Time travel does not change your current position at any given point in your time. It has been verified several times. The space station has been orbiting for over 3000 days at 8000 meters per second. The accumulated uncorrected time difference is just under 1/10 of one second. But the space station and our GPS satellites make tiny periodic clock adjustments because they understand this.

You can see that yes, you would need a really really fast space ship to notice any significant difference, approaching at least 1/2 the speed of light or more. The reality is if you could travel that fast and traveled to the next nearest star system and back, you would have aged just over a decade, but literally everyone you knew on earth would be long dead and gone.

Time travel is also lazy storytelling. It’s so freaking overdone and overused and abused. I’d be happy if another time travel plot never comes to be.

Maybe those UFOs that appear to instantly accelerate to incredible speeds are actually traveling in time rather than space. (or as well as in space).

Traveling in time is traveling in space. You need to know the coordinates of the place your going at the time you wish to be there. This would seem to be approaching a problem too difficult to solve with great enough accuracy. One would need the speed of that point and its direction at the precise time required. To solve that problem in one of my stories, the point in time and space is calculated, then the traveler is transported to a spot near enough to that calculated location to allow the traveler to move in on the target without those horrible possibilities over entering the point inside a rock or 50' above it, etc. In another I used a system of 4-brane matching, which is at best problematical. I've written several using time as the premise, but most of them ignore these problems or just give them lip service.

Oh indeed, that one would be displaced relative to the surface of the earth on several levels. To work as they do in science fiction, one would basically be teleporting through time and space.

You have to get Superman to turn the planet backwards, so everything un-happens.

Which begs the question- if he can do this to save Lois Lane, why can't he do it to solve every problem, every time?

(Secret answer- he only cares about Lois. Superman's a dick.)

Anchoring man! You gotta reference yourself (or whatever you are sending through time) to a physical thing. I’ve thought about this too. This may limit how far in time one could travel since nothing is permanent. Also it creates all kinds of questions about exactly what anchoring would be and what kind of things could be anchors. Perhaps something akin to particle entanglement.