International Journal of Astronomy and Astrophysics, 2015, 5, 95-105 Published Online June 2015 in SciRes. http://www.scirp.org/journal/ijaa http://dx.doi.org/10.4236/ijaa.2015.52013 How to cite this paper: Jain, M. and Aggarwal, R. (2015) Restricted Three Body Problem with Stokes Drag Effect. Interna- tional Journal of Astronomy and Astrophysics, 5, 95-105. http://dx.doi.org/10.4236/ijaa.2015.52013 Restricted Three Body Problem with Stokes Drag Effect Mamta Jain 1 , Rajiv Aggarwal 2 1 Department of Mathematics, Shri Venkateshwara University, Gajraula, India 2 Department of Mathematics, Sri Aurobindo College, University of Delhi, Delhi, India Email: mamtag27@gmail.com , rajiv_agg1973@yahoo.com Received 16 March 2015; accepted 8 June 2015; published 11 June 2015 Copyright © 2015 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ Abstract The existence and stability of stationary solutions of the restricted three body problem under the effect of the dissipative force, Stokes drag, are investigated. It is observed that there exist two non collinear stationary solutions. Further, it is also found that these stationary solutions are unstable for all values of the parameters. Keywords Restricted Three Body Problem, Libration Points, Linear Stability, Dissipative Forces, Stokes Drag 1. Introduction Two finite masses, called primaries, are moving in circular orbits around their common centre of mass, and an infinitesimal mass is moving in the plane of motion of the primaries. To study the motion of the infinitesimal mass is called the restricted three body problem. [1] proved that there existed five points of equilibrium, or points of libration (often denoted by L 1 , ….. L 5 ), which were the stationary solutions of the restricted problem. Out of them, three are collinear and two are non collinear. The collinear libration points are unstable for all val- ues of mass parameter µ and the triangular libration points are stable for 0 c µ µ < < , where 0.03852 c µ = ⋯ is a critical value of mass parameter [2]. As we know, dissipative forces are those where there is a loss of energy such as friction and one of the most important mechanisms of dissipation is the Stokes drag which is a force experienced by a particle moving in a gas, due to the collisions of the particle with the molecules of the gas. [3] has determined some results on the global dynamics of the regularized restricted three body problem with dissipative forces. Their investigations have motivated us to study the motion of the restricted three body prob- lem under dissipative forces such as Stokes drag. In the synodic frame, Stokes drag force is defined by [4]: