262. assignment (photonic propulsion)

A spaceship is being designed which can use the so-called ‘solar wind’ for propulsion. Once in orbit, a large sail will unfold, and form a square of area A. The idea is that a stream of photons, each with momentum p= hf /c (where f is its frequency), will collide with the sail, giving it a tiny kick with each collision. For the sake of simplicity, let us assume that all photons have the same frequency, that the sail is perpendicular upon the trajectory of the photons from the sun, and that the flux of the solar photons (the number of photons per unit area in unit time), is n. Calculate the total force on the sail in two scenarios:

(a) The sail is painted black - all photons are absorbed (i.e., the colision with a sail is completely inelastic).

(b) The sail is made of reflective mylar, and acts like giant mirror - all photons are reflected (i.e., the collision with a sail is elastic- photons bounce back towards the sun).

(c) Which design should be chosen?

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