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Already on earth the time is a bit of a problem with the time-zones. It is not that big a problem though, since we all "travel" at (nearly) the same speed.

Not so in space. With the time dilatation (and probably some other factors) one cannot simply rely on ones watch. So, how would it be done?

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    $\begingroup$ This would be on topic over at Physics, but I would say it's related to Space Exploration enough to warrant keeping it here. +1 $\endgroup$ – Undo Sep 21 '13 at 22:45
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    $\begingroup$ I think the use of multiple pulsars has been proposed for this type of problem. Such has certainly been demonstrated as useful for determining position. Wikipedia states "Certain types of pulsars rival atomic clocks in their accuracy in keeping time." Also Pulsar clock. $\endgroup$ – Paul A. Clayton Sep 22 '13 at 1:11
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    $\begingroup$ You explicitly mentioned time dilation. Strictly speaking, what you are asking cannot be done because simultaneity is relative. See en.wikipedia.org/wiki/Relativity_of_simultaneity. Special and general relativistic time dilation is inevitably going to make a mess of any attempt to synchronize clocks. However, since no human, or any space-faring device made by humans, has moved very fast (fast = one tenth light speed or greater) or very close to a black hole, we can ignore the non-linear aspects of relativity. That results in TDB, Barycentric Dynamic Time. $\endgroup$ – David Hammen Mar 6 '14 at 12:38
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With the time dilatation (and probably some other factors) one cannot simply rely on ones watch.

Ultimately, a "perfect watch" is all one can rely upon. A good approximation of a "perfect watch" is an atomic clock that is located at the center of mass of your (relativistic) spacecraft.

The basic problem is that simultaneity is relative even in special relativity. In general relativity, the simultaneity of relativity is a manyfold aggravated issue. Ben Franklin's statement that "Three can keep a secret, if two of them are dead" is very applicable to relativistic mechanics. How do you keep time, synchronously? As long as more than one are trying to do it, you can't.

We can (kind of) pretend that relativistic effects are linear, and in that case you end up with something like JPL's ephemeris time Teph or the IERS's/IAU's TCB (barycentric coordinate time) or TDB (barycentric dynamic time). None of them are perfect; they can't be.

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For the kind of space travel we are performing in this day and age, time dilation effects are too small to be of much concern for mission planning. The time coordination of most space missions is synchronized to the time at the mission control. The International Space Station does its scheduling and daily routine according to Coordinated Universal Time (UTC).

When you would perform space travel with relativistic speeds (note that we are entering the realm of science fiction here), you have to consider what goal you want to reach with your time-keeping. When you need to check on your fusion reactor temperature every hour, you would do so according to a conventional clock in your own reference frame, because your reactor wouldn't care about how much time has passed on Earth. But when mission control back on Earth expects hourly status reports from you, you would have to separately track the time according to Earth's frame of reference to ensure that they arrive on time. Your earth-clock would have to be aware of your current speed in earth's frame of reference so it can adjust its speed accordingly. Also keep in mind that information can only travel with the speed of light, so the earth-clock would also need to be aware of your current distance from Earth (in Earths reference frame), and add that number of light-seconds to the time it displays.

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    $\begingroup$ (pet peave): Please don't say "Greenwich Mean Time". That is a 40 year outdated concept, abandoned in 1972. The correct term is Coordinated Universal Time (UTC). People use GMT because it's a comfortable term. There is no such thing as GMT anymore. At least not officially. $\endgroup$ – David Hammen Mar 13 '14 at 21:22
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    $\begingroup$ Abandoned in this context, yes. It is very much alive in the UK, where it is the correct, and official term. $\endgroup$ – Rory Alsop Mar 14 '14 at 11:26
  • $\begingroup$ @DavidHammen - I thought that at least at this time, "GMT" and "UTC" were "synonymous". $\endgroup$ – Kevin Fegan Sep 27 '14 at 9:01
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    $\begingroup$ @KevinFegan - GMT was officially deprecated as a worldwide concept (Brits apparently are slow on the uptake) the day that UTC was made official. $\endgroup$ – David Hammen Sep 27 '14 at 9:53
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What exactly is being measured?

If it's one's own timeline while travelling, then a wristwatch is fine.

If it's mis-synchronization of clocks that are distant and possibly moving, then one clock must be chosen as a standard, either distant and unchangeable (pulsars) or local and convenient (an accurate clock in Greenwich).

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