The gravitational field of Phobos

The external gravitational field produced by a rigid body of uniform density but irregular shape is formulated in terms of spherical harmonics. The formalism is applied to the Martian satellite Phobos. Based on a three-dimensional shape model of Phobos by Duxbury (1989), the gravitational coefficients up to degree and order 4 for a homogeneous Phobos are computed. In particular, J2 is found to be 0.105. The in-plane libration amplitude of a homogeneous Phobos is predicted to be 0.97 deg, within the rather large uncertainty of the observed value of 0.78 + or - 0.4 deg.