Question

Lightsail-2 is a spacecraft launched in June 2019 by the Planetary Society driven by radiation pressure on a solar sail of area 30 square meters. It is currently in low earth orbit. Given the solar constant (solar power at the Earth’s surface) 1,388 W/m2 , estimate the force on the sail if it is oriented so that the solar radiation strikes the sail perpendicularly. Assume the sun emits pure yellow light of wavelength 570 nm, and that each photon is specularly reflected, with no absorption. (a) (5 pts) How many yellow photons hit the sail per second? (b) (5 pts) What is the force imparted to the sail?

Answer 1

Answer:

$2.655\times 10^{13}\ photons$

Explanation:

Area of the solar sail = A = 30 m2

Solar constant = I = 1388 W/m2

Planck's constant = h = 6.626 × 10⁻³⁴ m²kg/s

Speed of light = c = 3×10⁸ m/s

Wavelength of light = $\lambda$ = 570 nm

Pressure from radiation

$P=2\frac{I}{c}\\\Rightarrow P=2\frac{1388}{3\times 10^8}\\\Rightarrow P=9.253\times 10^{-6}\ W$

Energy of a photon

$E=\frac{hc}{\lambda}\\\Rightarrow E=\frac{6.626\times 10^{-34}\times 3\times 10^8}{570\times 10^{-9}}\\\Rightarrow E=3.487\times 10^{-19}\ J$

Number of photons

$n=\frac{P}{E}\\\Rightarrow n=\frac{9.253\times 10^{-6}}{3.487\times 10^{-19}}\\\Rightarrow n=2.655\times 10^{13}\ photons$

Number of photons is $2.655\times 10^{13}\ photons$