Are there any experimental data about potential time dilation caused by cyclical movement of heavy objects? 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?
 A: 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.
