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 circular 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 modified multiple shooting technique, and the problem is solved for a finite number of trajectory states at several time instants. The analysis involves computing the dynamical substitutes of the collinear points, as well as several Lagrange point orbits, for the the Sun–Earth, Sun–Jupiter, and Earth–Moon gravitational systems.