Ellipsoidal Harmonic expansions of the gravitational potential: Theory andapplication

Small bodies of the solar system are now the targets of space exploration. Many of these bodies have elongated, non-spherical shapes, and the usual sp herical harmonic expansions of their gravity fields are not well suited for the modelling of spacecraft orbits around these bodies. An elegant remedy is to use ellipsoidal harmonic expansions instead of the usual spherical on es. In this paper, we present their mathematical theory as well as a real a pplication: the simulation of a landing on the surface of a kilometer-sized comet. We show that with an ellipsoidal harmonic expansion up to degree 5, the error on the landing position is at the meter level, while the corresp onding error for the spherical harmonic expansion can reach tens of meters.