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.
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).
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.
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.
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'd like to believe that mass (and then by extension the Earth) "defines" the spacetime around it as much as it distorts spacetime near it. I suspect this may even be the underlying cause for the observation of speed of light being constant in the presence of earth/solar/galactic movement.
Ahummm, well actually, * adjusts monocle * time travel is not possible and since nobody has invented time machines yet, neither of these scenarios would happen in reality.
So either we would have to invent teleportation along with time travel/ have some sort of "magnet pad' that must exist and not break at all times on earth, or its the time machine type where it just fast forwards everything around you until somehow you're in a mall
If I was writing a fiction and felt the need to address this, I would make it so where you wind up is based on the location of the time machine in the time you travel. But also I probably wouldn't and just handwave it
It’s my belief that Time Machines aren’t immune to the effects of gravity. When time changes, the machine goes to the space it would be at if it was affect gravity for the whole time.