Planar librations of a gravity-oriented satellite under the influence of solar radiation pressure

Abstract

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 treated 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.