That was very helpful and I could only see 1 typo error in the whole post. ("This gives 700.666 km sec if we use the 149,003,113 Solar mass" was that supposed to be 140,003,113?) I sense Janus58 is a person who really knows what he/she is talking about.
OK so time dilation does not account for a sufficient part of the needed corrected mass (I know this poorly worded, for time dilation does not change mass). I was previously working on a project looking at correcting G rather than mass. If G varied in a function depending on distance from the central black hole maybe then we wouldn't need dark matter or adjusted mass. Have you ever considered G varying?
What you are talking about is is some type of MOND, or MOdified Newtonian Dynamics. The problem here is the there have been a lot of attempts to come up with a modified theory of gravity to replace DM, and they have all come up short. The problem they have is they can't account for
all observations. Not all galaxies are the same types or sizes and you just can't get a single modified gravity theory that can be made to fit them all.
One of the biggest blows to MOND theories is the already mentioned Bullet Cluster.
I'll explain:
With the Bullet cluster we are looking at the aftermath of a collision between two galaxy clusters. Now, during the collision there was interaction between the normal baryonic matter and energy was radiated away, which resulted in the clusters separating at a lesser speed than they came together. DM doesn't interact to the same degree, so you would expect the DM parts of the cluster not to lose as much speed. This would cause the DM to separate away form its parent cluster. Basically, the collision Knocks the DM loose of the cluster.
If the above is true, then we should see two distinct gravitational lensing silhouettes. One caused by the visible part of the cluster, and one caused by the DM that has been "knocked loose". When we examine the Bullet cluster, this is exactly what we see. We see the gravity lensing around the visible parts of the cluster, and offset from it, where there is no visible matter there is a second locus of gravitational lensing, just like we would expect. No MOND theory can explain how gravitational lensing can be knocked loose from the mass causing it unless the theory includes some DM.
In a reasonably simple way (at similar level in your "cut to the chase post") could you explain how the addition of DM to the galaxy overcomes this problem?
Thank you for helping us out.
It has to do with the way the mass is distributed. The visible baryonic mass is distributed as a central bulge and a thin disk. Once you leave the area of Bulge, the extra mass added inside your orbital sphere by the matter in the disk doesn't amount to much. However DM is spherically distributed. So it is the mass of DM within the entire orbital sphere that effects your orbital velocity and the volume of that sphere grows by the cube of the orbital radius. So what you have is the combination of the gravitational effect of the visible matter of the galaxy which falls off with distance, and the gravitational effect of the DM which increases with distance. the two act in opposition to flatten out the galaxy rotation curve.