Invariant Relative Orbits Taking into Account Third-Body Perturbation

Affiliation(s)

Department of Astronomy, Faculty of Science, Cairo University, Cairo, Egypt.

Observatoire de la C?te d’Azur, Grasse, France.

Department of Astronomy, Faculty of Science, Cairo University, Cairo, Egypt.

Observatoire de la C?te d’Azur, Grasse, France.

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.

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.

Cite this paper

W. Rahoma and G. Metris, "Invariant Relative Orbits Taking into Account Third-Body Perturbation,"*Applied Mathematics*, Vol. 3 No. 2, 2012, pp. 113-120. doi: 10.4236/am.2012.32018.

W. Rahoma and G. Metris, "Invariant Relative Orbits Taking into Account Third-Body Perturbation,"

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