Design of satellite orbits in the sun-earth-moon system

The treatment of the restricted three-body problem and its application to satellites in close Earth orbits appeared in many research papers and monographs. However for more general satellite orbits which circle between the Earth and the Moon, the impact of the Sun presence cannot be ignored and one has to consider these orbits in the context of the restricted four-body problem. For such satellites, we present in this paper a procedure that can be used to evaluate the thrust that is needed to keep them in a specified orbit. Specifically, we apply this procedure to two families of orbits which circle around the Earth and the Moon. The first family consists of elliptic orbits while the second consists of orbits in the shape of the figure eight (which resemble the orbit to be used by NASA for the Artemis project). We observe that in this paper we shall consider only satellite orbits in the Sun-Earth-Moon system. However, the methods described hereby can be adapted to other restricted four-body problems.