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Earth, Moon, and Planets

, Volume 110, Issue 3–4, pp 143–155 | Cite as

Stability of the Triangular Points Under Combined Effects of Radiation and Oblateness in the Restricted Three-Body Problem

  • Elbaz I. Abouelmagd
Article

Abstract

This paper deals with the existence of triangular points and their linear stability when the primaries are oblate spheroid and sources of radiation considering the effect of oblateness up to 10−6 of main terms in the restricted three-body problem; we see that the locations of the triangular points are affected by the oblateness of the primaries and solar radiation pressure. It is further seen that these points are stable for 0 ≤ μ ≤μ c ; and unstable for μ c  ≤ μ ≤1/2; where μ c is the critical mass value depending on terms which involve parameters that characterize the oblateness and radiation repulsive forces such that \( \mu_{c} \in (0,1/2) \); in addition to this an algorithm has been constructed to calculate the critical mass value.

Keywords

Restricted three-body problem Triangular points Stability Oblateness Radiation pressure 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Mathematics Department, Faculty of Science and ArtsKing Abdulaziz UniversityKhulaisSaudi Arabia

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