 Hydrostatic pressure support equation

ID: hydrostatic-pressure-support-equation

For a static spherically symmetric Newtonian star, balancing the inward gravitational force against the pressure gradient gives

\frac{d P}{d r} = - \frac{G m ( r ) ρ ( r )}{r ^{2}}, \frac{d m}{d r} = 4 π r^{2} ρ (r) .

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