Barycentric Dynamical Time

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Barycentric Dynamical Time (TDB) was a time standard used to take account of time dilation when calculating orbits of planets, asteroids, comets and interplanetary spacecraft in the Solar system. It was based on a Dynamical time scale but was not well defined and not rigorously correct as a relativistic time scale. It was subsequently deprecated in favour of Barycentric Coordinate Time (TCB), but at the 2006 General Assembly of the International Astronomical Union TDB was rehabilitated by making it a specific fixed linear transformation of TCB.

[edit] History

Since ancient times, planetary ephemerides were calculated using a time scale based on the Earth's rotation: Universal Time (UT). In the late nineteenth century it was realised that this time scale was not uniform: the observed timing of planetary positions did not match up correctly with UT. After atomic clocks were invented, they were used from 1960 to realise a new uniform time scale, Ephemeris Time (ET). ET was henceforth used for the time variable in planetary ephemeris calculations.

ET itself was not entirely satisfactory either. Although it was a uniform time scale within its reference frame, it was subject to time dilation when compared with the proper time experienced by other bodies in the Solar system. Because ET was based on subjective Earth time, the Earth's orbit introduced periodic non-uniformities when comparing ET against the true independent time variable of the ephemerides. Earth time ticks slower when it is near perihelion and speeds up in its orbit (in January) and faster near aphelion (in July).

In 1976 two time scales were defined to replace ET in 1984 ephemerides to take account of relativity. ET's direct successor in counting subjective Earth time was Terrestrial Dynamical Time (TDT). The new time scale to be used for planetary ephemerides was Barycentric Dynamical Time (TDB). TDB was to tick uniformly in a reference frame comoving with the barycentre of the Solar system, but over the long term tick at the same rate as TDT. TDT and TDB were defined in a series of resolutions at the same meeting of the International Astronomical Union.

It was soon 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. Furthermore, because the length of the TDB second is determined by clocks on Earth (as opposed to the barycentric reference frame itself) it disagrees with the SI second that would be determined by a clock at rest in the frame. As a result, in 1991 the IAU refined the notions of timescales by creating Barycentric Coordinate Time (TCB) and Geocentric Coordinate Time (TCG). TCB is a replacement for TDB, and TCG is its equivalent for use in near-Earth space. TDT was also renamed to Terrestrial Time (TT), because there is nothing dynamical about it.

[edit] Discussion

TDB is the direct successor of Ephemeris Time in that the values of physical constants, notably the Gaussian gravitational constant, match the traditional values from pre-relativistic days.

Despite IAU recommendations that TCB be used for all further calculations of solar system ephemerides, as of 2002 TDB and Ephemeris Time continue to be used, the latter by the producer of the important DE200 ephemeris and its successors at the Jet Propulsion Laboratory. This somewhat controversial approach is taken because the timescale is fitted to observed data for the planets, and to a lesser extent some of their satellites. To adopt TDB or TCB would be to force a timestream based on terrestrial clocks, albeit "corrected" for (some) general relativistic effects, on a data set with which it might not be quite compatible. That said, the differences between Ephemeris Time and TDB appear to be immeasurably small as of 2005.

Nevertheless, as greater accuracy is attained with International Atomic Time and Ephemeris Time differences may appear; thus it seems worthwhile to retain the two timestreams, Ephemeris Time and TDB or TCB, in hopes that we can learn from any measured differences. For practical purposes the only difference between TDB and TCB is that TCB ticks faster. This rate difference means, according to some scientists,[who?] that physical constants have different values in TCB than they do in TDB. Changing software from the traditional TDB values to the recommended TCB values would require considerable effort, but please note the considerations in the next paragraph.

Relativists accept Einstein's Principle of Equivalence (see general relativity), so that fundamental physical constants are the same in all inertial coordinate systems, and most do not use alternate definitions of the second as, for example, set up in TDB or TCB, these seeming to be fossils of early attempts to define absolute time. Relativists who are familiar with general relativity insist that there is no unambiguous way to compare the rates of clocks separated from each other in space or in time, or in relative motion to one another, nor to so compare measures of length and so on. Attempts to set up such comparisons are bound to fail when pursued to higher and higher accuracy. These comparisons and equations that model them may, however, be useful in limited contexts, though they are not normally regarded as a basis for defining different units.

[edit] External links