The luminosity of a star can be calculated by using the following equation.
L=4pir^2ot^4
In the luminosity equation, represents the luminosity in watts, represents the radius of the star in meters, represents a constant equal to 5.67 × 10-8 Wm-2K-4, and represents the surface temperature in Kelvins.
What is the approximate radius of a star with a luminosity equal to 2.532 × 1021 W and a surface temperature of 3,000 K? (Use pi= 3.14)
We can rearrange the luminosity equation to solve for the radius:
r = sqrt(L / (4*pi*o*t^4))
Substituting the given values:
r = sqrt(2.532 × 10^21 / (4*3.14*5.67 × 10^-8*3000^4))
r ≈ 5.45 x 10^9 meters or 5.45 million kilometers (rounded to two decimal places)