How To Derive The Eddington Limit

Help support this channel on Patreon:   / astrophil   Welcome, my name is Phil, and in this video I explain to derive the Eddington limit. The Eddington Limit is the maximum luminosity of a star while in hydrostatic equilibrium. If a star exceeds this luminosity it is unable to hold itself together against gravitational forces. To derive an expression for the Eddington Limit we first equation the gravitational forces and the out radiative pressure. We can then rearrange for luminosity. Since the only variable in the final equation is M, the mass of the star, we can put all the constant into one number. If we also put the equation in terms of solar luminosities we can get an idea for the most luminous stars in the universe. These stars have luminosities in excess of millions of solar luminosities.