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Unformatted text preview: Assignment #5 PHYSICS 8.284 due 11:04 am Friday 2006 March 17th â€¢ Reading: Hansen and Kawaler (Hayden reserve only): Â§Â§ 3.13.5 (eqn 3.67) on quan tum statistics, distribution functions and equations of state and Â§Â§ 7.17.2 (eqn 7.45) on polytropes. 1. Solve the LaneEmden equation for an n=3/2 polytrope using RungeKutta integra tion from Ï€ = to the point where the density first reaches zero. Plot n (which is proportional to density) and âˆ’ 4 Ï€ 2 d (which is proportional to the mass interior to d Ï€ ) as a function of Ï€ . 2. In class we derived an expression for the gravitational binding energy, , of a poly trope of index n. Use the virial theorem to derive and expression for the total in Â¯ ternal energy, U , of such a polytrope. Define the average temperature, T , such that Â¯ U = M 3 kT . Compute the ratio of the central temperature T c to this average tem Âµm p 2 perature....
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 Spring '06
 rappaport
 Physics, Atom, Mass, Binding energy, Fundamental physics concepts

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