Phobos’ degree-1 ellipsoidal harmonic gravity field recovery from two Mars Express flybys

ABSTRACT In this work, we model the gravity field of Phobos by employing an ellipsoidal harmonic coefficients representation instead of regular spherical harmonic coefficients up to degree-one (four gravity parameters in total) including the GM. Doppler tracking data from the combined flybys of Phobos by the Mars Express spacecraft in 2010 and 2013, with separate closest flyby distances of 70 and 59 km respectively, were processed. An improved estimate of the Phobos GM is presented with value as $(7.09962\pm 0.00197)\times 10^5$ m$^3$/s$^2$ ($3\sigma$). A comprehensive comparison between the spherical harmonic solution and the ellipsoidal harmonic solution reveals that the largest disparity in gravity potential occurs at the ends of Phobos’ elongated axis. The improved GM estimate suggests that the ellipsoidal harmonic expansion performs better than the spherical harmonic expansion for this case of an elongated body.