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1. /20 points) Consider the motion of a particle of massn in a central potential U(r) =ark where a and k can be either positive
1. /20 points) Consider the motion of a particle of massn in a central potential U(r) =ark where a and k can be either positive or negative, andk is an integer. (a) Are there any conditions (on both the parameters of the potential and the initial conditions) that would allow circular orbits? [10 points) (b) When are circular orbits stable? [10 points]
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