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Existence and Stability of Libration Points in the Restricted Three-Body Problem When the Primaries are Triaxial Rigid Bodies

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Abstract

This paper deals with the stationary solutions of the planar restricted three-body problem when the primaries are triaxial rigid bodies with one of the axes as the axis of symmetry and its equatorial plane coinciding with the plane of motion. It is seen that there are five libration points, two triangular and three collinear. It is further observed that the collinear points are unstable, while the triangular points are stable for the mass parameter 0 ≤ μ < μcrit(the critical mass parameter). It is further seen that the triangular points have long or short periodic elliptical orbits in the same range of μ.

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References

  • Bhatnagar, K. B. and Hallan, P. P.: 1979, ‘Effect of perturbed potential on the stability of libration points in the restricted problem’, Celest. Mech. & Dyn. Astr. 20, 95-103.

    Google Scholar 

  • El-Shaboury, S. M.: 1991, ‘Equilibrium solutions of the restricted problem of 2 + 2 axisymmetric rigid bodies’, Celest. Mech. & Dyn. Astr. 50, 199-208.

    Google Scholar 

  • Khanna, M. and Bhatnagar, K. B.: 1998, ‘Existence and stability of libration points in the restricted three-body problem when the smaller primary is a triaxial rigid body’, Indian J. pure appl. Math. 29(10), 1011-1023.

    Google Scholar 

  • Khanna, M. and Bhatnagar, K. B.: 1999, ‘Existence and stability of libration points in the restricted three-body problem when the smaller primary is a triaxial rigid body and the bigger one an oblate spheroid’, Indian J. pure appl. Math. 30(7), 721-733.

    Google Scholar 

  • McCusky, S. W.: 1963, Introduction to Celestial Mechanics, Addision Wesley.

  • Subba Rao, P. V. and Sharma, R. K.: 1975, ‘A note on the stability of the triangular points of the equilibrium in the restricted three-body problem’, Astron. Astrophys. 43, 381-383.

    Google Scholar 

  • Szebehely, V.: 1967, Theory of Orbits, Academic Press, New York.

    Google Scholar 

  • Vidyakin, V. V.: 1974, ‘A plane circular limited task pertaining to three spheroids (in Russian)’, Astron. Zh 51(5), 1087-1094.

    Google Scholar 

  • Wintner, A.: 1941, The Analytical Foundations of Celestial Mechanics, Princeton University Press, Princeton, 372.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Jamia Millia Islamia, Jamia Nagar, New Delhi, 110025, India

    Ravinder Kumar Sharma & Z. A. Taqvi

  2. Centre for Fundamental Research in Space Dynamics and Celestial Mechanics, IA/47C, Ashok Vihar, Delhi, 110052, India

    K. B. Bhatnagar

Authors
  1. Ravinder Kumar Sharma
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  2. Z. A. Taqvi
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  3. K. B. Bhatnagar
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Sharma, R.K., Taqvi, Z.A. & Bhatnagar, K.B. Existence and Stability of Libration Points in the Restricted Three-Body Problem When the Primaries are Triaxial Rigid Bodies. Celestial Mechanics and Dynamical Astronomy 79, 119–133 (2001). https://doi.org/10.1023/A:1011168605411

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  • DOI: https://doi.org/10.1023/A:1011168605411

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