Балкански 2010, Теория — Задача 4

The main problem and the three exercises are completely independent and can be solved in any order.

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

The exam is 4 hours long! The calculators are authorized.

Physical constants:

• Mass of the Earth: $M_E = 6{,}0.10^{24}kg$
• Mass of the Sun: $M_S = 2{,}0.10^{30}kg$
• Average Earth radius: $R_E = 6{,}4.10^{6}m$
• Average Sun radius: $R_S = 7{,}0.10^{8}m$
• Average radius of the Earth’s orbit around the Sun: $L = 1{,}5.10^{11}m$
• Time needed for one rotation of the Sun around its axe: $\theta_S = 2{,}6.10^{6}s$
• Universal gravitational constant: $G = 6{,}67.10^{-11}N.m^2.kg^{-2}$
• Perfect gaz constant: $\Re = 8{,}31J.K^{-1}.mol^{-1}$
• Avogadro’s number: $Na = 6{,}02.10^{23}mol^{-1}$
• Hydrogen molar mass: $M_H = 1{,}0.10^{-3}kg.mol^{-1}$
• Speed of light: $c = 3{,}0.10^{8}m.s^2$