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Unformatted text preview: Assignment #10 PHYSICS 8.284 Due 11:04 am Wednesday 3 May 2006 Reading: Binney and Tremaine, Chapter 4 through equation (4-45). (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 = =...
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- Spring '06