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

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.

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• Deep Theory of Functional Connections: A New Method for Estimating the Solutions of PDEs
• The Multivariate Theory of Functional Connections: Theory, Proofs, and Application in Partial Differential Equations
• Fuel-Efficient Powered Descent Guidance on Large Planetary Bodies via Theory of Functional Connections
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Cited by in corpus (6)

• Theory of functional connections applied to quadratic and nonlinear programming under equality constraints
• Orbit transfer using Theory of Functional Connections via change of variables
• Theory of Functional Connections and Nelder-Mead optimization methods applied in satellite characterization
• Tangent Velocity constraint for orbital maneuvers with Theory of Functional Connections
• Segmentation of the spacecraft transfer problem through overdetermined and continuity constraints based on the Theory of Functional Connections
• Connecting Earth and Moon via the L1 Lagrangian point