Analysis and control of satellite orbits around oblate earth using perturbation method

In this paper, we develop the dynamics of a particle satellite motion around the oblate earth using a special rotating reference frame. This dynamics is used to deduce the conditions under which the orbital plane of motion of the particle satellite remains fixed. Next, a two-scale perturbation analysis is performed to seek the analytical solution of tile particle satellite motion in the presence of the J(2) influence of tile oblate earth. The resulting analytical solution of the planar dynamics of the particle satellite is utilized to produce a planar motion controller so that tile perturbation forces in tile radial direction are tailored to guarantee that the particle satellite moves in a periodic trajectory. Finally, illustrative simulations are provided to demonstrate the effectiveness of the proposed framework.