This is covered in Randall Munroe’s book *What If?*, though that scenario uses shooting an arrow in low/no gravity.
You probably know him as the author of the webcomic XKCD.
I believe the arrow eventually slows to a stop, since there are some, rare, molecules in space.
“It’s happened to all of us. You’re in the belly of a vast space station and you’re trying to shoot someone with a bow and arrow.”
(I highly recommend this book to all of you at ELI5 – he tackles a lot of interesting hypothetical scenarios like the following scenario:
What would happen if a portal opened in the bottom of the ocean? What if that portal led to Mars? How would the worlds’ land masses change?)
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