A particle P of mass m is attracted towards a fixed origin O by a force of magnitude mγ /r3, where r is the distance of P from O and γ is a positive constant.
[It's gravity Jim, but not as we know it.] Initially, P is at a distance a from O, and is projected with speed u directly away from O. Show that P will escape to infinity if u2 > γ/a2.
For the case in which u2 = γ /(2a2), show that the maximum distance from O achieved by P in the subsequent motion is a, and find the time taken to reach this distance.