High‒degree gravity models from GRAIL primary mission data

Abstract

[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.

Lunar core structure investigation: Implication of GRAIL gravity field model

“…Yet another significant advancement in lunar gravity field resulted from the GRAIL mission. This mission observed lunar global gravity with highly accurate low-low satellite-to-satellite Ka-band tracking data, resulting in an improvement of the lunar gravity field model precision around 3 orders of magnitude compared with the SELENE models (Zuber et al, 2013;Konopliv et al, 2013;Lemoine et al, 2013). The significant differences between the mean moment inertia from the Lunar Prospector-based models and recent SGM100h and GRGM660PRIM models confirm the improvement of the mean moment of inertia stimulated by the gravity field model (Matsumoto et al, 2010;Yan et al, 2012;Lemoine et al, 2013).…”

Precession of Mercury’s Perihelion from Ranging to the MESSENGER Spacecraft

“…The mass parameters of Earth and Moon were derived from planetary and lunar laser ranging (Folkner et al 2014), which are compatible with results from satellite laser ranging of LAGEOS The residual precession angle has a linear fit removed (blue) and a quadratic plus periodic fit removed (green). (Ries et al 1992) and radio tracking of the GRAIL spacecraft (Konopliv et al 2013;Lemoine et al 2013;Williams et al 2014).…”

Application of Modern Fortran to Spacecraft Trajectory Design and Optimization

“…The segment class contains all the data necessary to propagate the segment by the integration method (t 0 , t f , x 0 , the force model, etc.). The Fortran Astrodynamics Toolkit is used to define the force model, which is an 8 × 8 GRAIL model [62] for the Moon, with the Earth and Sun included as pointmass third bodies. The equations of motion for this problem are shown in Fig.…”