It has been proposed that a spaceship might be propelled in thesolar system by r

Question

It has been proposed that a spaceship might be propelled in thesolar system by radiation pressure, using a large sail made offoil. How large must the surface area of the sail be if theradiation force is to be equal in magnitude to the Sun'sgravitational attraction? Assume that the mass of the ship + sailis 1500kg, that the sail is perfectly reflecting, and that the sailis oriented perpendicular to the Sun's rays. (With a larger sail,the ship is continually driven away from the Sun. Assume that thetotal radiation power of the Sun is 3.90 x 1026 W andits mass is 1.99 x 1030 kg.)

if a member could look up the answer and post it here i wouldbe greatful and will rate

Explanation / Answer

the radiation force is to be equal in magnitude to the Sun'sgravitational attraction therefore F = (GMm/r^2) the intensity radiated by Sun is equal to the intensityrecieved by the sail therefore I1 = I2 or (P1/A1) = (P2/A2) or A2 = P2 * (A1/P1) P2 = F,A1 = 4R^2 and P1 = 3.90 * 10^26 W A2 = F * (4R^2/3.90 * 10^26) or A2 = (GMm/r^2) * (4R^2/3.90 * 10^26) Here,r = R or A2 = (4 * GMm/3.90 * 10^26) G = 6.67 * 10^-11 Nm^2/kg^2 M = 1.99 * 10^30 kg m = 1500 kg

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