Barycentric Dynamical Time
Encyclopedia
Barycentric Dynamical Time (TDB) 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 planet
s, asteroid
s, comet
s and interplanetary spacecraft
in the Solar system
. TDB is now (since 2006) defined as a linear scaling of Barycentric Coordinate Time
(TCB), and 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.
TDB applies to the solar-system-barycentric reference frame, and was first defined in 1976 as a successor to the (non-relativistic) former standard of ephemeris time
(adopted by the IAU
in 1952 and superseded 1976). In 2006, after a history of multiple time-scale definitions and deprecation since the 1970s, a redefinition of TDB was approved by the IAU. TDB according to the 2006 redefinition can now be treated as equivalent, for practical astronomical purposes, to the long-established JPL ephemeris time argument Teph as implemented in JPL Development Ephemeris DE405 (in use as the official basis for planetary and lunar ephemerides in the Astronomical Almanac
, editions for 2003 and succeedng years).
. TCB diverges from both TDB and TT. TCB progresses faster at a differential rate of about 0.5 second/year, while TDB and TT remain close. As of the beginning of 2011, the difference between TDB and TCB is about 16.6 seconds.
where L = 1.550519768, TDB = −6.55 s, T = 2443144.5003725, and JD is the TCB Julian date
(that is, a quantity which was equal to T on 1977 January 1 00:00:00 TAI
at the geocenter and which increases by one every 86400 seconds of TCB).
From the 17th century to the late 19th century, planetary ephemerides were calculated using time scales based on the Earth's rotation: usually the mean solar time of one of the principal observatories, such as Paris or Greenwich. After 1884, mean solar time at Greenwich became a standard, later named Universal Time
(UT). But in the later nineteenth and early 20th centuries, with the increasing precision of astronomical measurements, it began to be suspected, and was eventually established, that the rotation of the Earth (i.e. the length of the day) showed irregularities on short time scales, and was slowing down on longer time scales. Ephemeris time
was consequently developed as a standard that was free from the irregularities of Earth rotation, by defining the time "as the independent variable of the equations of celestial mechanics", and it was at first measured astronomically, relying on the existing gravitational theories of the motions of the Earth about the Sun and of the Moon about the Earth.
After the cesium atomic clock
was invented, such clocks were used increasingly from the late 1950s as secondary realizations of ephemeris time (ET). These secondary realizations improved on the original ET standard by the improved uniformity of the atomic clocks, and (e.g. in the late 1960s) they were used to provide standard time for planetary ephemeris calculations and in astrodynamics.
But ET in principle did not yet take account of relativity theory. The size of the periodic part of the variations due to time dilation
between earth-based atomic clocks and the coordinate time
of the solar-system barycentric reference frame had been estimated at under 2 milliseconds, but in spite of this small size, it was increasingly considered in the early 1970s that time standards should be made suitable for applications in which differences due to relativistic time dilation could no longer be neglected.
In 1976, two new time scales were defined to replace ET (in the ephemerides for 1984 and afterwards) to take account of relativity. ET's direct successor for measuring time on a geocentric basis was Terrestrial Dynamical Time (TDT). The new time scale to supersede ET for planetary ephemerides was to be Barycentric Dynamical Time (TDB). TDB was to tick uniformly in a reference frame comoving with the barycenter of the Solar system. (As with any coordinate time
, a corresponding clock, to coincide in rate, would need not only to be at rest in that reference frame, but also (an unattainable hypothetical condition) to be located outside all of the relevant gravity well
s.) In addition, TDB was to have (as observed/evaluated at the Earth's surface), over the long term average, the same rate as TDT (now TT
). TDT and TDB were defined in a series of resolutions at the same 1976 meeting of the International Astronomical Union
.
