# Extra Credit Project: A Solar Sail

This project must be done by individuals.

Joe Aerospace decides to make a "solar sail" for his private spaceship. The "sail" uses radiation pressure from the Sun to move a ship, in the same way that a regular sail uses pressure from the wind. Joe uses ordinary aluminum foil (Reynolds Wrap or the equivalent) for his sail.

1. What is the mass per square meter of aluminum foil?

The Sun radiates a great deal of energy per second; see Appendix C for its power. Assume that all of this energy is emitted as photons of wavelengths 550 nanometers -- greenish-yellow light. These photons each have

energy      E = 3.61 x 10^(-19) Joules

momentum    p = 1.21 x 10^(-27) kg*m/s

2. How many photons of this sort does the Sun emit each second?

Joe's sail is a square, 100 meters on a side, located at the Earth's distance from the Sun. He orients it so that photons strike it face-on and bounce back towards the Sun.

3. How many photons strike Joe's sail each second?

4. If the photons are reflected perfectly back towards the Sun, how much momentum does a single photon transfer to the sail?

5. How much momentum is transferred to the sail each second?

6. Use impulse to calculate the force exerted on the sail by the photons.

7. Calculate the force of gravity due to the Sun on the sail.

8. What is the net acceleration of Joe's sail?