Not a troll here - looking to understand this better.
So, lets assume we have the galactic center, a star 1 a distance of x from the center and star 2 x+y from the center and in a galactic arm. Lets also assume we take a ray that forms a right angle from a tangent plane from the galactic center that transects S1 and S2, like a spoke in a wagon wheel. As S1 and S2 are observed to rotate around the galactic center, do they stay "within the spoke"? And relativistic models predict that S2 would lag behind the tangent ray that transects S1?
a tangent plane from the galactic center (represented as a sphere - the shape of the super massive black hole)
Yes, you’ve got the gist of it. The stars along a “spoke” from the center rotate such that their relative angles stay the same, even though that means the outer stars must revolve around the galactic center much faster than the inner stars, which is contrary to the standard laws of gravity.
So, either something besides gravity is driving their motion, or our understanding of gravity is flawed, or we do not know all the components of the gravitational system in a galaxy. Dark matter is choosing the third choice, scientists are assuming that nothing besides gravity drives the motion, and our gravitational equations are correct, so they are left to believe there must be a missing element we are not including in our equations to account for the motion of the system. They then “reverse engineer” what elements would make the equation work mathematically, and the result is the so-called “dark matter”.