On the best mean-square approximations to a planet's gravitational potential

Details On the best mean-square approximations to a planet's gravitational potential On the best mean-square approximations to a planet's gravitational potential

Feb 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985pazh...11..149l&link_type=abstract

(Pis'ma v Astronomicheskii Zhurnal, vol. 11, Feb. 1985, p. 149-155) Soviet Astronomy Letters (ISSN 0360-0327), vol. 11, Jan.-Feb

Astronomy and Astrophysics

Astronomy

Geopotential, Gravimetry, Planetary Gravitation, Spherical Harmonics, Approximation, Gravitational Fields, Legendre Functions, Mean Square Values, Polynomials, Stokes Theorem (Vector Calculus)

Scientific paper

The continuous problem of approximating the gravitational potential of a planet in the form of polynomials of solid spherical functions is considered. The best mean-square polynomials, referred to different parts of space, are compared with each other. The harmonic coefficients corresponding to the surface of a planet are shown to be unstable with respect to the degree of the polynomial and to differ from the Stokes constants.

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