High‒degree gravity models from GRAIL primary mission data

<jats:title>Abstract</jats:title><jats:p>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 <jats:italic>ℓ</jats:italic>=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, <jats:italic>k</jats:italic><jats:sub>20</jats:sub>=0.024615±0.0000914, <jats:italic>k</jats:italic><jats:sub>21</jats:sub>=0.023915±0.0000132, and <jats:italic>k</jats:italic><jats:sub>22</jats:sub>=0.024852±0.0000167, and a preliminary solution for the <jats:italic>k</jats:italic><jats:sub>30</jats:sub> Love number of <jats:italic>k</jats:italic><jats:sub>30</jats:sub>=0.00734±0.0015, where the Love number error sigmas are those obtained with VCE.</jats:p>