Балкански 2007, Теория — Задача 1. The solar sail

Concours Général de Physiques “Minko Balkanski” — 20 mai 2007 · 20 май 2007 г.

Указания

The two exercices are independent.

All the answers must be given in English or in French*. The clarity and the precision will be taken into account for the final note.*

The exam is 4 hours long.

Условие

The solar sail

Just like the ships that were once pushed by the wind, in the future we will travel from planet to planet by the help of sails driven by the solar radiation... This is no longer a fiction, but a scenario that is envisioned by a number of scientists and rocket engineers. Indeed, the radiation driven solar sails will not consume any fuel. In this problem we try to understand the way that they function and to estimate some orders of magnitude.

1. The solar sail is modelled by a mirror of reflectivity $R$, like in the figure above. A photon flow of energy $h\nu$ is incident on the sail, in the perpendicular direction, where $h$ is the Plank constant and $\nu$ the frequency of the radiation.

Let’s recall that a photon of energy $h\nu$ carries a momentum $p$ :

with $c$ the speed of light, $c = 3 \times 10^{8}\ ms^{-1}$.

1.a) Suppose that the incident photon is absorbed by the sail. What is the momentum transferred to the sail ?

1.b) Suppose now that the photon is reflected by the sail. What is the momentum transferred to the sail ?

1.c) If the photon is reflected with a probability $R$ and absorbed with a probability $1 - R$, what is the mean momentum transferred by each photon ?

1.d) The photon flow, or the number of photons arriving to the sail per unit surface and unit time is $\Phi$. If the sail surface is $S$, show that the force $F$ applied to the sail is

Решение

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Оригинал в Архива: CGP_2007_en.pdf