Балкански 2007, Теория — Задача 2. 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

2. We are now interested by the launching of the sail. In the following table we plot the solar energy flow, in $W/m^2$, at the vicinity of a planet, as a function of the planet-sun distance in Astronomical Units A.U. We recall that one astronomical unit is the distance between the Sun and the Earth : 1 A.U. $= 149.6 \times 10^{6}\ km$.

2.a) What is the relationship between the energy flow $\Phi_E$ and the flow of photons $\Phi$, if the mean energy per photon is $h\nu$ ? Give then a simplified expression of the radiation force on the sail.

2.b) If the sail is to attain a high speed, is it more advantageous to launch it in the vicinity of Mercury or Neptune ? Why ?

2.c) Fill up the forth column of the table by the product of the energy flow times the square of the planet-sun distance. What is to be noticed ? Provide an explanation.

2.d) Show then that the radiation fore can be written :

with $r$ the planet-Sun distance and $A$ a constant that will be calculated numerically, in S.I. units.

Решение

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Оригинал в Архива: CGP_2007_en.pdf