Analysis on the Near-Polar and Near-Circular Periodic Orbits Around the Moon with J2, C22 and Third-Body Perturbations

A method is introduced for the numerical continuation of the lunar-type, near-circular periodic orbits, with the background of middle-altitude lunar orbiters. In the Moon-Earth elliptic restricted three-body problem, some near-polar near-circular lunar-type periodic orbits are numerically continued from the Keper circular orbits by Broyden’s method. The integer ratio j/k of the mean motions between the inner and outer orbits can be in the range [9,150]. For the ratio j/k∈[38,70], the J2,C22 perturbations are added, and some near-polar periodic orbits are calculated. The orbital dynamics are well explained via the first-order double-averaged system. The linear stability can be studied by the characteristic multipliers, which are calculated from the linear variational system.