All or most time travel sci-fi assumes that the Earth isn't moving, because that's inconvenient. They focus on fixed points on Earth, but that's bunk. If time travel was based on a fixed point within our universe (whatever that means):
The Earth spins at about 1,675 km/hour at the equator. Ignoring all other movement, time travel forward or backward by 12 hours would put you on the other side of the Earth (likely in a mountain, or above the surface - extremely unlikely to re-appear with your feet on the ground).
The Earth revolves around the Sun at 18.5 miles/sec. If you are on the trailing edge of the earth and time-traveled 1 second into the past, you would appear 18.5 miles above the Earth. And about half a mile due East of your original position. Again, assuming that all other movement through the Universe doesn't exist.
The Sun revolves around the center of our galaxy at about 500,000 miles/h or 139 miles/sec. So we're actually moving 139±18.5 miles per second...considering the scenario above, you're more than halfway to the Moon's orbit.
The Milky Way itself is moving through space around "The Great Attractor" at approximately 1,300,000 miles/hour or 361 miles/sec. So now we're moving at 361±139±18.5 miles/sec or somewhere between about 518.5 and 203.5 miles per second, relative to "The Great Attractor", depending on the phases of each of our orbits. And who knows how fast that is moving through our expanding universe?
The only logical way around this, I think (besides a bunch of really complex math and uncanny precision with your time travel device) would be to create "time markers" you can jump to. This pretty much eliminates any ability to go back to the time of the dinosaurs. But when you walk through the time portal you create, remember that you could be dumped out onto your head...so be careful!
