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

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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.
Original languageEnglish
Article number13
Number of pages39
JournalCelestial Mechanics and Dynamical Astronomy
Volume133
DOIs
Publication statusPublished - 12 Mar 2021

Keywords

  • first order expansion
  • analytical solutions
  • low-thrust trajectories

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