How far away are the galaxies?

In 1929 Edwin Hubble discovered that the light of distant galaxies is redshifted.
This Doppler shift toward longer wavelengths indicates the source is moving away from us.
The familiar acoustical version is the drop in pitch of a siren as an ambulance rushes past us.
Hubble deduced the universe is expanding.
(This is a consequence of Einstein's original cosmological model, but Einstein first rejected it as philosophically unacceptable.)
Indeed, Hubble's law is that the velocity V of recession of galaxies is proportional to their distance R from us. Specifically,
V = H⋅R
The constant of proportionality is called Hubble's constant; measurements of Hubble's constant are the basis of estimates of the age of the universe.

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