Interesting problem about sun, photons, momentum?

by PhOtOnQuAnTiQuE

Question by erik_8991: Interesting problem about sun, photons, momentum?
The sun emits 3.9 × 10^26 W of power. NASA would like to use the flux of photons from the sun to move a spacecraft that is in the shape of a sail. This absorbing solar sail is d = 2 × 10^11 m from the sun and has an area of A = 10^6 m2. What is the change in momentum of the solar sail when it faces the sun for 60 seconds? (Note, you do not need to know the wavelength of sunlight to answer the question, but the sun does emit most of its photons at a wavelength of 500 nm.)

(a) 160 kg m/s
(b) 12 kg m/s
(c) 4.0 × 10^-19 kg m/s
(d) 1.3 × 10^-27 kg m/s
(e) The momentum does not change.

thanks!

Best answer:

Answer by DH
The intensity of the sun’s energy at d is P/4Ï€r^2 = 3.9×10^26W/(4Ï€*(2×10^11)^2) = 776W/m^2

The radiation pressure is I/c= 776w/M^2/3X10^8m/s = 2.59×10^-6 Pa

So the force on the sail is P*A = 2.59×10^-6*10^6 = 2.59N

The impulse would be F*t = 2.59N*60s = 155N-s = change in momentum

Rounded to 2 digits the answer is a) 160 kg-m/s

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