Solar System Research

, Volume 52, Issue 2, pp 168–179 | Cite as

Effect of Stellar Wind and Poynting–Robertson Drag on Photogravitational Elliptic Restricted Three Body Problem

  • A. Chakraborty
  • A. Narayan
Article
  • 5 Downloads

Abstract

The existence and linear stability of the planar equilibrium points for photogravitational elliptical restricted three body problem is investigated in this paper. Assuming that the primaries, one of which is radiating are rotating in an elliptical orbit around their common center of mass. The effect of the radiation pressure, forces due to stellar wind and Poynting–Robertson drag on the dust particles are considered. The location of the five equilibrium points are found using analytical methods. It is observed that the collinear equilibrium points L1, L2 and L3 do not lie on the line joining the primaries but are shifted along the y-coordinate. The instability of the libration points due to the presence of the drag forces is demonstrated by Lyapunov’s first method of stability.

Keywords

P–R drag Solar wind drag elliptic restricted three body problem Solar system 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abd El-Salem, F.A., Stability of triangular equilibrium points in the elliptic restricted three-body problem with oblate and triaxial primaries, Astrophys. Space Sci., 2015, vol. 357, p. 15. doi 10.1007/s10509-015-2308-5ADSCrossRefGoogle Scholar
  2. Ammar, M.K., The effect of solar radiation pressure on the Lagrangian points in the elliptic restricted three-body problem, Astrophys. Space Sci., 2008, vol. 313, pp. 393–408.ADSCrossRefMATHGoogle Scholar
  3. Bonavito, N.L., Der, G.J., and Vinti, J.P., Progress in Astronautics and Aeronautics: Orbital and Celestial Mechanics, Reston, VA: Am. Inst. Aeronaut. Astronaut., 1998. doi doi 10.2514/4.866487Google Scholar
  4. Burns, J.A., Lamy, P.L., and Soter, S., Radiation forces on small particles in the solar system, Icarus, 1979, vol. 40, pp. 1–48.ADSCrossRefGoogle Scholar
  5. Donnison, J.R. and Williams, I.P., The effect of a resisting medium on protoplanetary orbits, Mon. Not. R. Astron. Soc., 1977a, vol. 180, pp. 281–288.ADSCrossRefGoogle Scholar
  6. Donnison, J.R. and Williams, I.P., The resistive effect of the solar wind on the orbits of solid bodies in the solar system, Mon. Not. R. Astron. Soc., 1977b, vol. 180, pp. 289–296.ADSCrossRefGoogle Scholar
  7. Floria, L., On an analytical solution in the planar elliptic restricted three-body problem, Monogr. Semin. Mat. Garca Galdeano, 2004, vol. 31, pp. 135–144.MathSciNetGoogle Scholar
  8. Gyorgyey, J., On the nonlinear motions around the elliptical restricted problem of three bodies, Celest. Mech. Dyn. Astron., 1986, vol. 36, no. 3, pp. 281–285.CrossRefMATHGoogle Scholar
  9. Ishwar, B. and Kushvah, B.S., Linear stability of triangular equilibrium points in the generalized photogravitational restricted three-body problem with Poynting–Robertson drag, J. Dyn. Syst. Geom. Theor., 2006, vol. 4, pp. 1–5.MathSciNetMATHGoogle Scholar
  10. Kumar, S. and Ishwar, B., Solutions of generalized photogravitational elliptic restricted three-body problem, AIP Conf. Proc., 2009, vol. 1146, pp. 456–461.ADSCrossRefGoogle Scholar
  11. Kumar, S. and Ishwar, B., Location of collinear equilibrium points in the generalized photogravitational elliptic restricted three-body problem, Int. J. Eng., Sci. Technol., 2011, vol. 3, no. 2, pp. 157–162.CrossRefGoogle Scholar
  12. Kumar, V. and Choudhry, R.K., Non-linear stability of the triangular libration points for the photogravitational elliptic restricted problem of three bodies, Celest. Mech. Dyn. Astron., 1990, vol. 48, no. 4, pp. 299–317.ADSCrossRefMATHGoogle Scholar
  13. Kumari, R. and Kushvah, B.S., Equilibrium points and Zero velocity surfaces in the restricted four-body problem with solar wind drag, Astrophys. Space Sci., 2013, vol. 344, no. 2, pp. 347–359.ADSCrossRefMATHGoogle Scholar
  14. Kushvah, B., and Ishwar, B.S., Triangular equilibrium points in the generalized photogravitational restricted three-body problem with Poynting–Robertson drag, Rev. Bull. Cal. Math. Soc., 2004, vol. 12, pp. 109–114.MATHGoogle Scholar
  15. Liou, J-C., Zook, H.A., and Jackson, A.A., Linear stability of triangular equilibrium points in the generalized photo-gravitational restricted three body problem with Poynting–Robertson drag, Icarus, 1995, vol. 116, pp. 186–201.ADSCrossRefGoogle Scholar
  16. Lyapunov, A.M., The general problem of the stability of motion, Int. J. Control, 1992, vol. 55.Google Scholar
