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What is the difference between Satellite time, GPS time and UTC time? How are these calculated from one another?

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3 Answers 3

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Both GPS time and UTC are derived from the atomic time TAI, a reference used to define the time unit in SI, kept by 400 atomic clocks in the world. GPS time unit and UTC time unit are the TAI second. In addition GPS time and UTC were equal on January 6 1980. End of 2021 the relationship is this one:

enter image description here

While the TAI scale is invariant, the year duration varies, mostly due to Earth decreasing rotation rate under the braking effect of tides. As humans, we expect noon of some day (Sun at its zenith), e.g. on February 19, to really happen each year at the same legal time. So the scale for legal time has to be flexible, unlike TAI. We use UTC for this purpose$^{(1)}$. UTC is TAI with leap seconds. Solar noon is delayed each year by some tiny amount, a mean 0.75 second. UTC matching with solar time relies on two actions:

  • Earth rotation period measurement based on the direction of remote quasars sensed by very large interferometers, done by IERS. This defines another time scale, UT1, which second is not atomic: Any UT1 day has exactly 24 hours of 60 minutes of 60 seconds.
  • UTC adjustment when the difference with UT1 is close to 0.9s by adding an atomic leap second to UTC. Due to Earth complex motion, a negative adjustment might be required one day, but this never happened. UTC is adjusted the last day of June or the last day of December. This day lasts one second more than an ordinary day, and 23:59:60 UTC actually exists.
    enter image description here
    Clock displaying a leap second in timezone UTC+9, source

In practice, few clocks or applications behave this way, most ignore the leap second, and most which do not use it correctly (e.g. some will slice the additional duration and distribute it over several hours before and after midnight).

The consequence of adding a leap second is the next UTC day lags behind the corresponding TAI day by one additional second and repeating this operation UTC differs from TAI by an increasing number of seconds. If TAI was convertible to a date using a calendar, we would have a difference in the date around midnight. But a calendar is only a notion valid for UTC, neither TAI nor GPS time are convertible to a date, they are only expressed in their canonical form, a count of seconds since the origin (epoch), a precaution which also protects them against bissextile years complexity.

While UTC time is adjusted for Sun zenith at constant time of the day, UTC date is similarly adjusted by an additional days each 4 years or so, to prevent the vernal equinox and Spring date to lag more and more. The reason is 365 days is not enough for Earth to complete its revolution around the Sun, it needs about 6 more hours. This adjustment maintains the Spring equinox in the range 19 to 21 March.

GPS time is never resynchronized; its offset from TAI is the number of leap seconds which existed on January 6 1980, that is 19. GPS and TAI are uniform (continuous) times; UTC is discontinuous due to leap seconds.

Note none of the "times" we measure today is an absolute time (e.g. since the Big Bang), they are a duration since some conventional close landmark (e.g. TAI was reset in 1958, UTC in 1972, GPS time in 2019). The duration expressed in seconds is the same as long as the duration unit is the same. This is the case for TAI, GPS and UTC which all use the atomic second defined in the SI. things get complicated only when converting this duration into a date/time, using the specific starting point and unequal years, days, minutes and hours introduced by leap years and seconds, which needs to be inserted properly. UTC is a broker of uneasy compromises, using the invariable atomic second unit, but kept in sync with UT1 which uses the variable solar second unit.

TAI:

  • Synchronized on existing UT2 on January 1 1958.

UTC:

  • Redefined in 1970 to include leap seconds.
  • Resynchronized on January 1st 1972 to be exactly 10 seconds behind TAI.
  • 27 leap seconds have been introduced since then.
  • UTC is now 37 seconds behind TAI.
  • UTC = TAI - 37s at present.

GPS:

  • Defined as equal to UTC at midnight on January 6th 1980 when UTC was 19 seconds behind TAI.
  • 18 leap seconds were added to UTC since then.
  • GPS time is now 18 seconds ahead of UTC.
  • The internal representation of GPS time was reset (due to week counter finite size) on August 21 1999 and April 7 2019, and this may happen every 1024 weeks. Conversion programs have to take this into account. While the start time is changed each time, the offset with TAI is not modified.
  • GPS time = TAI - 19s (always).
  • GPS time = UTC + 18s at present.

Time in space and time references for space

Time aboard a satellite, is a bit different than on Earth due to relativistic effects and altitude. For example on a Navstar satellite (GPS), time is slowed down by velocity and accelerated by the lower gravity in altitude, giving a global accelerating factor of about $5.3 \times 10^{-10}$:

If not accounted for, in one day it could build up to a timing error that would translate into a navigational error of 13.7 km.

(source)

There are time references for the deep space which are neither based on a rotating Earth nor on Earth gravity, e.g. geocentric coordinate time (TCG) is the time coordinate for geocentric celestial reference system (GCRS) and barycentric coordinate time (TCB) the time for barycentric celestial reference system (BCRS). Time elapses faster than on Earth, from Wikipedia:

Because the reference frame for TCG is not rotating with the surface of the Earth and not in the gravitational potential of the Earth, TCG ticks faster than clocks on the surface of the Earth by a factor of about 7.0 × 10−10 (about 22 milliseconds per year).


$^{(1)}$: The use of UTC instead of TAI, while usually presented like I did as a need to keep in sync with Sun, is actually based on an imbroglio mixing legal reasons and administration poor understanding of the huge risks and difficulties created by leap seconds for a little practical benefit. WRC 2023 conference will decide whether leap seconds should continue to be used for another 8 years or die. The clock is ticking...

