It is believed that there are 2.7 × 1012 comets in the Oort Cloud, which has a radius of 71000.0 AU?
Calculate the average volume that each comet has to itself. Then take the cube root of the average volume per comet to find their typical spacing in AU.
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I was told there would be no math.
Wikipedia says Oort cloud extends from 2000 AU to 200,000 AU, but I'm going to ignore that, and treat the Oort cloud as a sphere of radius 71000 AU, as suggested in the problem.
((4/3)*pi*(71000 AU)^3)/(2.7 x 10^12)
= (4/3)*pi*(71 AU)^3 / (2700)
= 555 AU^3.
And the cube root of that is around 8.2 AU.
Radius = 71,000 AU. So the volume is (4/3) pi radius^3 = 1.5 x 10^15 AU^3. Per comet, that is 555.26 AU^3. The cube root of that is 8.2193 AU.