Spin-orbit corrections in the description of motion of compact binaries II.

Equations of motion for the angular quantities

Abstract

After the first direct detection of gravitational waves, the challenge is to get the most exact picture possible of the phenomena that can be observed using these waves, i.e. to realize the birth of gravitational wave astronomy. The binary systems formed by compact objects have a special role in this, since the waveforms emitted by them can be described with high accuracy over a wide range of parameters. In order to derive these waveforms, however, one needs to describe the motion of the binary system. We do this by using the post-Newtonian series expansion, taking into account the effects of the eccentricity of the orbit and the rotation of the objects. Earlier works have clarified the details of the changes of the length of the separation vector; however, to describe the emitted gravitational waves we need to describe the dynamics of the angular variables that characterize the vector orientations. In this paper the necessary equations are derived, and the methods to solve them are also described. The aim is also to explore and correct the errors of previous publications that we used as starting material.