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?

"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?