Answer:
The Eddington luminosity can be calculated using the formula:
L = 4πGMc / κ
where L is the Eddington luminosity, G is the gravitational constant, M is the mass of the star, c is the speed of light, and κ is the opacity of the star's material.
Assuming a typical opacity value of κ = 0.34 cm^2/g and a maximum mass of 100 solar masses (M = 100 M☉), we can calculate the maximum Eddington luminosity as follows:
L = 4πGMc / κ
L = 4π(6.67 × 10^-11 m^3/kg s^2)(100 M☉)(1.99 × 10^30 kg/M☉)(3 × 10^8 m/s) / (0.34 cm^2/g)(10^-4 m^2/cm^2)(1000 g/kg)
L ≈ 1.26 × 10^39 W
Therefore, the maximum luminosity of stars in the universe is approximately 1.26 × 10^39 watts.