The diagram from Hubble's original data only goes from 0 to 2 Mpc (see here), and yet our Local Group is not supposed to be expanding and it is 1.5 Mpc in radius. How can the data show that the universe is expanding when it mostly just includes the Local Group?
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The original diagram is I think referring to this one (with mislabelled y-axis units):
If you estmate the Hubble constant ($H_0$) from the solid straight line, you get $H_0 \simeq 500$ km/s per Mpc. This is about 7 times as big as the best estimates of $H_0$ today.
There are two reasons for this:
(1) Hubble was slightly fortunate; the galaxies he looked at were relatively nearby and not fully immersed in the "Hubble flow". In other words they would have been quite badly affected by the scatter caused by local peculiar motions, leading to a very noisy estimate of $H_0$. The scatter around the straight line is about 150 km/s.
(2) More imprtantly, Hubble got the distances wrong. The most distant 4 galaxies are in the Virgo cluster; a present-day distance estimate is 16.5 Mpc, i.e. 8 times further away than Hubble estimated. This means his Hubble parameter was about 8 times too big. Note that the distances, estimated in a few cases from Cepeid variables, but mostly using the apparent magnitudes of the brightest star(s) in each galaxy, would be uniformly wrong. i.e. It is just a calibration/scaling error on the x-axis, which should be about 7-8 times bigger.
A horizon of 16 Mpc for a Hubble diagram is still not very big and the peculiar motions of galaxies around the general Hubble flow would still play a big role here. Ideally, you would want measurements at $>50$ Mpc and Hubble diagrams today do cover a much larger volume of space. See for example Figure 3 in Kirshner (2003), showing a Hubble diagram for galaxies with type Ia supernovae going out to around 700 Mpc. More recent work expands this to several Gpc.
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$\begingroup$ Ah, yes, I remember now! I know that our local group is not expanding but is the space within it still expanding and the gravity holds everything back, and can we still use the cosmological redshift measurements, within it, after allowing for any peculiar velocity? $\endgroup$ Commented Jan 30 at 13:47
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$\begingroup$ This editor redlights REDSHIFT. Should we use 1 word or 2? $\endgroup$ Commented Jan 30 at 13:48
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1$\begingroup$ @CuriousCat: The Stack Exchange editor has no proofreading features, it's your browser (and/or OS and/or third-party software) doing that. Presumably its built-in dictionary was not compiled by cosmologists (but is at least still comprehensive enough to include the common English words "red" and "shift"). $\endgroup$ Commented Jan 30 at 19:49
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I don't know which Hubble diagram you're looking at but modern Hubble diagrams go up to hundreds of Mpc (see e.g. https://www.pnas.org/doi/10.1073/pnas.2536799100 Fig 3), well in the range where dark energy dominates.
If you're looking at Hubble's original diagram, do remember that the distance ladder has been much more accurately calibrated than in his day; we are able to estimate astronomical distances much better than Hubble could.
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$\begingroup$ Yes I did mean the original one. Yes but my question is still valid. $\endgroup$ Commented Feb 9 at 15:49