A global solution for the Mars static and seasonal gravity, Mars orientation, Phobos and Deimos masses, and Mars ephemeris

With the collection of six years of MGS tracking data and three years of Mars Odyssey tracking data, there has been a continual improvement in the JPL Mars gravity field determination. This includes the measurement of the seasonal changes in the gravity coefficients (e.g., J ¯ 2 , J ¯ 3 , C ¯ 21 , S ¯ 21 , C ¯ 31 , S ¯ 31 ) caused by the mass exchange between the polar ice caps and atmosphere. This paper describes the latest gravity field MGS95J to degree and order 95. The improvement comes from additional tracking data and the adoption of a more complete Mars orientation model with nutation, instead of the IAU 2000 model. Free wobble of the Marsʹ spin axis, i.e. polar motion, has been constrained to be less than 10 mas by looking at the temporal history of C ¯ 21 and S ¯ 21 . A strong annual signature is observed in C ¯ 21 , and this is a mixture of polar motion and ice mass redistribution. The Love number solution with a subset of Odyssey tracking data is consistent with the previous liquid outer core determination from MGS tracking data [Yoder et al., 2003. Science 300, 299–303], giving a combined solution of k 2 = 0.152 ± 0.009 using MGS and Odyssey tracking data. The solutions for the masses of the Marsʹ moons show consistency between MGS, Odyssey, and Viking data sets; Phobos GM = ( 7.16 ± 0.005 ) × 10 −4  km 3 / s 2 and Deimos GM = ( 0.98 ± 0.07 ) × 10 −4  km 3 / s 2 . Average MGS orbit errors, determined from differences in the overlaps of orbit solutions, have been reduced to 10-cm in the radial direction and 1.5 m along the spacecraft velocity and normal to the orbit plane. Hence, the ranging to the MGS and Odyssey spacecraft has resulted in position measurements of the Mars system center-of-mass relative to the Earth to an accuracy of one meter, greatly reducing the Mars ephemeris errors by several orders of magnitude, and providing mass estimates for Asteroids 1 Ceres, 2 Pallas, 3 Juno, 4 Vesta, and 324 Bamberga.