Question

3. ("Solar sail") A spaceship of mass m 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, as shown in the following picture Spaceship Copyright: NASA The idea is that a stream of photons from the sun, each with momentum p-h/λ (where X is its wavelength), 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 wavelength, and that the flux of the solar photons (the number of photons per unit area in unit time), is n. If the incidence angle of the photons (the angle between their direction and the line perpendicular to the surface of the sail) is θ, calculate the acceleration of the spaceship and indicate its direction on the figure in the following 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 a giant mirror - all photons are reflected (i.e., the colision with a sail is elastic-the photons bounce back towards the sun (c) Which design should be choosen? There are two considerations: (i) the magnitude of the acceleration, and (ii) maneuverability (namely, if the ship can be rotated in order to change the angle θ, can the direction of the acceleration be affected that way?). Explain your reasoning NB: it has recently been proposed to attach a tiny probe to a solar sail, and then shoot a strong laser beam from the Earth at the sail, and accelerate it toward Proxima Centauri b, an Earth-sized exoplanet in the habitable zone of Proxima Centauri.]

Answer 1

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