Third-body perturbation in orbits around natural satellites

An analytical and a numerical study of the perturbation imparted to a spacecraft by a third body is developed. There are several important applications of the present research, such as calculation of the effect of lunar and solar perturbations on high-altitude Earth satellites. The goal is to study the evolution of orbits around some important natural satellites of the solar system, such as the moon, the Galilean satellites of Jupiter, Titan, Titania, Triton, and Charon. There is special interest in learning under which conditions a near-circular orbit remains near circular. The existence of circular, equatorial, and frozen orbits are also considered for a lunar satellite, but 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. Then, a study is performed to estimate the lifetime of orbits around those natural satellites.