- #1
SHISHKABOB
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- 1
Homework Statement
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.
Homework Equations
[itex]\frac{dP}{dr} = -g\rho[/itex]
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...