Terrestrial Time

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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. [1] 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 (TDT or TD), [2] 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.

Contents

The unit of TT is the SI second, the definition of which is based currently on the caesium atomic clock, [3] but TT is not itself defined by atomic clocks. It is a theoretical ideal, and real clocks can only approximate it.

TT is distinct from the time scale often used as a basis for civil purposes, Coordinated Universal Time (UTC). TT is indirectly the basis of UTC, via International Atomic Time (TAI). Because of the historical difference between TAI and ET when TT was introduced, TT is 32.184 s ahead of TAI.

History

A definition of a terrestrial time standard was adopted by the International Astronomical Union (IAU) in 1976 at its XVI General Assembly and later named Terrestrial Dynamical Time (TDT). It was the counterpart to Barycentric Dynamical Time (TDB), which was a time standard for Solar system ephemerides, to be based on a dynamical time scale. Both of these time standards turned out to be imperfectly defined. Doubts were also expressed about the meaning of 'dynamical' in the name TDT.

In 1991, in Recommendation IV of the XXI General Assembly, the IAU redefined TDT, also renaming it "Terrestrial Time". TT was formally defined in terms of Geocentric Coordinate Time (TCG), defined by the IAU on the same occasion. TT was defined to be a linear scaling of TCG, such that the unit of TT is the "SI second on the geoid", [4] i.e. the rate approximately matched the rate of proper time on the Earth's surface at mean sea level. Thus the exact ratio between TT time and TCG time was , where was a constant and was the gravitational potential at the geoid surface, a value measured by physical geodesy. In 1991 the best available estimate of was 6.969291×10−10.

In 2000, the IAU very slightly altered the definition of TT by adopting an exact value, LG = 6.969290134×10−10. [5]

Current definition

TT differs from Geocentric Coordinate Time (TCG) by a constant rate. Formally it is defined by the equation

where TT and TCG are linear counts of SI seconds in Terrestrial Time and Geocentric Coordinate Time respectively, is the constant difference in the rates of the two time scales, and is a constant to resolve the epochs (see below). is defined as exactly 6.969290134×10−10. Due to the term the rate of TT is very slightly slower than that of TCG.

The equation linking TT and TCG more commonly has the form given by the IAU,

where is the TCG time expressed as a Julian date (JD). The Julian Date is a linear transformation of the raw count of seconds represented by the variable TCG, so this form of the equation is not simplified. The use of a Julian Date specifies the epoch fully. The above equation is often given with the Julian Date 2443144.5 for the epoch, but that is inexact (though inappreciably so, because of the small size of the multiplier ). The value 2443144.5003725 is exactly in accord with the definition.

Time coordinates on the TT and TCG scales are specified conventionally using traditional means of specifying days, inherited from non-uniform time standards based on the rotation of Earth. Specifically, both Julian Dates and the Gregorian calendar are used. For continuity with their predecessor Ephemeris Time (ET), TT and TCG were set to match ET at around Julian Date 2443144.5(1977-01-01T00Z). More precisely, it was defined that TT instant 1977-01-01T00:00:32.184 and TCG instant 1977-01-01T00:00:32.184 exactly correspond to the International Atomic Time (TAI) instant 1977-01-01T00:00:00.000. This is also the instant at which TAI introduced corrections for gravitational time dilation.

TT and TCG expressed as Julian Dates can be related precisely and most simply by the equation

where is 2443144.5003725 exactly.

Realizations

TT is a theoretical ideal, not dependent on a particular realization. For practical use, physical clocks must be measured and their readings processed to estimate TT. A simple offset calculation is sufficient for most applications, but in demanding applications, detailed modeling of relativistic physics and measurement uncertainties may be needed. [6]

TAI

The main realization of TT is supplied by TAI. The BIPM TAI service, performed since 1958, estimates TT using measurements from an ensemble of atomic clocks spread over the surface and low orbital space of Earth. TAI is canonically defined retrospectively, in monthly bulletins, in relation to the readings shown by that particular group of atomic clocks at the time. Estimates of TAI are also provided in real time by the institutions that operate the participating clocks. Because of the historical difference between TAI and ET when TT was introduced, the TAI realization of TT is defined thus: [7]

