Analytic continuation of expansions of the external potentials of ellipsoidal bodies

Details Analytic continuation of expansions of the external potentials of ellipsoidal bodies Analytic continuation of expansions of the external potentials of ellipsoidal bodies

Apr 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986azh....63..381b&link_type=abstract

(Astronomicheskii Zhurnal, vol. 63, Mar.-Apr. 1986, p. 381-388) Soviet Astronomy (ISSN 0038-5301), vol. 30, Mar.-Apr. 1986, p. 2

Astronomy and Astrophysics

Astronomy

Bodies Of Revolution, Celestial Mechanics, Ellipsoids, Potential Energy, Series Expansion, Convergence, Spherical Harmonics

Scientific paper

Gravitational external potential expansions of both level and homogeneous ellipsoids of revolution with large flattenings, as well as that of a circular disc with the surface density distribution μ(r) = μ(0)m√(1-r2/a2) have been constructed, where a means the radius of the disc and r is the distance from its centre to a point on its surface. In distinction to the earlier constructed series in spherical functions, each of these expansions converges in the whole exterior space down to the surface of the ellipsoid (or the disc) and it can be differentiated term by term an arbitrary number of times.

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