\frac{dp}{dz}= \rho(p) \cdot g

p(z) = p_0 + \rho \cdot g \cdot (z-z_0)

p(z) = p_0 \cdot \exp \left[ - \frac{M \, g}{R \, T} \cdot (z-z_0) \right]

 \frac{1+ c_0 \, p(z)}{1 + c_0 \, p_0}  = \exp \left[ \frac{ \rho_0 \, g \cdot (z-z_0)}{1+c_0 \, p_0} \right]