Delaunay variables in model problems of celestial mechanics and cosmodynamics

Abstract

One of the most important model problems of celestial mechanics and cosmodynamics is the two-body problem, which describes the interaction of two-point mass, moving under the action of mutual gravitational attraction according to Newton’s law of universal gravitation. Integration of differential equations of motion in the two-body problem is reduced to quadratures. The trajectory of a point with mass relative to a point with mass is a conical section. From the point of view of applications, the most important case is the case of the Keplerian elliptic orbit. Whereas in unperturbed problem a point with mass moves along an ellipse, to derive the equations of perturbed motion, the canonical Delaunay variables are used, which in unperturbed problem are the “action-angle” variables. The equations of motion in Delaunay variables are convenient to apply numerical and asymptotic research methods. This paper gives an example of using Delaunay variables in the model problem of motion of a satellite in the Earth’s gravitational field, modeled by an axisymmetric rigid body compressed along the axis of rotation.