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If a place is 500 light years away, then I set out to this place, then is it true to say that, the place which I set out from, will be 750 light years away from my destination, once I have reached it?

I am thinking of expanding space, as the reason for the additional distance possibly accumulated. Also to be considered for other galaxies separate from our own. Also what would be the estimated increase in the distance would it be half as much, or a quarter or third?

If the speed of light is 186 282 miles per second, then what would be the distance of expansion accumulated which occurred within the time it would take for a craft traveling at this speed to reach a galaxy beyond ours, or even a distance of 500 light years away, obviously there are innumerable distances of light years which could be applied to this calculation.

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    $\begingroup$ @DialFrost This is a repost of a question from a few weeks ago which was automatically deleted because the system thought it was abandoned. Some of the info in the question was added in response to comments. $\endgroup$
    – PM 2Ring
    Nov 3, 2022 at 5:31
  • $\begingroup$ @PM2Ring Ah my bad, I didn't look closely enough (I can't see deleted questions either) :3 (Close vote retracted) $\endgroup$
    – DialFrost
    Nov 3, 2022 at 5:34
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    $\begingroup$ 500 light-years from Earth is well within the Milky Way galaxy. As such, the overwhelming effect on the distance between your origin and destination on arrival is the relative motion of the two objects and your travel time, not universe expansion. $\endgroup$
    – notovny
    Nov 3, 2022 at 10:16
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    $\begingroup$ Not even just the overwhelming effect, but the entire effect! The galaxy isn't expanding. $\endgroup$
    – Sten
    Nov 3, 2022 at 13:40
  • $\begingroup$ You can't have a spacecraft travel at the speed of light. $\endgroup$
    – ProfRob
    Nov 5, 2022 at 18:11

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For the specific question on travelling to a point 500 light years away, the answer is no. There is enough matter in the Milky Way to keep space from expanding inside the Milky Way. So if the destination is not moving relative to the Earth, then it will still be 500 light years away when you reach it.

If you are travelling to a distant galaxy that is 500 000 000 light years away, then the expansion of space does become significant. The expansion of space means that the distant galaxy is moving away from the Earth, so by the time you reach the galaxy (in more than 500 000 000 years) it will have moved further away. The distance it had travelled would depend entirely on how long you had taken to reach the galaxy, and so would depend on your velocity.

There although distant galaxies are moving away from us due to the metric expansion of space, there is nothing very strange happening here. If I am running to catch up with a friend, but my friend is walking away from me, then I'll need to account for their motion.

Over even longer distances, the length of time required means that assumptions like "the rate of expansion is constant" are no longer valid.

But over "short" distances, like 500 lightyears, space isn't expanding.

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    $\begingroup$ Thanks for your swift response James, and for your understanding of what I meant when applied to galaxies beyond our own, it is very much appreciated 👍👌. $\endgroup$
    – Lux Magi
    Nov 6, 2022 at 6:57

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