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

Di Carlo, Marilena and da Graça Marto, Simão and Vasile, Massimiliano (2021) Extended analytical formulae for the perturbed Keplerian motion under low-thrust acceleration and orbital perturbations. Celestial Mechanics and Dynamical Astronomy, 133. 13. ISSN 0923-2958 (https://doi.org/10.1007/s10569-021-10007-x)

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Abstract

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.

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