Stabilization of Heliosynchronous Orbits of an Earths Artificial Satellite by Solar Pressure

The motion of a balloon satellite in the Earthʹs gravitational field under the effect of the light pressure of solar rays is considered. The satellite is assumed to be a specularly reflecting sphere with such mass and radius that satellite orbit perturbations, due to noncentrality of the Earthʹs gravitational field and to the light pressure, are of the same order of magnitude. Heliosynchronous orbits, the node of which moves with a mean angular velocity of the yearly motion of the Sun, are investigated. At first, the equations of motion of a satellite in osculating elements of the orbit are considered, which are averaged with respect to its mean anomaly. Solutions to these equations are constructed, which represent heliosynchronous orbits. These solutions turn out to be close to the steady-state ones. Then the heliosynchronous orbits are approximated more exactly by periodic solutions of a specifically constructed autonomous system of differential equations. Finally, a numerical integration of the satelliteʹs equations of motion on a prolonged time interval is carried out by the two-cycle method. Initial conditions of the calculated solutions correspond to the evaluated periodic orbits. It is demonstrated that there exist orbits which remain heliosynchronous for several years.