a) Show that the escape speed for a particle to leave the gravitational infuence of a planet is given by (2GM/R)^1/2, where M is the mass of the planet, R is its radius, and G is the gravitational constant. b) The temperature near the top of Jupiter's multicolored cloud layer is about 140K. The temperature at the top of the earth's troposphere, at an altitude of about 20km, is about 220k. Calculate the rms speed of huydrogen molecules (h2) in each of these environments. Give your answers in the m/s and as a fraction of the escape speed from the respective planet. c) Hydrogen gas is a rare element in the earth's atm. In the atmosphere of Jupiter, by contrast, 89% of all molecules are H2. Explain why, using your results from the previous part. d) Ceres is an asteroid with mass equal to .014 times the mass of the moon, a density of 2400kg/m^3 and a surface temp of about 200K. Suppose an astronomer claims to have iscovered an oxygen (O2) atmosphere on the asteroid Ceres. You are asked by a TV news reporter to comment on this claim. What would you say, and how would you support that? a) I don't fully understand what I have to calculate or demonstrate in this, can someone please break this down for me? Thanks! b) I need the formula Vrms = sqrt(3RT/M) M of H2 = 2g/mol = .002kg/mol Vrms Jupiter = sqrt(3x8.314x140k/.002kg) = 1.321x10^3 m/s Vrms Earth = sqrt(3x8.314x220k/.002kg)= 1.656x10^3 m/s I don't quite understand what I have to do to get the fraction of the escape speed relative to the planet. I suppose use the given formula (2GM/R)^1/2 to calculate each plantes escape and then divide that number by the Vrms of jupiter and Earth?? What is g, M, and R of jupiter?? Is 9.8m/s the gravitational force at 20km high in the earths atmosphere?? Please help! c) Im guessing this will have to do with the escape velocity of each planet? Maybe jupiter likes to hang on to it's H2 and earth lets them go? d) Lost me again on this one? Thanks for all the help..