Terrestrial Time
Encyclopedia
Terrestrial Time is a modern astronomical time standard
defined by the International Astronomical Union
, primarily for time-measurements of astronomical observations made from the surface of the Earth.
For example, the Astronomical Almanac
uses TT for its tables of positions (ephemerides
) of the Sun, Moon and planets as seen from the Earth. In this role, TT continues Terrestrial Dynamical Time (TDT), which in turn succeeded ephemeris time (ET)
.
The unit of TT is the SI second, the definition of which is currently based on the caesium atomic clock
, but TT is not itself defined by atomic clocks. It is a theoretical ideal, which real clocks can only approximate.
TT is distinct from the time scale often used as a basis for civil purposes, Coordinated Universal Time
(UTC). TT indirectly underlies UTC, via International Atomic Time
(TAI).
(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
(Earth surface at mean sea level). This left the exact ratio between TT time and TCG time as something to be determined by experiment. Experimental determination of the gravitational potential at the geoid surface is a task in physical geodesy
.
In 2000, the IAU very slightly altered the definition of TT by adopting an exact value for the ratio between TT and TCG time, as 1 − 6.969290134 × 10−10. (As measured on the geoid surface, the rate of TCG is very slightly faster than that of TT, see below, Relativistic relationships of TT.)
(TCG) by a constant rate. Formally it is defined by the equation
where TT and TCG are linear counts of SI
second
s in Terrestrial Time and Geocentric Coordinate Time respectively, LG is the constant difference in the rates of the two time scales, and E is a constant to resolve the epoch
s (see below). LG is defined as exactly 6.969290134 × 10−10. (In 1991 when TT was first defined, LG was to be determined by experiment, and the best available estimate was 6.969291 × 10−10.)
The equation linking TT and TCG is more commonly seen in the form
where JDTCG is the TCG time expressed as a Julian Date. This is just a transformation of the raw count of seconds represented by the variable TCG, so this form of the equation is needlessly complex. The use of a Julian Date does specify the epoch fully, however (see next paragraph). 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 LG). The value 2443144.5003725 is exactly in accord with the definition.
Time coordinates on the TT and TCG scales are conventionally specified using traditional means of specifying days, carried over from non-uniform time standards based on the rotation of the 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 exactly and TCG instant 1977-01-01T00:00:32.184 exactly correspond to the International Atomic Time
(TAI) instant 1977-01-01T00:00:00.000 exactly. 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 EJD is 2443144.5003725 exactly.
The main realization of TT is supplied by TAI. The TAI service, running since 1958, attempts to match the rate of proper time on the geoid, using an ensemble of atomic clock
s spread over the surface and low orbital space of the Earth. TAI is canonically defined retrospectively, in monthly bulletins, in relation to the readings that particular groups of atomic clocks showed 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:
Because TAI is never revised once published, it is possible for errors in it to become known and remain uncorrected. It is thus possible to produce a better realization of TT based on reanalysis of historical TAI data. The BIPM has done this approximately annually since 1992. These 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 table of differences from TT(TAI). The latest is [ftp://tai.bipm.org/TFG/TT(BIPM)/TTBIPM.10 TT(BIPM10)].
The international communities of precision timekeeping, astronomy
, and radio
broadcasts have considered creating a new precision time scale based on observations of an ensemble of pulsars. This new pulsar time scale will serve as an independent means of computing TT, and it may eventually be useful to identify defects in TAI.
. 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).
However,
TT is now actually defined as a coordinate time scale.
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 the Earth. TCG is used so far mainly for theoretical purposes in astronomy. From the point of view of an observer on the 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.
Time standard
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...
defined by the International Astronomical Union
IAU
IAU may refer to:*International Astronomical Union*International American University*International American University College of Medicine*International Association of Universities*International Association of Ultrarunners...
, primarily for time-measurements of astronomical observations made from the surface of the Earth.
For example, the Astronomical Almanac
Astronomical Almanac
The Astronomical Almanac is an almanac published by the United States Naval Observatory and Her Majesty's Nautical Almanac Office, containing solar system ephemeris and catalogs of selected stellar and extragalactic objects....
uses TT for its tables of positions (ephemerides
Ephemeris
An ephemeris is a table of values that gives the positions of astronomical objects in the sky at a given time or times. Different kinds of ephemerides are used for astronomy and astrology...
) of the Sun, Moon and planets as seen from the Earth. In this role, TT continues Terrestrial Dynamical Time (TDT), which in turn succeeded ephemeris time (ET)
Ephemeris time
The term ephemeris time can in principle refer to time in connection with any astronomical ephemeris. In practice it has been used more specifically to refer to:...
.
The unit of TT is the SI second, the definition of which is currently based on the caesium atomic clock
Atomic clock
An atomic clock is a clock that uses an electronic transition frequency in the microwave, optical, or ultraviolet region of the electromagnetic spectrum of atoms as a frequency standard for its timekeeping element...
