The luminosity a body would have to have for the force generated by radiation pressure to exceed the gravitational force.The force due to radiation pressure is given by
where L is the luminosity,
is the Thomson cross section,r is the radius, and c is the speed of light, and the gravitational force is
where G is the gravitational constant, M is the mass of the body, and m is the mass of a particle. Equating (2) and (1) gives
Since experimentally,
where
is the luminosity of the sun and 
is the sun's mass, a star will be unstable if
Using a 1/2 power instead,
Plugging in
gives
where m has been taken as the mass of a hydrogen atom.
(1)
where L is the luminosity,
is the Thomson cross section,r is the radius, and c is the speed of light, and the gravitational force is (2)
where G is the gravitational constant, M is the mass of the body, and m is the mass of a particle. Equating (2) and (1) gives
(3)
Since experimentally,
(4)
where
is the luminosity of the sun and is the sun's mass, a star will be unstable if(5)
Using a 1/2 power instead,
(6)
Plugging in
(7)
(8)
(9)
(10)
(11)
(12)
gives
(13)
where m has been taken as the mass of a hydrogen atom.
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