Question: A particle moves in a potential V (r) = C/(3r3). (a) Given L, find the maximum value of the effective potential. (b) Let the particle

A particle moves in a potential V (r) = −C/(3r3).
(a) Given L, find the maximum value of the effective potential.
(b) Let the particle come in from infinity with speed v0 and impact parameter b. In terms of C, m, and v0, what is the largest value of b (call it bmax) for which the particle is captured by the potential? In other words, what is the “cross section” for capture, πb2 max, for this potential?

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a b The effective potential is L 2mr2 Veff r 651 A circular orbit ... View full answer

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