This paper develops a semi-analytical study of the perturbation caused to a spacecraft by a third body involved in the dynamics. There are several important applications for this research, such as to calculate the effect of lunar and solar perturbations on high-altitude Earth satellites. In the present research the goal is to study the evolution of retrograde orbits around the Earth. There is a special interest to see under which conditions a near-circular orbit remains near-circular. The existence of circular, equatorial and frozen orbits are also considered, The results are valid for any system of primaries by making a time transformation that depends on the masses of the bodies involved. Several plots will show the time-histories of the Keplerian elements of the orbits involved.
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