Two algorithms to construct a consistent first order theory of equilibrium figures of close binary systems

Abstract

One of the main problems in celestial mechanics is the study of the shape adopted by extended deformable celestial bodies in its equilibrium configuration. In this paper, a new point of view about classical theories on equilibrium figures in close binary systems is offered.

Classical methods are based on the evaluation of the self-gravitational, centrifugal and tidal potentials. The most common technique used by classical methods shows convergence problems. To solve this problem up to first order in amplitudes two algorithms has been developed, the first one based on the Laplace method to develop the inverse of the distance and the second one based on the asymptotic properties of the numerical quadrature formulas.