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 = 5.80 x 105 m2 and mass m = 5.10 x 103 kg is placed in orbit facing the sun. Ignore all gravitational effects and assume a solar intensity of 1 370 W/m2 (a) What force is exerted on the sail? 5.29 (b) What is the sail's acceleration? 1.037E-3 m/s2 If you know the net force from part (a) and the mass from the problem statement, how do you find the acceleration? (c) Assuming the acceleration calculated in part (b) remains constant, find the time interval required for the sail to reach the Moon, 3.84 × 108 m away, starting from rest at the Earth. 8.6 problems involving constant acceleration X days This is a constant acceleration situation. It might be a good opportunity to review solution methods for

Explanation / Answer

a)

Radiatioj pressure is given by

P=2I/c =2*1370/(3*108)=9.13*10-6N/m2

Force exerted on the snail is

F=PA=(9.13*10-6)(5.8*105)

F=5.2973 N

b)

sail's acceleration

a=F/m =5.2973/(5.1*103) =1.0387*10-3 m/s2

1 um =10-6 m

a=1038.7 um/s2

c)

since d=(1/2)at2

3.84*108=(1/2)*(1.0387*10-3)*t2

t=8.6*105 s

in days

t=(8.6*105)/(24*60*60)

t=9.952 days

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