# How exactly is UT1 measured/calculated?

Background: I am an atomic physicist so I understand atomic time pretty well. But I'm not an astrophysicist or astronomer and I know very little about astronomical measurements.

I am interested in fine details about how UT1 time is measured. I roughly understand that UT1 time is related to the rotation of the Earth relative to either the sun or distant celestial objects (I think it's the latter but I'm not sure). I also know there are detailed challenges in measuring Earth's rotation due to various wobbles of the Earth's rotation axis. I'd like to understand all these ideas much better.

I think most of my questions will be answered by me getting a nicer understand of celestial orientation axes and how measurement are made but I don't quite know where to start.

Basically I understand that Earth rotates about an axis, but that that axis might change position with respect to Earth's crust because Earth is not a sphere. I understand that this axis + one point on Earth's crust (Greenwich, England?) defines a plane in space. I understand that this axis + a distant point defines another plane and that we can speak about the angle between these two planes.

I understand that if I have a clock synchronized with Greenwich England I can measure the rotation of my plane with respect to the Greenwich plane if an Astronomer in Greenwhich and myself both record the time of day that some celestial object is "directly overhead". i.e. when "my plane" with Earth's axis and the celestial objects plane overlap. This is related to "meridians". I guess in addition to the synchronized time we also need some idea about how fast Earth rotates in radians per second. What I DON'T understand is how we know when an object is on our meridian. That is, how do we measure "right ascension"? I also don't know how we measure the declination of celestial object. Does it involve a glorified plumb bob?

So then once we understand how right ascension and declination are measured, how does polar motion affect the story? I imagine that polar drift would be observed as observatories at different positions on Earth recording different rotation rates for Earth on some given day. Like I imagine two observatories measuring the duration from one object crossing their meridian once until it crosses their meridian the next day. I can imagine if the axis wobbles a little bit it could angle the Earth so that one observatory saw a shortened day and the other saw a long day. I think the difference in length of day at the two observatories would be related to the angle and velocity of the wobble?

How does all of this information get integrated to form what we call UT1? Also, are satellites and GPS necessary for our current realization of UT1 other than for synchronizing the clocks at each participating observatory? My guess is yes. If that is so I'm curious what their role is.

Some questions I'm interested in but a little less so: (1) knowing answers to all of the above, what is the difference between UT0 and UT1 (2) I'm curious for more specific details about the observatories used to measure time. I understand that they're probably based on very long baseline interferometry. How does these "telescopes" know which they're pointing with fine enough resolution to measure UT1? What collection of objects are they observing to define UT1?

I imagine some of my question here are very very basic for astronomers, but I imagine some of them are in the weeds of time keeping. I'm curious for answers that span this whole spectrum. My apologies if I've gotten anything so wrong my question doesn't make sense! Please let me know if there is anything I can clarify.

• A full description is way to involved for a post here. USNO Circular 179 is a descent place to start: spsweb.fltops.jpl.nasa.gov/portaldataops/mpg/MPG_Docs/… Mar 22 at 3:22
• Be aware that the "new" system is called ICRS where distant radio sources' RA/Dec coordinates are considered to be correct "by definition" and everything is based off of those. The old "equinox" system was based on the Earth's equator and orbital plane, and everything was based off of those. Mar 22 at 3:26
• @GregMiller Wow, it's so complicated. I think the story is something like: historical astrometric techniques were used to locate coordinates for a catalog of celestial objects. Then the positions of these objects were defined to be fixed. We now use these for astrometry. Using these we can measure how Earth rotates, but how Earth rotates is a bit complicated, but if we're smart we can measure and describe it. We have models for precession and nutation. We subtract these models off from the Earth rotation angle for calculating UT1 which is sort of a form of averaging. Mar 22 at 8:16
• This question was cross-posted at physics.SE, only that post was a bit earlier than this one. I'm not sure which is a better home as both astronomy (VLBI observations of quasars) and physics (VLBI synchronization of atomic clocks, and also GPS) are involved. However, the question should only be asked at one place. Ultimately one needs to be closed. Finally, asking for exactly is asking for a bit too much; you are asking us to write a book. Mar 22 at 11:19

("How exactly is UT1 measured/calculated?" -- with "interest in fine details about how UT1 time is measured.")

(edited 2023/Mch/27 to add references including text+image extract of IAU 2009 explanation showing continuing relation of UT1 to the sun.)

