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 5.9010 m2 and mass m 4,800 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 (in N) is exerted on the sail? (Enter the magnitude.) 4.47 If you know the intensity in a beam of light, how do you determine the radiation pressure?N (b) What is the sail's acceleration? (Enter the magnitude in imis.) um/s (e) Assuming the acceleration calculated in part () remains constant, find the time interval (in days) required for the sail to reach the Moon, 3.84 x 108 m away, starting from rest at the Earth days (d) What If? If the solar sail were initially in Earth orbit at an altitude of 360 km, show that a sail of this mass density could not escape Earth's gravitational pull regardless of size. (Calculate the magnitude of the gravitational field in m/s?.) my's (e) What would the mass density (in kg/m2) of the solar sail have to be for the solar sail to attain the same initial acceleration as that in part (b)? kg/m2

Answer 1

a)

radiation pressure is expressed as,

P = 2I / c

I = solar intensity

P = (2 x 1370) / (3 x 10^8)

P = 9.1333 x 10^-6 Pa

F = PA

F = 9.1333 x 10^-6 Pa x 5.90 x 10^5 m^2

F = 5.389 N

b)

a = F / m

a = 5.389 N / 4800 kg

a = 1.122 x 10^-3 m/s^2

c)

t = sqrt(2s / a)

t = sqrt[(2 x 3.84 x 10^8) / 1.122 x 10^-3)

t = 827340.3 sec

t = 827340.3 s x 1 day / 86400

t = 9.5757 days.