Celestial Mechanics and Dynamical Astronomy

, Volume 114, Issue 3, pp 229–254 | Cite as

Integrable approximation of J 2-perturbed relative orbits

  • M. Lara
  • P. Gurfil
Original Article


Most existing satellite relative motion theories utilize mean elements, and therefore cannot be used for calculating long-term bounded perturbed relative orbits. The goal of the current paper is to find an integrable approximation for the relative motion problem under the J 2 perturbation, which is adequate for long-term prediction of bounded relative orbits with arbitrary inclinations. To that end, a radial intermediary Hamiltonian is utilized. The intermediary Hamiltonian retains the original structure of the full J 2 Hamiltonian, excluding the latitude dependence. This formalism provides integrability via separation, a fact that is utilized for finding periodic relative orbits in a local-vertical local-horizontal frame and determine an initialization scheme that yields long-term boundedness of the relative distance. Numerical experiments show that the intermediary-based computation of orbits provides long-term bounded orbits in the full J 2 problem for various inclinations. In addition, a test case is shown in which the radial intermediary-based initial conditions of the chief and deputy satellites yield bounded relative distance in a high-precision orbit propagator.


Satellite relative motion Zonal harmonics Hamiltonian dynamics Integrability Cid’s intermediary 


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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.San FernandoSpain
  2. 2.Distributed Space Systems Lab, Faculty of Aerospace EngineeringTechnion—Israel Institute of TechnologyHaifaIsrael

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