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My thoughts on how to figure this out...

Calculate the momentum per unit area per unit time of the radiation leaving the Sun, which seems to me to be the pressure by this relation:

Pressure = Force/Area = momentum/(area*time)

Then find the force that arises from the pressure on the solar sail, and this needs to oppose the gravitational force of the Sun.

I think it is this: F = GMm/r

^{2}= Ut/c

where momentum p = U/c, and it's derivative is F = Ut/c

And U is energy coming from the Sun. This is more of my confusion. I know Luminosity is energy per unit time, I just don't really know how to use all of this to get what I need. I think I am just missing some of the conceptual part that would help me relate everything and simply plug in the given mass.