# Solar radius of a star

1. Nov 17, 2009

### snabelpablo

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?

2. Nov 17, 2009

### ideasrule

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.

3. Nov 17, 2009

### clamtrox

Perhaps one of the values given to you is incorrect. I'd guess it's the luminosity.

4. Nov 17, 2009

### snabelpablo

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.