The radiation pressure created by electromagnetic waves might someday be used to

Question

The radiation pressure created by electromagnetic waves might someday be used to power spacecraft through the use of a "solar sail".

a) Assuming total reflection, what would be the pressure on a solar sail located at the same distance from the Sun as the Earth (where I = 1350 W/m2)?

b) Suppose the sail material has a mass of 1×103 kg/m2 . What would be the acceleration of the sail due to solar radiation pressure?

c) A realistic solar sail would have a payload. How big a sail would you need to accelerate a 150-kg payload at 1×103 m/s2?

Explanation / Answer

a) pressure on a solar sail = 2 I / c = 2 * 1350 / (3 * 108)

= 9 * 10-6 N/m2

b) P = m a

9 * 10-6 = 1 * 10-3 * a

Acceleration of the sail a = 9 * 10-3 m/s2

c) m' = 0.001 * A + 150

F = pressure * a

m' * 1 * 10-3 = 9 * 10-6 A

(0.001 * A + 150) * 1 * 10-3 = 9 * 10-6 A

(0.001 * A * 1 * 10-3) - (9 * 10-6 * A) = -150 * 1 * 10-3

A = 18750 m2

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