Transformation of spherical harmonic coefficients to ellipsoidal harmonic coefficients

Abstract

Analytical expressions linking spherical harmonics gravity field expansions with ellipsoidal harmonics gravity field expansions are developed. Certain symmetries and simplifications for the transformation between the two are noted. Using the expressions, a numerical approach is developed and applied for the computation of ellipsoidal harmonic gravity coefficients using spherical harmonics coefficients as inputs. This method can be used to transform a measured spherical harmonic gravity field into an ellipsoidal harmonic gravity field for use within the Brillouin sphere of the original body. This would allow for the computation of spacecraft and natural trajectories close to the surface of an asteroid or comet using a measured gravity field.