The frozen orbits of the charged satellites under zonal harmonics perturbation

Abstract

In the present work, the problem of frozen orbits of a charged satellite around the Earth is treated. The geopotential is considered as oblate body up to J6 zonal harmonics. The first normalized Hamiltonian is utilized so as to compute families of the long-term frozen orbits for a charged satellite in the concerned model using the Lie transform method. Since the mathematical model of the problem is complicated, the Hamilton canonical equations have been solved numerically. Our numerical investigation of the considered dynamical system reveals no frozen orbits can be obtained for orbits with perigee point lies on the equator g∈0.0°, 0.180°. But, in the neighbouhood of these orbits, equilibria for a very nearly circular orbits as well as equatorial HEO exist. Our results reflected the remarkable effects of the electromagnetic perturbations on the frozen orbit dynamics, especially for the medium and high Earth orbits. Investigating charged satellites carrying different electronic charges, the phase space (I,e) is noticeably changed near the equilibria g=n(180°),n=0,1. It is observed also that a very little change in the amount of charge carried by the satellite, gives rise to a change in the phase space especially for the nearly circular orbits that have inclinations in between the two roots of critical of inclinations.