Hill Problem Analytical Theory to the Order Four : Application to the Computation of Frozen Orbits around Planetary Satellites

Abstract EN

Frozen orbits of the Hill problem are determined in the double-averaged problem, where short and long-period terms are removed by means of Lie transforms.

Due to the perturbation method we use, the initial conditions of corresponding quasi-periodic solutions in the nonaveraged problem are computed straightforwardly.

Moreover, the method provides the explicit equations of the transformation that connects the averaged and nonaveraged models.

A fourth-order analytical theory is necessary for the accurate computation of quasi-periodic frozen orbits.