This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 3.13.3. (12) (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 LaneEmden 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 ) = ....
View
Full
Document
 Spring '06
 rappaport
 Physics

Click to edit the document details