2. problem 2 (25%) titan is the largest moon of saturn and the only natural satellite known to have a dense atmosphere, which consists mostly of n2, ch4, and h2 titan's atmosphere has a surface pressure about 1.45× that of earth, gravitational acceleration of 1.35 m/s, a surface temperature of 94k, and a radius of 2575 km a) roughly, how many molecules per m3 are there in the air at titan's surface? what about on earth's surface? b) the composition of titan at the surface is about 95% n2 and 5% ch, by volume. estimate the atmospheric density in kg/m3 and scale height at titan's surface. c) prove that if the scale height is constant throughout the atmosphere, then the atmo- spheric density is: rho(z)-poe-s/h, where e is the height above the surface, h is the scale height, and is the surface density. d) crudely estimate the total mass of titan's atmosphere using your previous answers. how does this compare to the total mass of earth's atmosphere (matm~5x 1018 kg)? note: the key word is crudely - as long as you justify your approach and your answer is reasonable, you will be given credit.)