1 {scene: the Jurassic}
1 Terry: Quick! Activate the time machine!
1 Jane Goodall: We need to check the settings first. It could take us anywhere!
2 Terry: The question is, will it be taking us in one piece, or ripped into multiple bloody chunks?!
2 Allosaurus: RAAARRRHH!!
3 Jane Goodall: It depends. Some time machines don't permit the passage of living...
3 Terry: Aargh!! {presses a button on the time machine as the Allosaurus approaches}
3 SFX: press
4 SFX: ZUUURCH!! {they all vanish, including the Allosaurus}

It's a common and convenient assumption in many time travel stories that the time machine is capable of travelling not only in time, but also in space. This is often to avoid raising the awkward question of where exactly you end up if you travel in time, considering that the Earth is (a) rotating under you, (b) moving through space in its orbit around the sun, (c) moving around the centre of the Galaxy with the sun, and (d) drifting through intergalactic space along with the Galaxy.

To any sensible first approximation, for each year you travel through time, you should end up several million kilometres away from Earth.

Some authors explicitly get around this by proposing that the time vortex or whatever anchors itself to a local gravitaional field or somesuch, which effectively means that when you travel through time you end up in the same location on the surface of the Earth as when you left. Which is fine as far as it goes.

The first problem here is that the surface of the Earth moves up and down over large timescales. If you travel back a few tens of thousands of years without moving relative to the Earth, you're likely to end up either in mid air or buried inside rock. Again, this can be handwaved with some sort of appeal to local gravitational strength relative to an underlying geoid, or equipotential surfaces, or something similarly technobabblish. Which, again, can be fine if that's the way you want to go.

But the easy way out without appealing to technobabble is simply to posit a time machine that can also make arbitrary trips through space at the same time as it travels through time. This way you get exactly where you want to be without having to pull curtains over all the handwavey temporal physics that might be poking out from underneath.

The disadvantage is that if you don't know where the time machine is set to take you, you could end up both anywhen and anywhere.

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2024-03-17 Rerun commentary: The real upshot of this is that most time travel depicted in fiction is not just timey wimey but also spacey wacey.