Astronomy Olympiad Gravitation Qn Question:
Approximately once in 5 years people on Earth can observe bright comets whose nuclei have radius about 1km. The orbits of such comets are close to parabolic. Assuming that these nuclei are uniformly filling the volume of spherical Oort cloud with radius 10000 AU, estimate the number of large comet nuclei and mass of Oort cloud.

I'm not sure how to even start this question because I don't get how the comets uniformly fill Oort cloud yet on Earth we can only observe comets once every 5 years (unless there are some things blocking our views of these comets?). Would appreciate any help.  

P.S. Relativity should not be needed in this question...
Presumably you're supposed to start by calculating the minimum orbital period a comet can have for a 10,000 AU aphelion distance.

Then divide that period (number of years) by five, assuming we see on average one of these every five years.

That will give you an estimate for how many there are out there.

(I would also tell the person setting the question that there are some pretty wild assumptions implied in the question!)