A possible spacecraft design uses a solar sail made of aluminized plastic. As su

Question

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/m3, what is the maximum thickness of the sail for which the force due to radiation pressure exceeds the gravitational force on the sail?

If the sail's area is 2.7106 m2. its thickness is 1 µm, and the craft carries a 81.0 kg payload, what is its acceleration at the radius of the Earth's orbit?

Explanation / Answer

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 and R is the radius of the sun. Solve for d => d = 2600*Re^2/(c*G*M*density) = [2600*6.4^2*10^12]/[3*10^8*6.67*10^-11*1.99*10^30*625) = 4.28 * 10^(-15) m (ANS) one question at a time please.

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