International Journal of Innovative Research in Science, Engineering and Technology

International Journal of Innovative Research in Science, Engineering and Technology

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LOCATION OF LIBRATION POINTS IN THE GENERALISED PHOTOGRAVITATIONAL ELLIPTIC RESTRICTED THREE BODY PROBLEM

Dr. Om Prakash Raman1 and Dr. Ramashankar Sharma2
  1. Reader, Dept. of Mathematics, L.S. College, Muzaffarpur, India
  2. Lecturer, Dept. of Mathematics, Sant Kabir College, Samastipur, India
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International Journal of Innovative Research in Science, Engineering and Technology

Abstract

In this paper the location of libration points, triangular as well as collinear libration points in the generalized photogravitational elliptic restricted three body problem has been studied. The problem is generalized in the sense that the bigger primary is taken as an oblate spheroid and the smaller primary is considered as a source of radiation. It has been found that triangular and collinear libration points are different from those in classical case.

Keywords
Libration / Generalised / Photogravitational / Restricted

INTRODUCTION
Radzievskii [6] studied the location of the equilibrium points by taking more massive primary as the source of radiation in the restricted problem of three bodies. Danby [1] examined the stability of triangular points in the elliptic restricted problem of three bodies. Sharma [7] studied the photogravitational restricted three body problem aking smaller primary as an oblate spheroid. Haque and Ishwar [2] examined the non-linear stability in the perturbed photogravitational restricted three body problem. Markellos, Perdios and Labropoulou [4] studied the linear stability of the triangular equilibrium points in the photogravitational elliptic restricted problem. Khasan [3] discussed the librational solutions to the photogravitational restricted three body problem.
In the present paper we have studied the location of libration points triangular as well as libration points in the generalized photogravitational elliptic restricted three body problem. We have taken the bigger primary as an oblate spheroid and the smaller primary libration points contain eccentricity, oblateness and radiation factor which are different from those in classical case.

LOCATION OF TRIANGULAR LIBRATION POINTS:
THE EQUATIONS OF MOTION OF CONSIDERED PROBLEM ARE
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LOCATION OF COLLINEAR LIBRATION POINTS:
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References
  1. Danby, J.M.A.(1964): Astron. Journal 69, 165-172.
  2. Haque , M.N. and Ishwar, B.(1995): Bull Astv. Soc. India 23, 195-210.
  3. Khasan, S.N.(1996): Cosmic research vol. 34, No.2, 146-151.
  4. Markellos, V.V., Perdios, E. and Labropoulou, P.(1992): 1, Astrophysics and space science 194, 207-213.
  5. Mc Cuskey, S.W.(1963): Introduction to Celestial Mechanics, Addison-Wesley publishing Company, Inc. New York. [6] Radzievskii, V.V.(1953): Astron. Zh. 30, 256.
  6. Sharma, R.K.(1987): Astrophysics and Space Science,135, 271-281.
  7. Ray Ramashray: Ph. D. thesis, submitted to B. R. A. B. University; Muzaffarpur,2009.