[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, k 20 =0.024615˙0.0000914, k 21 =0.023915˙0.0000132, and k 22 =0.024852˙0.0000167, and a preliminary solution for the k 30 Love number of k 30 =0.00734˙0.0015, where the Love number error sigmas are those obtained with VCE.

We have derived a gravity field solution in spherical harmonics to degree and order 900, GRGM900C, from the tracking data of the Gravity Recovery and Interior Laboratory (GRAIL) Primary (1 March to 29 May 2012) and Extended Missions (30 August to 14 December 2012). A power law constraint of 3.6 ×10−4/ℓ2 was applied only for degree ℓ greater than 600. The model produces global correlations of gravity, and gravity predicted from lunar topography of ≥ 0.98 through degree 638. The model's degree strength varies from a minimum of 575–675 over the central nearside and farside to 900 over the polar regions. The model fits the Extended Mission Ka-Band Range Rate data through 17 November 2012 at 0.13 μm/s RMS, whereas the last month of Ka-Band Range-Rate data obtained from altitudes of 2–10 km fit at 0.98 μm/s RMS, indicating that there is still signal inherent in the tracking data beyond degree 900.

Knowledge of the average density of the crust of a planet is important in determining its interior structure. The combination of high‐resolution gravity and topography data has yielded a low density for the Moon's crust, yet for other terrestrial planets the resolution of the gravity field models has hampered reasonable estimates. By using well‐chosen constraints derived from topography during gravity field model determination using satellite tracking data, we show that we can robustly and independently determine the average bulk crustal density directly from the tracking data, using the admittance between topography and imperfect gravity. We find a low average bulk crustal density for Mars, 2582 ± 209 kg m−3. This bulk crustal density is lower than that assumed until now. Densities for volcanic complexes are higher, consistent with earlier estimates, implying large lateral variations in crustal density. In addition, we find indications that the crustal density increases with depth.