A recent survey of our part of the Milky Way failed to find any of the elusive dark matter posited to account for a presumed 83% matter shortfall needed to explain why galaxies don’t fly apart.
In the absence of dark matter it would seem that a productive avenue for explanation might be to reconsider the Gravitational Metric vis-a-vis the Visual Metric. That is to say, while the distance from the center to the arms of a galaxy may appear to be n miles or light years across, its gravitational distance might be entirely different.
This could come about in a number of ways. One way that suggests itself is to posit a granular universe composed of infinitely small units or grains. Gravitational distance would then be a function of the granular density - ie. the greater the density the further away the gravitational distance. Thus, planets, galactic spirals, black hole companions etc. would all have a “virtual gravitational orbit” determined by the number of gravitational units d between it and its sun, center or black hole.
Near a large body the radius of the virtual orbit would be greater than the radius of the visual orbit thus imparting to the object a greater rotational speed due to the conservation of angular momentum. For near Earth systems the difference between the visual and virtual orbits might be slight, but over large distances this difference might be considerable.
The radius of the virtual orbit would be given by nd where n is the number of gravitational units d. nd - r = Dr the difference between the radius of the virtual orbit and the radius of visual orbit. Dr should relate naturally to the curvature of space as well as giving a measure of the density of the gravitational units (nd/r = r). Where the gravitational and visual radii agree, r = 1.
The angular momentum L of a mass m moving in a circular orbit with linear speed v is given by: L =2pmr2/v.
Substituting nd for r the angular momentum of the virtual orbit is: L =2pm(nd)2/v. Since L is conserved and r is less than nd it follows that the angular velocity must increase which is precisely the observation that has led to positing the existence of dark matter.
By sampling enough anomalous galaxies and black hole satellites it should be possible to ascertain their virtual orbits and derive some measure of the size of these gravitational units and their relationship to h, c and G.