Extended analytical formulae for the perturbed Keplerian motion under low-thrust acceleration and orbital perturbations

• Published in: Celestial mechanics and dynamical astronomy Vol. 133; no. 3
• Main Authors: Di Carlo, Marilena, Graça Marto, Simão da, Vasile, Massimiliano
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.03.2021; Springer Nature B.V
• Subjects: Acceleration; Aerospace Technology and Astronautics; Astrophysics and Astroparticles; Classical Mechanics; Dynamical Systems and Ergodic Theory; Geophysics/Geodesy; Gravitational fields; Kepler laws; Mathematical analysis; Orbit perturbation; Orbital elements; Original Article; Physics; Physics and Astronomy; Solar orbits; Spacecraft; Thrust; Analytical solutions; First-order expansion; Low-thrust trajectories
• ISSN: 0923-2958; 1572-9478
• DOI: 10.1007/s10569-021-10007-x

This paper presents a collection of analytical formulae that can be used in the long-term propagation of the motion of a spacecraft subject to low-thrust acceleration and orbital perturbations. The paper considers accelerations due to: a low-thrust profile following an inverse square law, gravity perturbations due to the central body gravity field and the third-body gravitational perturbation. The analytical formulae are expressed in terms of non-singular equinoctial elements. The formulae for the third-body gravitational perturbation have been obtained starting from equations for the third-body potential already available in the literature. However, the final analytical formulae for the variation of the equinoctial orbital elements are a novel derivation. The results are validated, for different orbital regimes, using high-precision numerical orbit propagators.