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The Hubble law states that the recessional velocity of a galaxy is proportional to its distance from us.
It takes redshift and angular sizes (for distance) of the galaxy to determine velocity, and thus rate of expantion.
But I guess the factor of direction in which the galaxy is moving may substantially affect the 'expantion rate' calculations. i.e. If the galaxy A is moving in same direction as ours, will have less relative speed and the galaxy B moving in opposite direction will have more relative speed. The actual local speed may be the same.
I wonder whether this fact can be considered when we determine the expansion rate?

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The Hubble Constant was developed by looking at dozens, then hundreds, and finally hundreds of thousands of galaxies. One galaxy can't confirm, refute or even support the theory of the expansion of the universe. –  Marc Feb 6 at 21:36
Yes. That's the point. The Hubble constant is 'constant'. Ideally, H0 should 'vary' depending upon direction of the group of galaxies to minimize the margin of error due to relative speeds. (?) –  Vivek Feb 6 at 23:03
I think Brownian motion is a good comparison. We can expect a variation around the mean, but the mean clearly increases as temperature rises (a gas) or we are looking further away (Hubble) –  adrianmcmenamin Feb 6 at 23:34
In Brownian motion the temperature applies to all the particles and hence the mean would increase. But with the 'direction', it is not the case, it will not apply to all galaxies. Hence mean H0 would be misleading. –  Vivek Feb 7 at 0:34
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Yes, it can. For instance the Andromeda Galaxy is moving towards us, due to local gravitational attraction but that does not affect the validity of the theory of the expansion of spacetime because one result based on local factors is perfectly compatible with a cosmological theory which, by definition, includes every galaxy.

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Thats true. But I asked about 'distant' galaxies, moving 'away' from each other in opposite direction. –  Vivek Feb 6 at 22:58
why would you assume the physical laws of the universe are different there than here? The point is that local effects do not affect the validity of the theory and can be accounted for as 'statistical' variations. The further away the galaxies are then the greater the metrical effect in any case, so that will dwarf the local velocities. –  adrianmcmenamin Feb 6 at 23:32
Again, its not about local velocity (not about peculiar velocity). Its about relative velocity w.r.t. our galaxy. As our galaxy is also speeding, GR should be considered. That's my point. –  Vivek Feb 7 at 0:26
The expansion is of the spacetime metric - that effects all parts of the universe - no galaxy is moving towards us as a result of this expansion, so the only other changes are precisely local changes.Think of a surface of a balloon - as you blow it up all points move away from each other. Perhaps you could clarify your thinking/question if this does not answer it? –  adrianmcmenamin Feb 7 at 7:58
Back to the balloon example, I understand that all the galaxies are moving away from us. But 'on the surface' of the balloon, the galaxy adjacent or infront of us on the next layer of balloon is moving relatively slowly compared to galaxy exactly behind (on the other side of the balloon) which is moving in 'opposite direction' (discount the peculiar/local velocity). Even when the balloon is inflating equally in all directions, relative velocity of adjacent galaxy and the galaxy on the other side of balloon w.r.t. us is different. So, is this fact cosidered when we estimate expansion rate? –  Vivek Feb 7 at 18:30
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For galaxies it's difficult to determine their proper motions, but possible with the Very Long Baseline Array for nearby galaxies.

For more distant galaxies (more than several megaparsecs), relevant for the determination of the Hubble constant, no direct measurements are available.

An overall parallel motion relative to the majority of distant galaxies would be detected via redshift as radial motion when looking in any direction other than perpendicular to the motion.

A proper motion of the majority of distant galaxies circling us as observer without or with the same radial velocity would lead over time to at least one compactification and one thinning, according to the hairy ball theorem ("Any smooth vector field on a sphere has a singular point.") This would be possible to be observed.

Large-scale isotropy and homogeneity is in parts conjectural, but e.g. supported by the cosmic microwave background, although not quite undisputed.

More about the cosmological principle.

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