Do you think it's possible?
What's strange in those time-travel stories is that "space" is omitted out of the equation. Time and space are very closely related. A time machine should be able to do space traveling. Even John Titor said that the first problem they had with their time machine is that the machine would re-appear elsewhere, and it puzzled the engineers for a while (it was because the Earth is in motion, while the machine wasn't when operating.) Where are all the space travelers' stories?
This is a very insightful comment,... It sometimes pays of to waste time here
A "straight" time jump of even a few seconds would leave you in cold space. But that's assuming that time travel would somehow use a "fixed" referential. But if there is no such thing, there could still be problems, if time translation warps space translation.
You would add teleportation woes to timetravel headaches.
Not only earth is moving, the system and the galaxy are in motion as well.