Consider the motion of a point mass under the influence of an attractive central force. The potential for the force is proportional to the inverse distance from the central point O to the point mass. For every value of the angular momentum L of the object around O we have an equilibrium point in the radial direction, which corresponds to a circular orbit. We now consider a small perturbation of a circular orbit into a low eccentricity ellipse with the same angular momentum. If we look at the radial distance from O to the object on the elliptical orbit, we see that the distance changes from some rmin to rmax with some frequency f. If at L1=1 kg⋅m2/s we get f1=f(L1)=1 Hz, find the frequency f2 for L2=10 kg⋅m2/s in Hz.
Bonus thought: The value of the frequency at L3=0 (without angular momentum) is defined as the bare frequency. Is this a finite value?
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