Балкански 2007, Теория — Задача 3. 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

3. The force that is obtained in the previous question recalls the gravitational force between the Sun and an object of mass $m$, that reads :

with $G$ the gravitational constant, $G = 6.67 \times 10^{-11}\ m^{3}s^{-2}kg^{-2}$, and $M$ the solar mass, $M \approx 2 \times 10^{30}\ kg$.

3.a) What are the major differences between the two forces (4) and (3) ?

3.b) A solar sail of mass $m = 100\ kg$ is deployed in the orbit of the Earth. The sail reflectivity is $R = 0.9$. What is the surface of the sail $S$ requested so that the radiation force equilibrates exactly the gravitational force of the Sun ?

3.c) Consider a material of typical density $\rho = 1\ kgm^{-3}$. Does the value of $S$ obtained in the previous question seem realistic to you ?

3.d)* In fact, if the sail is launched from the Earth orbit, it is not necessary to compensate the Sun attraction. Why ? Explain how a solar sail, even with a surface much smaller than the one calculated before, can be successfully employed in inter-planetary trips.

Решение

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Оригинал в Архива: CGP_2007_en.pdf