8

The mining ship Red Dwarf left the solar system after the accidental radiation leak that killed the crew.

We know it travelled for 3 million years - and by the time season 1 was underway they hit light speed.

Do we know how far away from Earth the ship got?

5

According to the script for Back in the Red, Part I, the Red Dwarf is 3 million light years from Earth. I think we can assume this number has been rounded up or down slightly.

CMO: What's this rumour that we're three million light years into Deep Space, and Red Dwarf's changed shape?

HOLLISTER: That is classified information, Karen! Who the hell told you that?

Presumably the ship was traveling at a very appreciable fraction of lightspeed for the majority of its outward journey, then continued at an unspecified speed above lightspeed for several hours before finally coming to a halt. Their return journey was at a much lower speed, allowing them to stop the ship for fun and frolics.

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    That being said, the ship has traveled through time (on numerous occasions), been stolen, traveled into an alternate universe and navigated a system of wormholes. The fact that they even have the faintest clue where they are is nothing short of amazing. – Valorum Apr 1 '16 at 18:43
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    This also neglects to mention the fact that the Milky Way galaxy is only 100,000 light years wide. – Valorum Apr 1 '16 at 18:55

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