Looking at the example of the Andromeda galaxy and the Milky way galaxy.

Distance between the 2 galaxies - 2,537,000 ly = 0.78 Mpc

The closing speed of the 2 galaxies is 400,000 km/hr

Hubble constant - 260,000 km/hr/Mpc

Expansion rate of space between Andromeda and the Milky way: $$0.78 Mpc \times 260,000 km/hr/Mpc = 203,000 km/hr$$

So the relative movement __through space__ of the 2 galaxies __if there was no expansion__ would be 600,000 km/hr

Appreciated.

I will recap, the point, which is more or less quite popular, is that for nearby galaxies the cosmological expansion is overcome by gravity. This was being copy pasted or reiterated by NotEinstein couple of times, so I asked him to point out some scientific article with maths, which could establish it.

I also acknowledged that this overcome by gravity aspect appears quite plausible and prima facie non problematic to current models, but lacks maths. Exchemist naively linked back some popular article and NotEintein continued with word games.

You attempted some maths, great, but there is a problem in your argument, it does not conclude or establish that gravity overcomes metric expansion.

Lets see..

1.

1. We calculate the possible closing in speed due to gravity, say A.

2. Then we calculate the possible expansion speed due to Hubble, say B.

3. So the actual observed speed of Andromeda should be C = A-B

You have calculated B (that is 203000 km/hr, fine), and you have used observed closing in speed C (that is 400,000 km/Hr), to arrive at A = 600,000 km/Hr. Thats bad reasoning idealy should get C from A and B thus conclusively nailing it.

2.

You go one step further and make a claim that...

**At what distance is the closing speed through space equal to the expansion of space:**

$$\frac{600,000 km/hr}{ 260,000 km/hr/Mpc} = 2.3 Mpc$$

So simply looking at the current closing speed of the Andromeda galaxy, if the galaxy was 'magically' moved to > 2.3 Mpc from the Milky way galaxy, then they would be receding from each other. The actual velocity through space of the galaxy would be less than the expansion of space between the galaxies.

This is problematic. What you are implying that for Andromeda-Milky way mass with 2.3 Mpc at distance (Not Eisntein, read this carefully, you failed to understand the need of strategically massed and spaced earlier on) the relative speed between two will be nil and beyond that "only redshifts". There are no such observations, in fact there are around 7000 recorded galaxies with blue shift, many of them are at > 2.3 mpc and less bulkier (lesser gravitational effect still blue shifted).

The biggest conceptual issue which cannot be sidestepped for argument is: Hubble constant (260,000 km/hr/Mpc) is not so certain for such small distances. Hubble applicability is quite reliable if we talk of d > 1 bly, something more than 100 times the distance between Andromeda/MW. Face it, we have absolutely no observation of expansion at such cosmological small distance (2.3 Mpc).