Barycentric Dynamical Time

Barycentric Dynamical Time (TDB, from the French Temps Dynamique Barycentrique) is a relativistic coordinate time scale, intended for astronomical use as a time standard to take account of time dilation[1] when calculating orbits and astronomical ephemerides of planets, asteroids, comets and interplanetary spacecraft in the Solar System. TDB is now (since 2006) defined as a linear scaling of Barycentric Coordinate Time (TCB). 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,[2] and overall will remain at less than 2 milliseconds for several millennia.[3]

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in 1976 as a successor to the (non-relativistic) former standard of ephemeris time (adopted by the IAU in 1952 and superseded 1976).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,[4] a redefinition of TDB was approved by the IAU. The 2006 IAU redefinition of TDB as an international standard expressly acknowledged that the long-established JPL ephemeris time argument Teph, as implemented in JPL Development Ephemeris DE405, "is for practical purposes the same as TDB defined in this Resolution"[5] (By 2006, ephemeris DE405 had already been in use for a few years as the official basis for planetary and lunar ephemerides in the Astronomical Almanac; it was the basis for editions for 2003 through 2014; in the edition for 2015 it is superseded by DE430).[6]

Definition

IAU resolution 3 of 2006[7] defines TDB as a linear transformation of TCB. 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.[8] As of the beginning of 2011, the difference between TDB and TCB is about 16.6 seconds.

TDB = TCB − LB×(JDTCB − T0)×86400 + TDB0

where LB = 1.550519768×10−8, TDB0 = −6.55×10−5 s, T0 = 2443144.5003725, and JDTCB is the TCB Julian date (that is, a quantity which was equal to T0 on 1977 January 1 00:00:00 TAI at the geocenter and which increases by one every 86400 seconds of TCB).

History

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 19th 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 caesium 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,[2] 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[9] 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 wells.) 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.)[10] 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.

In 2006 TDB was redefined by IAU 2006 resolution 3; the 'new' TDB was expressly acknowledged as equivalent for practical purposes to JPL ephemeris time argument Teph; the difference between TDB according to the 2006 standard and TT (both as observed from the surface of the Earth), remains under 2 ms for several millennia around the present epoch.[11]

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 Laboratory.

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,[12] (the difference was close to zero at the start of 1977, and by 2009 was already over a quarter of a minute and increasing).[8]

References

  1. ^ Explanations given with (a) IAU resolutions 1991, under Resolution A.4, at 'Notes for recommendation III', and IAU 2006 resolution 3, and its footnotes; and (b) explanations and references cited at "Time dilation -- due to gravitation and motion together".
  2. ^ a b The periodic differences, due to relativistic effects, between a coordinate time scale applicable to the Solar-System barycenter, and time measured at the Earth's surface, were first estimated and are explained in: G M Clemence & V Szebehely, "Annual variation of an atomic clock", Astronomical Journal, Vol.72 (1967), p.1324-6.
  3. ^ IAU 2006 resolution 3, see Recommendation and footnotes, note 3.
  4. ^ (a)P K Seidelmann & T Fukushima (1992), "Why new time scales?", Astronomy & Astrophysics vol.265 (1992), pages 833-838: and (b) IAU resolution (1991) A.4(recommendation V), which recommended limiting the use of TDB (previously defined 1976-79) to cases "where discontinuity with previous work is deemed to be undesirable".
  5. ^ IAU 2006 resolution 3, see footnotes, note 4.
  6. ^ See US Naval Observatory (Naval Oceanography Portal), "History of the Astronomical Almanac" (accessed October 2015); also, for details of DE405:- E M Standish (1998), JPL Planetary and Lunar Ephemerides, DE405/LE405, Jet Propulsion Laboratory Interoffice Memorandum 312F-98-48, August 26, 1998; also, the Astronomical Almanac for 2015 commences use of the more recent JPL ephemeris version DE430, which is now based expressly on TDB, see section L, especially page L-4 Astronomical Almanac for 2015, page L-4 (accessed October 2015).
  7. ^ IAU 2006 resolution 3
  8. ^ a b Fig. 1 at p.835, a graph giving an overview of the rate differences and offsets between various standard time scales, present and past, defined by the IAU: for description see P K Seidelmann & T Fukushima (1992), "Why new time scales?", Astronomy & Astrophysics vol.265 (1992), pages 833-838.
  9. ^ They were defined in substance in 1976 but given their names in 1979.
  10. ^ E M Standish (1998), "Time scales in the JPL and CfA ephemerides", Astronomy and Astrophysics, v.336 (1998), p.381-384.
  11. ^ IAU 2006 resolution 3, see especially footnotes 3 and 4.
  12. ^ S A Klioner (2008), "Relativistic scaling of astronomical quantities and the system of astronomical units", Astronomy and Astrophysics, vol.478 (2008), pp.951-958, at page 953.

