canineraytube t1_j277ik4 wrote on December 30, 2022 at 3:33 AM

Reply to comment by Aseyhe in How fast does the Milky Way spin? How far does Earth move through space in a year? by Sabre-Tooth-Monkey

To what extent could it be said that the distribution of dark matter changes the effective dimensionality of our galaxy? I ask this because, in contrast to typical circular orbits in our 3+1 dimensional spacetime, which slow with increasing radius, all circular orbits around a given mass in 2+1 dimensional gravity (attenuating at 1/d^1) share the same velocity. Is this coincidental?

Aseyhe t1_j284skm wrote on December 30, 2022 at 9:21 AM

That's correct that the orbits within the extended galactic mass distribution resemble orbits about a point mass in two dimensions (or an infinite line mass in 3D). In both cases the gravitational potential is logarithmic with respect to distance. That's coincidental, and I'm not familiar with any mathematical tricks that take advantage of the correspondence.