Question

A solar sail is a means of spacecraft propulsion using reflected sunlight. The solar intensity is 1380 W/m2. When light is reflected from a reflecting surface it exerts a pressure on the surface of 2*(solar intensity)/(speed of light). If a solar sail of area 21,673.65 m2 and mass 793.86 kg were used to propel a spacecraft, what would its acceleration be in millimeters/s^2? Recall that Pressure=Force/Area.

Answer 1

The first step is for us to find out the pressure exerted by the solar radiation, which, according to the formula will be:

$P=\frac{2*1380}{c}=\frac{2*1380}{3*10^8}=9.2\mu Pa$

As we know, pressure is Force/Area, so we can find out the Force, which will be:

$F=P.A=9.2*10^{-6}*21673.65=0.19939758N$

But according to Newton's second law, Force is equal to the product between mass and acceleration, thus:

$a=\frac{F}{m}=\frac{0.19939758}{793.86}=2.51174*10^{-4}\frac{m}{s^2}=0.25\frac{mm}{s^2}$

Then, our final answer is a=0.25mm/s^2