Problem Set 9

# Problem Set 9 - Physics 341 Problem Set#9 due November 11 1...

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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Physics 341: Problem Set #9 due November 11 1. The Plummer model for a spherical star cluster is given by the density profile ⇢ ( r ) = 3 M 4 ⇡ a 2 ( r 2 + a 2 ) 5 / 2 where M is the total mass, and a is a core radius. (a) Show that the enclosed mass in the Plummer model is M ( r ) = Mr 3 ( r 2 + a 2 ) 3 / 2 You may need to make an appropriate substitution and use the fact that Z x 2 dx ( x 2 + 1) 5 / 2 = x 3 3( x 2 + 1) 3 / 2 + constant (b) Now calculate the total potential energy of the Plummer mass distribution. Hint: The answer should depend only on G , M , and a . After a substitution, you should find the following integral useful: R 1 x 4 dx/ ( x 2 + 1) 4 = ⇡ / 32. (c) If the mass distribution is in equilibrium, what is the total kinetic energy? What is the total energy? Again, your answers should depend only on G , M , and a . (d) The globular cluster ! Centauri can be described by a Plummer model with a total mass M = 5 ⇥ 10 6 M and core radius a = 4 . 5 pc. Use your derived total kinetic5 pc....
View Full Document

## This note was uploaded on 11/13/2011 for the course PHY 341 taught by Professor Gawsier during the Spring '11 term at Rutgers.

### Page1 / 2

Problem Set 9 - Physics 341 Problem Set#9 due November 11 1...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online