Frozen Orbits About the Moon

Frozen orbits are of special interest to mission designers of artificial satellites. On average the eccentricity and argument of the perigee of such orbits remain stationary. Frozen orbits correspond to equilibria in an averaged form of the zonal problem and are almost periodic solutions of the full (nonaveraged) problem. In the zonal problem of a satellite around the moon, we numerically continue natural families of periodic orbits with the polar component of the angular momentum as the parameter. Three families of frozen orbits are discovered.