Lunar Transfer and Perturbation Analysis for Proposed ESA Máni Mission: Comparing Hohmann, EML1 and ESL1 Trajectories with ESA GODOT

Abstract: This study explores trajectory optimisation for the Danish-led ESA Máni Mission by analysing multiple transfer strategies, including Two-Phase Patched Conic Transfer (TP), the use of the Lagrange Point-1 (L1) as either an intermediate apoapsis for ESL1 Lyapunov Bi-Elliptic Transfer or an intermediate step for EML1 Lyapunov Elliptic-Unstable Manifold Transfer. J2 and J4 perturbation effects of Earth, the Moon and the Sun are evaluated due to their oblateness. To avoid atmospheric drag effects, the study assumes that the satellite is parked at an altitude of 200 km for better visualisation of perturbative influences of Earth by introducing a modified method to analyse the perturbation potential along the orbit depending on the nature of the orbital transfer. In theoretical calculation, the three-body problem is utilised to analyse the L1 environment in Earth-Sun and Earth-Moon systems, and the SRP effects are evaluated in ESL1 Lyapunov Transfer due to the proximity of the Sun. Results show that while the Hohmann bi-elliptic transfer through ESL1 Transfer is inefficient due to the high-position error (2.93 km) when analysed in the Heliocentric frame resulting in 30-50 days transfer from ESL1 to the operation orbit, the EML1-assisted by the unstable manifold may offer a fuel-efficient transfer if the inclination correction burn is performed before the trans-lunar injection, and the TP Transfer would offer simplicity whilst maintaining fuel-efficiency despite the fact that the inclination burn is performed along an elliptic orbit. Through this, it is conclusive that the Kourou launch site is not optimal for the Lunar polar mission despite the advantage of getting higher orbital speed along the equatorial line. Additional Information: ESA Máni Mission's Information: ESA Máni Mission Activity Page Annual Danish Astronomy Meeting 2025: Annual Danish Astronomy Meeting 2025 | ADAM 2025 Funding: This research is funded by the Instrument Center for Danish Astrophysics (IDA) for travel, accomodation and fee award. Acknowledgements: I would like to thank Jens Frydenvang (KU/NBI) and Mads Toudal Frandsen (SDU/CP3/Galaxy) for enabling me to conduct this research through the student membership of the SDU Máni Science Team