Hypothetically, if you were to travel say, 6 months into the past with no spatial displacement, you would end up floating in space because the Earth would be on the opposite side of the sun.
I know when it comes to sci-fi, they can't account for everything and I don't expect them to. So I'm not nit-picking or anything, I'm just wondering if this is something that has been addressed to any detail, as it seems like it would have to be a major component of any time travel.
This question is discussed on p. 24 of Paul J. Nahin's Time Machines: Time Travel in Physics, Metaphysics, and Science Fiction (2nd edition, ISBN 0-387-98571-9):
Of course, one might argue that Wells' machine does actually move, because it is attached to the Earth, which is certainly moving, but it is not clear why this should result in the time machine arriving in the temporal past of the Earth, rather than in some past region of space (almost surely a vacuum.) The general problem of where things are for time travelers has been nicely illustrated by the physicist Gregory Benford in his novel Timescape. In that story the world of 1998 is on the verge of total ecological collapse, and an attempt is made to change the past by aiming a backward-in-time message via faster-than-light tachyons (see Tech Note 7) at the pivotal year 1963. When the principal scientist involved in this effort is explaining the process to a potential financial backer, he is asked, "Hold on. Aim for what? Where is 1963?" The scientist replies, "Quite far away, as it works out. Since 1963, the Earth's been going round the Sun, while the sun itself is revolving around the hub of the galaxy, and so on. Add that up and you find 1963 is pretty distant."
So there is one stfnal work that acknowledges the spatial-displacement aspect of time travel: the novel Timescape by Gregory Benford.
The other one Dr. Nahin mentions is an old short story, "Dead End" by Malcolm Jameson, in Thrilling Wonder Stories, March 1941 (available at the Internet Archive, click here for download options):
An understanding of the question "Where is everything?" actually goes quite a bit further back in fiction. For example, after looking through a TV-like gadget to view the past, one character in the 1941 story "Dead End" (Jameson) complains, "You said you'd find Captain Kidd's treasure, but all I can see is fog and static." He is told that's because "It's too far back—1698 or thereabouts. The Earth was billions of miles from here then, and there are too many cosmic rays between." The "cosmic rays" are presumably the cause of the interference.
P.S. Here's a better example, or at least an earlier one: "The Derelict of Space" (1931) by William T. Thurmond and Ray Cummings, originally published in Wonder Stories Quarterly, Fall 1931, available at the Internet Archive (click here for download options). I quote portions of Everett F. Bleiler's review in Science-Fiction: The Gernsback Years:
The exploratory spaceship sights a strange copper disk-like vessel in space. It is obviously derelict, and an elderly member of the crew recognizes it as the Deely time machine that left Earth around forty years earlier. The space men board the vessel, find six corpses and a manuscript kept by one of the time travelers. [. . .] The gimmick is that while the time machine moved in time, it was stationary in space; the universe moved away from it, leaving it isolated.
This story was actually written by Cummings based on a plot submitted as a contest entry by Thurmond. The time-travel "science" was criticized in a letter "Would Find the Earth Under Them" by reader Jack Cypin in Wonder Stories Quarterly, Winter 1932 (available at the Internet Archive, click here for download options), which was rebutted in a letter by Thurmond in Wonder Stories Quarterly, Spring 1932 (available at the Internet Archive, click here for download options).
P.P.S. This aspect of time travel is touched on in R. A. Lafferty's 1981 novelette "Bank and Shoal of Time":
"All ghost appearances are time trips. But time is sticky stuff, and it is always local," Rowena lectured them. "We are in a galactic drift of several billion miles a year, so there is no way we could return to any spot on earth in any past time according to absolute location in space. The spot on earth now would be billions of miles away from the same spot on earth then. But time clings to local physical objects, like a world, and all physical objects are deeply imbedded in time. Time is very cohesive and it can only be moved in quantum hunks, and we can only move out of the common time stream by quantum pushes. So a ghost has to bring part of his ambient with him when he comes, and his minimal ambient is his own clothes. This makes a difficulty for those who believe that travel in time consists of reconstructing people and things, molecule by molecule, in the visited time. How much more difficult the clothes would make it! And yet ghostly time visitants are almost always clothed.
Yes, this has been addressed.
The first example that comes to mind is Callahan's Con by Spider Robinson. During the course of the story a distraught mother travels into the future in an attempt to ascertain her daughter's fate. As she uses a relatively crude piece of time travel tech which she doesn't fully understand how to operate, she fails to account for the displacement of the planet over time. If you've got a copy lying around, you can find the details in chapters 10-12.
The Strontium Dog series, published in 2000AD, has this as a major component of one weapon - the time bomb:
...which can transport somebody minutes or hours forwards or backwards in time (by which time the planet has moved along in its orbit, so that the victim reappears in empty space).
Nasty stuff indeed. (As an aside, I do recall one occasion where our heroes used it as a means of transport.)
It's also curious that the series does feature conventional time-travel (e.g. in The Schicklgruber Grab) where this is not an issue.
Obviously there are differences, and obviously conventional time travel has this problem resolved, but I've no recollection of whether or not the creators ever made any comment on the matter.
You could come up with some technobabble about how while moving backwards the time machine is still affected by the Earth's gravity fields. Perhaps instead of moving instantly like teleportation it is moving more like an airplane flying. In that case you'd need some more technobabble about phase shifting its molecules or the time machine would be intersecting other matter and exploding all over the place.
Other possible technobabble might be the warping of space caused by gravity. Gravity is weird. One way of looking at inertia and gravity is that every object is actually following a straight line. It is only the space warped around it making it go in a circular orbit. And when you add a dimension for time it isn't circular either. The path then becomes a spiral through the time dimension that only looks circular. Except that because of the space warping effect of gravity the space-time path is perfectly straight. It is the big hypercube of spacetime that twists around it. So the technobabble would be that the time machine follows its own space-time path backwards in the same way that it follows it when moving forwards at the normal rate.
I can't remember the author or collection, but I have a short story somewhere on my shelves where they built a time machine and explicitly accounted for the motion of the Earth/Sun/Galaxy because of this very reason.
Unfortunately, after travelling a short while in time they realise that they universe is also in motion and they end up outside. Something suddenly appearing into nothing causes a new universe to spawn (at the loss of the time machines and occupants).
This has been addressed in some sci-fi stories.
e.g. in Steins;Gate, in a common scenario (assuming you want to time travel to the same point in space relative to earth), there are some complex math going on to ensure that you will in fact, land there.
This means that, yes, failed/miscalculated attempts ended up in test-subjects being time-travelled to space :)
I guess on other stories where the time travel machine is not explained that much, it was assumed.
At least a similar theme is found in Alfred Bester's Tiger! Tiger! (The Stars my Destination). People find out how to teleport, but their motion vector is unchanged during teleportation. Teleporting to a point right on the other side of the earth would mean you are moving with a huge speed relative to the ground (like 2000-3000 km/hr). 500km or so is the maximum an experienced person can teleport without suffering injuries.
Time travel was used deliberately as a way to achieve FTL by Gordon Dickson in Time Storm, and by Kay Kenyon in The Seeds of Time.
