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I am dealing with a completely fabricated scenarios (while trying to write a sci-fi book), so my thougts are completely hyphotetical. But I would like to ask you to help me find out if following experiment was ever executed:

Atomic clock A is paced in the line of Earths orbit but instead of orbiting Sun the clock is static in the space and does not orbit Sun. But it keeps the same distance from Sun as Earth had when the clock A was released. Clock B is placed on Earth. Clock A and B start at the same time (when clock A is realeased from Earth). After one year when Earth is pasing the clock A again the clock A is colected and the time compared.

I think that some difference can be caused by missig mass of planet Earth. If I made right assumption - it can somewhere like clock A has 5-10 seconds + compared to clock B...can someone please confirm that at least magnitude is right? That is in mater of few seconds...

Or will the clock show the same time?

And if there was experiment, and there was a difference, how much it was? Was it exactly how much the mathematic explains as missing mass of our planet?

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    $\begingroup$ What force is counteracting the sun's gravitational pull on Clock A? $\endgroup$ – WillO Aug 6 at 3:46
  • $\begingroup$ For an order of magnitude concerning the gravitational time dilation due to the proximity of Earth, see the diagram from this wiki page (we are interested in the green line, at its maximum value towards the right). You can see that we talk here of hundreds of picoseconds per second, so over one year the time offset would be less than a few seconds, more like a few milliseconds. $\endgroup$ – Stéphane Rollandin Aug 6 at 8:52
  • $\begingroup$ According to Wikipedia, clock A will be about 0.0219 seconds ahead of clock B. Also see Barycentric Coordinate Time and the various related articles. $\endgroup$ – PM 2Ring Aug 6 at 8:53
  • $\begingroup$ Thank you very much.I understand there is no reason to believe there is any connection between trajectory of motion in space and time dilatace . But I was wandering if there was ever a real experiment with atomic clock wher one of them was left motionless in the space for longer periods of time. $\endgroup$ – Miroslav Řešetka Aug 6 at 9:14
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Leaving a clock "motionless" in space is already science fiction. To do what you suggest, clock A would need substantial rockets running continuously to prevent it from falling directly into the sun on a radial line. I feel sure no one has ever done that as it would be practically impossible and, even if possible, not worth it.

Terrestrially, we have this experiment which is the closest match to what you suggested, although on aircraft not spacecraft: Hafele-Keating experiment.

In space, there are the GPS satellites. They obviously orbit the Earth, so they are not like your scenario, but the clocks on those have to be calibrated such that they keep the right time on orbit. That means they are "off" while still on the ground before launch. You could easily look up a lot on that.

I don't really understand the part of your question about "missing mass", but I don't see where that would matter. It is true that clocks run differently at different potential energies, and there would be a different gravitational pull, at some level, when the Earth was close to A vs far from A, but I don't think that would be very significant. You might be able to estimate that from the effect on the GPS satellites as mentioned above.

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