Article

# Invariant relative orbits for satellite constellations: A second order theory

Cairo University, Faculty of Science, Department of Astronomy, Cairo 12613, Egypt

Applied Mathematics and Computation (Impact Factor: 1.6). 10/2006; DOI: 10.1016/j.amc.2006.01.004 Source: dx.doi.org

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**ABSTRACT:**For a satellite in an orbit of more than 1600 km in altitude, the effects of Sun and Moon on the orbit canâ€™t be negligible. Working with mean orbital elements, the secular drift of the longitude of the ascending node and the sum of the argument 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 guarantee 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.Applied Mathematics. 02/2012; 3:113-120.

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