A baratropic star with  and  is stable if the quantity
is non-negative for all real functions  that conserve the total mass of the star .
where
* is the coordinate system fixed to the center of the star
* is the radius of the star
* is the volume of the star
* is the unperturbed density
* is the small perturbed density such that in the perturbed state, the total density is 
* is the self-gravitating potential from Newton's law of gravity
* is the Gravitational constant