Finally! Someone else made the same observation I did. All that "expected" rotation curve stuff is bullshit since it's based on Keplers laws, which don't apply to a flat disk.
They do that based on a misapplication of the divergence theorem. They assume that all the mass inside an orbital radius can be treated as a point-mass which is true for uniform spherical distributions. They also assume the mass outside the radius has no net infuence - which is true for uniform spherical shells. Neither of these is valid for non-uniform distributions - a flat disk in not symmetric in 3-space. If they'd just do some electrostatics problems they'd know the different formulas for disks and rings. I was going to google a sample page but there's too many to sift through and I gotta run an errand.
I really encourage you if you are actually interested in the arguments to progress beyond the entry level explanations. Binney & Tremaine (https://press.princeton.edu/titles/8697.html) is the standard work - I highly recommend it. At the very least, it will put to rest your notion that astrophysicists only consider spherically symmetric potentials or fail to consider the effects of a disks etc., which is just patently untrue.
And here I thought Hacker News was going to get the Nobel Prize! I can't believe quickly deriving something from first principles also occurred to the people devoting their lives to this field.
Thanks for the link. They have a .pdf of chapter one which I gave a look. Right there on page 14 when estimating the mass of our galaxy inside our suns radius we have:
"The approximation that the mass distribution is spherical is reasonable for the dark halo, but not for the flat stellar disk. Better models suggest that this estimate is probably high by about 30%, since a disk requires less mass to produce a given centripetal acceleration"
And there you have it. While he notes that a spherical distribution is different than a flat disk, he estimates the error at about 30%. The problem is that the error is not one of a constant factor, it's a different function. This unspecified better model also doesn't seem to care about the matter outside the solar radius - which also affects our velocity in a disk, but not in a sphere.
There is a lot of math in chapter one, but also a lot of hand waving.
They do that based on a misapplication of the divergence theorem. They assume that all the mass inside an orbital radius can be treated as a point-mass which is true for uniform spherical distributions. They also assume the mass outside the radius has no net infuence - which is true for uniform spherical shells. Neither of these is valid for non-uniform distributions - a flat disk in not symmetric in 3-space. If they'd just do some electrostatics problems they'd know the different formulas for disks and rings. I was going to google a sample page but there's too many to sift through and I gotta run an errand.
Welcome to the club - it's incredibly small...