Physics, 20.09.2020 15:01 natalie2sheffield
Consider Europa, the smallest moon of Saturn. It is thought that an ocean of liquid water exists under an outer crust. The ocean may be assumed static and incompressible, and the crust surrounding Europa will be neglected (i. e., assume Europa is only a spherical ocean). How will the ocean pressure vary as a function of radial position within the planet? The gravitational acceleration at the surface of a planet (9.81 m/s2 on earth) is defined as 2 , GM g R = where G is the universal gravitational constant, M is the mass of the planet, and R is the radius of the planet. Newton’s shell theorem states that the gravitational force experienced at a given radial position within a planet will only be dependent on the mass of the planet below the radial position considered such that we can write 2 ( ) , GM r g r = where M(r) is the mass of the planet within radial position r. Finally, the pressure-"height" relationship in spherical coordinates is given by . dp g dr = − Provide a relationship between pressure and radial position within the ocean planet (i. e., if two radial positions are selected, find a relationship describing the pressure at each of the positions).
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