If I had a time travel machine that could drop me into any point in space and time, could I accurately predict earth’s “position”? I know position is an improper term. Would it be possible to know exactly where to land so that you are at the same spot on the surface of Earth as when you “departed”?

  • $\begingroup$ No. The earth would have moved in its orbit around the sun; the sun, in its motion around the galactic center, the galaxy, relative to other galaxies in the cluster to which it belongs, the cluster, relative to other clusters, and other galaxies and clusters would have moved relative to the Milky Way. There'd be no reference points to figure out where in space your time machine would materialize relative to where the Earth would be at that moment in time. $\endgroup$ – BillDOe Apr 4 '18 at 19:14
  • $\begingroup$ There is no motion "through the universe". Space is not a thing, it's just a relationship between objects. If objects did not exist, space would not exist either. Motion is always relative to other objects. There is no motion in an absolute sense. So, when you ask about motion, you always have to specify "relative to this planet, or this star, or this rock", etc. $\endgroup$ – Florin Andrei Apr 4 '18 at 19:24
  • $\begingroup$ Relative to what? Since neither position nor velocity are absolute, you need to specify some kind of reference frame. I guess you could use the current position and orientation of your spacetime machine, or the comoving frame of the CMB, but it will be tricky to specify the coordinates of your destination precisely, even for relatively short hops, since the Earth is moving at roughly 369 km/s relative to the CMB frame, and its motion in that frame isn't exactly linear, being composed of various orbital motions (and of course its axial rotation, but at least that's regular and easy to compute). $\endgroup$ – PM 2Ring Apr 6 '18 at 12:14
  • $\begingroup$ Thanks, all. I understand that position is relative, so I suppose the question would be would we understand well enough Earth's position tomorrow relative to its position today. Given that we are moving in reference to the center of the solar system, in reference to the center of the galaxy, in reference to our galactic cluster, in reference to the CMB, etc. Have we quantified all of the points with which Earth is moving so that we could "launch" a spacetime machine forward into time, and know where to place it relative to all of the reference points in the future. $\endgroup$ – Michael James Apr 6 '18 at 17:46
  • $\begingroup$ You only need one reference point to position your machine relative to it, so since we know our position relative to the sun, yes we can do that. The fact that the sun moves relative to a galaxy (and so on) is irrelevant if you can place your machine relative to the sun. But you seem to be asking about whether we can place it in "absolute coordinates" and the answer of that remains unchanged: there is no absolute point. $\endgroup$ – Ingo Bürk Apr 6 '18 at 20:44

Surprisingly, we will soon be able to do this well enough to go back several hundred million years and place ourselves, if not in the solar system, inside the Galaxy and roughly in the right part of the Galaxy. It turns out that we know, with high accuracy, the Earth's motion with respect to the microwave background radiation, which provides a well defined frame of reference for motions. Therefore, we will be able to work out which direction and about how far the MW has moved with respect to this universal frame and separately the Earth with respect to the center of the galaxy. It requires solving for the growth of what is called the 'microwave dipole velocity' over time. Some of this velocity develops from nearby objects like the MW and the nearby groups of galaxies. So, we need to know their masses and relative motions a bit better than we presently do. But, by far, most of the velocity is from objects quite far away, and this allows us to use the simpler and well understood 'perturbation' techniques. The biggest uncertainty for the Earth's position might be the interactions with local stars back in time and what effects they had on perturbing the Suns orbital motion about the center of the galaxy. Again we need to know better the masses of local stars and their relative velocities to calculate the Earth's trajectory back in time. As it happens, the space telescope GAIA, which is about to make its second release of data, will greatly improve our knowledge of the motions and, indirectly, the masses of all these stars and nearby galaxies.

So, if you have got that time machine working, we are nearly ready to go!

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  • $\begingroup$ "We will soon be able to..."; what is the source of this extraordinary claim? Millions of years, perhaps, but not an entire Galactic rotation. The Gaia census does not include every object in the Galaxy. $\endgroup$ – Rob Jeffries Apr 9 '18 at 23:11
  • $\begingroup$ thanks! I feel I'll have to wait on the launch until we can at least land in my home solar system. is there an estimate on how far back one could go and position yourself on earth, if not earth's surface? $\endgroup$ – Michael James Apr 10 '18 at 0:28
  • $\begingroup$ CMB Dipole: Speeding Through the Universe: apod.nasa.gov/apod/ap140615.html $\endgroup$ – Wayfaring Stranger Apr 10 '18 at 15:27
  • $\begingroup$ @RobJeffries: GAIA will observe a large fraction of stars on this side of the Galaxy. No object outside of that region could have had a near fly by with us for several hundred million years because they are too far away and everything at our Galactic radius moves at roughly the same speed $\sim \pm$ 20 km/s. $\endgroup$ – eshaya Apr 11 '18 at 19:23
  • $\begingroup$ @MichaelJames: Well, I was optimistically thinking we could go back a billion years with an accuracy of a tenth of the galactic center (3,000 ly). The size of the solar system is 10 light hours. So, to hit the solar system one could go back $10*3600/(3000*3.1 \times 10^7) = 2 \times 10^{-7}$ of a billion years, which is $\approx 400$ years. $\endgroup$ – eshaya Apr 11 '18 at 19:43

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