Space Trajectories for a Spacecraft Travelling Under the Gravitational Forces of Two Bodies
by
Antonio Fernando Bertachini de Almeida Prado
Instituto Nacional de Pesquisas Espaciais - Brazil

In this paper we search for space trajectories under the non-linear mathematical model given by the restricted three-body problem. The orbits found here can be applied to transfer a spacecraft between any two or more points in the group formed by the secondary body and the Lagrangian points L3, L4, L5 with near-zero impulse in the systems Earth-Sun and Earth-Moon. The possibility of a close approach between the spacecraft and the celestial bodies involved is also considered and studied in some detail. Then, we also study a related problem, the gravitational capture in the planar and circular restricted three-body problem. It is a very interesting characteristic of some dynamical system, like the three- or four- body system in celestial mechanics. The basic idea is that a slightly hyperbolic orbit (with residual positive energy) around a celestial body can be transformed in a slightly elliptic orbit (with residual negative energy) without the use of any propulsive system. The only forces responsible for this capture are gravitational perturbations from one or more celestial bodies. Examples of trajectories obtained by numerical integration are shown, to explain the applicability of the topics. Most of the trajectories can be used by a spacecraft in a real mission.

Date received: January 4, 2000