One of the representative astrophysical application of the Thomson scattering is the Eddington Limit, the possibly maximum luminosity of a star, which can keep electrons from being blown out of the sphere.
As shown in FIG. 2, a free electron
can maintain within the sphere when the radiation pressure
is weaker than the gravitational force falling into the star center.
The radiation (photon ) energy flux at distance
from the center of the star is
Then the momentum transfer rate, i.e. the radiation force to a free electron is given by