A **time standard** is a specification for measuring time: either the rate at which time passes or points in time or both. In modern times, several time specifications have been officially recognized as standards, where formerly they were matters of custom and practice. An example of a kind of time standard can be a time scale, specifying a method for measuring divisions of time. A standard for civil time can specify both time intervals and time-of-day.

- Terminology
- Definitions of the second
- Current time standards
- Conversions
- Time standards based on Earth rotation
- Time standards for planetary motion calculations
- See also
- Notes
- References
- Citations
- Sources
- External links

Standardized time measurements are made using a clock to count periods of some period changes, which may be either the changes of a natural phenomenon or of an artificial machine.

Historically, time standards were often based on the Earth's rotational period. From the late 18 century to the 19th century it was assumed that the Earth's daily rotational rate was constant. Astronomical observations of several kinds, including eclipse records, studied in the 19th century, raised suspicions that the rate at which Earth rotates is gradually slowing and also shows small-scale irregularities, and this was confirmed in the early twentieth century. Time standards based on Earth rotation were replaced (or initially supplemented) for astronomical use from 1952 onwards by an * ephemeris time * standard based on the Earth's orbital period and in practice on the motion of the Moon. The invention in 1955 of the caesium atomic clock has led to the replacement of older and purely astronomical time standards, for most practical purposes, by newer time standards based wholly or partly on atomic time.

Various types of second and day are used as the basic time interval for most time scales. Other intervals of time (minutes, hours, and years) are usually defined in terms of these two.

The term "time" is generally used for many close but different concepts, including:

- instant
^{ [1] }as an object – one point on the time axis. Being an object, it has no value;- date
^{ [2] }as a quantity characterising an instant. As a quantity, it has a value which may be expressed in a variety of ways, for example "2014-04-26T09:42:36,75" in ISO standard format, or more colloquially such as "today, 9:42 a.m.";

- date
- time interval
^{ [3] }as an object – part of the time axis limited by two instants. Being an object, it has no value;- duration
^{ [4] }as a quantity characterizing a time interval.^{ [5] }As a quantity, it has a value, such as a number of minutes, or may be described in terms of the quantities (such as times and dates) of its beginning and end.

- duration
- chronology, an ordered sequence of events in the past. Chronologies can be put into chronological groups (periodization). One of the most important systems of periodization is the geologic time scale, which is a system of periodizing the events that shaped the Earth and its life. Chronology, periodization, and interpretation of the past are together known as the study of history.

There have only ever been three definitions of the second: as a fraction of the day, as a fraction of an extrapolated year, and as the microwave frequency of a caesium atomic clock.^{ [6] }

In early history, clocks were not accurate enough to track seconds. After the invention of mechanical clocks, the CGS system and MKS system of units both defined the second as 1⁄86,400 of a mean solar day. MKS was adopted internationally during the 1940s.

In the late 1940s, quartz crystal oscillator clocks could measure time more accurately than the rotation of the Earth. Metrologists also knew that Earth's orbit around the Sun (a year) was much more stable than Earth's rotation. This led to the definition of ephemeris time and the tropical year, and the ephemeris second was defined as "the fraction 1⁄31,556,925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time".^{ [7] }^{ [8] } This definition was adopted as part of the International System of Units in 1960.^{ [9] }

Most recently, atomic clocks have been developed that offer improved accuracy. Since 1967, the SI base unit for time is the SI second, defined as exactly "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom" (at a temperature of 0 K and at mean sea level).^{ [10] }^{ [11] } The SI second is the basis of all atomic timescales, e.g. coordinated universal time, GPS time, International Atomic Time, etc.

Geocentric Coordinate Time (TCG) is a coordinate time having its spatial origin at the center of Earth's mass. TCG is a theoretical ideal, and any particular realization will have measurement error.

International Atomic Time (TAI)^{ [12] } is the primary physically realized time standard. TAI is produced by the International Bureau of Weights and Measures (BIPM), and is based on the combined input of many atomic clocks around the world,^{ [13] } each corrected for environmental and relativistic effects (both gravitational and because of speed, like in GNSS). TAI is not related to TCG directly but rather is a realization of Terrestrial Time (TT), a theoretical timescale that is a rescaling of TCG such that the time rate approximately matches proper time at mean sea level.

Universal Time (UT1) is the Earth Rotation Angle (ERA) linearly scaled to match historical definitions of mean solar time at 0° longitude. At high precision, Earth's rotation is irregular and is determined from the positions of distant quasars using long baseline interferometry, laser ranging of the Moon and artificial satellites, as well as GPS satellite orbits.

