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[tex]U^*(\rho)=\frac{L^2}{2m\rho^2}+U(\rho) [/tex]

in many problems I found that particle will have stable circular orbit if [tex]U^*(\rho)[/tex] has minimum.

1. Why is that a case? Why circle? Why not ellipse for example?

2. Is this condition equivalent with

[tex]\frac{f'(\rho)}{f(\rho)}+\frac{3}{\rho}>0[/tex]?