Analytical Model to Find Frozen Orbits for a Lunar Orbiter

Analytical theories based on Lie-Deprit transforms are used to obtain families of periodic orbits for the problem of an orbiter around the moon. Low and moderately high orbit models are analyzed. Equilibria of the normalized equations of motion provide the representation of a global portrait of families of frozen orbits depending on values of the inclination, eccentricity, and semimajor axis. By means of the inverse transformation it is possible to refine the initial conditions for frozen orbits of a simplified model, and these initial conditions may be used as starters of numerical continuation methods when more complex models are considered.