Calculating Luminosity (Easy Atronomy Question)

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Capella, with a diameter ten times that of the Sun and the same temperature, is approximately 100 times more luminous than our star. The discussion revolves around using the formula R=sqrt(L)/Temp squared to calculate luminosity based on radius and temperature. Participants confirm that increasing the radius by a factor of ten results in a luminosity increase by a factor of 100. The method of dimensional analysis is validated as an effective approach for these types of problems. Understanding this relationship is crucial for solving similar astronomy questions.
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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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