The effect of a resisting medium which is either static (case I), or rotating freely (case II), or rotating uniformly (case III), on the size and shape of Keplerian orbits has been examined. Both direct and retrograde orbits (i.e. rotating with and against the medium) were considered. The signs for the instantaneous changes in the semi-major-axis a , eccentricity e , semi-latusrectum p , perihelion distance q were ascertained with regard to the position in the orbit and, in case III, also to the values a, e . The time-averages of the instantaneous changes in a and e over an orbital period were examined for sign for a law of resistance that varies as the relative velocity to power α and as the radial distance to power β , and were integrated to give the entire course of evolution of the orbital size and shape, for the four combinations ( α , β ) = (1, 0), (3, 0), (1, −2), (3, −2) in cases I and II, and for ( α , β ) = (1, 0) in case III. Detailed results are listed at the end of the paper. One particular result is that, if a freely rotating medium is effective enough to reduce the eccentricities of direct orbits appreciably, then it will reduce very considerably the perihelion distances of retrograde orbits. That the present-day planets all move in nearly circular orbits and that they all go round in the same sense may thus have been brought about by one and the same process.