On convergence of an asymmetrical body potential expansion in spherical harmonics

Details On convergence of an asymmetrical body potential expansion in spherical harmonics On convergence of an asymmetrical body potential expansion in spherical harmonics

Sep 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977cemec..16...45k&link_type=abstract

Celestial Mechanics, vol. 16, Sept. 1977, p. 45-60.

Physics

1

Asymptotic Methods, Gravitational Fields, Planetary Gravitation, Planetary Structure, Spherical Harmonics, Planetary Surfaces, Spheres

Scientific paper

The asymptotic behavior of the general term for the expansion of the gravitational potential of an arbitrary body in a series in terms of spherical harmonics is investigated. It is shown that on the general sphere for a body of smooth structure the general term decreases according to a power law. If the body has an analytic structure, the general term decreases in a geometric progression. For the terrestrial planets the n-th term of the potential expansion is of the order of n raised to the exponent -5/2.

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