Fast 2-impulse non-Keplerian orbit-transfer using the Theory of Functional Connections

TL;DR

This paper introduces a novel application of the Theory of Functional Connections to efficiently solve non-Keplerian orbit transfer problems, enabling rapid and accurate boundary condition satisfaction for complex perturbations.

Contribution

The study presents a new TFC-based method for solving TPBVPs in non-Keplerian transfers, achieving fast convergence and low computational cost for perturbed orbit transfer analysis.

Findings

Exact boundary condition satisfaction achieved.

Transfer costs comparable or better than existing solutions.

Rapid generation of perturbed pork-chop plots.

Abstract

This study applies a new approach, the Theory of Functional Connections (TFC), to solve the two-point boundary-value problem (TPBVP) in non-Keplerian orbit transfer. The perturbations considered are drag, solar radiation pressure, higher-order gravitational potential harmonic terms, and multiple bodies. The proposed approach is applied to Earth-to-Moon transfers, and obtains exact boundary condition satisfaction and with very fast convergence. Thanks to this highly efficient approach, perturbed pork-chop plots of Earth-to-Moon transfers are generated, and individual analyses on the transfers' parameters are easily done at low computational costs. The minimum fuel analysis is provided in terms of the time of flight, thrust application points, and relative geometry of the Moon and Sun. The transfer costs obtained are in agreement with the literature's best solutions, and in some cases are even slightly better.