Radiation Pressure and Solar Sail

[jmm5872]

Consider a spacecraft attached to a sheet of material, a "sail," that absorbs sunlight. Assume that the sail is positioned to face the Sun and that the combined mass of the spacecraft and the sail is m. How large does the area of the sail have to be to propel the spacecraft away from the Sun? m = 1000 kg.

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/r² = 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.

 

[Delphi51]

I think of it via the impulse formula F*Δt = change in momentum
For light, E = p*c so p = E/c and F = (E/Δt)/c = Intensity*Area/c.
The question doesn't say what distance from the sun. Earth orbit would be convenient; there the intensity is called the solar constant and it can be looked up in Wikipedia.