, but TT is not itself defined by atomic clocks. It is a theoretical ideal, which real clocks can only approximate.
TT is distinct from the time scale often used as a basis for civil purposes, Coordinated Universal Time
Coordinated Universal Time
Coordinated Universal Time is the primary time standard by which the world regulates clocks and time. It is one of several closely related successors to Greenwich Mean Time. Computer servers, online services and other entities that rely on having a universally accepted time use UTC for that purpose...
(UTC). TT indirectly underlies UTC, via International Atomic Time
International Atomic Time
International Atomic Time is a high-precision atomic coordinate time standard based on the notional passage of proper time on Earth's geoid...
(TAI).
Approximation
Sometimes times described in TT must be handled in situations where TT's detailed theoretical properties are not significant. Where millisecond accuracy is enough (or more than enough), TT can be summarized in the following ways:- To millisecond accuracy, TT runs parallel to the atomic timescale (International Atomic TimeInternational Atomic TimeInternational Atomic Time is a high-precision atomic coordinate time standard based on the notional passage of proper time on Earth's geoid...
, TAIInternational Atomic TimeInternational Atomic Time is a high-precision atomic coordinate time standard based on the notional passage of proper time on Earth's geoid...
) maintained by the BIPM. TT is ahead of TAI, and can be approximated as TT ~= TAI + 32.184 seconds. (The offset 32.184 s arises from the history.) - TT also runs in parallel with the GPS time scale, which has a constant difference from atomic time ( (TAI - GPS time) = +19 seconds), so that TT ~= GPS time + 51.184 seconds.
- TT is in effect a continuation of (but is more precisely uniform than) the former Ephemeris TimeEphemeris timeThe term ephemeris time can in principle refer to time in connection with any astronomical ephemeris. In practice it has been used more specifically to refer to:...
(ET). It was designed for continuity with ET, 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.) TT shares the original purpose for which ET was designed, to be free of the irregularities of mean solar time. - TT runs a little ahead of UT1 (a refined measure of mean solar time at Greenwich) by an amount known as deltaT = TT - UT1. DeltaT was measured at +65.7768 seconds (TT ahead of UT1) at 0h UTC on 1 January 2009; and by retrospective calculation, deltaT was close to zero around the year 1900. The difference deltaT, though somewhat unpredictable in fine detail, is expected to continue to increase, with UT1 becoming steadily (but irregularly) further behind TT in the future.
History
A definition of a terrestrial time standard was adopted by the International Astronomical UnionInternational Astronomical Union
The International Astronomical Union IAU is a collection of professional astronomers, at the Ph.D. level and beyond, active in professional research and education in astronomy...
(IAU) in 1976 at its XVI General Assembly, and later named Terrestrial Dynamical Time (TDT). It was the counterpart to Barycentric Dynamical Time
Barycentric Dynamical Time
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), which was a time standard for Solar system ephemerides, to be based on a dynamical time scale
Dynamical time scale
Dynamical time scale has two distinct meanings and usages, both related to astronomy:#In one use, which occurs in stellar physics, the dynamical time scale is alternatively known as the freefall time scale, and is in general, the length of time over which changes in one part of a body can be...
. 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
Geocentric Coordinate Time
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...
(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
Geoid
The geoid is that equipotential surface which would coincide exactly with the mean ocean surface of the Earth, if the oceans were in equilibrium, at rest , and extended through the continents . According to C.F...
(Earth surface at mean sea level). This left the exact ratio between TT time and TCG time as something to be determined by experiment. Experimental determination of the gravitational potential at the geoid surface is a task in physical geodesy
Physical geodesy
Physical geodesy is the study of the physical properties of the gravity field of the Earth, the geopotential, with a view to their application in geodesy.-Measurement procedure:...
.
In 2000, the IAU very slightly altered the definition of TT by adopting an exact value for the ratio between TT and TCG time, as 1 − 6.969290134 × 10−10. (As measured on the geoid surface, the rate of TCG is very slightly faster than that of TT, see below, Relativistic relationships of TT.)
Current definition
TT differs from Geocentric Coordinate TimeGeocentric Coordinate Time
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...
(TCG) by a constant rate. Formally it is defined by the equation
- TT = (1 − LG) TCG + E
where TT and TCG are linear counts of SI
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...
second
Second
The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....
s in Terrestrial Time and Geocentric Coordinate Time respectively, LG is the constant difference in the rates of the two time scales, and E is a constant to resolve the epoch
Epoch (reference date)
In the fields of chronology and periodization, an epoch is an instance in time chosen as the origin of a particular era. The "epoch" then serves as a reference point from which time is measured...
s (see below). LG is defined as exactly 6.969290134 × 10−10. (In 1991 when TT was first defined, LG was to be determined by experiment, and the best available estimate was 6.969291 × 10−10.)
