Commonly, the light output of a star – called the star’s luminosity – is compare

Question

Commonly, the light output of a star – called the star’s luminosity – is compared to the luminosity of our star, the Sun. Therefore, a star with the same light output of the Sun is said to have a luminosity of 1 solar luminosity (or 1 LSun). A star’s luminosity is calculated by comparing its radius (R) and temperature (T) to the Sun’s temperature using the equation:

If a star has a radius of 2.2 RSun and a temperature of 4800K, how luminous is it compared to the Sun?

0.469 LSun (0.469 times brighter than the Sun)

16.04 LSun (16.04 times brighter than the Sun)

23.42 LSun (23.42 times brighter than the Sun)

2.30 LSun (2.30 times brighter than the Sun)

10,560 LSun (10,560 times brighter than the Sun)

0.469 LSun (0.469 times brighter than the Sun)

16.04 LSun (16.04 times brighter than the Sun)

23.42 LSun (23.42 times brighter than the Sun)

2.30 LSun (2.30 times brighter than the Sun)

10,560 LSun (10,560 times brighter than the Sun)

Explanation / Answer

Answer : 2.30 LSun

Explanation : The luminousity is calculated as:

Lsun/Lstar = (Rsun2 * Tsun4) / (Rstar2 * Tstar4)

Now, Rstar = 2.2 Rsun (given)

Tstar = 4800K, Tsun = 5830K

So, Lsun/Lstar = (Rsun2 * 5830*5830*5830*5830)/((2.2*Rsun)2 * 4800*4800*4800*4800)

or, Lsun/Lstar = 33988900*33988900/23040000*23040000

or, Lstar = 23040000*2304/339889*339889 * Lsun

or, Lstar = 2.30 Lsun

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