Study on Equilibrium Positions of a Cable- Connected Satellites System under Several Influences

The present paper deals with the study of equilibrium positions of the motion of a system of two
artificial satellites connected by a light, flexible, inextensible and non-conducting cable under the
influence of solar radiation pressure, earth's oblateness, shadow of the earth and air resistance. Here,
we study the case of circular orbit of the centre of mass of the system. We derive differential
equations of motion of the system. To obtain the general solutions of the differential equations is
beyond our reach. On the other hand, the general solutions do not serve our purpose. Jacobean
integral of the system has also been obtained. Thereafter equilibrium positions of the motion of the
system have been obtained. The equilibrium position has wide applications in solving problems of
stability of a cable-connected satellites system in orbit. The work may be further modified, if wobbling
and nutation of the orbit of the system are taken into account.