(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider an isothermal atmosphere (T = const.) over a sufficiently small range of radii, so that you can assume that the gravitation acceleration g is constant. Use the equation for the gas pressure gradient in hydrostatic equilibrium to show that the gas pressure decreases exponentially with height.

2. Relevant equations

[itex]\frac{dP}{dr} = -g\rho[/itex]

3. The attempt at a solution

so I solve the differential equation for P and I get

[itex]P = -\rho gr = \frac{-GM\rho}{r}[/itex]

I think I'm doing something really dumb here...

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# Homework Help: Pressure Gradient in Hydrostatic Equilibrium

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