A New Representative for Small-Body Gravity Estimation

One of the options proposed in the 2009 Review of the U. S. Human Spaceflight Plans Committee calls for the consideration of robotic and human missions to asteroids. Beginning in 2000, the NEAR Shoemaker spacecraft inserted into orbit about the asteroid 433 Eros, and studied it for a year before landing. The Hayabusa satellite journeyed to 25143 Itokawa, and operated in a proximity of the asteroid for several months before landing to collect a return sample. Additionally, the DAWN satellite, which was launched in 2007, will explore the dwarf-planet Ceres and the asteroid 4 Vesta in the next three years. These are just several examples of current interests in exploring asteroids. In this paper, we explore an alternative for estimating the gravity field of a small body using observations of an orbiting satellite. Our approach uses two new mathematical tools, the quadratures (on a sphere) invariant under the icosahedral group, and a multiresolution representation of the gravity potential. With the near optimal quadratures on the sphere, we minimize the number of parameters needed to recover a function. Also, instead of estimating the coefficients of the spherical harmonics, the new quadratures allow us to estimate directly the values of the gravity field since they offer an analogue of the Lagrange-type interpolation.