The offset 32.184 s arises from history. The atomic time scale A1 (a predecessor of TAI) was set equal to UT2 at its conventional starting date of 1 January 1958, [8] when ΔT (ET − UT) was about 32 seconds. The offset 32.184 seconds was the 1976 estimate of the difference between Ephemeris Time (ET) and TAI, "to provide continuity with the current values and practice in the use of Ephemeris Time". [9]

TAI is never revised once published and TT(TAI) has small errors relative to TT(BIPM), [6] on the order of 10-50 microseconds. [10]

The GPS time scale has a nominal difference from atomic time (TAI − GPS time = +19 seconds), [11] so that TT ≈ GPS time + 51.184 seconds. This realization introduces up to a microsecond of additional error, as the GPS signal is not precisely synchronized with TAI, but GPS receiving devices are widely available. [12]

TT(BIPM)

Approximately annually since 1992, the International Bureau of Weights and Measures (BIPM) has produced better realizations of TT based on reanalysis of historical TAI data. BIPM's realizations of TT are named in the form "TT(BIPM08)", with the digits indicating the year of publication. They are published in the form of a table of differences from TT(TAI), along with an extrapolation equation that may be used for dates later than the table. The latest as of July 2024 is TT(BIPM23). [13]

Pulsars

Researchers from the International Pulsar Timing Array collaboration have created a realization TT(IPTA16) of TT based on observations of an ensemble of pulsars up to 2012. This new pulsar time scale is an independent means of computing TT. The researchers observed that their scale was within 0.5 microseconds of TT(BIPM17), with significantly lower errors since 2003. The data used was insufficient to analyze long-term stability, and contained several anomalies, but as more data is collected and analyzed, this realization may eventually be useful to identify defects in TAI and TT(BIPM). [14]

Other standards

TT is in effect a continuation of (but is more precisely uniform than) the former Ephemeris Time (ET). It was designed for continuity with ET, [15] and it runs at the rate of the SI second, which was itself derived from a calibration using the second of ET (see, under Ephemeris time, Redefinition of the second and Implementations). The JPL ephemeris time argument Teph is within a few milliseconds of TT.

TT is slightly ahead of UT1 (a refined measure of mean solar time at Greenwich) by an amount known as ΔT = TT − UT1. ΔT was measured at +67.6439 seconds (TT ahead of UT1) at 0 h UTC on 1 January 2015; [16] and by retrospective calculation, ΔT was close to zero about the year 1900. ΔT is expected to continue to increase, with UT1 becoming steadily (but irregularly) further behind TT in the future. In fine detail, ΔT is somewhat unpredictable, with 10-year extrapolations diverging by 2-3 seconds from the actual value. [17]

Relativistic relationships

Observers in different locations, that are in relative motion or at different altitudes, can disagree about the rates of each other's clocks, owing to effects described by the theory of relativity. As a result, TT (even as a theoretical ideal) does not match the proper time of all observers.

In relativistic terms, TT is described as the proper time of a clock located on the geoid (essentially mean sea level). [18] However, [19] TT is now actually defined as a coordinate time scale. [20] The redefinition did not quantitatively change TT, but rather made the existing definition more precise. In effect it defined the geoid (mean sea level) in terms of a particular level of gravitational time dilation relative to a notional observer located at infinitely high altitude.

The present definition of TT is a linear scaling of Geocentric Coordinate Time (TCG), which is the proper time of a notional observer who is infinitely far away (so not affected by gravitational time dilation) and at rest relative to Earth. TCG is used to date mainly for theoretical purposes in astronomy. From the point of view of an observer on Earth's surface the second of TCG passes in slightly less than the observer's SI second. The comparison of the observer's clock against TT depends on the observer's altitude: they will match on the geoid, and clocks at higher altitude tick slightly faster.

See also

Related Research Articles

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.

<span class="mw-page-title-main">Astronomical unit</span> Mean distance between Earth and the Sun

The astronomical unit is a unit of length defined to be exactly equal to 149,597,870,700 m. Historically, the astronomical unit was conceived as the average Earth-Sun distance, before its modern redefinition in 2012.

