Celestial Mechanics and Dynamical Astronomy

, Volume 114, Issue 3, pp 229–254

Integrable approximation of J2-perturbed relative orbits

Original Article

DOI: 10.1007/s10569-012-9437-8

Cite this article as:
Lara, M. & Gurfil, P. Celest Mech Dyn Astr (2012) 114: 229. doi:10.1007/s10569-012-9437-8


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 J2 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 J2 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 J2 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 

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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