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Brilliant Aberration
2009-Feb-06, 08:03 PM
I'm working on a homework set for my astronomy class, and I'm perplexed on one of the problems.

"Given that Beta Librae has a surface temperature of 12000K and a luminosity 130 times greater than that of the Sun, what is its radius in terms of the Sun's radius?"

I have:

L ~ R^2 * T^4

Sun == 1
Beta = 130 = R^2 * (12000/5800)^4 = 18.3*R^2 = 130

==> R = sqrt(130/18.3) = sqrt(7.1) = 2.7

But every literature source I've checked says its radius is more like 1.2 times the radius of the sun. But that would give it

L_beta = 1.2^2 * (12000/5800)^4 = 26.4*L_sun

What gives? Everything has matched up on all the other stars I've done for this. Am I just missing something?

grant hutchison
2009-Feb-06, 10:03 PM
For homework, you work with the parameters given.
If you're curious about the accuracy of your calculation for this spectral class, try checking the standard tables for the predicted radius of a B8V star.
If you're curious about this star, you'll need to track beyond Wikipedia sources, to see if you can find an origin for the mismatch between luminosity, temperature and radius.

Grant Hutchison

Brilliant Aberration
2009-Feb-06, 10:07 PM
Mostly I wanted to make sure I didn't make a mistake in my own understanding of the concepts. I'll see what backtracking I can do.

But now that you mention it, where can I find those standard tables?

George
2009-Feb-06, 10:22 PM
Your work looks quite correct. Grant, who understands the falibility of Wiki, is suggesting the mismatch has a source. Wiki references sometimes are a fair start.

You can Google for spectral classifications and find some sites that give radius and luminosity relationships.