Aluminized mylar film is a highly reflective, lightweight material that could be

Question

Aluminized mylar film is a highly reflective, lightweight material that could be used to make sails for spacecraft driven by the light of the sun. Suppose a sail with area 1.10 km2 is orbiting the Sun at a distance of 1.36 1011 m. The sail has a mass of 5.07 103 kg and is tethered to a payload of mass 2.08 104 kg.

(a) If the intensity of the sunlight is 1.34 103 W/m2 and the sail is oriented perpendicular to the incident light, what radial force is exerted on the sail?

(b) About how long would it take to change the radial speed of the sail by 1.00 km/s? Assume that the sail is perfectly reflecting.

(c) Suppose the light were supplied by a large , powerful laser beam instead of the Sun. (Such systems have been proposed.) Calculate the peak electric and magnetic fields of the laser light.

Emax=

Bmax=

Explanation / Answer

a)

Force exerted on the sail is

F=2IA/c =2*1340*(1.1*106)/(3*108)

F=9.8267 N

b)

acceleration

a=F/m =9.8267/(2.08*104)=4.72*10-4 m/s2

Time taken to change radial speed by 1 km/s

t=(V-U)/a =1000/4.72*10-4

t=2.1167*106 s

c)

Peak electric field

Emax =sqrt(2uoIc)=sqrt(2*4pi*10-7*1340*3*108)

Emax=1.005*103 N/C

Peak magnetic field

Bmax =Emax/c =1005/(3*108)

Bmax =3.35*10-6T

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