Effects of radiation on stability of triangular equilibrium points in elliptic restricted three body problem

Authors

  • Nutan Singh "Chattisgargh Swami Vivekanand Technical University"
  • Ashutosh Narayan "Chattisgargh Swami Vivekanand Technical University"

DOI:

https://doi.org/10.14419/ijamr.v3i1.1614

Published:

2014-02-01

Abstract

This paper deals with the stability of triangular Lagrangian points in the elliptical restricted three body problem, under the effect of radiation pressure stemming from the more massive primary on the infinitesimal. We adopted a set of rotating pulsating axes centered at the centre of mass of the two primaries Sun and Jupiter. We have exploited method of averaging used by Grebenikov, throughout the analysis of stability of the system. The critical mass ratio depends on the radiation pressure, eccentricity and the range of stability decreases as the radiation parameter increases.

 

Keywords: Dynamical system, elliptical restricted three body problems, lagrangian points, radiation pressure, and stability.

References

V. Szebehely, Theory of orbits, New York (1967).

E. A. Grebenikov, On the stability of the Lagrangian Triangular Solutions of the Restricted Elliptic Three Body problem, Soviet Astronomy –AJ 8 3 (1964) 567-578.

J.M.A. Danby, Stability of the triangular points in elliptic restricted problem of three bodies,” The Astronomical Journal 69 (1964) 165-172.

A. Bennett, Characteristic Exponent of the five equilibrium solutions in elliptically restricted problems, Icarus 4 (1965) 177-187.

E. Rabe, Elliptical restricted problem fourth-order stability analysis of the triangular points,Toply E.D Szebehely V. (els) ,Recent Advances in Dynamical Astronomy (1973) 155-160.

E. Rabe, Two new classes of periodic Trojan liberation in the elliptical restricted problem and there stabilities, In Giacaglia, G.E.O.(ed.) periodic orbits Stability and Resonance, (1970) 33-44.

R. Meire, The stability of the triangular points in the elliptical restricted problem, Celestial Mechanics 23 (1981) 89-95.

V. V. Markellos, E. Perdios ,P. Labropoulou, Linear Stability of the triangular equilibrium points in the photogravitational elliptical restricted problem, Astrophysics and Space Science, 194 (1992) 207-213.

G.E. Roberts, Linear stability of the elliptic Lagrangian triangle solution in the three body problem, J. Differential equation 182 (2002) 191-218.

A. S. Zimvoschikov ,V. N. Thakai, Instability of libration points and resonance phenomena in the photogravitaional in the elliptical restricted three body problem,Solar system Research 38 2 (2004) 155-163 .

M. K. Ammar, The effect of solar radiation pressure on the Lagrangian points in the elliptic restricted three body problems, Astrophys.space sci. 313 (2008) 393-408 .

S. N. Khasan, Liberation Solutions to the photogravitational restricted three body problem, Cosmic research 34 2 (1996) 146-151.

S. N. Khasan, Liberation Solutions to the photogravitational restricted three body problem, Cosmic research 34 2 (1996) 146-151.

D.Selaru , C. Cucu- Dumitrescu, An analysis asymptotical solution in the three body problem,Bom Astron. J 4 1 (1994) 59-67.

D.Selaru, C.Cucu-Dumitrescu, Infinitesimal orbit around Lagrange points in the elliptic restricted three body problem, Celest. Mech. Dyn. Astron. 61 4 (1995) 333-346.

J .Gyorgrey, on the non-linear stability of motion's around L_ {5} in the elliptic restricted problem of the three bodies, Celestial Mech.and Dyn. Astro. 36 3 (1985) 281-285.

V. Kumar and R.K. Choudhary, Nonlinear stability of the triangular libration points for the photo gravitational elliptic restricted problem of three bodies, Celestial Mech. and Dyn. Astro 48 4 (1990) 299-317.

B. Erdi, A parametric study of stability and resonance around L4 in the elliptical restricted three body problem, Celst. Mech.and Dyn. Astr. 104 (2009) 145-158.

C. Pinyol, Ejection collision orbits with the more massive primary in the planar elliptic restricted three body problem, Celest - Mech and Dyn Astro. 61 (1995) 315-331.

L.Floria, on analytical solutions in the planar elliptic restricted three body problem, Monografsem. Mat. Caracia de Galdeano 31 (2004) 135-144.

P.P Halan , N. Rana, The Existence and stability of equilibrium points in the Robe's restricted three body problem, Celest Mech and Dyn Astro. 79 (2001) 145-155.

A.P. Markeev, One special case of parametric resonance in problem of celestial mechanics, Dyn.Astronomy 31 5 (2005) 300-356.

A. Narayan, C. Ramesh, Stability of triangular equilibrium points in elliptical restricted three body problem under the effects of photogravitational and oblateness of primaries, International Journal of Pure and Applied Mathematics 70 5 (2011) 735-754.

A. Narayan , C. Ramesh, Existence and stability of collinear equilibrium points in elliptical restricted three body problem under the effects of photo gravitational and oblateness primaries, International Journal of Pure and Applied Mathematics 80 4 (2012) 477-494..

J. Singh, A. Umar, on the stability of triangular points in the elliptic R3BP under radiating and oblate primaries, Astrophysics and Space Science 341 (2012) 349-358.

J. Singh, an Umar, Motion in the photogravitational elliptic restricted three body problem under radiating oblate primaries, Astronomical Journal 143 (2012) 109-131.

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