Statistics – Computation
Scientific paper
Dec 2000
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000dps....32.6529c&link_type=abstract
American Astronomical Society, DPS Meeting #32, #65.29; Bulletin of the American Astronomical Society, Vol. 32, p.1645
Statistics
Computation
Scientific paper
Currrent and planned missions to small bodies of the Solar System (ROSETTA, NEAR, MUSES-C) have revived the interest of the scientific and engineering communities in the computation of spacecraft orbits around asteroids and cometary nuclei, possibly at very close range. The purpose of this paper is to address the problem of the divergence of the highly popular expansions of the potential in Spherical Harmonics inside the sphere that circumscribes the body (the Brillouin sphere). This is the question of the downward continuation, well known in classical Geodesy, where it still stirs debate. In the case of the highly irregular asteroids recently imaged, the problem is only exacerbated. Solutions have recently been proposed for the case of homogeneous bodies in terms of finite developments based on polyhedral approximations of their shape. As an alternative, we propose here the adoption of spheroidal (prolate or oblate) or ellipsoidal coordinates. These coordinates present triaxial ellipsoids or prolate/oblate spheroids as coordinate surfaces. Since these may better fit the shape of irregular bodies, the region of divergence comprised between the surface of the body and the Brillouin ellipsoid is now greatly reduced. In these alternative coordinates the Laplace equation is separable and the potential can be expresed in series of either the well-known Legendre functions of the first and second kind or the Lamé functions. Together with a review of results found in the classical literature we also present a strategy that has been undertaken for simulations studies within the ROSETTA mission.
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