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 1700 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

apply the formula for gravitational force F = mg

also radiation pressure for total refllection is given by Pr = F/A   = 2I/c

where I = intensity= power/area = Emax^2/(2uoC)

c = velocity of light = 3e8 m/s

so here now I = power/area

radius of sun = .695 e8 m

and

g on sun = 27.4 m/s^2

I = 3.9 e 26/(4*3.14 * 6.95 e 8* 6.95 e 8 )

I = 6.42 e 7 W/m^2

Area A = Fc/2I

A = mgc/2I

Area A = 1700 * 27.4 * 3e8/(2* 6.42 e 7)

A = 1.088 e 5 m^2 is the answer

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