Question

It looks like there is an earth sized planet in the habitable zone of Proxima Centauri, located 4.2 ly from the solar system. It would be cool to send a probe to check it out. Perhaps the most reasonable way of doing this is to construct a very small micro-spaceship connected to a large flat screen which absorbs radiation: a solar sail. We will model the sail as a perfectly absorbing flat screen, and the sun's radiation as plane waves.

(a) From the law of conservation of linear momentum, show that the pressure exerted by the sun's light is equal to the field energy per unit volume in the wave.

(b) Assume that the sun radiates 0.2 w/m^2. If the sail has a mass density of 10^-4g/cm^2, what would its acceleration be? How long would it take to get to a speed of 0.1c?

Answer 1

(a) pressure = force / area

so,

dF/dt = d / da * dP/dt

(momentum / volume ) * ( length / time) = ( energy * time / volume * length) ( length /time)

cancel all the like terms, we have

(momentum / volume ) * ( length / time) = energy / volume

so,

radiation pressure is simply the energy density.

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(b)

P = S / c

P = 0.2 / 3e8

P = 6.666e-10

so,

a = F / m

a = 6.666e-10 / 0.01

a = 6.67e-8 m/s²

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starting from rest, time taken to reach 0.1c

v = u + at

0.1c = 0 + 6.67e-8 * t

t = 4.5e14 seconds