Coordinated Universal Time (UTC) is an atomic time scale designed to approximate UT1. UTC differs from TAI by an integral number of seconds. UTC is kept within 0.9 second of UT1 by the introduction of one-second steps to UTC, the "leap second". To date these steps (and difference "TAI-UTC") have always been positive.

The Global Positioning System broadcasts a very precise time signal worldwide, along with instructions for converting GPS time (GPST) to UTC. It was defined with a constant offset from TAI: GPST = TAI - 19 s. The GPS time standard is maintained independently but regularly synchronized with or from, UTC time.

Standard time or civil time in a time zone deviates a fixed, round amount, usually a whole number of hours, from some form of Universal Time, usually UTC. The offset is chosen such that a new day starts approximately while the Sun is crossing the nadir meridian. Alternatively the difference is not really fixed, but it changes twice a year by a round amount, usually one hour, see Daylight saving time.

Julian day number is a count of days elapsed since Greenwich mean noon on 1 January 4713 B.C., Julian proleptic calendar. The Julian Date is the Julian day number followed by the fraction of the day elapsed since the preceding noon. Conveniently for astronomers, this avoids the date skip during an observation night. Modified Julian day (MJD) is defined as MJD = JD - 2400000.5. An MJD day thus begins at midnight, civil date. Julian dates can be expressed in UT1, TAI, TT, etc. and so for precise applications the timescale should be specified, e.g. MJD 49135.3824 TAI.^{ [14] }

Barycentric Coordinate Time (TCB) is a coordinate time having its spatial origin at the center of mass of the Solar System, which is called the barycenter.

Conversions between atomic time systems (TAI, GPST, and UTC) are for the most part exact. However, GPS time is a measured value as opposed to a computed "paper" scale.^{ [15] } As such it may differ from UTC(USNO) by a few hundred nanoseconds,^{ [16] } which in turn may differ from official UTC by as much as 26 nanoseconds.^{ [15] } Conversions for UT1 and TT rely on published difference tables which as of 2022^{ [update] } are specified to 10 microseconds and 0.1 nanoseconds respectively.

System | Description | UT1 | UTC | TT | TAI | GPS |
---|---|---|---|---|---|---|

UT1 | Mean Solar Time | UT1 | UTC = UT1 – DUT1 | TT = UT1 – DUT1 + LS + 32.184 s + DTT | TAI = UT1 – DUT1 + LS | GPS = UT1 – DUT1 + LS – 19 s |

UTC | Civil Time | UT1 = UTC + DUT1 | UTC | TT = UTC + LS + 32.184 s + DTT | TAI = UTC + LS | GPS = UTC + LS – 19 s |

TT | Terrestrial Time | UT1 = TT – 32.184 s - DTT – LS + DUT1 | UTC = TT – 32.184 s - DTT – LS | TT | TAI = TT – 32.184 s - DTT | GPS = TT – 51.184 s - DTT |

TAI | Atomic Time | UT1 = TAI – LS + DUT1 | UTC = TAI – LS | TT = TAI + 32.184 s + DTT | TAI | GPS = TAI – 19 s |

GPS | GPS Time | UT1 = GPS + 19 s – LS + DUT1 | UTC = GPS + 19 s – LS | TT = GPS + 51.184 s + DTT | TAI = GPS + 19 s | GPS |

Definitions:

- LS = TAI – UTC = Leap Seconds from USNO Table of Leap Seconds
- DUT1 = UT1 – UTC published in IERS Bulletins or U.S. Naval Observatory EO
- DTT = TT - TAI - 32.184 s published in BIPM's TT(BIPM) tables.

TCG is linearly related to TT as: TCG - TT = `L _{G}` * (JD -2443144.5) * 86400 seconds, with the scale difference

TCB is a linear transformation of TDB and TDB differs from TT in small, mostly periodic terms. Neglecting these terms (on the order of 2 milliseconds for several millennia around the present epoch),^{ [17] } TCB is related to TT by: TCB - TT = `L _{B}` * (JD -2443144.5) * 86400 seconds.

Apparent solar time or true solar time is based on the solar day, which is the period between one solar noon (passage of the real Sun across the meridian) and the next. A solar day is approximately 24 hours of mean time. Because the Earth's orbit around the Sun is elliptical, and because of the obliquity of the Earth's axis relative to the plane of the orbit (the ecliptic), the apparent solar day varies a few dozen seconds above or below the mean value of 24 hours. As the variation accumulates over a few weeks, there are differences as large as 16 minutes between apparent solar time and mean solar time (see Equation of time). However, these variations cancel out over a year. There are also other perturbations such as Earth's wobble, but these are less than a second per year.