External links

Astronomical constant

An astronomical constant is a physical constant used in astronomy. Formal sets of constants, along with recommended values, have been defined by the International Astronomical Union (IAU) several times: in 1964 and in 1976 (with an update in 1994). In 2009 the IAU adopted a new current set, and recognizing that new observations and techniques continuously provide better values for these constants, they decided to not fix these values, but have the Working Group on Numerical Standards continuously maintain a set of Current Best Estimates. The set of constants is widely reproduced in publications such as the Astronomical Almanac of the United States Naval Observatory and HM Nautical Almanac Office.

Besides the IAU list of units and constants, also the International Earth Rotation and Reference Systems Service defines constants relevant to the orientation and rotation of the Earth, in its technical notes.

The IAU system of constants defines a system of astronomical units for length, mass and time (in fact, several such systems), and also includes constants such as the speed of light and the constant of gravitation which allow transformations between astronomical units and SI units. Slightly different values for the constants are obtained depending on the frame of reference used. Values quoted in barycentric dynamical time (TDB) or equivalent time scales such as the Teph of the Jet Propulsion Laboratory ephemerides represent the mean values that would be measured by an observer on the Earth's surface (strictly, on the surface of the geoid) over a long period of time. The IAU also recommends values in SI units, which are the values which would be measured (in proper length and proper time) by an observer at the barycentre of the Solar System: these are obtained by the following transformations:

Astronomical unit

The astronomical unit (symbol: au, ua, or AU) is a unit of length, roughly the distance from Earth to the Sun. However, that distance varies as Earth orbits the Sun, from a maximum (aphelion) to a minimum (perihelion) and back again once a year. Originally conceived as the average of Earth's aphelion and perihelion, since 2012 it has been defined as exactly 149597870700 metres, or about 150 million kilometres (93 million miles). The astronomical unit is used primarily for measuring distances within the Solar System or around other stars. It is also a fundamental component in the definition of another unit of astronomical length, the parsec.

Barycenter

In astronomy, the barycenter (or barycentre; from the Ancient Greek βαρύς heavy + κέντρον center) is the center of mass of two or more bodies that orbit one another and is the point about which the bodies orbit. It is an important concept in such fields as astronomy and astrophysics. The distance from a body's center of mass to the barycenter can be calculated as a two-body problem.

If one of two orbiting bodies is much more massive than the other and the bodies are relatively close to one another, the barycenter will typically be located within the more massive object. In this case, rather than the two bodies appearing to orbit a point between them, the less massive body will appear to orbit about the more massive body, while the more massive body might be observed to wobble slightly. This is the case for the Earth–Moon system, in which the barycenter is located on average 4,671 km (2,902 mi) from Earth's center, 75% of Earth's radius of 6,378 km (3,963 mi). When the two bodies are of similar masses, the barycenter will generally be located between them and both bodies will orbit around it. This is the case for Pluto and Charon, one of Pluto's natural satellites, as well as for many binary asteroids and binary stars. When the less massive object is far away, the barycenter can be located outside the more massive object. This is the case for Jupiter and the Sun; despite the Sun being a thousandfold more massive than Jupiter, their barycenter is slightly outside the Sun due to the relatively large distance between them.In astronomy, barycentric coordinates are non-rotating coordinates with the origin at the barycenter of two or more bodies. The International Celestial Reference System (ICRS) is a barycentric coordinate system centered on the Solar System's barycenter.

