Automated Trajectory Refinement of Three-Body Orbits in the Real Solar System Model

In this paper, an automatic algorithm for the correction of orbits in the real solar system model is described. The differential equations governing the dynamics of a massless particle in the n-body problem are written as perturbation of the restricted three-body problem in a non-uniformly rotating, pulsating frame by using a Lagrangian formalism. The refinement is carried out by means of a multiple shooting technique, and the problem is solved for a finite set of variables. Results are given for the dynamical substitutes of the collinear points of several gravitational systems, as well as for periodic three-body orbits.