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The cosmic microwave background radiation should provide kind of a global reference frame, because you can determine your speed relative to it using the redshift.

Is it known how fast we are moving in relation to the CMB? If you subtract the various orbital motions (Earth around the Sun, Sun around the Galaxy), are we standing still in the expanding universe, or traveling in a certain direction?

cuckoo
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Yes, our (i.e. the Sun's) motion in the "global", or comoving, reference frame can be measured accurately from the dipole of the cosmic microwave background. The latest results from the Planck Collaboration et al. (2018) yielded a velocity of $$369.82\pm0.11\,\mathrm{km}\,\mathrm{s}^{-1} $$ in the direction $$ \begin{array}{rcl} \ell & = & 264.021º\pm0.011º\\ b & = & 48.253º\pm0.005º \end{array} $$ (in Galactic coordinates).

Since Earth orbits the Sun with some $30\,\mathrm{km}\,\mathrm{s}^{-1}$, there's a small, biannual correction to this result. On much larger timescales ($\sim100\,\mathrm{Myr}$) our motion round the Milky Way alters our comoving velocity with the order of $\sim100\,\mathrm{km}\,\mathrm{s}^{-1}$.

pela
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    How can the Planck results be precise to 0.11 km/s if there's a 60 km/s correction depending on the time of the year? – Allure Sep 27 '19 at 22:27
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    @Allure: The Earth's orbital velocity around the Sun is quite well known already. And even if it wasn't, they could just average it out over a whole year (or several). – Ilmari Karonen Sep 27 '19 at 22:30
  • @IlmariKaronen I was thinking more of, if the question is how fast are we moving with respect to the CMB, a precision of 0.11 km/s doesn't make sense because of the seasonal variation. Thinking about it, the quoted value of ~370 km/s must be the Sun's velocity with respect to the CMB. – Allure Sep 28 '19 at 03:33
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    @Allure Yes, exactly; that's why I wrote "our (i.e. the Sun's)" :) – pela Sep 28 '19 at 06:36
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    How can you move relative to the CMB when its expansion is always directly away from you in every direction? – nick012000 Sep 28 '19 at 10:00
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    @nick012000 Because what you've said isn't true. The small departure from this isotropy is what leads to the measurement quoted in the answer. – ProfRob Sep 28 '19 at 11:46
  • @RobJefferies My understanding is that inflation works like the “ant on an inflating balloon” metaphor where space between points on the balloon continuously increases without there being a “center point” for the expansion, and that motion of the ant relative to other objects is equivalent to the ant remaining stationary while everything else is moving around it. – nick012000 Sep 28 '19 at 14:29
  • @nick012000 Great, you've covered inflation. Now imagine that, in addition to that effect, the ant is simultaneously walking across the surface of the balloon. The sun isn't just plonked in the Universe and doesn't move at all. It's part of a vast network of interacting objects. Expansion of the universe notwithstanding, the Sun is moving in the Universe (e.g. around the Milky Way, and then there's galactic movement to consider, etc) – Lightness Races in Orbit Sep 28 '19 at 16:37
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    Personally I'm surprised it's so "slow". Nice calculation! – Lightness Races in Orbit Sep 28 '19 at 16:39
  • @LightnessRacesinOrbit Not just inflation. “that motion of the ant relative to other objects is equivalent to the ant remaining stationary while everything else is moving around it.” – nick012000 Sep 28 '19 at 20:46
  • @nick012000 You're right, this is not just inflation, but the analogy is good enough: Galaxies in an expanding universe (also inflationary expansion, though there were no galaxies around then) are like ants on a balloon surface. But the ants also crawl around slowly, which is exactly this so-called "peculiar" velocity that I quote above. – pela Sep 28 '19 at 20:51
  • @nick012000 That doesn't mean nothing moves. – Lightness Races in Orbit Sep 28 '19 at 23:46
  • @LightnessRacesinOrbit That's probably because there are no massively massive superclusters around into which the Home Galaxy can fall. – David Tonhofer Sep 29 '19 at 08:50
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    @nick I'm sure you've seen CMB images like this, which show that the CMB is isotropic to better than one part in 10,000. Such images have been corrected for our peculiar motion; otherwise, the CMB details would be swamped by the Doppler effect of the peculiar motion. A raw map of the CMB (i.e., without that correction), looks like this. – PM 2Ring Sep 29 '19 at 09:41
  • @DavidTonhofer That's a relief ;) – Lightness Races in Orbit Sep 30 '19 at 10:33
  • @LightnessRacesinOrbit A bit further there is the Great Attractor though, sadly invisible because hidden from view behind the galactic disk; which is also apparently not so great and may be surpassed by other Greats. It's the Nightland out there. – David Tonhofer Sep 30 '19 at 15:15