I am having trouble with this number density astrophysics question. Any help is greatly appreciated:(adsbygoogle = window.adsbygoogle || []).push({});

Consider a galactic disk with radius much larger than its thickness. Let R be the radius and the thickness be 2H where H is the ‘scale height’ of the disk. For a population of objects with large n3, the mean distance is small and a 3-dimensional approach can be taken. For a sparse population with large mean distance, a 2-dimensional (area) approach is appropriate where n2 is the integral of n3 through the disk vertically. At what mean distance does the transition from a 2D to 3D approach occur?

This question has to do with the relationship between number density and average distance, which is (I think) average distance = 1/cube root(density) for 3D space and 1/square root(density) for 2D space.

It involves calculus which I'm not too comfortable with and I'm not sure where to start... Please help!

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# Number density/average distance relationship question

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