Sidereal time is time by the stars. A sidereal rotation is the time it takes the Earth to make one revolution with rotation to the stars, approximately 23 hours 56 minutes 4 seconds. A mean solar day is about 3 minutes 56 seconds longer than a mean sidereal day, or 1⁄366 more than a mean sidereal day. In astronomy, sidereal time is used to predict when a star will reach its highest point in the sky. For accurate astronomical work on land, it was usual to observe sidereal time rather than solar time to measure mean solar time, because the observations of 'fixed' stars could be measured and reduced more accurately than observations of the Sun (in spite of the need to make various small compensations, for refraction, aberration, precession, nutation and proper motion). It is well known that observations of the Sun pose substantial obstacles to the achievement of accuracy in measurement.^{ [19] } In former times, before the distribution of accurate time signals, it was part of the routine work at any observatory to observe the sidereal times of meridian transit of selected 'clock stars' (of well-known position and movement), and to use these to correct observatory clocks running local mean sidereal time; but nowadays local sidereal time is usually generated by computer, based on time signals.^{ [20] }

Mean solar time was a time standard used especially at sea for navigational purposes, calculated by observing apparent solar time and then adding to it a correction, the equation of time, which compensated for two known irregularities in the length of the day, caused by the ellipticity of the Earth's orbit and the obliquity of the Earth's equator and polar axis to the ecliptic (which is the plane of the Earth's orbit around the sun). It has been superseded by Universal Time.

Greenwich Mean Time was originally mean time deduced from meridian observations made at the Royal Greenwich Observatory (RGO). The principal meridian of that observatory was chosen in 1884 by the International Meridian Conference to be the Prime Meridian. GMT either by that name or as 'mean time at Greenwich' used to be an international time standard, but is no longer so; it was initially renamed in 1928 as Universal Time (UT) (partly as a result of ambiguities arising from the changed practice of starting the astronomical day at midnight instead of at noon, adopted as from 1 January 1925). UT1 is still in reality mean time at Greenwich. Today, GMT is a time zone but is still the legal time in the UK in winter (and as adjusted by one hour for summer time). But Coordinated Universal Time (UTC) (an atomic-based time scale which is always kept within 0.9 second of UT1) is in common actual use in the UK, and the name GMT is often used to refer to it. (See articles Greenwich Mean Time, Universal Time, Coordinated Universal Time and the sources they cite.)

Versions of Universal Time such as UT0 and UT2 have been defined but are no longer in use.^{ [21] }^{ [22] }

Ephemeris time (ET) and its successor time scales described below have all been intended for astronomical use, e.g. in planetary motion calculations, with aims including uniformity, in particular, freedom from irregularities of Earth rotation. Some of these standards are examples of dynamical time scales and/or of coordinate time scales. Ephemeris Time was from 1952 to 1976 an official time scale standard of the International Astronomical Union; it was a dynamical time scale based on the orbital motion of the Earth around the Sun, from which the ephemeris second was derived as a defined fraction of the tropical year. This ephemeris second was the standard for the SI second from 1956 to 1967, and it was also the source for calibration of the caesium atomic clock; its length has been closely duplicated, to within 1 part in 10^{10}, in the size of the current SI second referred to atomic time.^{ [23] } This Ephemeris Time standard was non-relativistic and did not fulfil growing needs for relativistic coordinate time scales. It was in use for the official almanacs and planetary ephemerides from 1960 to 1983, and was replaced in official almanacs for 1984 and after, by numerically integrated Jet Propulsion Laboratory Development Ephemeris DE200 (based on the JPL relativistic coordinate time scale T_{eph}).

For applications at the Earth's surface, ET's official replacement was Terrestrial Dynamical Time (TDT), which maintained continuity with it. TDT is a uniform atomic time scale, whose unit is the SI second. TDT is tied in its rate to the SI second, as is International Atomic Time (TAI), but because TAI was somewhat arbitrarily defined at its inception in 1958 to be initially equal to a refined version of UT, TDT was offset from TAI, by a constant 32.184 seconds. The offset provided a continuity from Ephemeris Time to TDT. TDT has since been redefined as Terrestrial Time (TT).

