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Barycentric Coordinate Time

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Time standard for calculations pertaining to orbits

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Barycentric Coordinate Time (TCB, from theFrenchTemps-coordonnée barycentrique) is acoordinate time standard intended to be used as the independent variable of time for all calculations pertaining to orbits ofplanets,asteroids,comets, and interplanetaryspacecraft in theSolar System. It is equivalent to theproper time experienced by a clock at rest in a coordinate frameco-moving with thebarycenter (center of mass) of the Solar System^{[citation needed]}: that is, a clock that performs exactly the same movements as the Solar System but is outside the system'sgravity well. It is therefore not influenced by thegravitational time dilation caused by theSun and the rest of the system.TCB is the time coordinate for theBarycentric Celestial Reference System (BCRS).

TCB was defined in 1991 by theInternational Astronomical Union, in Recommendation III of the XXIst General Assembly.^[1] It was intended as one of the replacements for the problematic 1976 definition ofBarycentric Dynamical Time (TDB). Unlike former astronomical time scales, TCB is defined in the context of thegeneral theory of relativity. The relationships between TCB and other relativistic time scales are defined with fullygeneral relativistic metrics. The transformation between TCB andGeocentric Coordinate Time (TCG) may be approximated with an uncertainty not larger than $5\times 10^{-18}$ in rate as:^[2]

${\begin{aligned}TCB-TCG&=c^{-2}\left[\int _{t_{0}}^{t}\left({\frac {v_{E}^{2}}{2}}+w_{0ext}(\mathbf {x} _{E})\right)dt+v_{E}^{i}r_{E}^{i}\right]\\&-c^{-4}\left[\int _{t_{0}}^{t}\left(-{\frac {1}{8}}v_{E}^{4}-{\frac {3}{2}}v_{E}^{2}w_{0ext}(\mathbf {x} _{E})+4v_{E}^{i}w_{ext}^{i}(\mathbf {x} _{E})+{\frac {1}{2}}w_{0ext}^{2}(\mathbf {x} _{E})\right)dt\right.\\&\qquad \qquad \left.-\left(3w_{0ext}(\mathbf {x} _{E})+{\frac {v_{E}^{2}}{2}}\right)v_{E}^{i}r_{E}^{i}\right]\end{aligned}}$ where $x_{E}^{i}$ and $v_{E}^{i}$ are the barycentric coordinate position and velocity of the geocenter, $r_{E}^{i}=x^{i}-x_{E}^{i}$ with $x^{i}$ the barycentric position of the observer, $t=TCB$ , $t_{0}$ is the origin of TCB and TCG defined so that 1977 January 1, 00:00:00TAI is 1977 January 1, 00:00:32.184 TCG / TCB, $w_{0ext}(\mathbf {x} _{E})$ is the sum $\scriptstyle \sum _{A}{\frac {GM_{A}}{r_{A}}}$ ofgravitational potentials for all solar system bodies apart from the Earth evaluated at the geocenter, and $w_{ext}^{i}(\mathbf {x} _{E})$ is similarly the sum $\scriptstyle \sum _{A}{\frac {GM_{A}}{r_{A}}}v_{A}^{i}$ . The approximation discards higher powers of $r_{E}^{i}$ as they have been found to be negligible.^[3]

Because the reference frame for TCB is not influenced by thegravitational potential caused by the Solar System, TCB ticks faster than clocks on the surface of the Earth by 1.550505 × 10⁻⁸ (about 490 milliseconds per year). Consequently, the values of physical constants to be used with calculations using TCB 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 TCB is an ongoing task, and as of 2002^[update] many calculations continued to use TDB in some form.

Time coordinates on the TCB scale are specified conventionally using traditional means of specifying days, inherited from slightly non-uniform time standards based on the rotation of the Earth. Specifically, bothJulian Dates and theGregorian calendar are used. For continuity with its predecessorEphemeris Time, TCB was set to match ET at around Julian Date 2443144.5 (1977-01-01T00Z). More precisely, it was defined that TCB instant 1977-01-01T00:00:32.184 corresponds exactly to theInternational Atomic Time (TAI) instant 1977-01-01T00:00:00.000, at thegeocenter. This is also the instant at which TAI introduced corrections for gravitational time dilation.

References

[edit]

^"IAU(1991) Recommendation III". Archived fromthe original on 2007-09-27. Retrieved2006-04-28.
^Petit, Gerard."Comparision [sic] of "Old" and "New" Concepts: Coordinate Times and Time Transformations". p. 23. Archived fromthe original on 2022-01-20.
^Soffel, M.; Klioner, S. A.; Petit, G.; Wolf, P.; Kopeikin, S. M.; Bretagnon, P.; Brumberg, V. A.; Capitaine, N.; Damour, T.; Fukushima, T.; Guinot, B.; Huang, T.-Y.; Lindegren, L.; Ma, C.; Nordtvedt, K.; Ries, J. C.; Seidelmann, P. K.; Vokrouhlick, D.; Will, C. M.; Xu, C. (December 2003)."The IAU 2000 Resolutions for Astrometry, Celestial Mechanics, and Metrology in the Relativistic Framework: Explanatory Supplement".The Astronomical Journal.126 (6):2687–2706.arXiv:astro-ph/0303376.Bibcode:2003AJ....126.2687S.doi:10.1086/378162.S2CID 32887246.

v t e Time measurement andstandards
Chronometry Orders of magnitude Metrology
International standards	Coordinated Universal Time offset UT ΔT DUT1 International Earth Rotation and Reference Systems Service ISO 31-1 ISO 8601 International Atomic Time 12-hour clock 24-hour clock Barycentric Coordinate Time Barycentric Dynamical Time Civil time Daylight saving time Geocentric Coordinate Time International Date Line IERS Reference Meridian Leap second Solar time Terrestrial Time Time zone 180th meridian
Obsolete standards	Ephemeris time Greenwich Mean Time Prime meridian
Time in physics	Absolute space and time Spacetime Chronon Continuous signal Coordinate time Cosmological decade Discrete time and continuous time Proper time Theory of relativity Time dilation Gravitational time dilation Time domain Time-translation symmetry T-symmetry
Horology	Clock Astrarium Atomic clock Complication History of timekeeping devices Hourglass Marine chronometer Marine sandglass Radio clock Watch stopwatch Water clock Sundial Dialing scales Equation of time History of sundials Sundial markup schema
Calendar	Gregorian Hebrew Hindu Holocene Islamic (lunar Hijri) Julian Solar Hijri Astronomical Dominical letter Epact Equinox Intercalation Julian day Leap year Lunar Lunisolar Solar Solstice Tropical year Weekday determination Weekday names
Archaeology and geology	Chronological dating Geologic time scale International Commission on Stratigraphy
Astronomical chronology	Galactic year Nuclear timescale Precession Sidereal time
Otherunits of time	Instant Flick Shake Jiffy Second Minute Moment Hour Day Week Fortnight Month Year Olympiad Lustrum Decade Century Saeculum Millennium
Related topics	Chronology Duration music Mental chronometry Decimal time Metric time System time Time metrology Time value of money Timekeeper

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