Indian Journal of Science and Technology
Year: 2012, Volume: 5, Issue: 9, Pages: 1-14
F A Abd El-Salam1 and M I El-Saftawy2
1Department of Mathematics, Taibah University, Faculty of Science,
2 Department of Astronomy and Space, King Abdul-Aziz University, Faculty of Science, Jeddah, K.S.A 1 [email protected], [email protected]
Working with the mean orbit 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. By having both orbits drift at equal angular rates on the average, they will not separate over time due to the influence of the perturbative effects of the asphericity of the Earth. The relativistic corrections and the direct solar radiation pressure to the equations of motion, as is considered in this work. The problem is stated. The expressions for the time rate of change of the longitude of the ascending node and the sum of the argument of perigee and mean anomaly in terms of the augmented Delaunay canonical elements are obtained. The expressions for the second order conditions that guarantee that the drift rates of two neighboring orbits are equal on the average are derived.
Keywords: Invariant relative orbits, Spacecraft flying formations, Relativistic corrections, Direct solar radiation pressure.
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