But the location they started out at moved so the same space at a different time would be the vacuum of space and not the planet.A problem I have had with time travel stories recently is where the time machine moves through time but not space but they forget that the earth is not a static location. It moves all the time. When Marty went back to 1955 he shouldn't have ended up at that farm. He should have wound up in the cold vacuum of space.
No, because they are traveling through the time/SPACE continuum. Time and space are inseparably linked.
So you seriously think a device SO complex it can enable travel through time wouldn't, in all of the equations and variables presented, consider to adjust for the movement in space as well? Really?