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How are redshift, (recessional) velocity and distance of a galaxy related? I understand what v=HD states. So I assume that Hubble measured a direct relation between the distance and recessional velocity of a galaxy.

I get confused about the relation between the redshift and the other two. Is there a direct relation between the redshift and the distance and between the redshift and the velocity of a galaxy?

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Welcome to StackExchange. Good question. Hubble's Law says that an object's velocity away from an observer is directly proportional to its distance from the observer. In other words, the farther away something is the faster it is moving away from us. The redshift tells how fast a star is receding from us and we can therefore get the distance. Hubble's equation states that $v\ =\ H_0\cdot D$ where $H_0$ is Hubble's constant. It makes sense that the further away a star is the faster it has been moving.

The redshift is measured for a star and for small velocities relative to c it can be written that $z \approx \frac{v}{c}$. For larger speeds the equation is $z \approx \frac{H\cdot D}{v}-1$

A good general description is given here.

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