Would a time machine need to be a spaceship?

I’m glad I’m not the first person to think of the TARDIS…

I’d certainly like my theoretical time machine to have mobility, if only to account for changes to the landscape. Let’s say my lab is on the 20th floor of a modern university building. I go back to 1900, and suddenly that building doesn’t exist anymore. If I survive that mistake, I set up my machine at ground level. Then I travel back to the 1700s and sink into the former swampland my city was built on. Or perhaps I’d find myself in a dense forest, with my machine materialized inside a tree.

Possibly…from your point of view. I don’t know tech stuff

Actually I think no.

You take two gates connected by a wormhole in Year 0. You keep Gate 1 in the lab and send Gate 2 out on a spaceship traveling at the speed of light to return to it’s point of origin in 1000 years.

When you unload the ship back on Earth in Year 1000, Gate 1 will be also be in Year 1000 while Gate 2 will theoretically be back in year 0. But they will also now be moving forward in time at the normal rate. So you can only travel back and forth in time between these two gates offset 1000 years. You can probably set up additional gates for other stops in between. But you can’t go back before you invented the 1st gate.

See this is what I’m thinking of. Doc brown gets in his Delorean and decides to travel 10 days into the future. His time machine only goes through time not space (except in the way that a car moves through space), and presumably when his car disappears the forces of nature cease to operate until he instantaneously, from his perspective appears in the past or future, problem is he wasn’t “thinking 4th dimensionally” and not only are the train tracks not there but neither is the planet he used to be on.

Possibly. The other effect is that, rather than just vanishing now and reappearing in the future, your time vehicle would just appear to freeze or drastically slow down (thus remaining in place and solving the OP’s concern). If you were travelling into the future at 1/100th of a subjective second per second, bystanders would also have to exert 100 times the usual force to move you.

I can’t quite figure out what travel into the past would mean, because unlike the just-sticking-around mode of travel above, your vehicle would have to have-already-been there.

I think time travel to the past is a different class of thing to time travel to the future.