[Space] Mapping Large Flat Areas

[Ashtagon]

Originally Posted by Rupert

I don't know the answer to this problem, but here's what I understand it to be:

We have a two-dimensional space (so x,y co-ordinates) upon which are scattered a large number of points, at random. How do we determine the average distance between closest neighbours?

The actual answer to this questions depends on two points:

1) How many stars are in this space?
2) What is the size of this space?

Without this information, the best answer you'll get is a complicated formula that requires calculus.

[AlexanderHowl]

There are around 2,000 stars within 50 ly of Sol, many of which would appear quite close to each other on a 2D map without a 3D dimension. There are ~260,000 stars within 250 ly of Sol, many of which would appear quite close to each other on a 2D map without a 3D dimension. In the former case, there would effectively be effectively 1 star per 4 square ly of projection. In the latter case, there would effectively be 3 stars per 4 square ly of projection. You can start to see the complications with a 2D hyperspace real quickly, and that is without looking at the millions of galaxies below and above the Milky Way.

[Agemegos]

Originally Posted by Ashtagon

The actual answer to this questions depends on two points:

1) How many stars are in this space?
2) What is the size of this space?

Without this information, the best answer you'll get is a complicated formula that requires calculus.

I gave the formula in post #19. It's not complicated and doesn't require calculus. Average nearest-neighbour distance in two Euclidean dimensions = 0.5/sqrt(n/V).