<p>One way to determine the luminosity of a star is to first determine its distance, d.  Then one can use the formula, Luminosity = Flux * 4 * Pi * d$^2$.  Flux is related to the apparent brightness that is measured with a telescope (and CCD or photometer).  mag = -2.5 * Log(Flux) + c.  </p>

<p>If the star is relatively nearby, one can use <a href="https://astronomy.stackexchange.com/questions/1314/how-does-a-telescope-measure-parallax-angle">parallax</a> to get the distance.  If the star is in a binary system, one can solve for the distance from the period, orbital velocities and apparent size of the orbit.  If you know the velocities throughout one orbit, then one knows how far it has physically traveled.  Comparing this with the apparent size gives an approximate distance.  However, since one usually does not know the inclination, this causes uncertainty.  If it is an eclipsing binary, then you know that it is not very inclined and this works well.  On the other hand, if it is eclipsing, one can usually determine the radii of the binary pair and then get distances from Stefan Boltzmann Law.</p>

<p>Another method for estimating luminosity is to locate the star in the <a href="https://en.wikipedia.org/wiki/Hertzsprung%E2%80%93Russell_diagram" rel="nofollow noreferrer">HR Diagram</a> (Luminosity vs Color).   The color (difference between the magnitudes in two different filters) locates it horizontally, and <a href="https://en.wikipedia.org/wiki/Stellar_classification" rel="nofollow noreferrer">stellar class</a> locates it vertically in the diagram.  One needs a spectrum of the star to determine the class.</p>

<p>And we have one more trick up our sleeves.  If the star is a periodic variable such as a Cepheid or an RR Lyra, then there are relations between period of variability and luminosity.</p>

CC BY-SA 3.0
2015-09-15T21:32:10.473Z
This is a highly confusing answer to what is an extremely simple question.
ProfRob
CC BY-SA 3.0
2015-07-17T15:34:38.770Z
2015-07-17T15:34:38.770Z
2017-04-13T12:59:06.910Z
eshaya
<p>For example, if star 1 is 4x bigger than star 2 but both are the exact same temperature how do you determine which is more luminous?</p>

CC BY-SA 3.0
2015-07-16T18:47:34.463Z
Consider [Stefan–Boltzmann law](https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law). But the problem as stated seems highly artificial.
Stan Liou
CC BY-SA 3.0
2015-07-16T19:07:05.930Z
It's a conceptual question I pulled from my astronomy text book. The link below states that in order to determine the luminosity of a star that is twice as large as the sun you would use the following equation: L = (2 R⊙)2(T⊙)4 = 4L⊙ (the Hertzsprung-Russell Diagram). How do I apply this to my question? 

http://astro.unl.edu/naap/hr/hr_background2.html
Jay
CC BY-SA 3.0
2015-07-16T20:31:58.040Z
Just use 4 times the radius instead of two times the radius. I can't understand your difficulty, star 1 is $4^2$ times as luminous.
ProfRob
<amateur-observing><star-systems><luminosity>
How do you determine which star, between two, is more luminous?
Jay
# How do you determine which star, between two, is more luminous?

(Asked by: username_0 on 2015-07-16)

For example, if star 1 is 4x bigger than star 2 but both are the exact same temperature how do you determine which is more luminous?

**Tags:** amateur-observing, star-systems, luminosity
> **Comments:**
> **username_1**: Consider [Stefan–Boltzmann law](https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law). But the problem as stated seems highly artificial.  
> **username_0**: It's a conceptual question I pulled from my astronomy text book. The link below states that in order to determine the luminosity of a star that is twice as large as the sun you would use the following equation: L = (2 R⊙)2(T⊙)4 = 4L⊙ (the Hertzsprung-Russell Diagram). How do I apply this to my question?   http://astro.unl.edu/naap/hr/hr_background2.html  
> **username_2**: Just use 4 times the radius instead of two times the radius. I can't understand your difficulty, star 1 is $4^2$ times as luminous.  

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## 1 answers

### Answer by username_3 on 2015-07-17. Score: 1

One way to determine the luminosity of a star is to first determine its distance, d. Then one can use the formula, Luminosity = Flux \* 4 \* Pi \* d$^2$. Flux is related to the apparent brightness that is measured with a telescope (and CCD or photometer). mag = -2.5 \* Log(Flux) + c.

If the star is relatively nearby, one can use [parallax](https://astronomy.stackexchange.com/questions/1314/how-does-a-telescope-measure-parallax-angle) to get the distance. If the star is in a binary system, one can solve for the distance from the period, orbital velocities and apparent size of the orbit. If you know the velocities throughout one orbit, then one knows how far it has physically traveled. Comparing this with the apparent size gives an approximate distance. However, since one usually does not know the inclination, this causes uncertainty. If it is an eclipsing binary, then you know that it is not very inclined and this works well. On the other hand, if it is eclipsing, one can usually determine the radii of the binary pair and then get distances from Stefan Boltzmann Law.

Another method for estimating luminosity is to locate the star in the [HR Diagram](https://en.wikipedia.org/wiki/Hertzsprung%E2%80%93Russell_diagram) (Luminosity vs Color). The color (difference between the magnitudes in two different filters) locates it horizontally, and [stellar class](https://en.wikipedia.org/wiki/Stellar_classification) locates it vertically in the diagram. One needs a spectrum of the star to determine the class.

And we have one more trick up our sleeves. If the star is a periodic variable such as a Cepheid or an RR Lyra, then there are relations between period of variability and luminosity.

> **Comments:**
> **username_2**: This is a highly confusing answer to what is an extremely simple question.  

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