Consider an atmosphere atop a spherical rocky planet of mass M and radius R. The atmosphere is an ideal gas with mean molecular weight  and constant temperature T. The gravitational acceleration from the planet is g > 0. Near the ground, g is approximately constant. [8 points] (a) Measure the height from the ground as z  0. At the ground, the mass density of the atmosphere is (z = 0)  0. Write down a formula for the equilibrium density (z) in terms of the given variables and fundamental constants.