The Phobos gravitational field modeled on the basis of its topography

The parameters of the best-fitting ellipsoid have been derived using the latest spherical harmonics of the Phobos topography (Duxbury, 1989) by solution of non-linear overdetermined inverse problem. The lengths of the equatorial axes of the ellipsoid have been determined (a = 12.9 km, b = 11.4 km). They are nearly the same as established by Duxbury (ibid.) on the basis of the linearized relationship between the squared lengths of ellipsoidal axes and the topography coefficients C₂₀ and C_22. The length of the polar axis (c = 9.1 km) differs of about 20% from Duxbury's value. Supposing mass homogeneity of Phobos, the Stokes parameters of the external gravitational field have been derived up to those of the sixth degree and order. The large irregularities in the Phobos figure cause the values of the Duxbury's potential coefficients be fairly inaccurate except the harmonics C₂₀, C₃₂, S₄₃ and S₅₁, i.e. linearized relationship between gravity and topography cannot be applied for Phobos. Finally, positions of the centre of figure and the directions of the principal axes of inertia have been established.