On the validity of series expansion being used for the position of a point on a Roche equipotential |
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| Authors: | A K Lal S Saini C Mohan V P Singh |
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| Institution: | (1) School of Mathematics and Computer Applications, Thapar University, Patiala, Punjab, India;(2) Ambala College of Engineering and Applied Research, Ambala Cant., Haryana, India;(3) Department of Paper Technology, IIT Roorkee Campus, Saharanpur, U.P., India |
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| Abstract: | The concept of Roche equipotentials has been frequently used in literature to study the problems of rotating stars and stars
in binary systems. However in spite of using this simplifying concept, it is still not possible to express the position of
a point in the potential field of such a system in a closed analytic form. In order to carry out further analytic studies,
Kopal (Adv. Astron. Astrophys. 9:1–65, 1972), therefore, developed a series expansion for it. The series expansion of Kopal has often been used in the analysis of the
problem of equilibrium structure and the periods of oscillations of rotating stars and stars in binary systems, but its validity
and convergence has not been analytically established. It is important that this aspect of the problem is checked so that
one is sure of the correctness of subsequent analysis and results based on this series expansion. In the present brief note,
we have addressed ourselves to this problem and validated the correctness of the numerical results obtained through the use
of this series expansion. |
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| Keywords: | Roche equipotentials Rotating stars Binary stars Rotationally and tidally distorted stars |
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