Important Properties
There are many useful features of the effective potential. The condition for a particle of energy E flying by to be `trapped' and go into an orbit:
To find the radius of a circular orbit, we simply minimize the effective potential with respect to, or equivalently set the net force to zero and then solve for :
After solving for, plug this back into to find the maximum value of the effective potential
To find the frequency of small oscillations:
where the double prime indicates the second derivative of the effective potential with respect to .
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