Time and space are the same thing, if you’re traveling in time it seems like you could travel in space at the same time.

A time machine would necessarily need to have some way of defining what reference frame one is stationary in space relative towards, because there is no universal frame that everything moves relative to. This suggests that a time machine ought to let you move through space as well as time

Since relativity tells us there is no universal reference frame, then it having its reference tied to earth is perfectly valid.

Also sidenote: my favourite idea about time travel is that time travel is entirely possible, but will never be invented, because the timeline where its not invented is the only stable timeline. Because any timeline where it IS invented gets changed as soon as you use it, meaning the timeline changes over and over again every time time travel is invented repeatedly either infinitely or until someone accidentally creates a timeline where its never invented, only then does the timeline stop changing and we can actually experience it. So because we exist and can experience time, we can deduce that we will never invent time travel.

In most media time machines are also teleporters - many are explicitly so, with the destination space needing to be chosen at the same time as the destination time, but even when that's not shown they still make the time traveller suddenly vanish and then just suddenly reappear elsewhen.

One movie I've seen with a more "realistic" time machine is Primer. It's not at all a teleporter or portal. Very slight spoiler:

It sidesteps the whole issue that OP presents because the place where you exit the machine after traveling is just where the machine is when it's turned on to begin with. You can't time travel outside the machine, including to before it exists, and your path (in all four dimensions) is contiguous.

Guess this is why the TARDIS had to be a space ship as well.

Well, since this was posted in Science Memes, I'll be so pedantic that science does not support the idea of travelling back in time.

It does support travelling forwards in time, at various speeds, but you'll constantly be aware of where you are (even if one method involves travelling really fast and therefore may still leave you in empty space).

Time machines have been invented dozens of times since the 1800s; there's s trail of them drifting through deep space.

I like the idea that time machines are like phones in that you need a receiver to pick up the signal. A consequence is that you can only travel back to the time that the machine was turned on.

Use a space time machine. Problem solved.

This meme format having a redemption arc is my favorite. It wasn’t super sexist, but it was just unnecessarily sexist.

Someone should build a space machine so we can travel through space freely

Time machines don't exist and (as far as we know) cannot exist. Therefore, we can say they work however we want. If you can travel back in time, surely you can do that while remaining close to an arbitrary point of reference.

Jokes on you, space doesn't exist

I honestly think this would not happen because you would be time-travelling in the Earth's frame of reference

How, uh, far back in time did you want to go?

I have yet to stumble across a sci-fi short story about space travelers finding an entire civilization's worth of dead bodies floating round in space only to realize that they were all time travelers who only got part of the time traveling math correct. They figured out how to get through time but couldn't figure out how to get through space, but since all their volunteers died, they never figured it out and just kept sending people to their doom.

I think gravity is the solution to this problem. The time machine just has to be able to lock on to the earths gravitational force from across time

Why would you time travel to a position relative to anything other than the earth?