Astrophysics and Space Science

, Volume 338, Issue 1, pp 127–145 | Cite as

Radius of the Roche equipotential surfaces

  • A. PathaniaEmail author
  • T. Medupe
Original Article


In literature, there is no exact analytical solution available for determining the radius of Roche equipotential surfaces of distorted close binary systems in synchronous rotation. However, Kopal (Roche Model and Its Application to Close Binary Systems, Advances in Astronomy and Astrophysics, Academic Press, New York 1972) and Morris (Publ. Astron. Soc. Pac. 106:154, 1994) have provided the approximate analytical solutions in the form of infinite mathematical series. These series expressions have been commonly used by various authors to determine the radius of the Roche equipotential surfaces, and hence the equilibrium structures of rotating stars and stars in the binary systems. However, numerical results obtained from these approximating series expressions are not very accurate. In the present paper, we have expanded these series expressions to higher orders so as to improve their accuracy. The objective of this paper is to check, whether, there is any effect on the accuracy of these series expressions when the terms of higher orders are considered. Our results show that in most of the cases these expanded series give better results than the earlier series. We have further used these expanded series to find numerically the volume radius of the Roche equipotential surfaces. The obtained results are in good agreement with the results available in literature. We have also presented simple and accurate approximating formulas to calculate the radius of the primary component in a close binary system. These formulas give very accurate results in a specified range of mass ratio.


Methods: analytic Methods: numerical Binaries: close Binaries: general 


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© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Physics and ElectronicsNorth-West UniversityMafikengSouth Africa
  2. 2.South African Astronomical ObservatoryObservatorySouth Africa

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