Does time exist in space?

time is a human concept, it's simply a measurement

we used the earth as a reference

so in answer to your question, let's say you jumped in a space ship and zoomed off to a distant planet 1,000,000,000,000 light years away

Time would exist, if you wanted it to. You would have to create the measurement based on the characteristics of the new planet you landed on. You could say a year would be the time the planet circled it's sun. The only issue is that planet could circle it's sun in the same amount of time our planet circled our sun 100 times.

so 100 years on earth, would be 1 year in your measurements. You could use a different reference, say the new planets moon. or you could use our existing measurements, but that would be silly if you were on the other side of the galaxy. It's like saying aliens use our measurement of time, which would be highly unlikely.

does that make sense?

Yes, so what is the measurement in space? How do you calculate velocity without a time concept?
 
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