside of the Moon 4-29o subsatellites.Taking advantageof the high speedand in latitude and 4-100o in longitude, using both LOS memory capacity of more modern computers,this model accelerations and the estimation of discrete masses on represented the first realistic attempt to exhaust the the lunar surface. The Apollo subsatellitesmarked the gravity signalfrom the low periapsesatellites in a high- first time an extensive amount of data was acquired degreespherical harmonic solution. This model has ex- from a lunar satellite in low-altitude(100 km) near- cellent performance in terms of its root mean square circular orbit. The command and service modules of (RMS) fit to the trackingdata, and the map of the Table1. PreviousLunar Gravity Analyses Reference Data Used Comment Muller and $jogren[1968] Lunar Orbiters Discovery of lunar mascons. LoreIt and $jogren[1968] Lunar Orbiters 4x4 sphericalharmonic solution + zonals to 1=8. Wonget al. [1971] Apollo 8, 12 Solution for discrete masses on near side. Michael and Blackshear[1972] Lunar Orbiters 13x13 spherical harmonic solution. $jogrenet al. [1972a,b;1974b,c]; Apollos 14-17 Mappedline of sight(LOS) accelerations Muller et al. [1974] with data from as low as 12-20 km altitude. Sjogrenet al. [1974a] Apollo subsatellites Solve for LOS and discrete masses, Ferrari [1977] LO-5 and Apollo subsatellites 16x16 spherical harmonic solution. Ananda[1977] Solve for discrete masses. Bryant and Williamson[1974] Explorer 49 3x3 spherical harmonic solution from KeplerJan mean elements. Blackshearand Gapcynski[1977] Explorers 35 and 49 Zonal solution, J2 - Je only from Keplerian mean elements. Williams et al. [1973] Lunar laserranging (LLR) Ferrari et al. [1980] LLR and LO-4 Bills and Ferrari [1980] LLR, LO 1-5, Apo•o subsatellites, 16x16 spherical harmonic solution and Apollo 8,12 Konoplivet al. [1993] LO 1-5 and Apollo subsatellites 60x60 spherical harmonic solution. Dickey et al. [1994] LLR LEMOINE ET AL.: A 70TH DEGREE LUNAR GRAVITY MODEL (GLGM2) 16,341 lunar gravity anomaliesappears smooth when mapped the Jet PropulsionLaboratory (JPL), and the Johnson on a surface at 100 km altitude. However, the high- SpaceCenter (JSC). Explorers35 and 49 wereplaced in degreeterms have excessivepower, and when the grav- high lunar orbits, and were sensitiveto the low-degree ity anomalies are mapped onto the lunar surface, nu- harmonics[Bryant and Williamson,1974; Gapcynskiet merousartifacts becomeapparent, which make the mod- al., 1975; Blackshearand Gapcynski,1977]. In addi- el unsatisfactoryfor usein geophysicalstudies. The goal tion, these spacecraftwere tracked by VHF, not S band of the new analysiswas to developa lunar gravity model tracking,