Fundamentals of the LISA stable flight formation

The joint NASA ESA mission, LISA, relies crucially on the stability of the three-spacecraft constellation. Each of the spacecraft is in heliocentric orbit forming a stable triangle. In this paper we explicitly show with the help of the Clohessy Wiltshire equations that any configuration of spacecraft lying in the planes making angles of ±60° with the ecliptic and given suitable initial velocities within the plane, can be made stable in the sense that the inter-spacecraft distances remain constant to first order in the dimensions of the configuration compared with the distance to the Sun. Such analysis would be useful in order to carry out theoretical studies on the optical links, simulators, etc.