luminosity of star

Luminosity is the total amount of energy emitted per unit of time by a star. In SI units luminosity is measured in joules per second or watts.

A star’s luminosity depends on two things:

1. Radius measure
2. Surface temperature

Radius measure

If a star has the same surface temperature as the sun, but its radius is 4 solar (4 times the sun’s radius). Then its luminosity with respect to Sun is,

L is propotional to R²

L is propotional to 4² = 4 x 4 = 16 times the sun’s luminosity

where L = luminosity and R = radius

Surface temperature

Also, if a star has the same radius as the sun but its surface temperature is twice as that of Sun (5800 x 2 = 11600 Kelvin).

Then star’s luminosity, relative to the sun is,

L is propotional to T⁴
L is propotional to 2⁴ = 2 x 2 x 2 x 2 = 16 times the sun’s luminosity.

where L = luminosity and T = surface temperature

Luminosity of Star is propotional to R² x T⁴

The luminosity of any star is the product of the radius squared times the surface temperature raised to the fourth power. Given a star whose radius is 3 solar and a surface temperature that’s 2 solar, star’s luminosity is,

L is propotional to R² x T⁴
L is propotional to (3 x 3) x (2 x 2 x 2 x 2)

L is propotional to 9 x 16 = 144 times the sun’s luminosity

where L = luminosity, R = radius and T = surface temperature.