An Investigation on Jacobian Integral of the Equations of Motion of the System in the Elliptic Orbit of the Centre of Mass

In this article, we discuss the effect of earth’s oblateness and magnetic force on the motion and stability of the system for elliptic orbit of the centre of mass. We have got a set of non-linear, non-homogenous and non-autonomous equations. Generally, a system moving in space has to face some perturbative forces. These forces compel the system to change its orbit from circular to elliptic orbit. On account of this we have studied in details the problem in elliptic orbit of the centre of mass. This is simply the generalization of the particular case of the Keplerian orbit i.e. circular orbit. So, we analysed the effect of the earth’s oblateness and magnetic force on the existence and behavior of different equilibrium position of the system. Also, discuss the Jacobian Integral of the averaged equations of motion of the system, Two equilibrium solutions of the problem and after Hooke’s modulus of elasticity.