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ps6_nov2011

# ps6_nov2011 - Ge/Ay133 Problem Set#6 Revenge of...

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Ge/Ay133 – Problem Set #6 Revenge of the (Geo)Chemists Due November 17 th (1) This problem is to help you think about the thermal history of bodies that are assembled in the early solar system. Information of this sort is important when thinking about the core- instability model of Jovian planet formation and also about comets, asteroids and the differentiation of planetesimals and/or oligarchs. (a) Show that the gravitational potential energy of a spherical body of uniform density is given by - 3 G M 2 5R . Assuming a constant ρ and C p , and given no energy loss from the system, use this fact to generate an equation for the temperature of a body in terms of these constants. What does this relationship predict for the temperature for the moon and for the earth due to accretional energy alone? Why is this an upper limit to the temperature? For both, use a specific heat of C p = 10 7 erg/g/K, and use densities of ρ = 3.3, 5.5 g cm - 3 for the Moon and Earth. (b) In reality, only a fraction of the accretional energy is trapped as heat in the growing body. Let’s assume this efficiency of trapping, ǫ , is something like 2.5%. Recalculate the equations from (a), what temperatures do you derive? The largest asteroid, Ceres, has a radius of 487 km. Assuming

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ps6_nov2011 - Ge/Ay133 Problem Set#6 Revenge of...

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