A time travel question

Designing a time machine without taking into account spatial coordinates is like trying to build a radio that uses only electric fields. Radio waves are electromagnetic radiation and thus have two linked components, electric and magnetic.

Space and time are similarly linked as spacetime, as Einstein discovered. Any time machine is intrinsically also a space machine. Time travel stories ignore the space component for simplicity, but in this case the simplification is actually correct.

To clarify. Calculating spatial coordinates doesn't require special consideration, they are included in the time calculations. When the hero is shown to input the time coordinate he must also input the spatial coordinates but it is seldom shown. A bit like GPS coordinates shown in movies often omit altitude.

If you look into the film "Time After Time," this is partially addressed by [the fictional] H.G. Wells, where the machine actually moves west or east on the earth's surface when it travels. Moving east sends you back in time, moving west moves you forward in time, which is one reason when he went into the future to the 1970s to chase the bad guy, he ended up in San Francisco. There was also a special key he had built into the machine (which turned out to come in handy during the film's climax) where if you did not have it inserted into the machine when it was activated, your body would travel through time without the machine and you would be forever trapped that way in the 4th dimension, with no way to return.

Films or tv shows that use spaceship-type time machines address this issue a lot better, because they have to pick specific coordinates on a planet or in space in the chosen time period, not just the moment in time in which they want to go. The slingshot-thing around suns is particularly an interesting concept Star Trek brought up a couple of times.

Hollywood writers are science illiterate as a rule and the more details included, the more likely the writers will look stupid and the more likely the story will become boring. And not only does the Earth travel around the sun, but the sun around the galaxy, and the galaxy through the universe, so time travelers would travel very far indeed.