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The representation of the force functions of the Earth's and Moon's gravitation in ellipsoidal coordinates

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Abstract

This paper derives asymptotic expansions of ellipsoidal coordinates in Cartesian coordinates and an expansion in spherical harmonics of the dominant term for the solution of Laplace's equation corresponding to the gravitational force function for a two-dimensional finite body.

On comparing the expansion of the dominant term derived here with known expansions of the force functions of the Earth's and Moon's gravitation the author obtains values for the semimajor axes and eccentricities of the singular ellipses of these bodies in terms of the second degree harmonic coefficientsc 20 andc 22.

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Authors and Affiliations

  1. Dept. of Higher Mathematics, Institute of Power Engineering, Ivanovo, U.S.S.R.

    E. I. Burstein

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  1. E. I. Burstein
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Burstein, E.I. The representation of the force functions of the Earth's and Moon's gravitation in ellipsoidal coordinates. Celestial Mechanics 11, 255–264 (1975). https://doi.org/10.1007/BF01230547

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  • DOI: https://doi.org/10.1007/BF01230547

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