So I wonder if a star's gravity is mostly the mass of the star itself, but also, in small part, the huge amount of light that surrounds the star on all sides, being densest nearest the star itself.
There's some evidence that gravity may change a little during a solar eclipse http://en.wikipedia.org/wiki/Allais_effect and also the Pioneer anomaly, http://en.wikipedia.org/wiki/Pioneer_anomaly
I am most definitely not a physicist!