The equation linking TT and TCG is more commonly seen in the form
- TT = TCG − LG × (JDTCG − 2443144.5003725) × 86400
where JDTCG is the TCG time expressed as a Julian Date. This is just a transformation of the raw count of seconds represented by the variable TCG, so this form of the equation is needlessly complex. The use of a Julian Date does specify the epoch fully, however (see next paragraph). 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 LG). The value 2443144.5003725 is exactly in accord with the definition.
Time coordinates on the TT and TCG scales are conventionally specified using traditional means of specifying days, carried over from non-uniform time standards based on the rotation of the Earth. Specifically, both Julian Dates and the Gregorian calendar
Gregorian calendar
The Gregorian calendar, also known as the Western calendar, or Christian calendar, is the internationally accepted civil calendar. It was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582, a papal bull known by its opening words Inter...
are used. For continuity with their predecessor Ephemeris Time
Ephemeris time
The term ephemeris time can in principle refer to time in connection with any astronomical ephemeris. In practice it has been used more specifically to refer to:...
(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 exactly and TCG instant 1977-01-01T00:00:32.184 exactly correspond to the International Atomic Time
International Atomic Time
International Atomic Time is a high-precision atomic coordinate time standard based on the notional passage of proper time on Earth's geoid...
(TAI) instant 1977-01-01T00:00:00.000 exactly. This is also the instant at which TAI introduced corrections for gravitational time dilation
Gravitational time dilation
Gravitational time dilation is the effect of time passing at different rates in regions of different gravitational potential; the lower the gravitational potential, the more slowly time passes...
.
TT and TCG expressed as Julian Dates can be related precisely and most simply by the equation
- JDTT = EJD + (JDTCG − EJD) (1 − LG)
where EJD is 2443144.5003725 exactly.
Realization
TT is a theoretical ideal, not dependent on a particular realization. For practical purposes, TT must be realized by actual clocks in the Earth system.The main realization of TT is supplied by TAI. The TAI service, running since 1958, attempts to match the rate of proper time on the geoid, using an ensemble of atomic clock
Atomic clock
An atomic clock is a clock that uses an electronic transition frequency in the microwave, optical, or ultraviolet region of the electromagnetic spectrum of atoms as a frequency standard for its timekeeping element...
s spread over the surface and low orbital space of the Earth. TAI is canonically defined retrospectively, in monthly bulletins, in relation to the readings that particular groups of atomic clocks showed 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:
- TT(TAI) = TAI + 32.184 s
Because TAI is never revised once published, it is possible for errors in it to become known and remain uncorrected. It is thus possible to produce a better realization of TT based on reanalysis of historical TAI data. The BIPM has done this approximately annually since 1992. These 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 table of differences from TT(TAI). The latest is [ftp://tai.bipm.org/TFG/TT(BIPM)/TTBIPM.10 TT(BIPM10)].
The international communities of precision timekeeping, astronomy
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
, and radio
Radio
Radio is the transmission of signals through free space by modulation of electromagnetic waves with frequencies below those of visible light. Electromagnetic radiation travels by means of oscillating electromagnetic fields that pass through the air and the vacuum of space...
broadcasts have considered creating a new precision time scale based on observations of an ensemble of pulsars. This new pulsar time scale will serve as an independent means of computing TT, and it may eventually be useful to identify defects in TAI.
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 relativityTheory of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....
. 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
Proper time
In relativity, proper time is the elapsed time between two events as measured by a clock that passes through both events. The proper time depends not only on the events but also on the motion of the clock between the events. An accelerated clock will measure a smaller elapsed time between two...
of a clock located on the geoid
Geoid
The geoid is that equipotential surface which would coincide exactly with the mean ocean surface of the Earth, if the oceans were in equilibrium, at rest , and extended through the continents . According to C.F...
(essentially mean sea level).
However,
TT is now actually defined as a coordinate time scale.
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
Gravitational time dilation
Gravitational time dilation is the effect of time passing at different rates in regions of different gravitational potential; the lower the gravitational potential, the more slowly time passes...
relative to a notional observer located at infinitely high altitude.
The present definition of TT is a linear scaling of Geocentric Coordinate Time
Geocentric Coordinate Time
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...
(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 the Earth. TCG is used so far mainly for theoretical purposes in astronomy. From the point of view of an observer on the 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
- Time standardTime standardA 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...
- International Atomic TimeInternational Atomic TimeInternational Atomic Time is a high-precision atomic coordinate time standard based on the notional passage of proper time on Earth's geoid...
- Barycentric Coordinate TimeBarycentric Coordinate TimeBarycentric 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...
- Geocentric Coordinate TimeGeocentric Coordinate TimeGeocentric 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...