Astrophysics and Space Science

, Volume 351, Issue 1, pp 119–124

Robe’s circular restricted three-body problem with a Roche ellipsoid-triaxial versus oblate system

  • Jagadish Singh
  • Achonu Joseph Omale
  • Veronica Cyril Okeme
Original Article

DOI: 10.1007/s10509-014-1814-1

Cite this article as:
Singh, J., Omale, A.J. & Cyril Okeme, V. Astrophys Space Sci (2014) 351: 119. doi:10.1007/s10509-014-1814-1

Abstract

This paper investigates Robe’s circular restricted three-body problem for two cases: with a Roche ellipsoid-triaxial system and with a Roche ellipsoid-oblate system. Without ignoring any component in both problems, a full treatment is given of the buoyancy force. The relevant equations of motion are established, and the special case where the density of the fluid and that of the infinitesimal mass are equal (D=0) is discussed. The location of the libration point and its stability when the infinitesimal mass is denser than the medium (D>0) are studied and it is found that the point (0,0,0) is the only libration point and this point is stable.

Keywords

Robe’s restricted three-body problem Buoyancy force Roche ellipsoid Triaxiality and oblate system Libration point Linear stability 

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Jagadish Singh
    • 1
  • Achonu Joseph Omale
    • 1
  • Veronica Cyril Okeme
    • 1
  1. 1.Department of Mathematics, Faculty of ScienceAhmadu Bello UniversityZariaNigeria