Wouldn't systems near the core move faster and if they did wouldn't traveling through the cord would be different each time you would go through?
^^ That is a good question indeed :
Normally, one would expect indeed faster rotation near the core, and have it go slower as you move away*. (calculating it from the known visible matter (i.e. stars) distribution)
However, this is not what has been seen (-> measured). The velocity profile is in fact almost flat. This is generaly considered as one of the "clue" for the existance of
large amount of dark matter. (Or, modification of the law of gravity at large scale).
*Though, at very small radius (i.e. really close to the core), the radial velocity is nearly zero, then rises sharply to a max, and then
should go down,
but does not.
Also, the radial velocity is
only ~100km/s
. While it may seem a lot to us poor humans, at the scale considered it is indeed peanuts. After 10yrs, that would amount to 1/300 lyr.