Solution to the Clairaut-Laplace-Liapunov problem

Details Solution to the Clairaut-Laplace-Liapunov problem Solution to the Clairaut-Laplace-Liapunov problem

Jun 1976

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976azh....53..626t&link_type=abstract

Astronomicheskii Zhurnal, vol. 53, May-June 1976, p. 626-633. In Russian.

Astronomy and Astrophysics

Astronomy

Celestial Mechanics, Oblate Spheroids, Planetary Rotation, Stellar Rotation, Differential Equations, Integral Equations, Iterative Solution

Scientific paper

A successive-approximation solution is outlined for the Clairaut-Laplace-Liapunov problem concerning the figure of a slowly rotating nonuniform equilibrium body. The validity of employing the Laplace expansion to derive the equations for the figures of planets and stars is proven. In the analysis, Poisson's partial differential equation or the equivalent integral equation for a slowly rotating and gravitating equilibrium body is replaced by an infinite system of ordinary successive-approximation integrodifferential equations. The equation for the P12 harmonic is given along with values of the first seven computed nonzero coefficients of the planetary figure and field for a linear density distribution.

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