I've come across an issue with the concept of time travel that has been bugging me for a while now. I'm gonna use Back to the Future for my first example to get the idea across.
In Back to the Future, Marty McFly travels from October 25th, 1985 to November 5th, 1955. My issue is that not with the actual moving through time, but moving through space. In 1985, the location he starts at is a shopping mall, but when he arrives in 1955 he is outside the city because the mall hasn't been built yet. I think for it to be accurate he should have ended up in the middle of space with Earth nowhere insight. We used years to measure how long it takes for our planet to go around the sun, so we'll say for now that if he had come back to October 25th, 1955 that this might have been okay. But instead he came back 11 days later, with the planet having moved about 17 million miles away from where it was when he left.
The other issue is that not only is our planet constantly moving, but our solar system as well as everything else in the universe is constantly moving as well. I think the answer to maintaining your relative position to an object when time traveling requires the gravity being a component in your method. In that regard, I think Star Trek IV: The Voyage Home makes the most sense as far as keeping your relative position while traveling through time. In Star Trek, the former crew of the Enterprise slingshot around the Sun at warp speed to arrive 300 years in the past. Because the gravity of a massive object like the sun was a vital component in this method, it makes a lot more sense to me that they would arrive in the same relative position that they started in.
Anyways, this is not something that I think there's really an answer for since time travel isn't something that we know anything about. Atleast it will give me something to talk about next time I meet an astrophysicist.