It has been proposed that a spaceship might be propelled in the solar system by

Question

It has been proposed that a spaceship might be propelled in the solar system by radiation pressure, using a large sail made of foil. How large must the surface area (in m2) of the sail be if the radiation force is to be equal in magnitude to the Sun's gravitational attraction? Assume that the mass of the ship + sail is 1300 kg, that the sail is perfectly reflecting, and that the sail is oriented perpendicular to the Sun's rays. (With a larger sail, the ship is continuously driven away from the Sun.) The rate at which the Sun emits energy is 3.90

Explanation / Answer

Force of radiation = pressure * area =   2I/c * A   =   (2P /c 4pi r2 ) A

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force of gravity = G M m / r2

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Set forces equal

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         G M m /r2   = 2 P A / 4pi cr2         cancel r2 both sides

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         G M m 4 pic   = 2 P A

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   A = 2 pi c G M m / P = 2 pi * 3.00 x 108 * 6.67 x 10-11 *1.99 x 1030 * 1500 / 3.90 x 1026 =

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          =   833986.03m2   = 0.834 km2

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