Some spacecraft design uses a solar sail made of aluminized plastic. As sunlight reflects off the sail, radiation pressure drives the spacecraft outward away from the sun.

Question

a. If the sail material has a density of 700.0 kg/m3, what is the maximum thickness of the sail for which the force due to radiation pressure exceeds the gravitational force on the sail?

b. If the collector's area is 2e6 m^2. its thickness is 1 μm, and the craft carries a 100.0 kg payload, what is its acceleration at the radius of the Earth's orbit?

Answer 1

You need to know the radiation pressure due to solar radiation. This varies with (1/R^2), but so does the gravity force.

The solar flux at the Earth's distance from the sun is about
I = 1300 W/m^2, as I recall. You'd better look it up yourself. Divide that by c for the momentum flux.

(a) Let the sail area be A. (This will cancel out) and the thickness be d. For a balance with radiation pressure,
A*density*d*G*M/R^2 = 2*A*(1300/c)*(Re/R)^2

I am sure you recognize G as the universal constant of gravity. A cancels out. So does R^2.

The factor of 2 assumes perfect reflection of all incident light, for the momentum change.

M is the mass of the sun and Re is the radius of the earth;'s orbit. Solve for d

b. Use
2*A*(1300/c)*(Re/R)^2 for the force on the sail and the appropriate mass for that sail thickness.
Then use a = F/m for the acceleration

Answer 2

Thanks drwls. I'm having trouble with part b though. What is R? For the appropriate mass, am I suppose to use the density times the thickness to get the mass of the sail and with that, add the mass from payload?