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Luminosity of A Star: Radius & Surface Temperature



Two things determine the luminosity (intrinsic brightness) of any star:


1. Radius

2. Surface Temperature.


Let's take our Sun as the standard. The Sun's radius spans approximately 695,500 kilometers (432,450 miles) and its surface temperature is somewhere around 5830 Kelvin (10,034o Fahrenheit).

Photo of Sun on right, courtesy of NASA


Luminosity & Radius of Star


For simplicity, let's figure out the luminosity for stars that are larger and smaller than our Sun, but with the same surface temperature as the Sun. If you know the radius of any star relative to the Sun's radius, you can figure the star's luminosity relative to solar luminosity.

In the equation below L = luminosity and R = radius. Let's say the radius of the star is 5 times that of the Sun:


L = R2

L = 52

L = 5 x 5 = 25 times the luminosity of the Sun


Now let's figure the luminosity of a star whose radius is 1/5 that of the Sun:


L = R2

L = 1/52

L = 1/5 x 1/5 = 1/25 the luminosity of the Sun


Luminosity & Surface Temperature


Again, for simplicity, let's figure out the luminosity for stars that have a higher and a lower surface temperature than that of our Sun, but with the same solar radius. If you know the surface temperature of any star relative Sun's, you can figure the star's luminosity relative to solar luminosity.

In the equation below L = luminosity and T = surface temperature. Let's say the surface temperature = 17,490 Kelvin. That would make the star's surface temperature 3 times greater than the Sun's (17,490/5,830 = 3)


L = T4

L = 34

L = 3 x 3 x 3 x 3 = 81 times the luminosity of the Sun


Now let's figure the luminosity of a star whose surface temperature is 1/3 that of the Sun:


L = T4

L = 1/34

L = 1/3 x 1/3 x 1/3 x 1/3 = 1/81 the luminosity of the Sun


Note on HR diagram on right: Color (spectral type) reveals a star's surface temperature. Hot stars are blue whereas cool stars are red. Our yellow Sun indicates a moderate temperature between the two extremes. Hot main sequence stars are generally larger than our Sun, and cool main sequence stars are generally smaller. Click here to find out how astronomers figured this out.


Luminosity = Radius2 x Temperature4


Let's get brave and solve the star's luminosity for both size and surface temperature. Let's say the star's radius is 3 times that of the Sun and the surface temperature is 3 times as great. What's the star's luminosity relative to the Sun's luminosity?

In the equation below L = luminosity, R = radius and T = surface temperature.


L = R2 x T4

L = 32 x 34

L = (3 x 3) x (3 x 3 x 3 x 3) = 9 x 81 = 729 times the luminosity of the Sun


copyright 2013 by Bruce McClure


Stellar Luminosity Calculator


March 2013 Feature * May 2013 Feature