A note on the first-order theories of equilibrium figures of celestial bodies

Abstract

One of the main problems in celestial mechanics is the determination of the shape of the equilibrium configuration of celestial bodies. In this paper, a model of a fluid mass rotating in space like a rigid body will be developed. To this aim, the equipotential surfaces are developed by using the Neumann series with respect to the Clairaut coordinates, and from these developments, the equilibrium equations and the boundary conditions can be obtained. Classical methods involve convergence problems, and in this paper two methods are developed to solve this problem, one based on numerical quadrature methods and the other one based on an analytical development.

Keywords:

• figures of celestial bodies
• potential theory
• spherical harmonics
• celestial mechanics

2000 AMS Subject Classifications :

• 33E99
• 70F15
• 85A30

Acknowledgements

This research was partially supported by Grant 06I455.01/1 from the Fundación Bancaja and Grant GV/2009/027 from the Generalitat Valenciana. \reversemarginpar