Weird universe

Classical Mechanics Level 5

Suppose that we live in some crazy open universe, also the concentration of stars is constant and equal to \(n=10^9 \frac{1}{Mpc^3}\) and the mean radius of the star is \(R=\frac1{\sqrt \pi} 10^8 \text{ km}\). Find the average distance 'view' will travel before it 'hits' the star. Answer in \(Mpc\)

Example: if you look at tree 9m away from your eyes your look will travel distance of 9m.

\(*1Mpc=10^6\times 206265 \times 1.5\times 10^8 \text{ km}\)

This is one of short problems from IOAA 2015.

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