One possible means of achieving space flight is to place a perfectly reflecting

Question

One possible means of achieving space flight is to place a perfectly reflecting aluminized sheet into Earth's orbit and to use the light from the Sun to push this solar sail. Suppose such a sail, of area 7.00 x 10 4 m2 and mass 6200 kg, is placed in orbit facing the Sun. Ignore all gravitational effects, and assume a solar intensity of 1340 W/m2. (Hint: The radiation pressure by a reflected wave is given by 2 (average power per area)/c.) What force is exerted on the sail? F = N What is the sail's acceleration? a = m/s2 How long does it take for this sail to reach the Moon, 3.84 x 108 m away? t = days

Explanation / Answer

Solution:

(a):

Pressure = 2*I / c = (2*1340)/ 3*108 N/m2

Force = P*A = Pressure * 7.00*104 = 0.62533 N (answer (a) )

(b):

a = F/m = 0.62533/6200 = 1.0086 * 10-4 m/s2 (answer)

(c):

S = 1/2 * a * t2

=> t = underroot of (2*S/a)

= underroot of (2*3.84*108/1.0086 * 10-4)

= 32 days. (answer)

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