Planets lose their atmospheres over time unless they are replenished. A complete analysis of the overall process is very complicated and depends upon the radius of the planet, temperature, atmospheric composition, and other factors. Prove that the atmosphere of planets cannot be in an equilibrium state by demonstrating that the Boltzmann’s distribution leads to a uniform finite number density as r ---7 =. Hint. Recall that in a gravitational field the potential energy is V(r) = -GMm/r, where G is the gravitational constant, M is the mass of the planet, and m the mass of the particle.