A particle of mass m moves in a radial potential U(r) = -Uge- where Uo and A are positive constants. (a) If the particle is in a circular orbit, write a formula for the angular momentum in terms of m, r, and the parameters of the potential. (b) If the angular momentum is too large, a circular orbit will not exist, even if r is increased. What is the maximum allowed angular momentum for a circular orbit at any value of r?
A particle of mass m moves in a radial potential U(r) = -Uge- where Uo and A are positive constants. (a) If the particle is in a circular orbit, write a formula for the angular momentum in terms of m, r, and the parameters of the potential. (b) If the angular momentum is too large, a circular orbit will not exist, even if r is increased. What is the maximum allowed angular momentum for a circular orbit at any value of r?
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Transcribed Image Text:A particle of mass m moves in a radial potential U(r) = -Uge-Ar where Ug and A are
positive constants.
(a) If the particle is in a circular orbit, write a formula for the angular momentum in
terms of m, r, and the parameters of the potential.
(b) If the angular momentum is too large, a circular orbit will not exist, even if r is
increased. What is the maximum allowed angular momentum for a circular orbit at any
value of r?
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