For the calculation of ephemerides, Barycentric Dynamical Time (TDB) was officially recommended to replace ET. TDB is similar to TDT but includes relativistic corrections that move the origin to the barycenter, hence it is a dynamical time at the barycenter.^{ [24] } TDB differs from TT only in periodic terms. The difference is at most 2 milliseconds. Deficiencies were found in the definition of TDB (though not affecting T_{eph}), and TDB has been replaced by Barycentric Coordinate Time (TCB) and Geocentric Coordinate Time (TCG), and redefined to be JPL ephemeris time argument T_{eph}, a specific fixed linear transformation of TCB. As defined, TCB (as observed from the Earth's surface) is of divergent rate relative to all of ET, T_{eph} and TDT/TT;^{ [25] } and the same is true, to a lesser extent, of TCG. The ephemerides of Sun, Moon and planets in current widespread and official use continue to be those calculated at the Jet Propulsion Laboratory (updated as from 2003 to DE405) using as argument T_{eph}.

**International Atomic Time** is a high-precision atomic coordinate time standard based on the notional passage of proper time on Earth's geoid. TAI is a weighted average of the time kept by over 450 atomic clocks in over 80 national laboratories worldwide. It is a continuous scale of time, without leap seconds, and it is the principal realisation of Terrestrial Time. It is the basis for Coordinated Universal Time (UTC), which is used for civil timekeeping all over the Earth's surface and which has leap seconds.

In precise timekeeping, **Δ T** is a measure of the cumulative effect of the departure of the Earth's rotation period from the fixed-length day of International Atomic Time. Formally, Δ

The term **ephemeris time** can in principle refer to time in association with any ephemeris. In practice it has been used more specifically to refer to:

- a former standard astronomical time scale adopted in 1952 by the IAU, and superseded during the 1970s. This time scale was proposed in 1948, to overcome the disadvantages of irregularly fluctuating mean solar time. The intent was to define a uniform time based on Newtonian theory. Ephemeris time was a first application of the concept of a dynamical time scale, in which the time and time scale are defined implicitly, inferred from the observed position of an astronomical object via the dynamical theory of its motion.
- a modern relativistic coordinate time scale, implemented by the JPL ephemeris time argument T
_{eph}, in a series of numerically integrated Development Ephemerides. Among them is the DE405 ephemeris in widespread current use. The time scale represented by T_{eph}is closely related to, but distinct from, the TCB time scale currently adopted as a standard by the IAU.

**Greenwich Mean Time** (**GMT**) is the local mean time at the Royal Observatory in Greenwich, London, counted from midnight. At different times in the past, it has been calculated in different ways, including being calculated from noon; as a consequence, it cannot be used to specify a particular time unless a context is given. The term *GMT* is also used as one of the names for the time zone UTC+00:00 and, in UK law, is the basis for civil time in the United Kingdom.

A **leap second** is a one-second adjustment that is occasionally applied to Coordinated Universal Time (UTC), to accommodate the difference between precise time and imprecise observed solar time (UT1), which varies due to irregularities and long-term slowdown in the Earth's rotation. The UTC time standard, widely used for international timekeeping and as the reference for civil time in most countries, uses TAI and consequently would run ahead of observed solar time unless it is reset to UT1 as needed. The leap second facility exists to provide this adjustment. The leap second was introduced in 1972 and since then 27 leap seconds have been added to UTC with the most recent leap second occuring on December 31, 2016.

The **second** is the unit of time in the International System of Units (SI), historically defined as 1⁄86400 of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds each. "Minute" comes from the Latin *pars minuta prima* , meaning "first small part", and "second" comes from the *pars minuta secunda* , "second small part".

**Terrestrial Time** (**TT**) is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of Earth. For example, the Astronomical Almanac uses TT for its tables of positions (ephemerides) of the Sun, Moon and planets as seen from Earth. In this role, TT continues **Terrestrial Dynamical Time**, which succeeded ephemeris time (ET). TT shares the original purpose for which ET was designed, to be free of the irregularities in the rotation of Earth.

**Universal Time** is a time standard based on Earth's rotation. While originally it was mean solar time at 0° longitude, precise measurements of the Sun are difficult. Therefore, UT1 is computed from a measure of the Earth's angle with respect to the International Celestial Reference Frame (ICRF), called the Earth Rotation Angle. UT1 is the same everywhere on Earth. UT1 is required to follow the relationship

**Sidereal time** is a system of timekeeping used especially by astronomers. Using sidereal time and the celestial coordinate system, it is easy to locate the positions of celestial objects in the night sky. Sidereal time is a "time scale that is based on Earth's rate of rotation measured relative to the fixed stars".