Δ<i>T</i> (timekeeping) Measure of variation of solar time from atomic time

In precise timekeeping, ΔT 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, ΔT is the time difference ΔT = TT − UT between Universal Time and Terrestrial Time. The value of ΔT for the start of 1902 was approximately zero; for 2002 it was about 64 seconds. So Earth's rotations over that century took about 64 seconds longer than would be required for days of atomic time. As well as this long-term drift in the length of the day there are short-term fluctuations in the length of day which are dealt with separately.

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:

  1. 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.
  2. a modern relativistic coordinate time scale, implemented by the JPL ephemeris time argument Teph, in a series of numerically integrated Development Ephemerides. Among them is the DE405 ephemeris in widespread current use. The time scale represented by Teph is closely related to, but distinct from, the TCB time scale currently adopted as a standard by the IAU.
<span class="mw-page-title-main">Second</span> SI unit of time

The second is a unit of time, 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.

<span class="mw-page-title-main">Caesium standard</span> Primary frequency standard

The caesium standard is a primary frequency standard in which the photon absorption by transitions between the two hyperfine ground states of caesium-133 atoms is used to control the output frequency. The first caesium clock was built by Louis Essen in 1955 at the National Physical Laboratory in the UK and promoted worldwide by Gernot M. R. Winkler of the United States Naval Observatory.

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.

<span class="mw-page-title-main">Earth radius</span> Distance from the Earth surface to a point near its center

Earth radius is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid, the radius ranges from a maximum of nearly 6,378 km (3,963 mi) to a minimum of nearly 6,357 km (3,950 mi).

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).

The astronomical system of units, formerly called the IAU (1976) System of Astronomical Constants, is a system of measurement developed for use in astronomy. It was adopted by the International Astronomical Union (IAU) in 1976 via Resolution No. 1, and has been significantly updated in 1994 and 2009.

An astronomical constant is any of several physical constants used in astronomy. Formal sets of constants, along with recommended values, have been defined by the International Astronomical Union (IAU) several times: in 1964 and in 1976. In 2009 the IAU adopted a new current set, and recognizing that new observations and techniques continuously provide better values for these constants, they decided to not fix these values, but have the Working Group on Numerical Standards continuously maintain a set of Current Best Estimates. The set of constants is widely reproduced in publications such as the Astronomical Almanac of the United States Naval Observatory and HM Nautical Almanac Office.

<span class="mw-page-title-main">Theoretical astronomy</span> Applied and interdisciplinary physics

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.

The Astronomical Almanac is an almanac published by the United Kingdom Hydrographic Office; it also includes data supplied by many scientists from around the world. On page vii, the listed major contributors to its various Sections are: H.M Nautical Almanac Office, United Kingdom Hydrographic Office; the Nautical Almanac Office, United States Naval Observatory; the Jet Propulsion Laboratory, California Institute of Technology; the IAU Standards Of Fundamental Astronomy (SOFA) initiative; the Institut de Mécanique Céleste et des Calcul des Éphémerides, Paris Observatory; and the Minor Planet Center, Cambridge, Massachusetts. It is considered a worldwide resource for fundamental astronomical data, often being the first publication to incorporate new International Astronomical Union resolutions. The almanac largely contains Solar System ephemerides based on the JPL Solar System integration "DE440", and catalogs of selected stellar and extragalactic objects. The material appears in sections, each section addressing a specific astronomical category. The book also includes references to the material, explanations, and examples. It used to be available up to one year in advance of its date, however the current 2024 edition became available only one month in advance; in December 2023.

<span class="mw-page-title-main">Dynamical time scale</span> Time standard

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.

<span class="mw-page-title-main">Coordinated Universal Time</span> Primary time standard

Coordinated Universal Time (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.

<span class="mw-page-title-main">Atomic clock</span> Clock that monitors the resonant frequency of atoms

An atomic clock is a clock that measures time by monitoring the resonant frequency of atoms. It is based on atoms having different energy levels. Electron states in an atom are associated with different energy levels, and in transitions between such states they interact with a very specific frequency of electromagnetic radiation. This phenomenon serves as the basis for the International System of Units' (SI) definition of a second:

The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency, , the unperturbed ground-state hyperfine transition frequency of the caesium-133 atom, to be 9192631770 when expressed in the unit Hz, which is equal to s−1.

