Volume 45 | Number 3 | Year 2017 | Article Id. IJMTT-V45P526 | DOI : https://doi.org/10.14445/22315373/IJMTT-V45P526
We have investigated the existence and stability of non-collinear libration points in the restricted three body problem (R3BP) with dissipative force Stokes drag. The bigger primary is taken as spherical and smaller one as a finite straight segment. There exist five libration points, out of which two are non-collinear with the primaries and three are almost collinear with the primaries. The location of libration points for different values of parameters, and l are evaluated numerically and shown graphically. The linear stability of non-collinear libration points is also discussed.
[1] Bulletin of Astronomical Society of India, 34, 327-356, 2006.
[2] R. Aggarwal and B. Kaur, “Robe’s restricted problem of 2+2 bodies with one of the primaries an oblate body,” Astrophys and Space Science, 352(2), 467-479, 2014.
[3] M. Jain and R. Aggarwal, “Existence and Stability of Non-collinear libration points in the restricted problem with Poynting Robertson Light Drag Effect,” Int. J. of Mathematics Trends and Technology, 19, 20-33, 2015.
[4] M. Jain and R. Aggarwal, “Restricted three body problem with Stokes drag effect,” Int. J. Astron. Astrophys., 5, 95-105, 2015.
[5] M. Jain and R. Aggarwal, “A study of non-collinear libration points in the restricted three body problem with Stokes drag effect when smaller primary is an oblate spheroid,” Astrophys and space Science, 358, 51, 2015.
[6] D. Kumar, R. Aggarwal and M. Jain, “Combined effects of finite straight segment and oblateness on the libration points in the restricted three body problem,” Int. J. Tech., 6(2), 185-190, 2016.
[7] M. Khanna and K.B. Bhatnagar,”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, 1999.
[8] J. C. Liou, H. A. Zook and A. A. Jackson, “Radiation pres-sure, Poynting-Robertson drag and solar wind drag in the restricted three body problem,” Icarus, 116, 186-201, 1995b.
[9] V. K. Mishra, J. P. Sharma and B. Ishwar, “Stability of triangular equilibrium points in the Photogravitational elliptic restricted three body problem with Poynting-Robertson drag,” International Journal of Advanced Astronomy, 4(1), 33-38, 2016.
[10] C. D. Muray, “Dynamical effects of drag in the circular restricted three body problems: 1. Location and stability of the Lagrangian equilibrium points,” Icarus, 112, 465-484, 1994.
[11] A. Riaguas, A. Elipe and M. Lara, “Periodic Orbits Around a Massive Straight Segment,” Celestial Mechanics and Dynamical Astronomy, 73(1), 169-178, 1999.
[12] A. Riaguas, A. Elipe, and T. Lopez-Moratalla, “Non-Linear Stability of the equilibria in the gravity field of a finite straight segment,” Celestial Mechanics and Dynamical Astronomy, 81, 235-248, 2001.
[13] R.K. Sharma, “The linear stability of libration points of the photogravitational restricted three body problem when the smaller primary is an oblate spheroid,” Astrophys and Space Science, 135(2), 271-281, 1987.
[14] V. Szebehely, “Theory of Orbits, the Restricted Problem of Three Bodies,” Academic Press, New York, (1967).
Dinesh Kumar, Mamta Jain, Rajiv Aggarwal, Satyendra Kumar Satya, "Stability of L4,5 in the R3BP Under the Combined Effects of Stokes Drag and Finite Straight Segment," International Journal of Mathematics Trends and Technology (IJMTT), vol. 45, no. 3, pp. 200-206, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V45P526