How long could it take for the Earth to be in the exact same place as it was?

[SitPlutoSit]

Okay, so this might seem a bit simplistic, but who knows, maybe not...

How long would it theoretically take for the Earth to return to its exact same position as it was before? The major factors I'm including are its angle and relative distance from "local" cosmic bodies. I'm guessing its actual "same" position in the universe would include an absolute "never" but that's why I'm asking you :)

 

[Chronos]

Given the peculiar motion of the solar system relative to nearby stars [which are orbiting a galaxy which is hurdling through space hundreds of kilomenters per second, I think 'never' is the logical answer.

 

[DaveC426913]

How long would it theoretically take for the Earth to return to its exact same position as it was before?

What are you using as a reference for "exact same position"? Its position in the solar system? Local neighborhood? Galaxy?

The question cannot be answered because it is poorly formed.

However, the answer is never (but not it the 'it will not happen' sense; in the 'it can not happen by definition' sense).

 

[sophiecentaur]

The question assumes that there is some three-dimensional Cosmic graph paper out there and that we have an absolute position (Cartesian Space). It seems that there isn't and we don't. So, with respect, the question has no meaning - except if you were to suggest that everything, one day could come back into the identical relative pattern that it's in now. But even that's out of the question because things are constantly getting more jumbled up (entropy) and masses are being created and destroyed all over the place.
It's downhill all the way, I fear.

 

[eachus]

First, there is a universal sense in which there are absolute positions. Interactions with the vacuum which show up in Feynman diagrams are relative to an inertial zero for any point in space. Measuring this speed using nuclear reactions can probably get you within 0.1 or 0.2 c of what it means to be at rest. Measuring all the surrounding galaxies and their velocities with respect to the solar system can probably get closer...

Once you have that data, or an assumed definition for at rest in the vicinity of Earth, now you have to look at the Earth's motion around the sun. The combination can result in the answer "never," but if the Earth's orbital plane matches the motion of the solar system relative to rest, there can be two occasions per year where the Earth's orbit crosses last year's orbit.

 

[russ_watters]

First, there is a universal sense in which there are absolute positions. Interactions with the vacuum which show up in Feynman diagrams are relative to an inertial zero for any point in space. Measuring this speed using nuclear reactions can probably get you within 0.1 or 0.2 c of what it means to be at rest.

Sorry, there is no absolute position in the universe and no experiment that can detect such a thing. That's the entire point of the first postulate of Special Relativity.

 

[eachus]

Sorry, there is no absolute position in the universe and no experiment that can detect such a thing. That's the entire point of the first postulate of Special Relativity.

Sorry, the first principle of Special Relativity doesn't hold in my universe.* Does it hold in yours? Or to phrase it differently will your reconciliation of quantum mechanics and relativity be published in time to be considered for next year's Nobel Prize in Physics? No, maybe the year after? I'm amazed that no one else thought of discarding general relativity... (End sarcasm mode.)

I spoke of something which is (measurably) true in quantum mechanics--the energy of the vacuum defines a zero speed reference for every point in the universe. (Probably all of them are different, but that waits on someone's grand unification paper.) This point is not theory--the LHC could not work without considering the effect. (Well, you could try to adjust and align all the magnets "by hand," good luck with that. Oops, too much caffiene. But at least this time the sarcasm is pointed back at me.)

It happens to be easier to measure the speed of the solar system relative to the cosmic background radiation. (The CMB also defines a specific zero velocity at any point in space.) That value is 627±22 km/sec (about ten times the Earth's velocity in its orbit around the sun).

Some of the errors in that number are systemic. So don't put too much faith in the error bars, which are relative to the data. But still, the Earth probably never passes through the same point relative to the CMB twice.

*To clarify, I am saying that the Principle of Relativity doesn't hold in my universe. The Principle of Invariant Light Speed does. I've seen explanations of SR which reorder these principles or turn them into postulates. You seem to be referring to the Principle of Relativity which, as indicated, is not true in general relativity. Gravity, which is not considered as such in SR, is most of what GR is about.

 

[SitPlutoSit]

Kool, well, thanks everyone for the info. I totally realize the problems and difficulties with answering the question itself (hence the little posit at the beginning) and the answers that were given are actually more than enough for me to work with, so definitely, thanks.

This was actually in order to gain a bit of perspective that I might use for a work of fiction, so there's not any real universal laws that are paramount. I just wanted to see about the probables/possibles that I could work with while being able to blend them in with the unlikely and the nevers. Take care, all :)