Translunar Trajectory Analysis and Design for the European Student Moon Orbiter

Abstract Background The European Student Moon Orbiter (ESMO) is planned to be the first European mission to the Moon to be completely designed, developed, built, tested and operated by students across the European Space Agency (ESA) Member States and ESA Cooperating States, and it is the only mission planned by ESA to fly around Earth's natural satellite. The mission analysis of ESMO is conducted by the Space Advanced Research Team at the University of Glasgow, which is designing a Weak Stability Boundary (WSB) transfer for it. This kind of transfer is particularly cost-effective because the spacecraft takes advantage of a gravity assist from the Sun at the L 1 Lagrange point of the Sun-Earth system, which raises the spacecraft's perigee allowing it to be captured by the Moon. As a result, the required amount of propellant is reduced by 5 to 10% with respect to a direct Hohmann transfer, with either a subsequent increase of the payload capacity of the spacecraft or minor launch costs. However, the trasfer time is increased up to three months, and the spacecraft's behaviour at the WSB region is quite unpredictable, which makes it highly sensitive to errors and hard to find new transfers for any given day. This is a strict constraint, since ESMO will fly as a secondary payload and the launch date will be chosen by the primary payload owner. Therefore, a new method is required to find new transfer trajectories in a systematic and reliable way . The purpose of this report is to present a possible procedure to optimize the first guess solution of a test WSB transfer for ESMO, leaving from an Ariane 5 standard GTO. First of all, two optimization methods are compared: a Newton method, based on the State Transition Matrix (STM) and acting on initial and final burns, and a Direct Optimization code based on the fmincon MA TLAB function and acting on the Master Thesis Report page III