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F. A. Abd El-Salam, I. A. El-Tohamy, M. K. Ahmed, W. A. Rahoma and M. A. Rassem, “Invariant Relative Orbits for Satellite Constellations: A Second Order Theory,” Applied Mathematics and Computation, Vol. 181, No. 1, 2006, pp. 6-20. doi:10.1016/j.amc.2006.01.004

has been cited by the following article:

• TITLE: Invariant Relative Orbits Taking into Account Third-Body Perturbation

  AUTHORS: Walid Ali Rahoma, Gilles Metris

  KEYWORDS: Invariant Relative Orbits; Third-Body Perturbation; Hamiltonian

  JOURNAL NAME: Applied Mathematics, Vol.3 No.2, February 23, 2012

  ABSTRACT: For a satellite in an orbit of more than 1600 km in altitude, the effects of Sun and Moon on the orbit can’t be negligible. Working with mean orbital elements, the secular drift of the longitude of the ascending node and the sum of the argu-ment of perigee and mean anomaly are set equal between two neighboring orbits to negate the separation over time due to the potential of the Earth and the third body effect. The expressions for the second order conditions that guaran-tee that the drift rates of two neighboring orbits are equal on the average are derived. To this end, the Hamiltonian was developed. The expressions for the non-vanishing time rate of change of canonical elements are obtained.