# Velocity of most distant galaxies

Taking Hubble's law into account, what is the velocity of the most distant galaxies relative to Earth? Yes, I know that it is actually space that is expanding, (so, it is not their real velocity), but at what speed relative to Earth are they receding from us?

• Roughly $3.3c$.
– pela
Commented Jun 9, 2017 at 10:52
• No it's not, it's 2.3c. @pela Commented Jun 18, 2017 at 23:08
• @RobJeffries: Yes, if you interpret the question as the most distant known galaxy. I interpreted it as the most distant galaxy in the observable Universe (assuming the cosmological principle holds true, so that there are galaxies out there, even though we won't see them because the lookback time is so large that it looks to us as though they haven't formed yet).
– pela
Commented Jun 19, 2017 at 8:12
• @pela We cannot say anything about the recession velocities of things that are causally outside the observable universe. In the observable universe we know (or think) that galaxies cannot have formed prior to redshift 20. This gives an upper limit to the recession velocity of 2.5c. Commented Jun 19, 2017 at 11:13
• @RobJeffries: I understand what you mean. It's merely a question of how the OP is interpreted. What I mean is that, if the cosmological principle holds true, then there are galaxies all the way out to the "edge" of the observable Universe (and probably beyond, but I don't consider those). These galaxies exist right now, they are at the same evolutionary state as the Local Universe, and they recede at v = 3.3c. You are of course right that, because of the finite speed of light, we look so far back in time that, to us, they haven't formed yet.
– pela
Commented Jun 19, 2017 at 13:45

The most distant galaxy currently known is at a redshift $Z=11.1$ (Oesch et al. 2016). According to Ned Wright's cosmology calculator, for a set of concordance cosmological parameters, this corresponds to a comoving distance of 9.88 Gpc (32 billion light years) and a recession velocity (now) from Hubble's law of 2.28c (i.e. 684,000 km/s).

Of course galaxies could exist at greater distances, although they do need time to form after the big bang. Theoretical simulations (e.g. Bromm 2011) suggest star forming galaxies might be present at redshifts of 20, only 200 million years after the big bang. Such galaxies, if they exist, would have recession velocities of 2.5c. This is the maximum possible recession velocity for any galaxy that is observable by us now (or in the near future).

There is no possibility of observable galaxies having recession velocities as high as 3.3c, since that would place them at redshifts of $>1000$ and they would need to have formed even before the epoch of hydrogen recombination.

However, as Pela and Zephyr are pointing out, there are (likely) galaxies that exist now, but that we cannot observe now and never will be able to measure, that are more distant than this and which are receding faster. We are reasonably sure that the universe probed by current observations of the cosmic microwave background is isotropic to comoving distances of about 14.1 Gpc (46 billion light years; "the edge of the observable universe"). Thus galaxies that are currently there, but which are just perturbations in the CMB as we see them now, will have recession velocities of 3.3c. Equally, there could be more distant galaxies than that in a much larger, or possibly infinite, universe and these could have much larger recession velocities still (that we also cannot observe or measure), and indeed they, like the galaxies we do observe, are possibly accelerating away from us.

• The question doesn't necessarily ask about galaxies known to or observed by us. As pela stated, there are certainly going to be galaxies at the edge of the observable universe which we are not observable in their present state, but they still almost assuredly exist and are receding from us. Commented Jun 20, 2017 at 12:57
• @Zephyr But then what is special about the edge of the observable universe? Galaxies will (probably) exist beyond this and have even faster recession velocities. I have struggled to edit my answer to make your point, but I'm not entirely sure what it is. 3.3c is the recession velocity of the cosmic microwave background. Commented Jun 20, 2017 at 17:37
• There's nothing special. I was just pointing out that possibly the question is asking about galaxies at the edge of the universe, be they visible or not. I think the question was just, how fast are the fastest things moving away from us (in the observable universe). I guess its all in how you interpret the question. Commented Jun 20, 2017 at 17:53

The speed relative to Earth is greater than the speed of light. This is consistent with Relativity as the space between us and the distant galaxies has stretched.

The speed is given by

$$(\mathrm{Hubble\ constant}) \times (\mathrm{radius\ of\ the\ observable\ universe\ in\ Mpc})$$

Which, as noted by Pela in a comment, is roughly 3.3 times the speed of light.

There is a general misunderstanding of Relativity. Relativity primarily uses 'Relative Time', (t) whereas the 'traveller' uses Proper time, (t0). (t) is invariably greater than (t0), and the ratio: (t)/(t0) is referred to as time dilation, or Gamma, and has the positive range only of unity to infinity. The realationship between (t) and (t0) is dependant upon a Right Triangle, wherein the base represents distance in Light-seconds, and the height represents Proper time, (t0) in seconds.
The Hypotenuse then represents Relative time (t) in seconds. If, in one second of Proper time, (t0), the vessel carrying the Proper clock covers a distance of one Light-second, then the perceived velocity, as observed by the pilot of the vessel, will be one Light-second per second. However, the 'static' observer will perceive relative time, which is here represented by the Hypotenuse of the Right Triangle, which under these circumstances will be root(2) seconds, so the Observed Relative velocity will be measured as 1/(root(2)) Light-seconds per second.

Einstein sets no limit on Proper velocity. When the Proper velocity approaches infinity, then, for any distance covered, the Height of the triangle approaches zero, so that the length of the Hypotenuse approaches the length of the base. Thus in the limiting case, where Height is zero, Base and Hypotenuse are equal, so the Reltive velocity as perceived by the static observer will be one light-second per second, or c.

Back to Hubble, and recessional velocity. Both Hubble, and Doppler work on Proper velocity.

The point I am trying to make is that space is not expanding, but Proper velocities are without limit. Only RELATIVE velocities are limited by the factor of 'c'. Dopper shift is wrt Proper velocity, and the CMBR indicates recessive Proper velocities in excess of 50,000 x c

• This is not an answer to the question. In fact, I don't really understand what it is, but it seems that most of your text would be more easily understandable with some sort of diagram.
– pela
Commented Jul 9 at 12:35
• Sadly I do not know how to put graphics here. Perhaps if you look at Einstein's thought experiment in a railway carriage, wherein time is measured using a light beam clock, where a beam is fired vertically from the clock unit on the carriage floor, and having struck a mirror in the carriage roof, is reflected back into the clock, so defining a unit of time. What Einstein then explains is that for a track-side observer, the light beam is no-longer vertical, because the carriage has moved wrt the observer while the beam is in transit, so its path is longer, so the 'tick' is longer. Commented 2 days ago
• Sorry, I don't get your point. It seems you're describing special relativity, but that has little to do with the expansion of the Universe.
– pela
Commented yesterday
• The universe is expanding, but space is not expanding. Commented 14 hours ago