Time travel from stationary position?

This is my first question on this site, which I recently found and can't get enough of.

In many time travel scenarios, the machine is static in space. My question is how to explain this. For example, in HG Wells' works, it's always in the same location. I'm referring the earth rotating around the sun, as well as the sun moving across the cosmos.

Even if you made a timeship, moving a couple hundred years could mean light years, without FTL you are stuck in deep space.

I have also contemplated using a time machine as a sort of FTL calculating some time in the past or present when another star system will be in the same location we currently are.

Is there a realistic answer to why we stay grounded in the same space while moving through time? It might be easily answered by the theory of relativity, and I just don't understand.

Note: I'm not thinking about using near light speed time travel, because obviously you would be moving anyway. Thinking more of the getting inside and flipping some switches.

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Time travel from stationary position?

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