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 #5 PHYSICS 8.284 due 11:04 am Friday 2006 March 17th Reading: Hansen and Kawaler (Hayden reserve only): 3.13.5 (eqn 3.67) on quan tum statistics, distribution functions and equations of state and 7.17.2 (eqn 7.45) on polytropes. 1. Solve the LaneEmden equation for an n=3/2 polytrope using RungeKutta integra tion from = to the point where the density first reaches zero. Plot n (which is proportional to density) and 4 2 d (which is proportional to the mass interior to d ) as a function of . 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 ternal energy, U , of such a polytrope. Define the average temperature, T , such that U = M 3 kT . Compute the ratio of the central temperature T c to this average tem m p 2 perature....
View
Full
Document
 Spring '06
 rappaport
 Physics

Click to edit the document details