Planar librations of a gravity-oriented
satellite under the influence of solar radiation pressure
Satellite oscillations about its centre of mass in the circular orbit plane are dealt with.
The satellite is assumed symmetrical about a plane permanently coinciding with the orbit plane.
A gravity-gradient torque and a torque of solar radiation pressure on an unshadowed flat plate—a part
of the satellite—are taken into account. The centre of pressure is supposed to belong to the principal axis
of inertia. Effects of entering the Earth's shadow are neglected. A simplification that the orbit lies in the
ecliptic plane is adopted. Under the assumptions made, the satellite motion is described by a non-
autonomous differential second-order equation. A problem is to find symmetrical and nonsymmetrical
periodic motions of orbital period and to determine their stability. For the case of small radiation
disturbance, the Krylov-Bogolyubov asymptotic approach is used in the analysis. The libration in the
vicinity of the main resonance has been elaborated. For the satellite dynamically resembling a sphere the
investigation is trea'.ed with the Volosov-Morgunov averaging method. A resonant value of the radiation
torque parameter has been found. A question of periodic motions bifurcation is cleared up. For the
satellite with an arbitrary tensor of inertia under non-small radiation disturbance the problem has been
solved numerically. The main results are represented as a chart graphically demonstrating regions of
existence and stability of possible periodic librations of the satellite on parametric plane.
V.V.Beletsky, E.L.Starostin.
Acta Astronautica, 1989, v. 19, No. 3, pp. 201-213. doi:10.1016/0094-5765(89)90034-9
Abstract