

Well, it depends. I mean the original story “The Time machine” I think very deliberately had a machine that was on the ground. I guess if you’re “travelling” through time then you could follow your local location in the same way you do when it is moving forward at the normal rate.
The argument is more true for time machines that instantly move through time, like back to the future. Since yes it would need some way to account for planetary movement.
No, he used a Delorean because of the style, and something about the stainless steel construction that we’ll never know the rest of. :P