Electromagnetism HW question?

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 6.50 x10^5 m2 and mass 5800 kg is placed in orbit facing the Sun.

(a) What force is exerted on the sail?

___ N

(b) What is the sail's acceleration?

___ m/s^2

(c) What time interval is required for the sail to reach the Moon, 3.84 x10^8 m away? Ignore all gravitational effects, assume the acceleration calculated in part (b) remains constant, and assume a solar intensity of 1370 W/m^2.

___ days

Answer 1

energy reaching the sail per second is E=1370*6.5e5=8.905e8 J;

on the other hand this is kinetic energy of photons reaching the sail per second, that is E=mc^2, where m is mass of these photons moving with speed of light c=3e8m/s; meanwhile this mass of photons is carrying momentum L1=mc=E/c; after reflection these photons are carrying momentum L2=-mc; the difference of momentum ΔL=L1-L2=2E/c is being translated to the sail; thus increase of momentum per second of the sail is ΔL=M*Δv, where M=5800kg, Δv is increase of speed of the sail per second, that is acceleration a=Δv;

(a) F=M*a = ΔL =2E/c = 8.905e8/ 3e8 = 2.97 N;    

(b) a=F/M =5.12e-4 m/s^2;

(c) S=0.5*a*t^2, where S=3.84e8 m;

thence t=√(2S/a) =1225006s =340.28h =14.18 days; correct?