1. a) A possible spacecraft design uses a solar sail made of aluminized plastic.
ID: 1963548 • Letter: 1
Question
1. a) A possible 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. If the sail material has a density of 625.0 kg/m^3, 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 2 x 10^6 m^2. its thickness is 1 µm, and the craft carries a 91.0 kg payload, what is its acceleration at the radius of the Earth's orbit?
Explanation / Answer
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
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