Forced Keplerian orbits in the Earth-Moon system

Motivated by the fact that the mass of the Moon is about one percent of the Earth mass we consider in this paper Keplerian orbits of satellites (or spacecrafts) in the Earth-Moon system. These orbits represent approximate solutions of the basic equations of motion. As a result a satellite in one of these orbits will require some thrust to stay in orbit. In spite of this issue these orbits might be of interest when satellites orbits have to satisfy some practical constraints. In this paper we explore two types of such orbits. The first is around the Earth-Moon center of mass. The second consists of orbits whose center is along the line from Earth to the Moon but at some distance from Earth-Moon center of mass. As examples we consider briefly orbits for an Earth observation station and an Earth-Moon cycler (Casoliva et al., 2008). (In the following we use the term "Earth-Moon shuffle" to mean "Earth-Moon cycler"). Throughout this paper we use symbiosis between analytical and numerical methods to derive the desired results.