The representation of the external potentials of ellipsoidal bodies of revolution in the form of a series of spherical functions

Details The representation of the external potentials of ellipsoidal bodies of revolution in the form of a series of spherical functions The representation of the external potentials of ellipsoidal bodies of revolution in the form of a series of spherical functions

Feb 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987azh....64..158b&link_type=abstract

Astronomicheskii Zhurnal (ISSN 0004-6299), vol. 64, Jan.-Feb. 1987, p. 158-166. In Russian.

Statistics

Computation

Computational Astrophysics, Functions (Mathematics), Gravitational Fields, Rotating Bodies, Series Expansion, Density Distribution, Disk Galaxies, Ellipsoids, Elliptical Galaxies, Spiral Galaxies

Scientific paper

Gravitational potential expansions of both level and homogeneous oblate ellipsoids of rotation with arbitrary oblateness have been constructed in terms of solid spherical functions. The series converge in the whole external space of ellipsoids and at their surfaces. A similar expansion has been derived as a limit case for the gravitational potential of a circular disk with the surface density distribution μ(r) = μ(0)√(1-r2/a2) where a means the radius of the disk and r is the distance from its centre to a point on its surface. The expansion constructed can be used for representing the external potentials of some elliptical, spiral, and disk galaxies as well as of lunar mascons.

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