A particle P of mass m moves under the attractive inverse square field F = -(mγ /r2). Initially P is at a point C, a distance c from O, when it is projected with speed (γ /c)½ in a direction making an acute angle α with the line OC.
Find the apsidal distances in the resulting orbit. Given that the orbit is an ellipse with O at a focus, find the semi-major and semi-minor axes of this ellipse.