A possible means of space flight is to place a perfectly reflecting aluminized s

Question

A possible means of space flight is to place a perfectly reflecting aluminized sheet into orbit around the Earth and then use the light from the Sun to push this "solar sail." Suppose a sail of area A = 6.10 x 10^5 m2 and mass m = 6.10 x 10^3 kg is placed in orbit facing the Sun. Ignore all gravitational effects and assume a solar intensity of 1 370 W/m2. What force is exerted on the sail? N What is the sail's acceleration? pm/s^2 Assuming the acceleration calculated in part remains constant, find the time interval required for the sail to reach the Moon, 3.84 x 10^8 m away, starting from rest at the Earth. days

Explanation / Answer

Energy reaching the sail per second , E= 1370 * 6.10 *10^5 = 8.357 * 10^8 J
This is kinetic energy of photons reaching the sail per second, that is E=mc^2,
where m is mass of these photons
c is speed of light c = 3*10^8 m/s
This mass of photons is carrying momentum L1=mc=E/c;
after reflection these photons are carrying momentum L2=-mc;

Difference of momentum L=L1-L2 = 2E/c
Increase of momentum per second of the sail is L=M*v,
where M=6.10 * 10^3 Kg
v is increase of speed of the sail per second,
that is acceleration a=v;

(a)
F = M*a = L =2E/c = 2*8.357 * 10^8/ 3*10^8 = 5.57 N

(b)
a = F/M = 5.57 / 6.10 * 10^3 = 9.13*10^-4 m/s^2

(c)
S = 0.5*a*t^2,
where S= 3.84*10^8 m
thence t=(2S/a)
t = sqrt((2*3.84*10^8) /(9.13*10^-4) )
t = 9.17 * 10^5 s
t = 10.61 Days.

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