What is the solar radius of Rigel and Procyon B?

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The discussion focuses on calculating the solar radius of Rigel and Procyon B using their luminosity and surface temperature. For Rigel, an initial calculation suggested a radius of 231 solar radii, but this was corrected to approximately 73 solar radii after identifying the luminosity as 2.7 * 10^31 W instead of the initially stated 2.7 * 10^32 W. For Procyon B, the calculated solar radius was found to be 0.0078, which is significantly lower than Wikipedia's figure of 0.01234. The discrepancies highlight potential inaccuracies in the provided luminosity values. Accurate luminosity is crucial for determining the correct solar radii of these stars.
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A star's surface sends out energy in form of electromagnetic radiation and has an emissivity close to 1. Find the solar radius of Rigel that emits energy at a rate of 2,7 * 10^32W and has a surface temperature of 11000K. You may assume the star is spherical.

Attempt at solution:
Formula for the heat current in radiation: H = AeσT^4.
Solve this with respect to A gives surface area: A = H / (eσT^4) =
2.7 * 10^32 / (1 * (5,67 * 10^-8) * 11000^4) = 3,25 * 10^23 m^2.

Formula for the area of a sphere: A = 4πr^2.
Solve this with respect to r gives radius: r = (A / 4π)^0,5 =
(3,25 * 10^23 / 4π)^0,5 = 1,61 * 10^11 m.

The radius of the sun: 6,96 * 10^8 m.
Solar radius = (1,61 * 10^11) / (6,96 * 10^8) = 231,06Rsun.

The Rigel radius is 231 times the radius of the sun. However, Wikipedia says 78. I've also seen 63, 98 etc., but 231 sounds a bit high. What have I done wrong?
 
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The star's luminosity should be 2.7*10^31 W, not 2.7*10^32 W. With the correct luminosity, you get 23 solar radii, very close to Wikipedia's figure.
 
Perhaps one of the values given to you is incorrect. I'd guess it's the luminosity.
 
You are correct! The luminosity is in fact 2,7 * 10^31 W for Rigel giving it a solar radii of 73 using my formulas.

However, I have to do this for a second star as well, Procyon B.
Calculating its solar radius with the same formulas using H = 2,1 * 10^23W and T = 10000K I get:

A = 3,7 * 10^14 m^2.
r = 5,43 * 10^6 m.
Rsun = 0,0078.

Wikipedia says 0,01234 - almost twice what I got.
 
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