Rotationally and Tidally Perturbed Orbital Elements of Close Binary Stars

Abstract

This paper summarizes some relatively recent work on the effects that rotational and tidal forces can produce on the orbital elements of a close binary system.

In the case of rotational distortion the six elements of the orbit have been expressed by means of the unperturbed true anomaly measured from the ascending node. First-order approximations are obtained for the following values of orbital inclination,

• (i) i = any value and

• (ii) i = very small.

In the case of tidal distortion the elements of the orbit have been presented as functions of the unperturbed true anomaly measured from the periastron. Our study includes the effects produced by the second, third, and fourth tidal harmonic distortions. The results obtained have been expressed by means of Hansen coefficients.

First order approximations for tidal distortion have been produced for the following cases,

• (i) Tides do not lag, and,

• (ii) Tides are lagging in longitude or in latitude.