Celestial Mechanics and Dynamical Astronomy

, Volume 123, Issue 1, pp 85–103 | Cite as

Analytic propagation of near-circular satellite orbits in the atmosphere of an oblate planet

  • Vladimir Martinusi
  • Lamberto Dell’Elce
  • Gaëtan Kerschen
Original Article


In the present paper, an averaging perturbation technique leads to the determination of a time-explicit analytic approximate solution for the motion of a low-Earth-orbiting satellite . The two dominant perturbations are taken into account: the Earth oblateness and the atmospheric drag. The proposed orbit propagation algorithm comprises the Brouwer–Lyddane transformation (direct and inverse), coupled with the analytic solution of the averaged equations of motion. This solution, based on equinoctial elements, is singularity-free, and therefore it stands for low inclinations and small eccentricities as well. The simplifying assumption of a constant atmospheric density is made, which is reasonable for near-circular orbits and short-time orbit propagation. Two sets of time-explicit equations are provided, for moderate and small eccentricities (\(\mathcal {O} ( e^{4}) =0\) and \(\mathcal {O}( e^{2}) =0,\) respectively), and they are obtained by performing (1) a regularization of the original averaged differential equations of motion for the vectorial orbital elements, and (2) Taylor series expansions of the aforementioned equations with respect to the eccentricity. The numerical simulations show that the errors due to the use of the proposed analytic model in the presence of drag are almost the same as the errors of the Brouwer first-order approximation in the absence of drag.


Atmospheric drag Oblate planet Time-explicit solution Brouwer-Lyddane transformation Onboard orbit propagation 



This work was supported by the Belgian National Fund for Scientific Research (FRIA) and the Marie Curie BEIPD-COFUND programme at the University of Liège, Belgium. The Authors also thank Dr. Martin Lara, as well as the other anonymous Reviewer, for their valuable comments and suggestions.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Vladimir Martinusi
    • 1
  • Lamberto Dell’Elce
    • 1
  • Gaëtan Kerschen
    • 1
  1. 1.Space Structures and Systems Lab, Department of Aerospace and Mechanical EngineeringUniversity of LiègeLiègeBelgium

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