Gregory Benford’s book, Timescape dealt with the Earth’s movement, though the time travel wasn’t physical. In an attempt to change the past just enough to avoid ecological disaster, a lab in 1998 had to aim a tachyon beam at a lab in 1962, which was running an experiment that might be capable of detecting the types of anomalies interactions with tachyons could cause. That meant that they had to calculate the Earth’s movement relative to their own with a fairly high degree of precision. An unintended effect was that one of the scientists who got involved in the past project ran with the idea that it was an alien message, since the beam was coming from the vicinity of a prominent galactic cluster, near where the 1998 Earth would be in the sky relative to the 1962 Earth.
Aren’t time and space entwined in such a way that travel through one means travel through the other anyway? What I mean is that should you travel through time you would also be traveling through space to the correct point (disregarding the frame of reference issues)
You still haven’t explained why you feel that you need to time travel with a Hoover bag over your head.