On the Evolution of Balloon Satellite Motions in a Plane Restricted Planetary Four-Body Problem with Light Pressure

Abstract

In this paper, we consider the plane restricted four-body problem taking into account the light pressure forces when the Earth’s orbit is a Keplerian ellipse with a focus at the Sun, the Moon’s orbit is a Keplerian ellipse with a focus at the Earth, and the balloon satellite is a passively gravitating body. The averaged perturbing function of the problem in osculating elements is obtained in the nonresonant case, when the unperturbed orbit of the Earth satellite lies in the outer sphere of the Earth’s gravitational influence, located beyond the lunar Hill sphere. It is found that the integrals of averaged equations in the osculating elements are the semimajor axis of the satellite orbit as well as the average value of the force function. The stationary modes of oscillations and their bifurcation depending on the light pressure coefficient and the semimajor axis are investigated. Phase oscillation portraits are constructed for different values of the light pressure coefficient. The librational and rotational orbits of the satellite in the ecliptic plane are calculated.