"UT1" is a standard measure of time currently close to mean solar time at longitude 0, and has been (re)defined in the last ~40 years successively by several IAU standards (1982, 2000, 2006). Effectively these standards are much-modified conventional descendants of results of older methods from optical astronomy for accurate determination of mean solar time, dating largely from the 18th and 19th centuries. The modifications have effectively discarded some part of the physical basis and rationale that originally underlay determinations of time (see also below).

Although UT1 is usually obtained now in practice from the difference with the uniform time scale UTC by using the quantity UT1 − UTC (available from the IERS), fundamental redefinitions for UT1 as a standard over the last ~40 years have been offered as follows:

1982 standard (in official use from 1984): S Aoki et al (1982) "New Definition of Universal Time", Astronomy & Astrophysics 105: 359-361

2000 standard (in official use from 2003): N Capitaine et al (2003) "Expressions to implement the IAU 2000 definition of UT1", Astronomy & Astrophysics 406: 1135-1149.

The IAU 2000 standard introduced an officially-preferred alternative to the traditional equinox-based calculations, involving a 'non-rotating origin' (NRO) and an 'earth rotation angle' (ERA). Full details, too long to reproduce here, are given in the paper of Capitaine et al (2003) linked above. The 2000 standard has often been found since to be in need of explanation, and the following extract is from a presentation by N Capitaine & P Wallace, "Implementation of the IAU2000 definition of UT1 in astronomy" at the 2009 27th General Assembly of the IAU (JD06, IAU Gen. Assembly 2009):
The presentation showed that the sun's mean position (in hour angle) is still intended to be represented by UT1, also in the context of use of the ERA formulae (constants shown above in their post-2006 revised values). The details of this representation have previously been discussed in Astronomy SE, at (Does Universal Time really track mean solar time?).

The UT1 definition underwent indirect modification effected by IAU 2006 resolution incorporating latest precession-nutation data in the standard calculation of earth-rotation angle and hence of UT1: see P Wallace & N Capitaine (2006), "Precession-nutation procedures consistent with IAU 2006 resolutions", Astronomy & Astrophysics 459: 981-985.

The standard definitions are effectively available as C and Fortran algorithms at the IAU SOFA ('Standards of Fundamental Astronomy') webpages at (https://www.iausofa.org/), where there is also a guide to 'SOFA Time Scale and Calendar Tools' .

A summary of the recent position on time standards including UT1 was given for example in October 2019 at the conference "Journees 2019" by N Capitaine (https://syrte.obspm.fr/astro/journees2019/journees_pdf/SessionII_1/CAPITAINE_Nicole.pdf).

Further information about implementation of current standard UT1 can be found via: (https://ui.adsabs.harvard.edu/abs/2006A%2526A...459..981W), (https://www.cambridge.org/core/journals/proceedings-of-the-international-astronomical-union/article/implementation-of-the-iau-2000-definition-of-ut1-in-astronomy/D1C56574CA4CCBB263A8C212D3B25475),
SOFA earth-rotation page.

These UT1 standards are no longer strictly in accord with the classical physical basis that a mean solar time naturally depends on two independent variables, related respectively to angular rates of the earth's axial rotation, and of the earth's orbital motion around the sun. The standard UT1 calculations have effectively condensed these two dependencies into a single conventional constant, thus losing one of the independent variables of the natural physical model (discussed on Astronomy SE at (Does Universal Time really track mean solar time?)); but the adopted conventional relationship is expected to hold to adequate closeness for an extended period of time into the future. (The redefinition of UT1, in some ways physically obscure, has also had some critiques of principle, e.g. Xu et al (1986) "Discussion of Meaning and Definition of UT" (IAU Symposia 109 "Astrometric Techniques", 13-17).)

In view of the wider-ranging matters asked in this question, it may be helpful to add the following:-

A good source on the physical foundations underlying determinations of mean time, especially in the 19th-century period shortly before the adoption of UT, is still F Brünnow's 'Spherical astronomy' (1865, New York).

