On convergence of an asymmetrical body potential expansion in spherical harmonics |
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| Authors: | Constantin Kholshevnikov |
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| Institution: | (1) Celestial Mechanics Department, Mathematical Faculty, University of Leningrad, U.S.S.R. |
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| Abstract: | The gravity potential of an arbitrary bodyT is expanded in a series of spherical harmonics and rigorous evaluations of the general termV
n
of the expansion are obtained. It is proved thatV
n
decreases on the sphere envelopingT according to the power law if the body structure is smooth. For a body with analytic structure,V
n
decreases in geometric progression. The exactness of these evaluations is proved for bodies having irregular and analytic structures. For the terrestrial planetsV
n
=O (n
–5/2).
               I              I   V
n
  IV
n
I . . IV
n
I .  I. IV
n
=O(n
–5/2
)
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| Keywords: | |
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