**Solar time** is a calculation of the passage of time based on the position of the Sun in the sky. The fundamental unit of solar time is the day, based on the synodic rotation period. Traditionally, there are three types of time reckoning based on astronomical observations: apparent solar time and mean solar time, and sidereal time, which is based on the apparent motions of stars other than the Sun.

**Barycentric Dynamical Time** is a relativistic coordinate time scale, intended for astronomical use as a time standard to take account of time dilation when calculating orbits and astronomical ephemerides of planets, asteroids, comets and interplanetary spacecraft in the Solar System. TDB is now defined as a linear scaling of Barycentric Coordinate Time (TCB). A feature that distinguishes TDB from TCB is that TDB, when observed from the Earth's surface, has a difference from Terrestrial Time (TT) that is about as small as can be practically arranged with consistent definition: the differences are mainly periodic, and overall will remain at less than 2 milliseconds for several millennia.

**Barycentric Coordinate Time** is a coordinate time standard intended to be used as the independent variable of time for all calculations pertaining to orbits of planets, asteroids, comets, and interplanetary spacecraft in the Solar System. It is equivalent to the proper time experienced by a clock at rest in a coordinate frame co-moving with the barycenter of the Solar System : that is, a clock that performs exactly the same movements as the Solar System but is outside the system's gravity well. It is therefore not influenced by the gravitational time dilation caused by the Sun and the rest of the system. TCB is the time coordinate for the Barycentric Celestial Reference System (BCRS).

**Geocentric Coordinate Time** is a coordinate time standard intended to be used as the independent variable of time for all calculations pertaining to precession, nutation, the Moon, and artificial satellites of the Earth. It is equivalent to the proper time experienced by a clock at rest in a coordinate frame co-moving with the center of the Earth : that is, a clock that performs exactly the same movements as the Earth but is outside the Earth's gravity well. It is therefore not influenced by the gravitational time dilation caused by the Earth. The TCG is the time coordinate for the Geocentric Celestial Reference System (GCRS).

**DUT1** is a time correction equal to the difference between Universal Time (UT1), which is defined by Earth's rotation, and Coordinated Universal Time (UTC), which is defined by a network of precision atomic clocks.

**Theoretical astronomy** is the use of analytical and computational models based on principles from physics and chemistry to describe and explain astronomical objects and astronomical phenomena. Theorists in astronomy endeavor to create theoretical models and from the results predict observational consequences of those models. The observation of a phenomenon predicted by a model allows astronomers to select between several alternate or conflicting models as the one best able to describe the phenomena.

In the theory of relativity, it is convenient to express results in terms of a spacetime coordinate system relative to an implied observer. In many coordinate systems, an event is specified by one time coordinate and three spatial coordinates. The time specified by the time coordinate is referred to as **coordinate time** to distinguish it from proper time.

**Earth's rotation** or **Earth's spin** is the rotation of planet Earth around its own axis, as well as changes in the orientation of the rotation axis in space. Earth rotates eastward, in prograde motion. As viewed from the northern polar star Polaris, Earth turns counterclockwise.

In time standards, **dynamical time** is the independent variable of the equations of celestial mechanics. This is in contrast to time scales such as mean solar time which are based on how far the earth has turned. Since Earth's rotation is not constant, using a time scale based on it for calculating the positions of heavenly objects gives errors. Dynamical time can be inferred from the observed position of an astronomical object via a theory of its motion. A first application of this concept of dynamical time was the definition of the ephemeris time scale (ET).

A **tropical year** or **solar year** is the time that the Sun takes to return to the same position in the sky – as viewed from the Earth or another celestial body of the Solar System – thus completing a full cycle of astronomical seasons. For example, it is the time from vernal equinox to the next vernal equinox, or from summer solstice to the next summer solstice. It is the type of year used by tropical solar calendars.

**Coordinated Universal Time** or **UTC** is the primary time standard globally used to regulate clocks and time. It establishes a reference for the current time, forming the basis for civil time and time zones. UTC facilitates international communication, navigation, scientific research, and commerce.

