Optimising LISA orbits: The projectile solution

LISA is a joint space mission of the NASA and the ESA for detecting low frequency gravitational waves (GW) in the band $10^{-5} - 0.1$ Hz. The proposed mission will use coherent laser beams which will be exchanged between three identical spacecraft forming a giant (almost) equilateral triangle of side $5 \times 10^6$ kilometres. The plane of the triangle will make an angle of $\sim 60^{\circ}$ with the plane of the ecliptic. The spacecraft constituting LISA will be freely floating in the ambient gravitational field of the Sun and other celestial bodies. To achieve the requisite sensitivity, the spacecraft formation should remain stable, one requirement being, the distances between spacecraft should remain as constant as possible - that is the flexing of the arms should be minimal. In this paper we present a solution - the projectile solution - which constrains the flexing of the arms to below 5.5 metres/sec in a three year mission period. This solution is obtained in the field of the Sun and Earth only, which principally affect the motion of the spacecraft, especially the flexing of LISA's arms.