Hello I am to solve whether it is possible for body of mass $m$ to move around stable circular orbit in potentials: ${V_{1} = \large\frac{-|\kappa|}{r^5}}$ and ${V_{2} = \large\frac{-|\kappa|}{r^{\frac{1}{2}}}}$. I have read about Bertrand's Problem and is it sufficient to check if the parametr $\beta^{2} = 3 + \large\frac{r_{0}F'_{r}(r_{0})}{F_{r}(r_{0})}$$>0$ in my problem? $r_{0}$ denotes point where derivative of effective potential is zero. I also assume that $L$ is not equal to zero.
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$\begingroup$ Why the downvote? Is it because the post sounds like a homework question? The OP has obviously done some research and he wants a clarification if he is on the right track. $\endgroup$– FlatterMannCommented Jan 25 at 9:27
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