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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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2 Answers 2

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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, 2016 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, 2016 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, 2016 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. $\endgroup$ Oct 6, 2016 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, 2016 at 21:22
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Andromeda is moving toward us. It isn't a peculiar motion superimposed on a cosmological recession; it's just ordinary relative motion.

The FLRW geometry is not a background of expanding space on which matter moves. It's just what you get when you stitch together a bunch of Schwarzschild patches representing individual moving objects. If you zoom in, you see masses moving past each other, orbiting each other, and occasionally colliding. If you zoom out, you see a bumpy spacetime manifold with roughly the shape of a FLRW manifold. The farther you zoom out, the smaller the bumps look.

You can model the evolution of the universe at a large scale as a FLRW manifold, or you can model it at a smaller scale as individual gravitating lumps, but if you do both and add the results, you'll get nonsense (or, at best, twice the correct answer). There are surprisingly many published papers that do that, and the paper by Iorio that is mentioned in James K's answer is one of them. Iorio considers "a localized gravitationally bound binary system immersed in an expanding Friedmann-Lemaître-Robertson-Walker", or to put it another way, a system of clumped matter immersed in the same matter, but unclumped. The unclumped matter isn't there, so none of the effects considered in the paper exist.

See this longer answer that discusses another paper that makes the same mistake.

(If you're wondering how ordinary relative motion can lead to superluminal expansion at large scales, see this answer to the question "Can space expand with unlimited speed?". The short version is that superluminal recession speeds are possible even in special relativity if you use the cosmological definition of recession speed.)

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  • $\begingroup$ I'll have to take quite a bit of time to really comprehend this and the implications! $\endgroup$
    – Fattie
    Sep 19, 2022 at 15:09
  • $\begingroup$ At this point, it sounds like "the expansion of the universe" is completely undefined, and there is no decisive agreement or understanding as to what it is or even means. (Perhaps like the various "interpretations" of quantum physics.) $\endgroup$
    – Fattie
    Sep 19, 2022 at 15:10
  • $\begingroup$ @Fattie It's not completely undefined. It's a description of the shape of the spacetime manifold on a large scale. It's statistical like temperature, so there is a little but of fuzziness in it, but it's still well-defined to high precision. This isn't like quantum interpretations, which, if they're really just interpretations, make the same predictions as standard QM for every experiment. Iorio's paper says that a certain force exists that doesn't exist according to the standard cosmological model. It's just a mistake, not an alternate model. $\endgroup$
    – benrg
    Sep 19, 2022 at 15:27
  • $\begingroup$ It seems difficult to get a straight answer on questions like "is 'space itself' expanding, or is stuff expanding in the background 'space'"? There indeed seems to be various philosophical-level "interpretations" of the issues. I bet, you could provide better answers to these questions for example! :) physics.stackexchange.com/q/235654/10319 $\endgroup$
    – Fattie
    Sep 19, 2022 at 18:04

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