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What's the average distance to the next point when 7 points are distributed equally throughout a cube?
A globular cluster of stars is estimated to have a density of 7 stars per cubic light year. On the average, what is the inter-stellar distance from any star to the next closest one? Can you show this mathematically?
I wonder how our differently our civilization, mathematics, and science might have developed if the nearest stars were 8x closer. Our understanding of gravitation, electro-magnetic propagation, motion, even time-space might might have advanced farther and more quickly than it has, so far, in our given time on earth. I imagine that even the arts - visual, poetic, musical, etc.- would all be profoundly affected.
1 Answer
- ronwizfrLv 71 decade agoFavorite Answer
A density of 7 stars per cubic light year means that there is one star per 1/7 lyr^3, which is a cube with a length of 0.52 light year. So that's the average distance between two stars.
Well, not quite.
One out of two stars is double or triple. So of these 7 stars, 2 are on their own while 5 are grouped in 2 star systems. So their are only four systems in the lyr^3, for an average distance of 0.63 light years.
