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
Number of pages42
JournalCelestial Mechanics and Dynamical Astronomy
DOIs
Publication statusAccepted/In press - 18 Nov 2020

Keywords

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

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