References

  1. ↑ The 1991 definition refers to the scale agreeing with the SI second "on the geoid", i.e. close to mean sea level on Earth's surface, see IAU 1991 XXIst General Assembly (Buenos Aires) Resolutions, Resolution A.4 (Recommendation IV). A redefinition by resolution of the IAU 2000 24th General Assembly (Manchester), at Resolution B1.9, is in different terms intended for continuity and to come very close to the same standard.
  2. ↑ TT is equivalent to TDT, see IAU conference 1991, Resolution A4, recommendation IV, note 4.
  3. ↑ IAU conference 1991, Resolution A4, recommendation IV, part 2 states that the unit for TT is to agree with the SI second 'on the geoid'.
  4. ↑ "IAU(1991) RECOMMENDATION IV". IERS.
  5. ↑ "Resolution B1.9 of the IAU XXIV General Assembly, 2000".
  6. 1 2 Guinot, B. (1 March 1988). "Atomic time scales for pulsar studies and other demanding applications". Astronomy and Astrophysics. 192 (1–2): 370–373. Bibcode:1988A&A...192..370G. ISSN   0004-6361.
  7. ↑ IAU conference 1991, Resolution A4, recommendation IV, note 9.
  8. ↑ L Essen, "Time Scales", Metrologia, vol.4 (1968), 161-165, at 163
  9. ↑ IAU Commission 4 (Ephemerides), Recommendations to IAU General Assembly 1976, Notes on Recommendation 5, note 2
  10. ↑ "TT(BIPM22)" . Retrieved 14 December 2023.
  11. ↑ Steve Allen. "Time Scales". Lick Observatory . Retrieved 13 August 2017.
  12. ↑ "GPS time accurate to 100 nanoseconds". Galleon. Archived from the original on 14 May 2012. Retrieved 12 October 2012.
  13. ↑ "Index of /ftp/pub/tai/ttbipm". webtai.bipm.org. Retrieved 8 July 2024.
  14. ↑ Hobbs, G.; Guo, L.; Caballero, R. N.; Coles, W.; Lee, K. J.; Manchester, R. N.; Reardon, D. J.; Matsakis, D.; Tong, M. L.; Arzoumanian, Z.; Bailes, M.; Bassa, C. G.; Bhat, N D R.; Brazier, A.; Burke-Spolaor, S.; Champion, D. J.; Chatterjee, S.; Cognard, I.; Dai, S.; Desvignes, G.; Dolch, T.; Ferdman, R. D.; Graikou, E.; Guillemot, L.; Janssen, G. H.; Keith, M. J.; Kerr, M.; Kramer, M.; Lam, M. T.; et al. (2020). "A pulsar-based time-scale from the International Pulsar Timing Array". Monthly Notices of the Royal Astronomical Society. 491 (4): 5951–5965. arXiv: 1910.13628 . Bibcode:2020MNRAS.491.5951H. doi: 10.1093/mnras/stz3071 . S2CID   204961320.
  15. ↑ P K Seidelmann (ed.) (1992), 'Explanatory Supplement to the Astronomical Almanac', at p.42; also IAU Commission 4 (Ephemerides), Recommendations to IAU General Assembly 1976, Notes on Recommendation 5, note 2.
  16. ↑ US Naval Observatory (USNO) data file online at https://web.archive.org/web/20190808224315/http://maia.usno.navy.mil:80/ser7/deltat.data (accessed 27 October 2015).
  17. ↑ "Delta T: Past, Present and Future". The Astronomical Almanac Online. 2020. Archived from the original on 18 September 2022.
  18. ↑ For example, IAU Commission 4 (Ephemerides), Recommendations to IAU General Assembly 1976, Notes on Recommendation 5, note 1, as well as other sources, indicate the time scale for apparent geocentric ephemerides as a proper time.
  19. ↑ B Guinot (1986), "Is the International Atomic Time a Coordinate Time or a Proper Time?", Celestial Mechanics, 38 (1986), pp.155-161.
  20. ↑ IAU General Assembly 1991, Resolution A4, Recommendations III and IV, define TCB and TCG as coordinate time scales, and TT as a linear scaling of TCG, hence also a coordinate time.
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