## Special Solutions in a Simplified Restricted Three-Body Problem with Gravitational Radiation Taken into Account

Celestial Mechanics and Dynamical Astronomy, 85(3), 269-291 (2003)

**Keywords**:
general relativity, gravitational radiation, restricted three-body problem, binary pulsar systems

### Abstract

The distinctive feature of the relativistic restricted three-body problem within the c−5 order of accuracy (2 1/2 post-Newtonian approximation) is the presence of the gravitational radiation. To simplify the problem the motion of the massive binary components is assumed to be quasi-circular. In terms of time these orbits have linearly changing radii and quadratically changing phase angles. By substituting this motion into the Newtonian-like equations of motion one gets the quasi-Newtonian restricted quasi-circular three-body problem sufficient to take into account the main indirect perturbations caused by the binary radiation terms. Such problem admits the Lagrange-like quasi-libration solutions and rather simple quasi-circular orbits lying at large distance from the binary.