<Dd> L ∝ M 3 (\ displaystyle L \ varpropto M ^ (3)) </Dd> <P> One may distinguish between the cases of small and large stellar masses by deriving the above results using radiation pressure . In this case, it is easier to use the optical opacity κ (\ displaystyle \ kappa) and to consider the internal temperature T directly; more precisely, one can consider the average temperature in the radiation zone . </P> <P> The consideration begins by noting the relation between the radiation pressure P and luminosity . The gradient of radiation pressure is equal to the momentum transfer absorbed from the radiation, giving: </P> <P> d P r a d d r = − κ ρ c L 4 π r 2, (\ displaystyle (\ frac (dP_ (rad)) (dr)) = - (\ frac (\ kappa \ rho) (c)) (\ frac (L) (4 \ pi r ^ (2))),) </P>

Relationship between mass and radius of a star