Modeling and Optimization of Earth-Moon Transfers

Abstract

This thesis aims to calculate optimal trajectories from a user-defined Earth-bounded orbit to a user-defined Moon-bounded orbit using a bi-impulse direct transfer ultimately under the influence of a full dynamical model with perturbations, hence reflecting the actual physical environment.

Two tools are developed to achieve this goal. The first tool employs a global optimization algorithm, in particular a Particle Swarm Optimizer (PSO), to find an initial guess within a simplified dynamics model, exploring the user-defined search space. The second tool employs a gradient-based Sequential Linear Least SQuares Programming (SLLSQP) optimizer to refine the initial guess and include the relevant perturbations that act in real life. Additionally, the tools are supported by methods for evaluating the results, providing plotting and analysis tools to make the most out of the obtained solutions.

For the initial guess calculation, the dynamics model includes the point-mass gravity field of Earth and the Moon. The output provides the required DeltaV for the transfer and the epochs at which each maneuver should be performed. The SLLSQP optimizer subsequently corrects the initial guess considering the user-specified perturbations, optimizing the time in the first orbit, the different components of both maneuvers, and the time of flight to reach the required orbit in an optimal way.

The capabilities of the tools are demonstrated through several test cases. The first test involves transferring from a circular low Earth orbit (LEO) to a circular near-polar low lunar orbit (LLO), resulting in a total DeltaV of 4716.62 m/s. A second and a third test case involving transfers from a LEO or a geostationary transfer orbit (GTO) to an eccentric lunar orbit are also conducted, obtaining a DeltaV of 3859.81 m/s when transferring from the LEO and of 1512.95 m/s when doing so from a GTO, corresponding to a decrease of around 60%. The solution obtained from the transfer from the GTO leads to a 4.5% improvement compared to preliminary results found in literature. The forth test comprises transfers from another circular LEO orbit to a high-altitude lunar polar orbit, requiring a DeltaV of 3996.44 m/s, being 4.6% higher than the solution found in literature.

These test cases validate the functionality of the code and showcase its versatility in handling various scenarios. In conclusion, the developed tools provide efficient and robust solutions for optimizing direct transfers from Earth to the Moon under the influence of real-life perturbations.