Study of Stability of Equilibrium Points in The Pcr3bp on the Circumference of FEC

Authors

  • Vikash Kumar  Research Scholar, University Department of Mathematics, B. R. A. Bihar University, Muzaffarpur, Bihar, India
  • Dr. K. B. Singh  P. G. Department of Physics, L. S. College, Muzaffarpur, B. R. A. Bihar University, Muzaffarpur, Bihar, India
  • Dr. M. N. Haque  P. G. Department of Mathematics, M. S. College, Motihari, B. R. A. Bihar University, Muzaffarpur, Bihar, India

DOI:

https://doi.org//10.32628/IJSRST229658

Keywords:

RTBP, CRTBP, Three Body Problem.

Abstract

The Three Body Problem The three body problem studies the motion of three masses whose gravitational attraction have an effect on each other. The dynamics of the three-body problem are essentially different from those of two bodies, because in the latter case, an analytical solution may be found that admits orbits in the form of conic sections. This problem has been studied at great length and is the basis of most of today’s orbit planning and trajectory design for satellites. However, the two-body problem is valid on close to a single massive body, compared to which the target body (the object whose motion is desired) is essentially a massless particle. In deep space, when there may be two or more massive bodies to affect the motion of our test particle, the two-body solution obviously fails. It then becomes essential to study the three-body problem.

References

  1. Bhatanagar, K.B. and Hallan, P.P. (1978), “Effect of perturbation in coriolis and centrifugal forces on the stability of libration points in restricted problem”, Cele. Mech., 18: pp. 105.
  2. Brumberg, V.G., 1972. Relativistic Celestial Mechanics, Nauka, Moscow.
  3. Deprit, A and Deprit-Bartholome, A. (1967), “Stability of the triangular Lagrangian points” Astro. J.,vol. 72 No. 2: pp. 173-179.
  4. Douskos, C.N. (2011), “Equilibrium points of the restricted three body problem with prolate and radiating primaries and their stability”, Astrophys. Space Sci., 333: pp. 79-87.
  5. Fawzy, A and Abd El-salam (2012), “Discovery of an equilibrium circle in the circular restricted three body problem”, Americ. J. App. Sci., 9: pp-1378-1384.
  6. Haque, M.N. (1992), “Effect of perturbations on the stability of equilibrium points in the photogravitational restricted problem of three bodies” Ph.D. thesis, Submitted to BRA Bihar University, Muz.
  7. Haque, M.N. and Vikash Kumar (2014), “Location and stability of equilibrium points in a PRTBP under perturbations, bigger primary is an oblate spheriod ”, IJSR, vol. 3: pp-1139-1140.
  8. Kumar, S. and Ishwar, B. (2011), “Location of collinear equilibrium points in the generalised photogravitational elliptic restricted three body problem”, Int. J. Eng. Sci. Techol., 3: pp-157-163.
  9. Kishor, R. and Kushvah, B.S. (2012) “Periodic orbits in the generalised photogravitational Chermnykh-Like problem with power profile”,
  10. Leontovich, A.M. (1962), “On the stability of the restricted problem of three bodies”, Soviet Math. Dokl., 3: pp. 425-428.
  11. Markeew, A.P. (1969), “On the stability of triangular libration points in the circular bounded three body problem”, J. Applied Math. Mech., 33: pp. 105-110.
  12. Murray, C.D. and Dermott, S.F. (1999), “Solar system dynamics”, Cambridge University Press, Cambridge.
  13. Narayan, A. and Ramesh, C. (2008), “Stability of triangular points in the generalised restricted three body problem”, J. Mod. Ex-B, France.
  14. Szebehely, V.G. (1967), “Theory of orbits”, Academics press, New York.
  15. Subbarao, P.V. and Sharma, R.K. (1975), “A note on the stability of the triangular points of equilibrium in the restricted three body problem” Astronomy and Astrophysics, 43: pp. 381-383.
  16. Singh, R.B. (2006), “Some Problems of Space Dynamics” Celestial Mechanics, Recent Trends” pp. 237-244, Narosa Publishing House, New Delhi.
  17. Singh, J. (2011), “Nonlinear stability in the restricted three body problem with oblate and variable mass”, Astrophys. Space Sci., 333: pp. 105-110.

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Published

2022-12-30

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Section

Research Articles

How to Cite

[1]
Vikash Kumar, Dr. K. B. Singh, Dr. M. N. Haque, " Study of Stability of Equilibrium Points in The Pcr3bp on the Circumference of FEC, International Journal of Scientific Research in Science and Technology(IJSRST), Online ISSN : 2395-602X, Print ISSN : 2395-6011, Volume 9, Issue 6, pp.395-401, November-December-2022. Available at doi : https://doi.org/10.32628/IJSRST229658