Analysis of balloon satellite motion in the planetary restricted four-body problem taking into consideration light pressure forces

Abstract

A plane restricted four-body problem was examined taking into consideration the light pressure forces under the following conditions: the Earth’s orbit is a Keplerian ellipse with focus in the Sun, the Moon’s orbit is a Keplerian ellipse with focus in the Earth and a balloon satellite is the passively gravitating body. The problem force function was obtained, provided that resonances between the mean motions of the main bodies and the mean motion of the satellite unperturbed orbit was missing. It was demonstrated that semimajor axis of the satellite orbit and average value of the force function were the integrals of averaged equations in the osculating elements. Stationary modes of vibrations and their bifurcation depending on the coefficient of light pressure were investigated. Phase portraits of vibrations were constructed for different values of the light pressure coefficient.