ORBITING BELOW THE BRILLOUIN SPHERE USING TRANSLATED SPHERICAL HARMONICS

Spacecraft trajectories near the south pole of Enceladus violate the Brillouin sphere associated with the convergence radius of spherical harmonics models. In this study, a shifted coordinate frame is demonstrated to ensure a convergent model is available in regions of operational interest. A hypothetical experiment is per-formed around a celestial body where the truth exterior gravity field is known exactly. The divergence of the harmonics below the Brillouin sphere of the un-shifted model is demonstrated, while the shifted harmonics model converges. The method is applied to the flight-derived gravity field for Enceladus, including un-certainties. Using these low degree and order reference models, expected for use in an operational setting, the results show that the shifted and body-centered har-monics models agree to near machine precision for all evaluations at or above the surface, and no divergence is noticed. The results imply that mission designers and navigation engineers can safely use a traditional spherical harmonics field for Enceladus, even in regions that dip below the Brillouin sphere. The experiments conducted in this study are applicable for low-flying missions to any non-spherical celestial body.