Spacecraft stability, dynamics and control near the triangular Lagrange points influenced by multiple Trojan asteroids

Abstract

In view of the importance of Lagrange points to the exploration and development of space, the dynamics and stability of a satellite were studied under multiple Trojan asteroids influence. Through the use of a numerical simulator developed in MATLAB, consideration was given to the effects of gravitational forces exerted by the asteroids themselves, simulating the resulting insignificant influence of the Trojan asteroids on a satellite placed at the triangular Lagrange points. The study of optimized satellite transfers between triangular Lagrange points allowed the enforcement of multiple, specific, non-linear constraints on critical mission parameters of maximum thrust, mission duration, propellant consumption and accelerations. The optimized transfer trajectory between the two triangular Lagrange points was direction sensitive. That is, the minimum thrust optimized transfer trajectory for a satellite from L 4 to L 5 was unique and vastly different to that from L 5 to L 4 . A further exciting discovery highlighted that superposition of the latter trajectories formed a perfectly smooth, uninterrupted kidney-shaped loop, fused at the two relevant points of connection. Implications for this phenomenon extend directly to future mission planning.