The time it takes for a probe of mass \(\mu\) to move from one radius to another under the influence of a central spring force was shown in the chapter to be

where \(E\) is the energy, \(k\) is the spring constant, and \(\ell\) is the angular momentum. Evaluate the integral in general, and find (in terms of given parameters) how long it takes the probe to go from the maximum to the minimum value of \(r\).

Transcribed Image Text:

t(r) = r dr Er k1/2 - 12/21" ro