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Unformatted text preview: Assignment #11 PHYSICS 8.284 Due 11:04am Wednesday 10 May 2006 Reading: Binney and Tremaine Chapter 10; 8.902 notes on Cosmology 3.1-3.3. (1-2) (20 points) This is a longish problem, requiring that you use a computer to solve a differential equation, but it is VERY similar to the solution Lane-Emden equation. Find the function which is the solution of the isothermal sphere equation, 1 d d 2 = e 2 d d with boundary conditions (0) = and (0) = 0. Plot a) log / c as a function of log over the interval 1 < log < 2 and b) v c / as a function of over the interval < < 30. Remember that is the one dimensional velocity dispersion and that the square of the circular velocity, v 2 = GM ( < r ) /r . c (3) Consider a spherically symmetric galaxy in which the number density of stars as a function of radius, and the isotropic one dimensional velocity dispersion, 2 are given by 1 5 / 2 2 1 1 / 2 ( r ) = ; 2 ( r ) = ....
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- Spring '06