How fast do galaxies 1 billion light-years away move away from us?

[Dreksler]

TL;DR Summary

If a galaxy that is 1 megaparsec away from us is moving away at a speed of 70 km/s. Does that mean that a galaxy that is 312 megaparsecs away is moving away at a speed of 22k km/s (312 times greater speed)?

We know that galaxies that are 1 megaparsec away from us (3.2 million light-years) are moving away from us here at a speed that is approximately 70km/s. Given that that is the case would that also imply that galaxies that are 312 megaparsecs (1 billion light-years) away from us are moving away from our position here at a speed of about 22,000 km/s?
Since they are 312 times further away would they also recede from our position here at a speed that is 312 greater?

 

[PeroK]

Yes, recession velocity is proportional to distance.

 

[phinds]

Summary:: If a galaxy that is 1 megaparsec away from us is moving away at a speed of 70 km/h. Does that mean that a galaxy that is 312 megaparsecs away is moving away at a speed of 22k km/h (312 times greater speed)?

We know that galaxies that are 1 megaparsec away from us (3.2 million light-years) are moving away from us here at a speed that is approximately 70km/s. Given that that is the case would that also imply that galaxies that are 312 megaparsecs (1 billion light-years) away from us are moving away from our position here at a speed of about 22,000 km/s?
Since they are 312 times further away would they also recede from our position here at a speed that is 312 greater?

Your use of "velocity" and "speed" is incorrect. The movement you are talking about HAS to be described as "recession velocity", not velocity or speed because those terms imply proper motion and there is none (or only a trivial amount) in the cases you are describing. You'll note that Perok was careful to say "recession velocity" because of the condition I just stated. That is, recession is NOT movement in the way you normally think of movement.