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Andromeda is about 2.5 million ly away.

Actually, in this universe, at what "speed" (in km/h) are two objects separating cosmologically - I mean strictly due to the "expansion of the universe" - if they are 2.5 million ly apart?

I do understand that local "ordinary" or "peculiar" motion completely swamps this effect. If I'm not mistaken, the "local" "ordinary" motion of Andromeda per our galaxy happens to be about 400,000 km/h towards us.

Is the "speed" due to the "expansion of the universe" drastically smaller than this?

I assumed that the expansion of the universe (or "of the spacetime metric") is even everywhere: it's well known that it only affects "the largest structures" but I still assumed that the expansion is the same in my room, my galaxy, my cosmological region. Perhaps this assumption is totally wrong?

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The rate of expansion, measured in the customary units of (km/s)/Megaparsec is not known with great accuracy. Recent measurements include 67.6 (SDSS-III), 73(HST) 67.8 (Plank) 69.3 (WMAP) [wikipedia]

The Andromeda galaxy is 0.78 Mpc from us, so taking the Hubble constant to be about 70, gives a recession of about 55 km/s. This is not a very great speed: compare with the orbital velocity of the sun around the galaxy at over 200 km/s, or the escape velocity of the galaxy (over 500km/s)

As you note, this is pretty much swamped by the proper relative motion of our galaxies. Its blueshift indicates that Andromeda is approaching us at over 100 km/s. For galaxies outside of the the Local group, the Hubble flow dominates.

Now the value of 55km/s assumes that space is smooth and homogeneous. This is approximately true on a universal scale, but it is not true on the scale of a galaxy cluster, where local gravitational effects dominate the curvature of spacetime. The general expansion of spacetime has very little effect on the motion of galaxies in the local group, as discussed by Iorio's paper on the motion of a gravitationally bound binary system

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    $\begingroup$ Whoa! Thank you so much for the prompt answer - which is very clear, thanks - so the answer is 200,000 km/h. That's amazing, totally unbelievable. I thought it would be some tiny figure like "ten km/h". So Andromeda is "really" moving towards us at 600,000 km/h, the metric expansion of space is 200,000 km/h, resulting in 400,000 km/h towards us. Fantastic, amazing, surprising. $\endgroup$ – Fattie Oct 6 '16 at 16:15
  • $\begingroup$ Again I'm astounded to learn that that hubble flow, if you will, between us and Andromeda is the same order of magnitude as our local jiggly motion: I thought, James, the answer would be maybe nine or ten orders of magnitude smaller than it is. Amazing! $\endgroup$ – Fattie Oct 6 '16 at 16:21
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    $\begingroup$ @JoeBlow You misunderstood. The expansion of space is hardly affecting the Milky Way to M31 separation. The apparent velocity is not the vector sum of two effects. The Friedmann eqn that leads to Hubble's law assumes that the density of the universe is smooth and homogeneous. It isn't on small scales like the local group. $\endgroup$ – ProfRob Oct 6 '16 at 17:35
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    $\begingroup$ @JoeBlow, to echo Rob Jeffries, when James K says that Andromeda is moving towards us at 100 km/s, he means that is the actual measured velocity of Andromeda approaching us. You shouldn't add in the expansion of the universe to get the "real" value; 100 km/s is the "real" value. $\endgroup$ – NeutronStar Oct 6 '16 at 18:41
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    $\begingroup$ @JoeBlow Just looking at this paper: the consensus appears to be that a gravitationally bound 2-body system does not experience any expansion effect at all (in GR). arxiv.org/pdf/1208.1523v4.pdf So it is not that the effect is "swamped"; it is not there at all. $\endgroup$ – ProfRob Oct 6 '16 at 21:22

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