Question

Since force is dp/dt, the force due to radiation pressure reflected off of a solar sail can be calculated as 2 times the radiative momentum striking the sail per second. In the vicinity of Earth's orbit around the Sun, the energy intensity of sunlight is about 1300 W/m2. What is the approximate magnitude of the pressure on the sail?

Answer 1

Step-by-step explanation:

Given that,

Force = dp/dt

Where p is momentum

Sun intensity I = 1300 W/m²

For a photon, the momentum is given as

p = E / c

Where E is photon energy and c Is speed of light

c is a constant c = 3 × 10^8m/s

So, substituting p into the differential

F = d(E/c) / dt

Since we know that c is constant

F = 1/c dE/dt

This is then double for a complete reflection of light

F = 2 × 1/c dE/dt

F = 2/c dE/dt

The energy of each photon depend on its wavelength. Sunlight contain wide spectrum of wavelength, but if the sail reflects all the wavelength equally we can sum the contribution from all the photon and use the intensity of light given I = 1300W/m²

So, intensity is given as

I = Power / Area

And power is Workdone/time

I = E/t / A

So, intensity can be related to

I = dE/dt / A

Therefore, dE/dt = I•A

We have,

F = 2/c dE/dt

F = 2/c × I•A

Since we know that,

Pressure is force divided by area

P = F / A

Then,

F / A = 2/c × I

P = 2 × I / c

P = 2× 1300 / 3 × 10^8

P = 8.67 × 10^-6 N/m²