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Highdegree Gravity Models from GRAIL Primary Mission Data JOURNAL OF GEOPHYSICAL RESEARCH: PLANETS, VOL. 118, 1676–1698, doi:10.1002/jgre.20118, 2013 High-degree gravity models from GRAIL primary mission data Frank G. Lemoine,1 Sander Goossens,1,2 Terence J. Sabaka,1 Joseph B. Nicholas,1,3 Erwan Mazarico,1,4 David D. Rowlands,1 Bryant D. Loomis,1,5 Douglas S. Chinn,1,5 Douglas S. Caprette,1,5 Gregory A. Neumann,1 David E. Smith,4 and Maria T. Zuber4 Received 5 June 2013; revised 25 July 2013; accepted 1 August 2013; published 23 August 2013. [1] We have analyzed Ka-band range rate (KBRR) and Deep Space Network (DSN) data from the Gravity Recovery and Interior Laboratory (GRAIL) primary mission (1 March to 29 May 2012) to derive gravity models of the Moon to degree 420, 540, and 660 in spherical harmonics. For these models, GRGM420A, GRGM540A, and GRGM660PRIM, a Kaula constraint was applied only beyond degree 330. Variance-component estimation (VCE) was used to adjust the a priori weights and obtain a calibrated error covariance. The global root-mean-square error in the gravity anomalies computed from the error covariance to 320 320 is 0.77 mGal, compared to 29.0 mGal with the pre-GRAIL model derived with the SELENE mission data, SGM150J, only to 140 140. The global correlations with the Lunar Orbiter Laser Altimeter-derived topography are larger than 0.985 between ` = 120 and 330. The free-air gravity anomalies, especially over the lunar farside, display a dramatic increase in detail compared to the pre-GRAIL models (SGM150J and LP150Q) and, through degree 320, are free of the orbit-track-related artifacts present in the earlier models. For GRAIL, we obtain an a posteriori fit to the S-band DSN data of 0.13 mm/s. The a posteriori fits to the KBRR data range from 0.08 to 1.5 μm/s for GRGM420A and from 0.03 to 0.06 μm/s for GRGM660PRIM. Using the GRAIL data, we obtain solutions for the degree 2 Love numbers, k20=0.024615˙0.0000914, k21=0.023915˙0.0000132,andk22=0.024852˙0.0000167,and a preliminary solution for the k30 Love number of k30=0.00734˙0.0015, where the Love number error sigmas are those obtained with VCE. Citation: Lemoine, F. G., et al. (2013), High-degree gravity models from GRAIL primary mission data, J. Geophys. Res. Planets, 118, 1676–1698, doi:10.1002/jgre.20118. 1. Introduction Lunar Gravity Ranging System (LGRS) measures precisely the range between the two co-orbiting spacecraft [Klipstein [2] The pair of spacecraft comprising the NASA Dis- covery Gravity Recovery and Interior Laboratory (GRAIL) et al., 2013]. The GRAIL mission is the latest and the mission successfully mapped the gravity field of the Moon most comprehensive effort to map the lunar gravity field. from a mean altitude of 55 km between 1 March and 29 Asmar et al. [2013, Table 1] give a detailed summary of the May 2012 [Zuber et al., 2013a]. The GRAIL mission used differences and similarities between GRACE and GRAIL. a modified version of the precision intersatellite ranging [3] The earliest efforts to determine the lunar gravity field system used on the Gravity Recovery and Climate Experi- date to the 1960s and 1970s and used the S-band Doppler ment (GRACE) mission [Tapley et al., 2004a]. The GRAIL tracking of the Lunar Orbiters 1–5, the Apollo Command Modules, and the Apollo 15 and 16 subsatellites. Muller and Sjogren [1968] demonstrated the existence of mascons over Additional supporting information may be found in the online version the large lunar maria from an analysis of Lunar Orbiter data. of this article. The data from the Apollo Command Module and Apollo 1NASA Goddard Space Flight Center, Greenbelt, Maryland, USA. 16 subsatellite were acquired from very low altitude orbits 2 CRESST, University of Maryland, Baltimore County, Baltimore, (12–30 km altitude); however, the tracking coverage pro- Maryland, USA. 3Emergent Space Technologies, Greenbelt, Maryland, USA. vided only localized sampling of the lunar gravity field using 4Department of Earth, Atmospheric and Planetary Sciences, S-band Doppler [Gottlieb et al., 1970; Sjogren et al., 1972, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA. 1974; Phillips et al., 1978]. The S-band Doppler of this 5Stinger Ghaffarian Technologies Inc., Greenbelt, Maryland, USA. era had a precision of a few mm/s, while the GRACE and Corresponding author: F. G. Lemoine, Planetary Geodynamics Labora- GRAIL Ka-band range rate (KBRR) data have a precision of tory, Code 698 NASA Goddard Space Flight Center, Greenbelt, MD 20771, 0.1 μm/s or better. The Lunar Orbiter and Apollo subsatel- USA. ([email protected]) lite data provided low-altitude coverage over the equatorial ı ©2013. American Geophysical Union. All Rights Reserved. regions to ˙30 latitude. In the early 1990s, the S-band data 2169-9097/13/10.1002/jgre.20118 to the Apollo-era lunar orbiters were reanalyzed with the 1676 LEMOINE ET AL.: HIGH-DEGREE GRAIL GRAVITY MODELS development of updated spherical harmonic models such as The Lunar Orbiter Laser Altimeter (LOLA) was designed to Lun60d to 60 60 [Konopliv et al., 1993] and GLGM2 to map the Moon with 5 m footprint and a vertical resolution of 70 70 [Lemoine et al., 1997], where GLGM2 incorpo- 10 cm. To satisfy the LRO orbit determination requirements rated data from the Clementine mission. The Soviet Union and aid in the accurate geolocation of the laser altimeter data, sent a series of spacecraft to the Moon, which occupied a Mazarico et al. [2012] developed a tuned gravity model of variety of inclinations and periapse altitudes. The tracking the Moon to degree 150 that combined LRO S-band tracking data from the Luna satellites were combined into a 16 16 data, altimetric data in the form of altimeter crossovers, and model by Sagitov et al. [1986] and later reprocessed by Akim the historical U.S. Lunar spacecraft data into the 150 150 and Golikov [1997]. So far as we are aware, logistical and model, LLGM-1. This model resulted in LRO orbit accura- technical efforts appear to have stymied efforts to combine cies of 20 m, a substantial improvement over what could be tracking data from the Soviet Luna orbiters and the U.S. achieved with respect to the untuned models (e.g., GLGM3). historical orbiters into a single combined solution for the For GRAIL though, we did not notice any benefit of using lunar gravity field. LLGM-1 and thus preferred to use SGM150J as a priori. [4] The tracking data from Lunar Prospector provided [8] Detailed simulations showed that the intersatellite a substantial leap in knowledge due to the low-altitude, tracking data obtained from GRAIL over the 3 months of the near-polar orbit of the spacecraft. Whereas during the pri- primary mission of GRAIL would provide a factor of 100 to mary mission (January to December 1998) the spacecraft 1000 improvement over gravity models based on the earlier orbited the Moon at an average altitude of 100 km, during data [Park et al., 2012]. As we will show in this paper, the the extended mission (January to July 1999) the spacecraft results we obtain substantiate and in some respects exceed altitude was lowered to an average of 30 km. The Lunar these pre-mission expectations. Prospector data, in combination with the previous lunar mis- [9] Under the auspices of the GRAIL Science Team, two sion data, were used to develop the LP150Q [Konopliv, groups at the NASA Goddard Space Flight Center (NASA 2000; Konopliv et al., 2001] and GLGM3 [Mazarico et al., GSFC) and at the Jet Propulsion Laboratory (JPL) were 2010] models to degree 150 in spherical harmonics. tasked to analyze the Level 1B tracking and produce geopo- [5] There is evidence that the Lunar Prospector tracking tential models as Level 2 products [Zuber et al., 2013a]. The data contain information to higher degree than can be reli- results of the JPL analyses are discussed by Konopliv et al. ably extracted from the tracking data. Han et al. [2011] [2013], including the development of models to 660 660 used the Lunar Prospector data tracking data residuals to in spherical harmonics. The model GL420A model devel- derive a solution to degree 200 with localized harmonics oped by the JPL team was presented in Zuber et al. [2013b] that increased the resolution of nearside features, while not in the first publication of GRAIL results from the primary changing the a priori farside gravity model. However, due to mission. This paper focuses on the development of the lunar the synchronous rotation of the Moon, none of the historical gravity models from GRAIL primary mission data by the missions just mentioned could obtain direct Doppler track- NASA GSFC team and discusses the development of models ing over the lunar farside. As a result, the farside gravity to 420 420, 540 540,and660 660 in spherical har- field in those models was poorly determined, as evidenced, monics. This paper is structured as follows: In section 2, we for example, by the errors in the gravity anomalies com- summarize the GRAIL mission and describe the Deep Space puted using the error covariance of the GLGM3 model Network (DSN) and KBRR data; in section 3, we describe [cf. see Mazarico et al., 2010, Figure 4]. the force and measurement models applied; in section 4, [6] A variety of mission concepts were proposed over we describe the strategy used to analyze the tracking data several decades to try and obtain direct tracking data over the and the inversions strategies that were employed to obtain lunar farside.
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