Approximate solution of third-order Clairaut theory of rotational sectorial figures of Jupiter and Saturn

Physics

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Jupiter (Planet), Planetary Rotation, Saturn (Planet), Approximation, Differential Equations, Distortion, Equipotentials, Numerical Integration

Scientific paper

The aim of this paper is to investigate numerical solutions of third-order Clairaut theory, under the boundary conditions given in El Shaarawy (1974). This solution gives an explicit form of the shape and rotational distortion, due to third-order sectorial harmonic terms, of the equipotential surfaces of the two rapidly rotating planets, Jupiter and Saturn, at the different levels inside these planets owing to a certain internal density distribution model (Zharkov, 1975). Each of them is considered as a heterogeneous self-gravitating fluid mass in hydrostatic equilibrium.

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