A possible means of interplanetary space travel utilizes a perfectly refelcting

Question

A possible means of interplanetary space travel utilizes a perfectly refelcting sheet that harnesses sunlight to push the ship. Consider a sail plus ship that has a mass of 6000 kg with a sail surface area of 1.2 x 105 m2 that directly faces the Sun. Note: assume that the intesnity of the sunlight is that near Earth's orbit, 1300 W/m2.

a) Determine the force exerted on the ship/sail.

b) What is the acceleration of the ship/sail? (Ignore any gravitational effects).

c) How long will it take the sail to reach the position of the Moon given that the Moon is 3.84 x 105 km away from the Earth and it starts from rest relative to the Earth and Moon.

Explanation / Answer

m =6000 kg ,A =1.2*10^5 m^2, I =1300W/m^2

Velocity of light c = 3*10^8 m/s

(a) Radiation pressure P = 2I/c

Pressure P = Force/Area =F/A

F = P*A = (2IA)/c

F = (2*1300*1.2*10^5)/(3*10^8)

F =1.04 N

(b) From Newtons second law F =ma

a = F/m =1.04/6000

a = 1.73*10^-4 m/s^2

(c) u=0

from kinematci equations

S = ut +(1/2)at^2

3.84*10^8 =0 +(0.5*1.73*10^-4*t^2)

t = 2.11*10^6 s

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