First Integral of Motion of a Tether Connected Satellites System Under Several Influences of General Nature: Circular Orbit

Abstract

Here, we are interested to obtain Jacobean integral of motion of a system of two elastic cable connected satellites in circular orbit under the influence of some perturbative forces of general nature. These perturbative forces are Geo-magnetic field, solar radiation pressure, shadow of the earth and air drag. We also consider elasticity of the cable as one of the perturbative forces i.e., elasticity of the cable also influences motion of the system as a whole. Shadow of the earth is taken to be cylindrical and the entire system is allowed to pass through the shadow beam.  Off course, gravitational force of the earth is the main force that governs motion of the system. The cable connecting the two satellites is taken to be light flexible, non-conducting and elastic in nature. Since, masses of the satellites are small and distance between the   satellites is very large, the gravitational forces of attraction between the two satellites and other celestial bodies including the sun have been neglected. We do not consider nutation and wobbling of the orbit.