Calculating Luminosity (Easy Atronomy Question)

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In summary, based on the formula R=sqrt(L)/Temp squared, the star Capella must be about 100 times as luminous as our sun due to its temperature and diameter being approximately ten times larger.
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zoiberg137
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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:​
 

FAQ: Calculating Luminosity (Easy Atronomy Question)

What is luminosity?

Luminosity refers to the total amount of energy a star emits in a given time period. It is a measure of the star's intrinsic brightness and is often expressed in terms of the sun's luminosity, which is equivalent to 3.828 x 10^26 watts.

How do you calculate luminosity?

Luminosity can be calculated using the formula L = 4πR^2σT^4, where L is the luminosity, R is the radius of the star, σ is the Stefan-Boltzmann constant, and T is the temperature of the star in Kelvin. This formula is known as the Stefan-Boltzmann law.

What is the Stefan-Boltzmann constant?

The Stefan-Boltzmann constant (σ) is a physical constant that relates the temperature and energy radiated by a black body. Its value is approximately equal to 5.67 x 10^-8 watts per square meter per Kelvin to the fourth power (W/m^2K^4).

Can luminosity change?

Yes, the luminosity of a star can change over time. This can happen due to changes in the star's temperature, size, or mass. For example, as a star ages and runs out of fuel, its luminosity will decrease.

What is the difference between luminosity and apparent brightness?

Luminosity is a measure of the total amount of energy a star emits, while apparent brightness is a measure of how bright a star appears in the sky from Earth. Apparent brightness depends on both the luminosity and distance of the star, so a star with a high luminosity may appear dim if it is very far away.

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