Journal
CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY
Volume 79, Issue 4, Pages 235-275Publisher
KLUWER ACADEMIC PUBL
DOI: 10.1023/A:1017555515763
Keywords
ellipsoidal harmonic; Lame's function; gravitational potential; small bodies; divergence of series
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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 spherical 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 ones. In this paper, we present their mathematical theory as well as a real application: 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 corresponding error for the spherical harmonic expansion can reach tens of meters.
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