planeparatm consider an isothermal atmosphere on the surface of a star, which has a very small height and is in hydrostatic equilibrium. this means that the atmosphere can be treated as plane parallel: in the equation of hydrostatic equilibrium, dp/dr can be replaced by dp/dz, where z is the height above the surface of the star. moreover, the surface gravity, g, is constant over the height of the atmosphere (a) under these assumptions, start with the equation of hydrostatic equilibrium and derive a differential equation for the density of this atmosphere (b) solve this equation to obtain the density as a function of height above the surface of the star (c) in your solution, identify the "scale height," i. e. a quantity with dimensions of length, which represents the height over which the density of the atmosphere changes appre- ciably. (d) calculate the pressure at the base of the atmosphere. (e) using the ideal gas equation of state and your solution for the density structure of the atmosphere from part (b), compute the pressure at the surface of the star. compare your answer to what you found in part (d). what do you conclude from this exercise?