= Entropy dependence of a polytropic mass-radius relation
{title2=$R\propto K^{n/(3-n)}M^{(1-n)/(3-n)}$}
For a finite regular <polytrope> with fixed index, the scale $\alpha^2\propto K\rho_c^{(1-n)/n}$ implies $M^{n-1}R^{3-n}\propto K^n$. Thus, for $n\ne3$, $R\propto K^{n/(3-n)}M^{(1-n)/(3-n)}$. For $n=3/2$, $R\propto KM^{-1/3}$. Fixed composition makes the cold <electron degeneracy pressure> coefficient approximately fixed, but a convective <ideal gas> has $K$ controlled by <entropy>. A stellar sequence with changing entropy therefore need not follow the fixed-$K$ negative slope.
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