A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2018 Oct 6, 11:01 -0700
David, you wrote:
"What had I forgotten from my school geometry, and what fraction of the 28mm Neptune should I have taken to make a 14mm Neptune?"
Only one-eighth of the original. And it really is hard to believe, for anyone, until you start messing around with lumps of clay. Geometry is surprising for our monkey brains.
But we can make our little, linear primate brains happier if we switch to general relativity instead of clay (not often you get to say that!). If you take two black holes, each a mile across, and you merge them (ignoring radiative losses), you will get a black hole that is two miles across. And if you take that two-mile black hole and merge a one-mile black hole with it, you get a three-mile black hole. And so it goes... If you have a million-mile wide black hole at the center of a galaxy and add a one-mile wide black hole to it, the resulting black hole adds one mile to its diameter. Isn't that nice!
Nice? Well, up to a point. This is why you should be careful about tossing little black holes into big black holes -- the volume of space within event horizons (inside black holes) increases far more rapidly than the rate for fixed-density objects. If you're not careful, you can end up with your whole galactic neighborhood inside a black hole.