[tlb]

The constant rotational speed is the observation that requires dark matter to exist. Otherwise, small galaxies would rotate faster just like close planets do.

[marcosdumay]

Dark matter theory tells why galaxies rotate faster than they should. The fact that this speed is constant requires some other explanation.

[avip]

It's not "constant" though, it's "cosmologically constant". Cosmologists would routinely assert that 1 == 1000 holds true.

[tzs]

Couldn't a large galaxy rotate as fast as a small galaxy, without the need for dark matter, if the large galaxy had a sufficiently more massive black hole at its center than the small galaxy.

The formula for the orbital period around a central mass is:

               3  1/2
           /  R  \
  T = 2 Pi |-----|
           \ G M /

where T is the period, R is radius of the orbit, G is the gravitational constant, and M is the mass of the central body. That's Newtonian, but I think that is good enough for this.

This says that if Big Galaxy has a radius k times that of Small Galaxy, it won't rotate slower than Small Galaxy as long as Big Galaxy's mass is at least k^3 times Small Galaxy's mass.

[salty_biscuits]

You are right that this could explain the velocity at a particular radius, but it's the radial velocity profile as you go out that hints at dark matter. The velocity as a function of radius is strange.

[wuliwong]

I don't believe it is just one thing. I believe the observed shape of galaxies is another problem that is dark matter is a proposed solution.

Edit---

I was just reading more and there is also the fact that galaxies stay together at all. Apparently without including dark matter, they wouldn't "hold together." Sounds like the problem with the atom back before quantum mechanics. :)

[Retra]

Dark matter also has a measurable gravitational lensing effect, as I understand it.