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Orbital evolution dynamics of two satellites in encounter phase using multiple scales expansion

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Abstract

An approximate solution of the encounter problem of two small satellites describing initially elliptical orbits around a massive oblate primary is obtained. The equations of motion of the center of mass of the two masses are developed in the most general form without any restrictions on the orbital elements. The method of multiple scales which seeks a solution whose behavior depends on several time scales is used. To overcome the singularity the equations of motion are transformed to the Struble variables. An analytical second order theory of the evolution dynamics is obtained. A MATHEMATICA program is constructed. The evolution dynamics of the orbital parameters between the perturbed and the unperturbed cases are plotted. The effect of changing eccentricity and changing inclination on the orbital parameters are highlighted.

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Acknowledgements

The author is deeply indebted and thankful to the deanship of the scientific research and his helpful and distinct team of employees at Taibah university, Medina, KSA. This research work was supported by a grant No. (3017/1434).

The author would also wish to record here his indebtedness and thankfulness to the Professors Mohammad Radwan and Fawzy Ahmed Abd El-Salam for their valuable help during the preparation and reviewing process through finalizing this work. Also the author wish to thank the reviewers for their valuable and fruitful comments as well as for their potential reading and suggestions.

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  1. S. E. Abd El-Bar

    Present address: Department of Math., Faculty of Science, Taibah University, Medina, Kingdom of Saudi Arabia

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  1. Department of Mathematics, Faculty of Science, Tanta University, Tanta, 31527, Egypt

    S. E. Abd El-Bar

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Abd El-Bar, S.E. Orbital evolution dynamics of two satellites in encounter phase using multiple scales expansion. Astrophys Space Sci 350, 155–168 (2014). https://doi.org/10.1007/s10509-013-1744-3

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