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  • $\begingroup$ FYI, the often quoted claim of a 13km/day error is not correct. GPS location is computed by comparing the times of the several GPS signals, not comparing any of them to an earth based clock. Because all are at similar orbits all will be similarly affected, relativistic errors would be small, small enough not to be a deal breaker for the original purposes of GPS if they weren't accounted for. $\endgroup$ Dec 17, 2021 at 18:49
  • $\begingroup$ @whatsisname: As the relativistic drift is time cumulative, there is a difference in how drift progresses on each individual satellite if orbits are not exactly circular with the same radius. I guess this difference is sufficient to create pseudo-range errors after a certain time. But I have no figures, I'm interested in related documentation. $\endgroup$
    – mins
    Dec 17, 2021 at 19:46
  • $\begingroup$ physics.stackexchange.com/a/128951/63383 $\endgroup$
    – Tim
    Dec 17, 2021 at 22:18
  • $\begingroup$ @Tim: Thanks. The answer you point to is based on the idea the pseudo-ranges are not computed from actual travel times ("It doesn't measure how long the signal took to get from satellite A to GPS"), and therefore there is no need to know the time of arrival, only the (common) departure time. But its not correct. The 4 signals don't have to leave the satellites at the same time and the travel times are computed and the receiver clock error estimated (both at once), This is a regular multi-lateration without a central clock. $\endgroup$
    – mins
    Dec 18, 2021 at 0:24
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    $\begingroup$ Small but important correction: GMT does not exist anymore. You correctly note that GMT and UT1 are similar ideas, but only the latter is still rigorously defined, or even measured. Using GMT for modern timekeeping is an anachronism (albeit and regrettably, an extremely common one). $\endgroup$
    – imallett
    Dec 18, 2021 at 0:48
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GPS time is the exact number of seconds since January 1, 1980, at 00:00:00 UTC. Some systems may (incorrectly) represent that as a date and time by assuming days of exactly 86,400 seconds.

UTC time truly has two parts: the date and the time within that date. Most days are 86,400 seconds long, but they may occasionally be 86,401 or 86,399 seconds long (due to “leap seconds”) to keep UTC in sync with Earth’s slightly irregular rotational period. Some systems may (incorrectly) represent that as a count of seconds.

GPS ephemera helpfully includes the net number of leap seconds added or subtracted under UTC, which is +18 as of 2021, so you can easily derive the current UTC date and time if that’s what you actually need.

Other satellite systems may have their own definitions of time.

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  • $\begingroup$ Hi can you please elaborate more . Let say satellite transmit 10:41:30 as time then how would the GPS time be calculated $\endgroup$ Dec 17, 2021 at 5:18
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    $\begingroup$ @SourabhJain the satellite won't "transmit 10:41:30", but rather they will transmit "the exact number of seconds since January 1, 1980, at 00:00:00 UTC", as the answer says. That's GPS time. $\endgroup$
    – Federico
    Dec 17, 2021 at 9:26
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    $\begingroup$ note: GPS time is a linear count of SI seconds as observed on the surface of Earth. On the satellites, the clock tick a little slow to compensate for relativistic time dilation, which is (IIRC) on the order of 10¯⁶ while the clock have to be accurate to at least 10¯¹⁰ (more because the synchronization isn't every second) to provide the navigation accuracy they have. $\endgroup$
    – Jan Hudec
    Dec 17, 2021 at 11:14
  • $\begingroup$ Of course, defining a day as exactly 86400 seconds basically means that it has to be the seconds that vary in length, at least sometimes... Which is exactly what I understand Google did and which at least some NTP servers support. Also, obligatory xkcd: xkcd.com/2266 $\endgroup$
    – ilkkachu
    Dec 18, 2021 at 16:50
  • $\begingroup$ @ilkkachu The “smearing” of leap seconds is pretty common these days because too much software breaks when time goes backwards under dumber handling of leap seconds. If POSIX time were TAI rather than UTC, it would be a lot simpler for everyone. $\endgroup$
    – StephenS
    Dec 18, 2021 at 17:18
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Disclaimer: Since I am using Wikipedia references below, this answer itself should not be used as a separate source for a any wiki article. Please look at the respective articles for the direct references to ensure they are the most current, accurate, and provide the proper source references.

When I was doing some Supplemental reading this question prompted I found this archived article from InsideGNSS, which talks about how time is compared between the GPS and Galileo, but also talks about the way the GPS System time is related to UTC. I added emphasis for the specific for this question but included the section for context. If you want more information you should probably review the article on the main site which may have more up to date information since none of the various systems are completely static.

Galileo runs on Galileo system time (GST), which is generated on the ground at the Galileo Control Center in Fucino, Italy, by the Precise Timing Facility (PTF), based on averages of different atomic clocks. GPS system time is computed by the GPS control segment using an assembly of clocks — the GPS Composite Clock, which consists of all operational monitor station and satellite frequency standards. GPS system time, in turn, is referenced to the U.S. Naval Observatory’s Master Clock and steered to Coordinated Universal Time — UTC(USNO), corrected for leap seconds (which GPS time doesn't use).

These two internal times are derived independently of one another but are kept close to the world’s reference time, coordinated universal time or UTC, with the offset between the two being precisely calculated on a continuous basis for the Galileo system by the PTF.

It would appear that at least these two GNSS providers reference back to UTC. UTC itself is derived from TAI (International Atomic Time), which is itself based on a weighted average of 400 atomic clocks spread around the world.

I did see one thing in reading that TAI article that I do not have the experience to resolve. It appears TAI currently uses GPS system time to validate the timings between different atomic clocks. This would seem to lead to a cyclic Self Referencing error so I can only hope that was some how mitigated.

It could be that the nature of an encyclopedia entry is necessarily simplified leading to the apparent confusion. For practical purposes the time difference are probably extremely small.

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