Essential tools for the classical determination of mean solar time at the local meridian of an observatory were, in the 19th century --

• (a) an observatory clock keeping sidereal time as closely as possible, subject to observational corrections,
• (b) a transit instrument, i.e. a telescope aligned to the local meridian (meaning for stations at northern latitudes, pointing due south), and mounted on horizontal bearings for adjustable pointing to objects at various altitudes but always in the meridian direction, and
• (c) tables giving positions in right ascension (expressed as time) of well-characterized "clock stars" and their slow precessional motions, plus tables of the motion of the 'mean sun' (expressed as mean longitude from the equinox, given in units of time, where 360 degrees converts to 24 hr), taken from a theory of solar motion then currently accepted as most accurate. (During the early 19th-c. this usually meant the solar theory of Delambre as arranged by Carlini, displaced in the 1860s by LeVerrier's improved solar theory).

A bare bones summary of the practice was then to:--

• (i) record the times of observed transit of some "clock stars" past the central 'wire' in the viewing field of the transit instrument, using the observatory sidereal-time clock;
• (ii) evaluate the clock-correction needed for the meridian transit of each observed star to occur at a (corrected) clock sidereal time equal to the current right ascension of the star: the so-corrected clock then gave (local) sidereal time to the accuracy of the observations;
• (iii) compute the local mean solar time at the meridian of the observatory, for any instant, as the difference "local sidereal time minus sun's mean longitude in terms of time". The principle of this conversion is described in: (Does Universal Time really track mean solar time?) in the section headed "Classical method for determining mean solar time (Nautical Almanac, 19th-c.)". After adoption of the conventional standards, GMT or UT could then be derived from local mean solar time by applying the difference between the longitudes of Greenwich and of the local observatory expressed as time, up to the accuracy of the longitude determinations.

Greenwich Mean Time used to be the local mean solar time at Greenwich derived by those methods; it was renamed in the 1880s to Universal Time ('UT') and then renamed again in the 1950s to 'UT0' to make room for further versions, especially UT1, which originally was UT0 with corrections intended to remove small fluctuations due to the effect of polar motions on the longitude of the observatory.

The mean sun's position in celestial longitude used to be considered as what would result from observations after calculation to free them from all discoverable periodic variations (see e.g. J C Adams (1884) "On the definition of mean solar time", Observatory 7: 42-44, and A Cayley (1884), Monthly Notices R Astron Soc 77: 84-5).

• thanks for the answer. I'm parsing through it. Is there no simple way to say what UT1 is? For example TAI is our best guess at how many radiation resonant with an ideal Cs ground state hyperfine transition has oscillated since it became the standard. It is essentially realized by a fleet of atomic clocks whose answers to the question of how many oscillations have occurred lately are averaged together for better statistics. Is there not such a simple story for UT1? I'm wishing for something like: Every day a fleet of observatories measures X and their answers are averaged (1/2) Mar 23 at 0:45
• together to give us some rotation angle of the Earth (however that is defined) at that is linearly proportional to UT1. But it seems like somehow UT1 requires many complicated model-dependent algebraic expressions, averaging, subtracting off effects etc. Perhaps UT1 is just somehow much more complicated than TAI... I'm continuing to look through the references in this answer and other comments. (2/2) Mar 23 at 0:47
• @Jagerber48 Well, first, the answer does include as simple of a definition as I think there is. And second, you did write that you are interested in fine details of the measurement. The simplest descriptive definition is the one telling that mean solar time is 'local sidereal time minus sun's mean longitude', then how that transfers to LMT at Greenwich for UT (renamed UT0), then that UT1 originally resulted from removal of polar-motion fluctuations: finally you have full links to the (complicated!!) redefinitions after that. If there was anything else that you wanted, let me know. Mar 23 at 1:01
• there are a lot of words here, but somehow I don't feel like I understand what UT1 is so I can't accept this answer. I understand that UT1 is linearly proportional to Earth's Rotation Angle (ERA). How is ERA measured? Perhaps equivalently: You say that IERS makes UT1 - UTC available. What does IERS do to generate UT1 - UTC? I expect something like: We make certain measurements, we process them this way, and that allows us to produce the time scale. Perhaps I'm needing more focus on the measurements and less focus on algorithms? Mar 26 at 7:04
• @jagerber Misunderstanding arises from misleadingly obscure new definitions, concealing complication. Any solar time is not proportional to earth rotation, it depends on two motions not proportional to each other, i.e. earth rotation and orbital motion round the sun. No amount of redefinition alters that physical fact about the solar system and solar time. Universal Time was defined as a kind of solar time. New UT1 hides within itself a simulation of the orbital component, independent of the real orbital motion. Its nature is not as simple as its name and definition may suggest. Mar 27 at 0:23