Motion in central orbits

Question

A particle moves in a plane under inverse square law towards a fixed point.The point is surrounded by a gas,which revolves about it in such a way that the velocity of the gas at any point is inversely proportional to square root of radius vector at right angles to the radius vector.The resistance of the medium produces on the particle a retardation equal to k times the velocity of the particle relative to the medium in its neighbourhood,where k is a constant.Find the equations of motion and if the particle is slightly disturbed from motion in a circle,then find the expression for radius vector in the subsequent motion.