Using the hydrostatic law for a uniform density star gives the stellar pressure as a function of radius r as
where is the density, G is the gravitational constant, and R is the stellar radius. Applying the ideal gas law at the star's center then gives
where m is the molecular mass and k is Boltzmann's constant. Therefore, assuming only hydrostatic equilibrium (i.e., ignoring thermonuclear fusion), the temperature at the center of the star is
where M is the mass of the star.
