What is the solar radius of Rigel and Procyon B?

In summary, using the formula for heat current in radiation, we can calculate the surface area of a star and then use the formula for the area of a sphere to find its radius. For Rigel, with a luminosity of 2.7 * 10^31 W and a surface temperature of 11000K, the solar radius is approximately 73 times that of the sun. However, for Procyon B, with a luminosity of 2.1 * 10^23 W and a surface temperature of 10000K, the solar radius is only about 0.008 times that of the sun, which is significantly smaller than the value reported on Wikipedia. This could be due to an incorrect value given for
  • #1
snabelpablo
7
0
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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  • #2
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
Perhaps one of the values given to you is incorrect. I'd guess it's the luminosity.
 
  • #4
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.
 

What is the solar radius of a star?

The solar radius of a star is a measure of its size, specifically the distance from its center to its outer edge. It is typically measured in terms of the radius of our own sun, which is approximately 695,700 kilometers.

How is the solar radius of a star determined?

The solar radius of a star is determined through various methods such as measuring the star's luminosity, temperature, and distance from Earth. These measurements are then compared to known values for our sun to calculate the star's radius.

What is the average solar radius of a star?

The average solar radius of a star can vary greatly, as stars come in different sizes. However, for stars similar to our sun, the average solar radius is around 695,700 kilometers.

Can the solar radius of a star change over time?

Yes, the solar radius of a star can change over time. As a star ages, it may expand or contract, causing changes in its radius. This can also occur due to external factors such as interactions with other stars or planets.

Why is the solar radius of a star important to study?

The solar radius of a star is important to study because it provides insight into the physical characteristics and behavior of stars. It can also help us better understand the life cycle of stars and their impact on their surrounding environments.

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