Homework 7 Solutions

5k r 365 4 g 9m 2 r 3 7 5 10 f 8 g 365 13 12

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: bstituting this in for ρc: 2.5K R = 3.65 4πG 9M 2πR3 7 5 × 10 f (η) 8πG = 3.65 −1/3 1/2 1/2 9 2π −1/3 M −1/3 moving the R1/2 over to the left side and squaring gives: R = (3.65) = R0 25 × 107 f (η) 8πG 9 2π η2 1+η+ 1 + η R1/2 −1/3 M −1/3 where the constant R0 can be solved numerically: R0 = 3.5 × 1017 M −1/3 m kg1/3 = 2.8 × 10 1/3 M M 7 m (c) [15 pts] Using your result from part (b), show that η can be written as η = 3×10 −9 M M Tc 4/3 R R0 2 and evaluate this for (i) the Sun and (ii) a 0.1 M, 0.1 R low-­‐mass star with a core temperature of 5x106 K. Start with our definition of η evaluated in the core: ηc = 8 × 10−4 Tc 2/3 ρc substitute in the average density/core density relationship for n=1.5 polytrope: η = 8 × 10 −4 Tc −2/3 9M 2πR3 = 6.3 × 10−4 Tc M −2/3 R2 Now normalize the mass term to solar masses, and the radius term to R0, usi...
View Full Document

This document was uploaded on 02/26/2014 for the course PHYS 160 at UCSD.

Ask a homework question - tutors are online