Barycentric

Barycentric can refer to:

In astronomy,

Barycenter or barycentre, the center of mass of two or more bodies that orbit each other

Barycentric coordinates, coordinates defined by the common center of mass of two or more bodies (see Barycenter)

Barycentric Coordinate Time, a coordinate time standard in the Solar system

Barycentric Dynamical Time, a former time standard in the Solar SystemIn geometry,

Barycentric subdivision, a way of dividing a simplicial complex

Barycentric coordinates (mathematics), coordinates defined by the vertices of a simplex

Barycentric Coordinate Time

Barycentric Coordinate Time (TCB, from the French Temps-coordonnée barycentrique) 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. It is equivalent to the proper time experienced by a clock at rest in a coordinate frame co-moving with the barycenter of the Solar system: that is, a clock that performs exactly the same movements as the Solar system but is outside the system's gravity well. It is therefore not influenced by the gravitational time dilation caused by the Sun and the rest of the system.

TCB 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 problematic 1976 definition of Barycentric Dynamical Time (TDB). Unlike former astronomical time scales, TCB is defined in the context of the general theory of relativity. The relationships between TCB and other relativistic time scales are defined with fully general relativistic metrics.

Because the reference frame for TCB is not influenced by the gravitational 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 many calculations continue to use TDB in some form.

Time coordinates on the TCB 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, 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 exactly corresponds to the International Atomic Time (TAI) instant 1977-01-01T00:00:00.000 exactly, at the geocenter. This is also the instant at which TAI introduced corrections for gravitational time dilation.

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 (but not all) coordinate systems, an event is specified by one time coordinate and three spatial coordinates. The time specified by the time coordinate is referred to as coordinate time to distinguish it from proper time.

In the special case of an inertial observer in special relativity, by convention the coordinate time at an event is the same as the proper time measured by a clock that is at the same location as the event, that is stationary relative to the observer and that has been synchronised to the observer's clock using the Einstein synchronisation convention.

Dynamical time scale

In time standards, dynamical time is the time-like argument of a dynamical theory; and a dynamical time scale in this sense is the realization of a time-like argument based on a dynamical theory: that is, the time and time scale are defined implicitly, inferred from the observed position of an astronomical object via a theory of its motion. A first application of this concept of dynamical time was the definition of the ephemeris time scale (ET).In the late 19th century it was suspected, and in the early 20th century it was established, that the rotation of the Earth (i.e. the length of the day) was both irregular on short time scales, and was slowing down on longer time scales. The suggestion was made, that observation of the position of the Moon, Sun and planets and comparison of the observations with their gravitational ephemerides would be a better way to determine a uniform time scale. A detailed proposal of this kind was published in 1948 and adopted by the IAU in 1952 (see Ephemeris time - history).

Using data from Newcomb's Tables of the Sun (based on the theory of the apparent motion of the Sun by Simon Newcomb, 1895, as retrospectively used in the definition of ephemeris time), the SI second was defined in 1960 as:

the fraction 1/31,556,925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time.Caesium atomic clocks became operational in 1955, and their use provided further confirmation that the rotation of the earth fluctuated randomly. This confirmed the unsuitability of the mean solar second of Universal Time as a precision measure of time interval. After three years of comparisons with lunar observations it was determined that the ephemeris second corresponded to 9,192,631,770 ± 20 cycles of the caesium resonance. In 1967/68 the length of the SI second was redefined to be 9,192,631,770 cycles of the caesium resonance, equal to the previous measurement result for the ephemeris second (see Ephemeris time - redefinition of the second).

