[LDL (OP)]

For any height above a mass (M) there is a speed in each opposing direction that will generate a satellites orbit. These orbital speeds produce the proper rotational rate from M's gravitational field that deviates a satellite's motion into an orbital path. A satellite orbiting cw has its lateral motion deviated by a cw rotating gravitational field. A satellite orbiting ccw has its lateral motion deviated by a ccw rotating gravitational field. With no relative lateral motion, only inward fall will occur.

Consider three motionless satellites in a linear formation, with s1 below s2 and s2 below s3. Below them moving left is a body of mass we will label as M. When M is directly below the satellites moving left at speed v, we will determine the horizontal speeds required for each satellite to put them in a cw or ccw orbit around M.

We do this by first giving s1 a speed equal to v left, which puts it in a non-rotational relationship with M, before the orbital speeds required for its elevation (r1) in either direction is added. s2 is given the same left lateral speed v before adding the orbital speeds required for r2. And again, s3 also is given the same left lateral speed of v before we add the orbital speeds for r3.

Initially as M passes by, the satellites reside in M's cw rotational gravitational field. When speed v-left is added to the satellites, there will be no relative lateral motion between M and the satellites and M's gravitational field no longer rotates. We will call speed v the non-rotational speed (nr).

It is important to note that nr is the same for any elevation that the satellites are at.

If a left moving M produces a cw rotational gravitational field above it, what happens if we maintain M stationary but put it in ccw spin?

What is the primary motion affecting the field above M? The top half of M which moves left should have more influence because of its closer proximity to the surface. Certainly not to the extent of moving M fully left but significant none-the-less. A ccw spinning body should produce a cw rotational gravitational field around the whole circumference surrounding M.

Since the above cw rotational space above M is caused by left lateral motion from M's spin, nr (the non-rotating speed) can be reached by left lateral motion of the above satellites. If the satellites surpass the tangential speed of the surface of spinning M, they are certainly in a ccw rotating space. Somewhere at or below the tangential speed, this non-rotating speed must exist.

For the satellites to orbit around a ccw spinning M body in a ccw direction, they must first overcome the cw rotating space and reach nr. From nr, the orbital speed around a non-spinning M body (original orbital speed) is then added which will result in the correct rotational rate from the gravitational field to secure an orbital path. To achieve orbital speed in the cw direction, less added speed is required (original orbital speed nr) since the satellites starting position is already under a certain amount of cw rotation.

We can imagine any circular orbital pathway, of any diameter, around a ccw spinning M to be turning ccw with the peripheral lateral speed always being nr. The satellites original orbital speeds in either direction stay relative to the rotating circular space.

nr is dependent on the spin rate of M. As the spin increases nr increases. Original orbital speeds don't change. What if we increase the spin rate of M till nr is so large that the original orbital speeds all become minor add on-s. The viewed orbital speeds at all levels converge towards speed nr.

This process should flatten a rotation curve.

Does there exist a galaxy with a flat rotation curve that doesn't have an internal spinning core?