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

N. N. Tscherbakova, V. V. Beletskii, and V. V. Sazonov

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 123042 Russia

Received June 30, 1998

Abstract—The motion of a balloon satellite in the Earth’s gravitational field under the effect of the light pres-
sure 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 Earth’s 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. Solu-
tions 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 inte-
gration of the satellite’s 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 demon-
strated that there exist orbits which remain heliosynchronous for several years.

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