Abstract: With the abundance of exploration data of Mars and moon，the traditional

rectangular coordinate gravity potential model is not suitable for the forward and

inverse processing of the gravity of such small bodies. To solve this problem，a

spherical model based on Newton's gravitational is presented，which is expanded by

spherical harmonic expansion.It is shown that the gravity potential of spherical topography can be

estimated by the topography and its higher order spherical harmonic expansion coefficient，which

simplifies the complicated quadrature process of traditional numerical integration.Results also

indicate that the influence of higher topography is less than 7 orders，

and within 5 orders are generally better to meet the accuracy requirements.The algorithm is

applied to the estimation of the gravity potential on the surface of Mars，and the results

are consistent with the topography characteristics of Mars，which shows that the proposed

algorithm is reasonable to some extent.

Key words: small celestial bodies, topography on sphere, gravity potential, spherical harmonic expansion