IJPAM: Volume 79, No. 1 (2012)

ANALYTICAL APPROACH TO THE PROBLEM OF CLOSE
APPROACH OF TWO SMALL MASSES IN THE FIELD OF
MASSIVE OBLATE PRIMARY

Mohamad Radwan$^1$, Sultan Z. Alamri$^2$
Department of Applied Mathematics
Faculty of Applied Sciences
Taibah University
Madinah Munawwarah, KINGDOM OF SAUDI ARABIA


Abstract. The present work deals with the encounter problem of two small masses $m_{2}$ and $m_{3}$ describing initially elliptical orbits around a massive oblate primary. The equations of motion of the center of mass of $m_{2}$ and $m_{3}$ are developed in the most general form without any restrictions on the orbital elements. To avoid the appearance of mixed secular terms, we applied the method of multiple variables expansion. To facilitate the application of this method we first transform to the Struble variables.

Received: October 29, 2011

AMS Subject Classification: 58D30

Key Words and Phrases: encounter problem, multiple variables expansion, Struble variables

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 79
Issue: 1