It forms an interesting and topical example in particle dynamics to investigate the effect of a small frictional perturbation on an elliptic orbit. In this paper the frictional force is assumed to be proportional to the square of the velocity and the eccentricity of the orbit is assumed to be small. Formulae are deduced for the rates of change of the major axis and eccentricity of the ellipse in terms of the rate of change of periodic time, numerical values being compared with the rather sparse information on Sputnik I.