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I read that the clocks of GPS satellites seem to run slower than the clock of stationary observer, because of their speed (special relativity) and seem to run faster than the clock of stationary observer because of their altitude (general relativity). http://osg.informatik.tu-chemnitz.de/lehre/old/ws0809/sem/online/GPS.pdf

From this, can you model the speed $\upsilon(t)$ and the altitude $r(t)$ of a spaceship launched from the ground vertically at $t=0$ such that the clock of the spaceship will always seem to be synchronised to the clock of the observer on the ground (from the observer's frame of reference)?

Qmechanic
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newzad
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  • It's not really correct to say "the clock of GPS satellite's run slow". The difference is not in the behavior of the clocks, it is in the nature of time. – dmckee --- ex-moderator kitten May 12 '13 at 02:50
  • for reasons @dmckee pointed out, the correct way to phrase it would be GPS clock appears to tick more slowly. I don't quite your question. As my understanding goes, there is no generic way to synchronize clocks in 2 frames of reference(unless it is an inertial reference frame connected by a simple translation). You are limited to using a special event as the definition of the moment when the clock are synchronized, and they will not remain synchronized indefinitely. One can correct the moving clock continuously, to account for this, but that is a different matter. – Prathyush May 12 '13 at 03:50
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    Time dilatation due to the speed is proportional to the kinetic energy (with a factor $m$), and time dilatation due to the altitude is proportional to the minus potential energy (with the same factor $m$). So you just have to keep $E_K-E_P=0$ at any time, and any such flight would give you a solution. – firtree May 12 '13 at 05:26
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    Possible duplicate: http://physics.stackexchange.com/q/62222/ – John Rennie May 12 '13 at 07:56

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