- ↑ IEC 60050-113:2011, item 113-01-08
- ↑ IEC 60050-113:2011, item 113-01-012: "mark attributed to an instant by means of a specified time scale
- ↑ IEC 60050-113:2011, item 113-01-010; ISO 80000-3:2006, item 3–7
- ↑ IEC 60050-113:2011, item 113-01-013: "range of a time interval (113-01-10)"
- ↑ ISO 80000-3:2006, item 3–7
- ↑ U.S. Naval Observatory. "Leap Seconds". Archived from the original on 2019-10-19. Retrieved 19 October 2019.
- ↑
*Whitaker's Almanac 2013*(ed. Ruth Northey), London 2012, p. 1131, ISBN 978-1-4081-7207-0. - ↑ "Leap Seconds". Time Service Department, United States Naval Observatory. Archived from the original on March 12, 2015. Retrieved November 22, 2015.
- ↑ "SI Brochure (2006)" (PDF).
*SI Brochure 8th Edition*. BIPM. p. 112. Archived (PDF) from the original on May 3, 2019. Retrieved May 23, 2019. - ↑ McCarthy, Dennis D.; Seidelmann, P. Kenneth (2009).
*Time: From Earth Rotation to Atomic Physics*. Weinheim: Wiley. pp. 231–232. - ↑ "Base unit definitions: Second". NIST. Archived from the original on 17 April 2011. Retrieved 9 April 2011.
- ↑ TAI
- ↑ "BIPM - clock comparisons". Archived from the original on 2019-08-10.
- ↑ Matsakis, Demetrios. "Systems of time". Archived from the original on 2019-09-30. Retrieved 30 September 2019.
- 1 2 "International Time Scales and the B.I.P.M. — Naval Oceanography Portal".
*www.usno.navy.mil*. Retrieved 23 March 2022. - ↑ "USNO GPS Time Transfer — Naval Oceanography Portal".
*www.usno.navy.mil*. Retrieved 23 March 2022.GPS time is automatically steered to UTC(USNO) on a daily basis to keep system time within one microsecond of UTC(USNO), but during the last several years has been within a few hundred nanoseconds.

- 1 2 "IAU 2006 Resolution B3: Re-definition of Barycentric Dynamical Time, TDB" (PDF). p. 2. Archived (PDF) from the original on 2022-10-09. Retrieved 4 April 2022.
- ↑ "IAU (1991) RECOMMENDATION III".
*www.iers.org*. Note 1. - ↑ See H A Harvey, "The Simpler Aspects of Celestial Mechanics", in Popular Astronomy 44 (1936), 533-541.
- ↑ A E Roy, D Clarke, 'Astronomy: Principles and Practice' (4th edition, 2003) at p.89.
- ↑ Urban & Seidelmann 2013, p. 81.
- ↑ Schlyter, Paul. "Time Scales: UT1, UTC, TAI, ET, TT, GPS time".
*www.stjarnhimlen.se*. Retrieved 21 March 2022.UT2 is nowadays considered obsolete.

- ↑ W Markowitz, R G Hall, L Essen, J V L Parry (1958), 'Frequency of caesium in terms of ephemeris time', Phys Rev Letters v1 (1958), 105-107; and Wm Markowitz (1988) 'Comparisons of ET(Solar), ET(Lunar), UT and TDT', in (eds.) A K Babcock & G A Wilkins, 'The Earth's Rotation and Reference Frames for Geodesy and Geophysics', IAU Symposia #128 (1988), at pp 413-418.
- ↑ V Brumberg, S Kopeikin (1990), 'Relativistic time scales in the solar system', Celestial Mechanics and Dynamical Astronomy (1990), Vol. 48, 23-44
- ↑ P K Seidelmann & T Fukushima (1992), "Why new time scales?",
*Astronomy & Astrophysics*vol.265 (1992), pages 833-838, including Fig. 1 at p.835, a graph giving an overview of the rate differences and offsets between various standard time scales, present and past, defined by the IAU.

- Urban, Sean; Seidelmann, P. Kenneth, eds. (2013).
*Explanatory Supplement to the Astronomical Almanac*(3rd ed.). Mill Valley, California: University Science Books. *Explanatory Supplement to the Astronomical Almanac,*P. K. Seidelmann, ed., University Science Books, 1992, ISBN 0-935702-68-7.

- Current time according to the bservatory (get the current time)
- Systems of Time by Demetrios Matsakis, Director, Time Service Dept., United States Naval Observatory
- USNO article on the definition of seconds and leap seconds Archived 2012-06-11 at the Wayback Machine
- A history of astronomical time scales by Steve Allen
- Why is a minute divided into 60 seconds, an hour into 60 minutes, yet there are only 24 hours in a day Ask the Experts – March 5, 2021. SCIENTIFIC AMERICAN

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