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...
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 Fall '08
 Norman,M
 Physics, Work, pts, η, Helium3, Polytrope

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