It was eventually realized that TDB was not well defined because it was not accompanied by a general relativistic metric and because the exact relationship between TDB and TDT had not been specified. (It was also later criticized as being not physically possible in exact accordance with its original definition: among other things the 1976 definition excluded a necessary small offset for the initial epoch of 1977.) After the difficulties were appreciated, in 1991 the IAU refined the official definitions of timescales by creating additional new time scales: Barycentric Coordinate Time
(TCB) and Geocentric Coordinate Time
(TCG). TCB was intended as a replacement for TDB, and TCG was its equivalent for use in near-Earth space. TDT was also renamed to Terrestrial Time
(TT), because of doubts raised about the appropriateness of the word "dynamical" in that connection.
.
Arguments have been put forward for the continued practical use of TDB rather than TCB based on the very small size of the difference between TDB and TT, not exceeding 0.002 second, which can be neglected for many applications. It has been argued that the smallness of this difference makes for a lower risk of damage if TDB is ever confused with TT, compared to the possible damage of confusing TCB and TT, which have a relative linear drift of about 0.5 second per year, (the difference was close to zero at the start of 1977, and is now (2009) over a quarter-minute, increasing).
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...
scale, intended for astronomical use as a 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...
to take account of time dilation
Time dilation
In the theory of relativity, time dilation is an observed difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from gravitational masses. An accurate clock at rest with respect to one observer may be measured to tick at...
when calculating orbits and astronomical 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 planet
Planet
A planet is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.The term planet is ancient, with ties to history, science,...
s, asteroid
Asteroid
Asteroids are a class of small Solar System bodies in orbit around the Sun. They have also been called planetoids, especially the larger ones...
s, comet
Comet
A comet is an icy small Solar System body that, when close enough to the Sun, displays a visible coma and sometimes also a tail. These phenomena are both due to the effects of solar radiation and the solar wind upon the nucleus of the comet...
s and interplanetary spacecraft
Spacecraft
A spacecraft or spaceship is a craft or machine designed for spaceflight. Spacecraft are used for a variety of purposes, including communications, earth observation, meteorology, navigation, planetary exploration and transportation of humans and cargo....
in the Solar system
Solar System
The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...
. TDB is now (since 2006) defined as a linear scaling of 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), and a feature that distinguishes TDB from TCB is that TDB, when observed from the Earth's surface, has a difference from Terrestrial Time (TT)
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....
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.
TDB applies to the solar-system-barycentric reference frame, and was first defined in 1976 as a successor to the (non-relativistic) former standard of 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:...
(adopted by the IAU
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...
in 1952 and superseded 1976). In 2006, after a history of multiple time-scale definitions and deprecation since the 1970s, a redefinition of TDB was approved by the IAU. TDB according to the 2006 redefinition can now be treated as equivalent, for practical astronomical purposes, to the long-established JPL ephemeris time argument Teph as implemented in JPL Development Ephemeris DE405 (in use as the official basis for planetary and lunar ephemerides in 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....
, editions for 2003 and succeedng years).
Definition
IAU resolution 3 of 2006 defines TDB as a linear transformation of TCBBarycentric 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 diverges from both TDB and TT. TCB progresses faster at a differential rate of about 0.5 second/year, while TDB and TT remain close. As of the beginning of 2011, the difference between TDB and TCB is about 16.6 seconds.
- TDB = TCB − L×(JD − T)×86400 + TDB
where L = 1.550519768, TDB = −6.55 s, T = 2443144.5003725, and JD is the TCB Julian date
Julian day
Julian day is used in the Julian date system of time measurement for scientific use by the astronomy community, presenting the interval of time in days and fractions of a day since January 1, 4713 BC Greenwich noon...
(that is, a quantity which was equal to T on 1977 January 1 00:00:00 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...
at the geocenter and which increases by one every 86400 seconds of TCB).
History
See also Ephemeris time - History for further information and sources.From the 17th century to the late 19th century, planetary ephemerides were calculated using time scales based on the Earth's rotation: usually the mean solar time of one of the principal observatories, such as Paris or Greenwich. After 1884, mean solar time at Greenwich became a standard, later named Universal Time
Universal Time
Universal Time is a time scale based on the rotation of the Earth. It is a modern continuation of Greenwich Mean Time , i.e., the mean solar time on the Prime Meridian at Greenwich, and GMT is sometimes used loosely as a synonym for UTC...
