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 #10 PHYSICS 8.284 Due 11:04 am Wednesday 3 May 2006 Reading: Binney and Tremaine, Chapter 4 through equation (445). (1) In casting the Boltzmann equation in spherical coordinates we found we needed the quantities v r , v , and v . There are several ways to obtain these. One is to use La granges equations. The other is to assume spherical symmetry, write down expres sions for E , L 2 , and L z , all of which are conserved, and differentiate these. The sec ond approach has the shortcoming that it looses generality, dropping terms / and / . Using one method or the other, derive the equations 2 v 2 + v v r = , r r v r v cot v 2 1 v = and r + r r v r v cot v v 1 v = . r r r sin (2) The Cartesian Jeans equation yields a particularly simple equation for the special case of a plane parallel stellar system with 2 independent of distance z from the zz plane, d 2 ln d 2 2 dz 2 = =...
View
Full
Document
 Spring '06
 rappaport
 Physics

Click to edit the document details