  17. Markeev, A.P., Tochki libratsii v nebesnoi mekhanike i kosmodinamike (Libration Points in Celestial Mechanics and Cosmic Dynamics), Moscow: Nauka, 1978.Google Scholar
  18. Markellos, V.V., Perdios, E., and Labropoulou, P., Linear stability of the triangular equilibrium points in the photogravitational elliptic restricted problem, I, Astrophys. Space Sci., 1992, vol. 194, no. 2, pp. 207–213.ADSCrossRefMATHGoogle Scholar
  19. Markellos, V.V., Perdios, E., and Georghiou, C., Linear stability of the triangular equilibrium points in the photogravitational elliptic restricted problem, II, Astrophys. Space Sci., 1993, vol. 199, pp. 23–33.ADSCrossRefMATHGoogle Scholar
  20. Murray, C.D., Dynamical effects of drag in the circular restricted three-body problem: 1. Location and stability of the Lagrangian equilibrium points, Icarus, 1994, vol. 112, pp. 465–484.ADSCrossRefGoogle Scholar
  21. Narayan, A. and Shrivastav, A., Existence of resonance stability of triangular equilibrium points in circular case of the planar elliptical restricted three-body problem under the oblate and radiating primaries around the binary system, Adv. Astron., 2014, vol. 17, art. ID 287174.Google Scholar
  22. Narayan, A. and Singh, N., Motion and stability of triangular equilibrium points in elliptic restricted three-body problem under the radiating primaries, Astrophys. Space Sci., 2014a, vol. 352, pp. 57–70.ADSCrossRefGoogle Scholar
  23. Narayan, A. and Singh, N., effects of radiation on stability of triangular equilibrium points in elliptic restricted three-body problem, Int. J. Appl. Math. Res., 2014b, vol. 3, pp. 45–53.Google Scholar
  24. Narayan, A. and Usha, T., Stability of triangular equilibrium points in elliptic restricted three bodies with radiating and triaxial primaries, Astrophys. Space Sci., 2014, vol. 351, no. 1, pp. 135–142.ADSCrossRefGoogle Scholar
  25. Poynting, J.H., The pressure of light, Inquirer, 1903, pp. 195–196.Google Scholar
  26. Radzievskii, V.V., The restricted problem of three bodies taking account of light pressure, Astron. Zh., 1950, vol. 27, pp. 250–256.MathSciNetGoogle Scholar
  27. Radzievskii, V.V., The space photogravitational restricted three-body problem, Astron. Zh., 1953, vol. 30, pp. 265–273.Google Scholar
  28. Ragos, O., Perdios, E.A., Kalatonis, V.A., and Vrahatis, M.N., On the equilibrium points of the relativistic restricted three-body problem, Nonlinear Anal., 2001, vol. 47, pp. 3413–3418.MathSciNetCrossRefMATHGoogle Scholar
  29. Robertson, H.P., Dynamical effects of radiation in the solar system, Mon. Not. R. Astron. Soc., 1937, vol. 97, pp. 423–438.ADSCrossRefMATHGoogle Scholar
  30. Schuerman, D.W., The restricted three-body problem including radiation pressure, Astrophs. J., 1980, vol. 238, pp. 337–342.ADSMathSciNetCrossRefGoogle Scholar
  31. Singh, J. and Aminu, A., Instability of triangular liberation points in the perturbed photogravitational R3BP with Poynting–Robertson drag, Astrophys. Space Sci., 2014, vol. 351, pp. 473–482.ADSCrossRefGoogle Scholar
  32. Singh, J. and Amuda, T.O., Poynting–Robertson (P–R) drag and oblateness effects on motion around triangular equilibrium points in the photo-gravitational RTBP, Astrophys. Space Sci., 2014, vol. 350, pp. 119–126.ADSCrossRefGoogle Scholar
  33. Singh, J. and Umar, A., On the stability of triangular points in the elliptic R3BP under radiating and oblate primaries, Astrophys. Space Sci., 2012a, vol. 341, pp. 349–358.ADSCrossRefMATHGoogle Scholar
  34. Singh, J. and Umar, A., Motion in the photogravitational elliptic restricted three-body problem under an oblate primary, Astron. J., 2012b, vol. 143, no. 5, p. 109. http://stacks.iop.org/1538-3881/143/i=5/a=109.ADSCrossRefGoogle Scholar
  35. Szebehely, V., Theory of Orbits: The Restricted Problem of Three Bodies, New York: Academic, 1967.MATHGoogle Scholar
  36. Usha, T., Narayan, A., and Ishwar, B., Effects of radiation and triaxiality of primaries on triangular equilibrium points in elliptic restricted three-body problem, Astrophys. Space Sci., 2014, vol. 349, pp. 151–164.ADSCrossRefGoogle Scholar
  37. Zimvoschikov, A.S. and Thkai, V.N., Instability of libration points and resonance phenomena in the photogravitational elliptical restricted three-body problem, Sol. Syst. Res., 2004, 38, no. 2, pp. 155–163.ADSCrossRefGoogle Scholar
  38. Zsoft, S. and Erdi, B., Sympletic mapping for the trojantype motion in the elliptic restricted three-body problem, Celest. Mech. Dyn. Astron., 2003, vol. 86, pp. 301–319.ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  • A. Chakraborty
    • 1
  • A. Narayan
    • 1
  1. 1.Bhilai Institute of TechnologyDurgIndia

Personalised recommendations