Stability of Collinear Points in the Generalized Photogravitational Robes Restricted Three-Body Problem

Author(s)
AbdulRazaq AbdulRaheem

ABSTRACT

In studying the effects of radiation and oblateness of the primaries on the stability of collinear equilibrium points in the Robes restricted three-body problem we observed the variations of the density parameter k with the mass parameter μ for constant radiation and oblateness factors on the location and stability of the collin-ear points L1, L2and L3. It is also discovered that the collinear points are unstable for k > 0 and stable for k < 0.

In studying the effects of radiation and oblateness of the primaries on the stability of collinear equilibrium points in the Robes restricted three-body problem we observed the variations of the density parameter k with the mass parameter μ for constant radiation and oblateness factors on the location and stability of the collin-ear points L1, L2and L3. It is also discovered that the collinear points are unstable for k > 0 and stable for k < 0.

Cite this paper

nullA. AbdulRaheem, "Stability of Collinear Points in the Generalized Photogravitational Robes Restricted Three-Body Problem,"*International Journal of Astronomy and Astrophysics*, Vol. 1 No. 1, 2011, pp. 6-9. doi: 10.4236/ijaa.2011.11002.

nullA. AbdulRaheem, "Stability of Collinear Points in the Generalized Photogravitational Robes Restricted Three-Body Problem,"

References

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[1] A. AbdulRaheem and Singh, “Combined Effects of Perturba-tions, Radiation and Oblateness on the Stability of Equilibrium points in the Restricted Three-Body Problem,” Astronomical Journal, Vol. 131, No. 3, 2006, pp. 1880-1885.

[2] R. K. Sharma, Z. A. Taqvi and K. B. Bhatnagar, Celest. Mech. and Dyn. Astr., Vol. 79, 2001, pp. 119-133.

[3] J. Singh, Indian J. of Pure and Appl. Math., Vol. 34, No. 2, 2003, pp. 335-345.

[4] S. K. Shaoo and B. Ishwar, Bull. of Astr. Society. of India, Vol. 28, 2000, pp. 579-586.

[5] B. Ishwar and A. Elipe, As-trophysics and Space Science, Vol. 277, 2001, pp. 437-446.

[6] A. L. Kunisyn, Jour. of Appl. Math. and Mech., Vol. 64, No. 5, 2000, pp. 757-763.

[7] A. L. Kunisyn, Jour. of Appl. Math. and Mech., Vol. 65, No. 4, 2001, pp. 703-706.

[8] D. V. Schuerman, Astronomical Journal, Vol. 238, 1980, pp. 337-342.

[9] V. V. Szebehely, Astronomical Journal, Vol. 72, No. 1, 1967, pp. 7-9.

[10] H. A. G. Robe, Celestial Mechanics, Vol. 16, 1977, pp. 345-351.

[11] A. K. Shrivastava and D. Garain, Celest.and Mech. Dyn. Astr., Vol. 51, 1991, pp. 67-73.

[12] C. M. Giordano, A. R. Plastino and A. Plastino, Celest. Mech. and Dyn. Astr., Vol. 66, 1997, pp. 229-242.

[13] P. P. Hallan and N. Rana, Celest . Mech.and Dyn. Astr., Vol. 66, 2001, pp. 145-155.

[14] P. P. Hallan and N. Rana, Indian J. of Pure and Appl. Math., Vol. 35, No. 3, 2004, pp. 401-413.