Abstract
The expansion of the external gravitational potential of solid, irregular bodies of non-near spherical shape in terms of Spheroidal Harmonics is introduced as a way to minimize the divergence region, or Brillouin sphere, associated with the use of the more usual Spherical Harmonics. A method for the numerical evaluation of the spheroidal Stokes coefficients is proposed.
The support of the Italian Space Agency (ASI) is gratefully acknowledged.
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References
Casotto, S. (2001): Numerical Experiments on the Convergence of Spherical and Spheroidal Harmonic Representations of the External Potential inside the Brillouin Sphere, AAS/AIAA Space Flight Mechanics Meeting, Paper AAS 01–226, Santa Barbara, California, 11–15 February 2001.
Garmier, R. and J.-P. Barriot (2001): Ellipsoidal Harmonic Expansion of the Gravitational Potential: Theory and Applications, Cel. Mech. and Dyn. Astron., 79, 235–275.
Gerstl, M. (1980): On the Recursive Computation of the Integrals of the Associated Legendre Functions, Manuscripta Geodaetica, 5, 181–189.
Heiskanen, W. A. and H. Moritz (1967): Physical Geodesy, Freeman, San Francisco.
MacRobert, T. M. (1967): Spherical Harmonics, Pergamon Press, Oxford.
Vanícek, P. and E. J. Krakiwski (1982): Geodesy: The Concepts, North-Holland, Amsterdam.
Wang, Z. X. and D. R. Guo (1989): Special Functions, World Scientific, Singapore.
Wangerin, A., Theorie des Potentials und der Kugelfunktionen, 2 Bände, De Gruyter, Berlin, 1921.
Werner, R. (1994): The Gravitational Potential of an Homogeneous Polyhedron or Don’t Cut Corners, Cel. Mech. and Dyn. Astron., 59, 253–278.
Wimp, J. (1984): Computations with Recurrence Relations, Pitman, Boston.
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Casotto, S. (2002). On the Expansion of the External Gravitational Potential in Spheroidal Harmonics. In: Celletti, A., Ferraz-Mello, S., Henrard, J. (eds) Modern Celestial Mechanics: From Theory to Applications. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2304-6_23
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DOI: https://doi.org/10.1007/978-94-017-2304-6_23
Publisher Name: Springer, Dordrecht
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