Atmospheric physics 2: Homogeneous atmosphere

The air pressure $P(z)$ at altitude $z$ corresponds to the weight $F = m(z) g$ of the overlying atmospheric layers. The partial mass $m(z)$ is obtained by integrating the air density $\rho(z)$ over the volume between the altitudes $z$ and $z_0$ : $\begin{aligned} m(z) &= \int_{z}^{\infty} \rho(z') \cdot A dz' = \int_{z}^{z_0} \rho_0 \cdot A dz' = \rho_0 A (z_0 - z) \\ \Rightarrow \quad P(z) &= \frac{m(z) g}{A} = \rho_0 g (z_0 - z) = P_0 \left(1 - \frac{z}{z_0}\right) \end{aligned}$ Here, the pressure decreases linearly with the altitude and becomes zero at the interface to space (comparable to the hydrostatic pressure of water).