Assignment #10

(3) Convince me! (4 pts.) We know that Saturn has a density less than that of water - so the planet would float in a giant bath tub. If you tell your friends that a planet could float, they are likely to laugh at you. Describe HOW we know the density of Saturn is less than that of water by observing it from here on Earth - what quantities have been measured (units?)? Which formula (or formulae) is (are) used? To figure out the density of the Saturn, according to the formula ρ = m V , we need to know both the mass of Saturn and volume of the Saturn separately. To determine the mass, we need to figure out the gravitational force that depends on the mass of Saturn and its moon: F grav = G M Saturn M moon r 2 , since the force is perpendicular to the momentum, the force will change the direction of the momentum and not the magnitude. So G M Saturn M moon r 2 also = M moon r ( 2 pi T ) 2 , so M Saturn = 4 pi 2 r 3 / GT 2 , to calculate this, we just need to measure the size of the orbit, the period of the orbit for its moon and the G, which is the universal gravitational constant. To determine the volume, according to: V = 4 3 pi R 3 , so we just need to measure the radius of the Saturn so that we can calculate the volume. (4) Layers upon layers. (5 pts.) Jupiter have several distinct layers of clouds. Why are these clouds separated into several distinct layers, so that clouds composed of a highly volatile gas such as ammonia found higher in the atmosphere than water? The reason these clouds are separated into several distinct layers is that different types of gases possess different densities, which form different layers by gravitational force. The ammonia is found higher in the atmosphere than water is due to the lower density of the ammonia gas, which result in precipitation of water with high density to the bottom, compared to the ammonia gas.