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

S.E. Abd El-Bar
Organization: Department of Mathematics, Faculty of Science, Tanta University
Journal / Anthology

Atrophysics and Space Science
Year: 2014
Volume: 350
Issue: 1
Page range: 155-168

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.

*Science > Physics > Astrophysics

Encounter problem, Multiple variables expansion, Struble variables