(UT). But in the later nineteenth and early 20th centuries, with the increasing precision of astronomical measurements, it began to be suspected, and was eventually established, that the rotation of the Earth (i.e. the length of the day) showed irregularities on short time scales, and was slowing down on longer time scales. 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:...
was consequently developed as a standard that was free from the irregularities of Earth rotation, by defining the time "as the independent variable of the equations of celestial mechanics", and it was at first measured astronomically, relying on the existing gravitational theories of the motions of the Earth about the Sun and of the Moon about the Earth.
After the cesium 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...
was invented, such clocks were used increasingly from the late 1950s as secondary realizations of ephemeris time (ET). These secondary realizations improved on the original ET standard by the improved uniformity of the atomic clocks, and (e.g. in the late 1960s) they were used to provide standard time for planetary ephemeris calculations and in astrodynamics.
But ET in principle did not yet take account of relativity theory. The size of the periodic part of the variations due to time dilation
Time dilation
In the theory of relativity, time dilation is an observed difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from gravitational masses. An accurate clock at rest with respect to one observer may be measured to tick at...
between earth-based atomic clocks and the coordinate time
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...
of the solar-system barycentric reference frame had been estimated at under 2 milliseconds, but in spite of this small size, it was increasingly considered in the early 1970s that time standards should be made suitable for applications in which differences due to relativistic time dilation could no longer be neglected.
In 1976, two new time scales were defined to replace ET (in the ephemerides for 1984 and afterwards) to take account of relativity. ET's direct successor for measuring time on a geocentric basis was Terrestrial Dynamical Time (TDT). The new time scale to supersede ET for planetary ephemerides was to be Barycentric Dynamical Time (TDB). TDB was to tick uniformly in a reference frame comoving with the barycenter of the Solar system. (As with any coordinate time
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...
, a corresponding clock, to coincide in rate, would need not only to be at rest in that reference frame, but also (an unattainable hypothetical condition) to be located outside all of the relevant 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...
s.) In addition, TDB was to have (as observed/evaluated at the Earth's surface), over the long term average, the same rate as TDT (now TT
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....
). TDT and TDB were defined in a series of resolutions at the same 1976 meeting of 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...
.
It was eventually realized that TDB was not well defined because it was not accompanied by a general relativistic metric and because the exact relationship between TDB and TDT had not been specified. (It was also later criticized as being not physically possible in exact accordance with its original definition: among other things the 1976 definition excluded a necessary small offset for the initial epoch of 1977.) After the difficulties were appreciated, in 1991 the IAU refined the official definitions of timescales by creating additional new time scales: 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) and 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). TCB was intended as a replacement for TDB, and TCG was its equivalent for use in near-Earth space. TDT was also renamed to 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), because of doubts raised about the appropriateness of the word "dynamical" in that connection.
Use of TDB
TDB is a successor of Ephemeris Time (ET), in that ET can be seen (within the limits of the lesser accuracy and precision achievable in its time) to be an approximation to TDB as well as to Terrestrial Time (TT) (see Ephemeris time - Implementations). TDB in the form of the very closely analogous, and practically equivalent, time scale Teph continues to be used for the important DE405 planetary and lunar ephemerides from the Jet Propulsion LaboratoryJet Propulsion Laboratory
Jet Propulsion Laboratory is a federally funded research and development center and NASA field center located in the San Gabriel Valley area of Los Angeles County, California, United States. The facility is headquartered in the city of Pasadena on the border of La Cañada Flintridge and Pasadena...
.
Arguments have been put forward for the continued practical use of TDB rather than TCB based on the very small size of the difference between TDB and TT, not exceeding 0.002 second, which can be neglected for many applications. It has been argued that the smallness of this difference makes for a lower risk of damage if TDB is ever confused with TT, compared to the possible damage of confusing TCB and TT, which have a relative linear drift of about 0.5 second per year, (the difference was close to zero at the start of 1977, and is now (2009) over a quarter-minute, increasing).