I have a question to consult you. Even though I know the relationship between time scales like UT1, UTC, TAI, and TT, I do not know which one is the key point for the computation. That is, from which parameter I can derive others.

For example, if I wanna compute UT1, I must know UT1-UTC. But how to derive UT1-UTC normally? Actually, I know there is some place to distribute the table for UT1-UTC. But compared to that, I prefer to know how to derive that.

In my opinion, all the key point maybe the TAI. We can derive the TAI-UT1 by astronomical observation and then compute other time scales with the relationship formula. Am I right? I hope for the right and professional answer.


TAI, International Atomic Time, ticks according to the second defined by the International System of Units. TT, Terrestrial Time, is separated from TAI by 32.184 seconds.

The second was once defined by the rotation of the Earth, with 86400 seconds per mean solar day. This concept is the basis for UT1, Universal Time. Atomic Time and Universal Time are rather distinct time scales. The Earth's rotation rate is ever so slowly slowing down.This means that a UT1 second is not equal to a TAI second.

Coordinated Universal Time, UTC, is a hybrid time scale. It has seconds that tick in sync with Atomic Time but also has leap seconds introduced intermittently so as to keep UTC and UT1 within 0.9 seconds of one another.

In my opinion, all the key point maybe the TAI. We can derive the TAI-UT1 by astronomical observation and then compute other time scales with the relationship formula. Am I right?

No, you're not. The very slow slowing down of the Earth's rotation rate due to transfer of angular momentum to the Moon is compounded with changes that occur over multiple time scales, varying from centuries to days long (or even shorter; earthquakes are hypothesized to change the Earth's inertia tensor and hence the rotation rate). Some of these changes are predictable, to some extent; others are not predictable at all.

The unpredictability means that $\Delta T \equiv TT - UT1$ is not predictable. This is why the primary job of a number of observational scientists is to collect data regarding the observed Earth rotation rate and publish it via various means. You can receive these data from the International Earth Rotation and Reference System Service (IERS) via its Bulletins A and B. You can also subscribe to these bulletins via email.

Side note regarding the acronyms:
TAI obviously does not jibe with International Atomic Time. (It does jibe in French.) A time scale that I didn't mention, GMST (Greenwich Mean Sidereal Time), does jibe with its acronym, in English. UTC doesn't jibe with Coordinated Universal Time in any language. The acronyms for these internationally recognized time scales are the same in every language.

IERS also obviously does not jibe with International Earth Rotation and Reference System Service. It did do so, once upon a time (in English), when the organization's name was shorter. The acronym remains IERS, in every language.

  • $\begingroup$ Thanks for your answer first, but a little helpless..., 'cause most of them are not related to my general question: how to determine one key time scale or the difference of two time scales, which can be used to compute other time scales by the rigid relationship formula? But from your comments, I get some information which might be useful. As I know, there is a relationship between earth rotation rate and UT1. Does that mean we can derive UT1 directly from earth rotation rate observation? $\endgroup$ – alex Nov 29 '18 at 11:43
  • $\begingroup$ Nevertheless, when we observe the solar or extragalactic radio source, which time scale could be used to determine solar or other celestial body's duration? In my opinion, the Atomic second could be used in current observation. We can get the difference between the atomic second and the period of celestial body directly. $\endgroup$ – alex Nov 29 '18 at 11:44
  • $\begingroup$ @alex - regarding your first comment, that is exactly how UT1 is derived. The inherent unpredictability of UT1 means that it is a purely observational time scale. The IERS (with the US Naval Observatory as the lead) combines data from radio telescopes and VLBI observations to determine what the difference between UT1 and UTC is now / was a few days ago. (It takes time to process these data.) $\endgroup$ – David Hammen Nov 29 '18 at 11:59
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    $\begingroup$ Regarding your second comment, the best radio observations of extragalactic sources are ground-based radio telescopes. The operators of those ground-based observatories need to know the Earth's orientation very precisely so they can aim those telescopes toward the object of interest. Knowing time as ticked by the Earth's rotation is key for pointing the antennae in the right direction. However, time as ticked by an atomic clock is key for interpreting the observed results. $\endgroup$ – David Hammen Nov 29 '18 at 12:04

The fundamental issue is we want to agree on what time it is, but all methods of measuring time have issues. Firstly all measurement methods have limited accuracy, secondly thanks to relativity elapsed time is only really defined in a given reference frame. Thirdly when most people talk about time they don't really care about some scientific definition of time, they care about how many days have passed and what time of day it is but those astronmic phenomina are not entirely stable.

TT is a theoretical scientific ideal, measuring time in the earth's reference frame using SI seconds.

TAI is an attempt to realise that ideal (though for historical reasons it has an offset from TT) by averaging results from a bunch of atomic clocks.

The UT0/1/1R/2 series on the other hand are based around attempts to measure earths orbit astronmically. Rather than a second being a SI second, a day is a rotation of the earth and a second is a fraction of a day. The problem here is that the earths rotation is not entirely stable, so the length of a second varies a bit. The different variants apply various smoothing and corrections to try to make the length of a second more consntat.

Since a SI second is not precisely 1/86400 of an earth day the TT time of day will drift over time from the astronomical time of day. On the other hand for short time intervals atomic time with it's relatively stable seconds is usually considered preferable.

UTC makes a compromise, in the short term it is defined by atomic time, but in the long term it is adjusted to keep it reasonably close to UT1. In the early days both frequency adjustments and irregular time steps were used, but since 1971 UTC seconds have been identical to TAI seconds and time steps have always been exactly 1 second.

Since we have two fundamentally different sources of truth here no formula can precisely predict the future relationship between the astronomical and atomic time scales.

  • $\begingroup$ The second sentence in the fourth paragraph isn't a sentence. It's missing something at the end: Rather than a second being a SI second, a day is a rotation of the earth and a . $\endgroup$ – David Hammen Jan 6 at 12:38

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