Question concerning Time Travel locations

[Agamemnon]

Now be gentle with me on this one please!

Right then, after a good night's entertaining with friends a question was raised in a humourous manner..........."If I travelled back in time, say 500 years to 1507, would I still be in the same place"?
Now the meaning to this question is that when you generally see time travel portreyed, the person(s) travelling back in time start and re-appear in the same spot on the earth, with just their surround different. Our question was that with the changing path of earth's orbit, and the moving of continents, and the revolution of the earth itself, someone travelling back in time from say, Times Square in New York in 2007, could re-appear somewhere in the Atlantic ocean in 1507!
Is this possible, or am I ballsing the time travelling theory up completely?

[Samadhi]

Well, it's even worse. The earth is rotating around the sun. And the sun is rotating around the center of the galaxy at some ungodly speed. And then there's the expansion of the universe.

Yeah, your best case is that you end up in vacuum (probably 99.9999%+ likely), next most likely but clearly the worst, you'd find yourself merging with solid matter somewhere that would be really uncomfortable (probably 99.9999%+ or the remainder), then there's the off chance you actually appear, say, on the surface of a planet that has an atmosphere/gravity/etc that you can survive.

Oh and I probably undercut those probabilities by an incredibly unimaginable amount.
_________________
And he lived happily ever after. Except for the dieing at the end and the heartbreak in between.

[Chuck]

No matter what your intended destination, you'd probably end up in 20th century Los Angeles. Many time travelers end up there in time travel movies.

We're all traveling forward slowly through time right now and not changing our locations relative to the earth. Maybe if you travel backward slowly you'd stay put.

[Lepton*]

If you can travel arbitrarily through time, you should be able to use the same technique to travel arbitrarily through space. Then it just becomes a matter of finding a covariant reference frame against which to operate (no small task!).

[raekuul]

Aguably, a time machine should use the time and 4-space coordinates adjusted to the origional frame of reference. Take Resurant at the end of the universe for example. They specified no 4-space coords, so they went to the nearest resturaunt in 4-space, regardless of the time.