Estimate (!) the number of atoms in the Sun given that it takes the light about t=8.3 min to reach us.

Use the following constants: light speed in vacuum c=310^8 m/s , gravitational constant G=6.67408 × 10^{-11} m^3 kg^{-1} s^{-2} and Avogadro's constant A =6.02214086 × 10^{23} mol^{-1}.Assuming that Earth moves in an almost circular orbit we can equate centripetal force F1={mv^2}/{R} to the force from the Newton's law of gravity F2=G*{mM}/{R^2} such that F1=F2.Knowing the period of Earth's rotation to be around T= 365 days we can find Earth's orbital velocity in the following way: v={length of the orbit}/{period}={2piR}/{T}={2pict}/{T}. After equating forces and plugging in the expression for the velocity we have M={v^2R}/{G}={(2pi)^2*(ct)^3}/{GT^2}. We assume that the Sun is made up only from single hydrogen atoms (wich actually makes up about 71% of Sun's mass) which have molar mass of n=0.001 kg /mol. Now we find the number of moles of hydrogen in the Sun and multiply the answer by Avogadro's constant to get the number of atoms N={MA}/{n}={(2\pi)^2*(ct)^3A}/{GT^2n}. Now we just plug in the numbers and get the final value which should be of an order 10^57.Questions similar to this can be part of the interview when applying for physics or engineering degree at Oxbridge.