Restricted Three- Body Problem in Parabolodial Coordinate System

Abstract

In this paper, the equations of motion for the spatial circular restricted three- body problem in sidereal parabolodial coordinates system were established. Initial value procedure that can be used to compute both the parabolodial and Cartesian sidereal coordinates and velocities was also developed. The application of the procedure was illustrated by numerical example of a hypothetical Trojan asteroid in the Sun Jupiter system and by graphical representations of the variations of the two sidereal coordinate systems.