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\centerline{Plot for assignment 24 set 7.} \bigskip 

Calculation of $r_{\min}$ defined by 
$U^{\min}_{\rm eff}=U_{\rm eff}(r_{\min})$:

$$ U'_{\rm eff}(r) = \frac{\alpha}{r^2} - \frac{L^2}{\mu\,r^3} $$
$$ 0 = \alpha - \frac{L^2}{\mu\,r^{\min}} $$
$$ r^{\min} = \frac{L^2}{\alpha\,\mu} = 1~~{\rm for}~~
   \alpha=\mu=L=1\ .$$

The orbit is a circle with radius $r^{\min}=1$.
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