Primaries Oblateness Effects on the Collinear Libration Points in the Restricted-three Body Problem
M. N. Ismail *
Department of Astronomy, Faculty of Science, Al-Azhar University, Cairo, Egypt.
A. H. Ibrahim
Department of Astronomy, Faculty of Science, Al-Azhar University, Cairo, Egypt.
G. H. F. Mohamadin
National Institute of Astronomy and Geophysics, NRIAG, Helwan, Cairo, Egypt.
W. A. Okasha
National Institute of Astronomy and Geophysics, NRIAG, Helwan, Cairo, Egypt.
*Author to whom correspondence should be addressed.
Abstract
In this work, the canonical Hamiltonian form of the restricted three- body problem including the effects of primaries oblateness is presented. Moreover, the collinear libration points are obtained. In addition to this, the relation between position of libration points and variation in (mass ration , oblateness coefficients A1 and A2) is studied. The results obtained are a good agreement with Perdios [1] & Singh [2]. The Poincare surface section PSS is used to illustrate the stability of motion around each of the collinear libration points. A numerical application on the real system Earth-Moon is presented.
Keywords: Restricted three body problem, oblateness effects, Poincare surface of section, stability motion, libration points