Invariant relative orbits for satellite constellations: A second order theory

• Published in: Applied mathematics and computation 2006-10, Vol.181 (1), p.6-20
• Main Authors: Abd El-Salam, F.A., El-Tohamy, I.A., Ahmed, M.K., Rahoma, W.A., Rassem, M.A.
• Format: Article
• Language: English
• Subjects: Atomic and molecular physics; Exact sciences and technology; Exotic atoms and molecules (containing mesons, muons, and other unusual particles); Global analysis, analysis on manifolds; Invariant relative orbits; Mathematics; Physics; Satellite constellations; Sciences and techniques of general use; Studies of special atoms, molecules and their ions; clusters; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2006.01.004

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, 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 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.