The post-Newtonian relative orbit of the two-body system. Gravitational radiation
The average loss of energy over one period of the elliptical motion of the two-body system is given, within the quadrupole approximation, by using the relative motion in the post-Newtonian centre of the mass frame. More explicit formulae are derived for the elliptical orbits and detailed results are presented for the circular orbits assuming small orbital velocities compared to the velocity of light. On the other hand, using the defined Lagrangian we give the integrals of motion.
elliptical motion of the two-body system
scientific article; zbMATH DE number 4031081