The stability of eccentric polar orbits around the Moon.

The possibility of the decrease of eccentricity in the orbit of lunar orbiting satellites due to perturbation by the earth is examined analytically. The orbital influence of third-body perturbations is studied by estimating the ratio of the orbital radius vector over the third-body radius vector in the Lagrange planetary equations. Long-term behavior is characterized by the first order terms and averaging the equations over one revolution of the satellite. Attention is given to a polar lunar eccentric orbit, with validation deriving from the stroboscopic method. Consideration is given the moon oblateness and the earth gravitational pull for a periselenium between 0-360 deg. It is shown that the eccentricity of an elliptic lunar orbit can be reduced through the influence of earth perturbation. Examples are provided.