Geocentric Coordinate Time
Encyclopedia
Geocentric Coordinate Time (TCG - Temps-coordonnée géocentrique) 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.
TCG was defined in 1991 by the International Astronomical Union
, in Recommendation III of the XXIst General Assembly. It was intended as one of the replacements for the ill-defined Barycentric Dynamical Time
(TDB). Unlike former astronomical time scales, TCG is defined in the context of the general theory of relativity
. The relationships between TCG and other relativistic time scales are defined with fully general relativistic
metrics
.
Because the reference frame for TCG is not rotating with the surface of the Earth and not in the gravitational potential of the Earth, TCG ticks faster than clocks on the surface of the Earth by about 7.0 × 10−10 (about 22 milliseconds per year). Consequently, the values of physical constants to be used with calculations using TCG differ from the traditional values of physical constants. (The traditional values were in a sense wrong, incorporating corrections for the difference in time scales.) Adapting the large body of existing software to change from TDB to TCG is a formidable task, and as of 2002 many calculations continue to use TDB in some form.
Time coordinates on the TCG scale 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 its predecessor Ephemeris Time
, TCG was set to match ET at around Julian Date 2443144.5 (1977-01-01T00Z). More precisely, it was defined that TCG instant 1977-01-01T00:00:32.184 exactly corresponds to TAI
instant 1977-01-01T00:00:00.000 exactly. This is also the instant at which TAI introduced corrections for gravitational time dilation.
TCG is a Platonic
time scale: a theoretical ideal, not dependent on a particular realisation. For practical purposes, TCG must be realised by actual clocks in the Earth system. Because of the linear relationship between Terrestrial Time
(TT) and TCG, the same clocks that realise TT also serve for TCG. See the article on TT for details of the relationship and how TT is realised.
Barycentric Coordinate Time
(TCB) is the equivalent of TCG for calculations relating to the solar system beyond Earth orbit. TCG is defined by a different reference frame
from TCB, such that they are not linearly related. Over the long term, TCG ticks more slowly than TCB by about 1.6 × 10−8. In addition there are periodic variations, as Earth moves within the Solar system. When the Earth is at perihelion in January, TCG ticks even more slowly than it does on average, due to gravitational time dilation from being deeper in the Sun
's gravity well and also velocity time dilation from moving faster relative to the Sun. At aphelion in July the opposite holds, with TCG ticking faster than in does on average.
Coordinate time
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...
time standard
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...
intended to be used as the independent variable of time for all calculations pertaining to precession
Precession
Precession is a change in the orientation of the rotation axis of a rotating body. It can be defined as a change in direction of the rotation axis in which the second Euler angle is constant...
, nutation
Nutation
Nutation is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behavior of a mechanism...
, the Moon
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...
, and artificial satellites of the Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
. It is equivalent to 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...
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
Gravity well
A gravity well or gravitational well is a conceptual model of the gravitational field surrounding a body in space. The more massive the body the deeper and more extensive the gravity well associated with it. The Sun has a far-reaching and deep gravity well. Asteroids and small moons have much...
. It is therefore not influenced by the 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...
caused by the Earth.
TCG was defined in 1991 by the International Astronomical Union
International 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...
, in Recommendation III of the XXIst General Assembly. It was intended as one of the replacements for the ill-defined 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). Unlike former astronomical time scales, TCG is defined in the context of the general theory of relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
. The relationships between TCG and other relativistic time scales are defined with fully general relativistic
Theory 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....
metrics
Metric tensor (general relativity)
In general relativity, the metric tensor is the fundamental object of study. It may loosely be thought of as a generalization of the gravitational field familiar from Newtonian gravitation...
.
Because the reference frame for TCG is not rotating with the surface of the Earth and not in the gravitational potential of the Earth, TCG ticks faster than clocks on the surface of the Earth by about 7.0 × 10−10 (about 22 milliseconds per year). Consequently, the values of physical constants to be used with calculations using TCG differ from the traditional values of physical constants. (The traditional values were in a sense wrong, incorporating corrections for the difference in time scales.) Adapting the large body of existing software to change from TDB to TCG is a formidable task, and as of 2002 many calculations continue to use TDB in some form.
Time coordinates on the TCG scale 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 its 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:...
, TCG was set to match ET at around Julian Date 2443144.5 (1977-01-01T00Z). More precisely, it was defined that TCG instant 1977-01-01T00:00:32.184 exactly corresponds to TAI
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...
instant 1977-01-01T00:00:00.000 exactly. This is also the instant at which TAI introduced corrections for gravitational time dilation.
TCG is a Platonic
Platonic idealism
Platonic idealism usually refers to Plato's theory of forms or doctrine of ideas,Some commentators hold Plato argued that truth is an abstraction...
time scale: a theoretical ideal, not dependent on a particular realisation. For practical purposes, TCG must be realised by actual clocks in the Earth system. Because of the linear relationship between Terrestrial Time
Terrestrial Time
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....
(TT) and TCG, the same clocks that realise TT also serve for TCG. See the article on TT for details of the relationship and how TT is realised.
Barycentric Coordinate Time
Barycentric Coordinate Time
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...
(TCB) is the equivalent of TCG for calculations relating to the solar system beyond Earth orbit. TCG is defined by a different reference frame
Reference frame
Reference frame may refer to:*Frame of reference, in physics*Reference frame , frames of a compressed video that are used to define future frames...
from TCB, such that they are not linearly related. Over the long term, TCG ticks more slowly than TCB by about 1.6 × 10−8. In addition there are periodic variations, as Earth moves within the Solar system. When the Earth is at perihelion in January, TCG ticks even more slowly than it does on average, due to gravitational time dilation from being deeper in the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
's gravity well and also velocity time dilation from moving faster relative to the Sun. At aphelion in July the opposite holds, with TCG ticking faster than in does on average.