Consider the motion of a point mass m in the potential
V(r)=-k/r , k>0
Show that there is a solution x(t) of the equations of motion which is a circular motion
with constant circular frequency ω. Determine the relation between ω and the radius of the
circular motion. Show explicitely that energy and angular momentum are conserved along
the motion curve, by computing their values. Show also that the radius of the circular
motion coincides with the radius where the corresponding eective potential takes its
γ(t)=(rcos(ωt); r sin(wt)); r > 0; ω> 0;
The Attempt at a Solution
I am not really sure where to start. Maybe one can find the arc length for a piece of the curve γ, using this
s(t0,t1)=∫ from t0 to t1√(∑γ'k^2dx) and then go into the details, but for the moment I can't conjure up anything.
Any help would be highly appreciated.