Sure you can, but you need to adjust your position due to centrifugal forces all the time. A time machine would have to do that as well.
If a ball is flying in a straight line through space with a speed of 1m/s I can predict without much math where it will be at any point in time. In fact, if the reference frame is chosen such that the ball is stationary you don’t need any math at all, because the ball doesn’t move!
However, if you have a set of two balls orbiting each other you will always have to do math to calculate their position. I mean technically you could choose the reference frame that is rotating in sync with the balls. But still you need to do math to check that the centrifugal force, which is a real force coming from nowhere in this reference frame, exactly cancels out the gravitational pull between the two balls. Because rotating reference frames are not equivalent to each other!
I really don’t get why the time machine would have to do any calculations at all. The time machine is in this reference frame. You seem to assume that by going back through time you’d be teleporting through time, which leaves the open question of where you’d appear. However, I’d much rather assume that you’d actually be “going” through time. You wouldn’t cease to exist until you reappeared somewhere. Instead you’d be in the machine for some time until you’d get out of the machine again. That’d mean neither you nor the machine ever leave the reference frame.
Since I stay on earth now when I’m moving forward in time why wouldn’t I stay on earth when I move backward through time?
Sure you can, but you need to adjust your position due to centrifugal forces all the time. A time machine would have to do that as well.
If a ball is flying in a straight line through space with a speed of 1m/s I can predict without much math where it will be at any point in time. In fact, if the reference frame is chosen such that the ball is stationary you don’t need any math at all, because the ball doesn’t move!
However, if you have a set of two balls orbiting each other you will always have to do math to calculate their position. I mean technically you could choose the reference frame that is rotating in sync with the balls. But still you need to do math to check that the centrifugal force, which is a real force coming from nowhere in this reference frame, exactly cancels out the gravitational pull between the two balls. Because rotating reference frames are not equivalent to each other!
I really don’t get why the time machine would have to do any calculations at all. The time machine is in this reference frame. You seem to assume that by going back through time you’d be teleporting through time, which leaves the open question of where you’d appear. However, I’d much rather assume that you’d actually be “going” through time. You wouldn’t cease to exist until you reappeared somewhere. Instead you’d be in the machine for some time until you’d get out of the machine again. That’d mean neither you nor the machine ever leave the reference frame.
Fair enough :)