What is the solar radius of Rigel and Procyon B?

  • Thread starter Thread starter snabelpablo
  • Start date Start date
  • Tags Tags
    Radius Solar Star
Click For Summary

Homework Help Overview

The discussion revolves around calculating the solar radius of the stars Rigel and Procyon B based on their luminosity and surface temperature. The original poster presents calculations for Rigel, questioning the accuracy of their results compared to external sources, while also attempting similar calculations for Procyon B.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to apply the Stefan-Boltzmann law to determine the surface area and radius of Rigel, but questions the validity of their calculated solar radius in light of differing values found online. They also apply the same method to Procyon B and express uncertainty about the results.

Discussion Status

Participants are actively engaging with the calculations, with one suggesting a correction to the luminosity value for Rigel, which significantly alters the calculated solar radius. There is an ongoing exploration of the values used in the calculations and their implications for accuracy.

Contextual Notes

There is a noted discrepancy between the calculated solar radius for Rigel and the values reported in external sources, leading to questions about the accuracy of the initial luminosity value. The calculations for Procyon B are also yielding results that differ from established figures, indicating potential issues with the input data or assumptions made.

snabelpablo
Messages
7
Reaction score
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?
 
Physics news on Phys.org
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.
 

Similar threads

  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 1 ·
Replies
1
Views
4K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
1
Views
2K
Replies
1
Views
6K
  • · Replies 8 ·
Replies
8
Views
2K