It's possible to assume that the professor did the math.

But yeah any time machine would also basically have to have space travel built in to compensate.

They knew that when they wrote Dr Who (IE the time travel machine is called a TARDIS (Time and Relative Dimension in Space).

There's a ton of issues with time travel. That could be one, but most fictional time-travel devices can be said to accommodate for the difference in distance. It would just be boring to explain on-screen.

floating astronaut with pistol always has been

That's why doctor who works, its very clear about the fact that TARDIS travels in spacetime, it can do only time, only space or both space and time and they can get away with time traveling and still staying on earth

It could be explained as a time and space machine but just saying time machine is easier.

That's how ive always thought of these things in my head.

That's what einstein said. There is no fixed reference frame, but only relative ones. Every "inertial"(meaning, motion without any external force) frame of reference is equally valid as any other inertial frame movibg with respect to it.

But for sure we can tell earth's orbit is not inertial since circular motion occur, which is due to external force of gravity.

Edit:typo

This is why Doctor Who has a time and space machine. Also because the BBC didn’t have the effects budget to show him flying around.

There is not central point in the universe, and no way to calculate a position. Everything is relatove

I was under the impression that gravity was a constant force keeping the atoms closer together

They are not, that would require changes in the strong force.

I hear police boxes and phones booths are popular as well.

Clark Ashton Smith wrote a similar short story where the inventor failed to take it into account. Upon realizing his mistake he decided to just wait for another planet to reach him, turning his time machine into a spaceship.

Math is hard.

It's even cooler if you remember we send something to the moon even with all this variables and no calculators humans were able to know where the moon would be

Of course the moon is relatively close but still

At least in Doctor Who, the T.A.R.D.I.S. can teleport through space as well as through time, solving that problem. But most time machines don't

Magic exists in that universe though and they're using some of the most powerful objects in the universe. So like if it's granting a wish, you just wish that everyone comes back to earth or whatever. It's not even really a suspension of disbelief. It feels more silly to think that genius scientists using wish granting artifacts wouldn't remember to account for the movement of the earth through space.

Can't they just float and follow the Earth? Or would it be too fast? What's the terminal velocity of a ghost?