If I had two tennis balls, one meter apart, at what velocity are they moving away from each other due to Hubble flow? (Assume they are in a zero G environment, and nothing impedes their movement.)
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I'm amused that you ask for "understandable" distances - given that as the answers show, all this gets you is "un-understandable" speeds. – Kyle Oman Jun 03 '15 at 21:06
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Good point. Except something very slow is similar to 0. Something really huge is hard to grasp. – Jiminion Jun 03 '15 at 21:09
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Astronomers often get questions like "How can one grasp such crazy distances and masses?" I don't think we really think of a number like 1e22 or 1e-22 being vastly different from 1, and I think the reason is that we tend to think logarithmically. That is, we compare numbers like 22, -22, and 0. Then we never have to consider numbers larger than (±) 100. Would you agree, @KyleOman? – pela Jun 04 '15 at 07:19
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By that notion, then basically every number is 1. I think in terms of domains of where stuff works. Hubble is obviously at work at the supra-galactic level. Even makes me wonder if the phenomena could perhaps be explained by other means. – Jiminion Jun 04 '15 at 13:48
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1@pela Well, we do compare logarithms, but it's important to keep in mind that 10 orders of magnitude is a factor of 10 billion - and even more important to emphasize this when talking to the public. In fact it's probably best to avoid scientific notation and logs in this case. It gets tedious talking about "factors of a billion billion" and such, but realistically I think that's often the best strategy. – Kyle Oman Jun 04 '15 at 15:09
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@KyleOman: I agree! – pela Jun 05 '15 at 15:36
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Can we talk about points in the intergalactic medium instead (i.e. between the galaxies and thus far from any gravitating matter), rather than two tennis balls? Because on such small scales, the Universe doesn't expand, instead being held together by gravity.
Anyway, the present-day Universe expands at a rate of $H_0 = 70\,\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$. That means that if the two points are 1 Mpc apart, they recede at $70\,\mathrm{km}\,\mathrm{s}^{-1}$. If they are 0.5 Mpc apart, they recede at $35\,\mathrm{km}\,\mathrm{s}^{-1}$, and if they are 1 m apart, they recede at $$v_\mathrm{rec} = H_0 \, d = 70\,\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1} \,\times \, \frac{1\,\mathrm{m}}{3.08\times10^{22}\,\mathrm{m}\,\mathrm{Mpc}^{-1}} = 2.2\times10^{-21}\,\mathrm{km}\,\mathrm{s}^{-1}.$$
You can compare this to the gravitational field from a tennis ball at the distance of $r = 1\,\mathrm{m}$. A tennis ball weighs $m_\mathrm{tb} = 58.5\,\mathrm{g}$, so the acceleration is $$g = \frac{G\,m_\mathrm{tb}}{r^2} = 3.9\times10^{-10}\,\mathrm{cm}\,\mathrm{s}^{-2},$$ which is small, but sufficient to accelerate the tennis balls to collide with each other in roughly $t \sim \sqrt{2r/g} \sim$ one week, with a terminal velocity of $3\times10^{-4}\,\mathrm{cm}\,\mathrm{s}^{-1}$, i.e. 12 orders of magnitude larger than the expansion of the Universe.
Oh… now I ended up talking about tennis balls anyway…
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@Jiminion The intergalactic medium is a fancy term for saying the space between galaxies – Jim Jun 03 '15 at 15:13
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@Jiminion: JimtheEnchanter got it right; I edited the text, and also made a comparison to the mutual attraction of the tennis balls. – pela Jun 03 '15 at 19:16
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Hubble Constant is about 70 km/sec per Megaparsec.
Given the Milky Way Galaxy is about 34K parsecs in diameter, that means the velocity between the edges of the galaxy due to Hubble Flow is about 2.38 km/sec.
With additional math, we can see two objects 1 meter apart are moving away from each other at about 2.26x10^-18 meters/sec. So after 10,000 years, they would be 10^-7 meters further away from each other.
Not sure of the math exactly, but it is clear Hubble flow is really small at understandable distances.
Jiminion
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