Calculating Luminosity (Easy Atronomy Question)

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SUMMARY

Capella, with a diameter ten times that of the Sun, is approximately 100 times more luminous than the Sun. The calculation is based on the formula R=sqrt(L)/Temp squared, where R represents the radius and L represents luminosity. By applying dimensional analysis, it is confirmed that increasing the radius by a factor of ten results in an increase in luminosity by a factor of one hundred. This method effectively demonstrates the relationship between radius and luminosity in stellar calculations.

PREREQUISITES
  • Understanding of stellar luminosity and temperature relationships
  • Familiarity with the formula R=sqrt(L)/Temp squared
  • Basic knowledge of dimensional analysis
  • Concept of radius in astronomical contexts
NEXT STEPS
  • Study the application of the Stefan-Boltzmann Law in stellar physics
  • Learn about the Hertzsprung-Russell diagram and its significance in astronomy
  • Explore the concept of absolute magnitude and its calculation
  • Investigate the properties of other stars for comparative luminosity analysis
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Astronomy students, astrophysics enthusiasts, educators teaching stellar properties, and anyone interested in understanding luminosity calculations in stars.

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Capella is the same temperature as our sun, but about ten times the suns diamter; it must be about_____ times as luminous as our star.

Could someone please tell me how to solve this type of problem??

I am aware of the formula R=sqrt(L)/Temp squared.

But I'm not sure how to apply that here. Inserting my own made up radius of 2 for the sun and 20 for Capella, I come up with the answer being "100 times as luminous". But I fee like I am missing something...

Thanks!
 
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hi zoiberg137! :smile:
zoiberg137 said:
I am aware of the formula R=sqrt(L)/Temp squared.

But I'm not sure how to apply that here. Inserting my own made up radius of 2 for the sun and 20 for Capella, I come up with the answer being "100 times as luminous". But I fee like I am missing something...

no, that's fine :smile: …

that's exactly how these "dimensional analysis" questions work …

R2/L is a constant

so if you multiply R by 10, you do multiply L by 100 :wink:​
 

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