In 1976, however, the IAU resolved that the theoretical basis for ephemeris time was wholly non-relativistic, and therefore, beginning in 1984 ephemeris time would be replaced by two further time scales with allowance for relativistic corrections. Their names, assigned in 1979, emphasized their dynamical nature or origin, Barycentric Dynamical Time (TDB) and Terrestrial Dynamical Time (TDT). Both were defined for continuity with ET and were based on what had become the standard SI second, which in turn had been derived from the measured second of ET.

During the period 1991–2006, the TDB and TDT time scales were both redefined and replaced, owing to difficulties or inconsistencies in their original definitions. The current fundamental relativistic time scales are Geocentric Coordinate Time (TCG) and Barycentric Coordinate Time (TCB); both of these have rates that are based on the SI second in respective reference frames (and hypothetically outside the relevant gravity well), but on account of relativistic effects, their rates would appear slightly faster when observed at the Earth's surface, and therefore diverge from local earth-based time scales based on the SI second at the Earth's surface. Therefore, the currently defined IAU time scales also include Terrestrial Time (TT) (replacing TDT, and now defined as a re-scaling of TCG, chosen to give TT a rate that matches the SI second when observed at the Earth's surface), and a redefined Barycentric Dynamical Time (TDB), a re-scaling of TCB to give TDB a rate that matches the SI second at the Earth's surface.

Ephemeris time

The term ephemeris time (often abbreviated ET) can in principle refer to time in connection with any astronomical ephemeris. In practice it has been used more specifically to refer to:

a former standard astronomical time scale adopted in 1952 by the IAU, and superseded in the 1970s. This time scale was proposed in 1948, to overcome the drawbacks of irregularly fluctuating mean solar time. The intent was to define a uniform time (as far as was then feasible) based on Newtonian theory (see below: Definition of ephemeris time (1952)). Ephemeris time was a first application of the concept of a dynamical time scale, in which the time and time scale are defined implicitly, inferred from the observed position of an astronomical object via the dynamical theory of its motion.

a modern relativistic coordinate time scale, implemented by the JPL ephemeris time argument Teph, in a series of numerically integrated Development Ephemerides. Among them is the DE405 ephemeris in widespread current use. The time scale represented by Teph is closely related to, but distinct (by an offset and constant rate) from, the TCB time scale currently adopted as a standard by the IAU (see below: JPL ephemeris time argument Teph).Most of the following sections relate to the ephemeris time of the 1952 standard.

An impression has sometimes arisen that ephemeris time was in use from 1900: this probably arose because ET, though proposed and adopted in the period 1948–1952, was defined in detail using formulae that made retrospective use of the epoch date of 1900 January 0 and of Newcomb's Tables of the Sun.The ephemeris time of the 1952 standard leaves a continuing legacy, through its ephemeris second which became closely duplicated in the length of the current standard SI second (see below: Redefinition of the second).

Geocentric Coordinate Time

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 a factor of 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 analog of TCG, used 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 (about 0.5 seconds per year). 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 it does on average.

Hourglass

An hourglass (or sandglass, sand timer, sand clock or egg timer) is a device used to measure the passage of time. It comprises two glass bulbs connected vertically by a narrow neck that allows a regulated trickle of material (historically sand) from the upper bulb to the lower one. Factors affecting the time it measured include sand quantity, sand coarseness, bulb size, and neck width. Hourglasses may be reused indefinitely by inverting the bulbs once the upper bulb is empty. Depictions of hourglasses in art survive in large numbers from antiquity to the present day, as a symbol for the passage of time. These were especially common sculpted as epitaphs on tombstones or other monuments, also in the form of the winged hourglass, a literal depiction of the well-known Latin epitaph tempus fugit ("time flies").

List of astronomy acronyms

This is a compilation of initialisms and acronyms commonly used in astronomy. Most are drawn from professional astronomy, and are used quite frequently in scientific publications. A few are frequently used by the general public or by amateur astronomers.

The acronyms listed below were placed into one or more of these categories:

Astrophysics terminology – physics-related acronyms

Catalog – collections of tabulated scientific data

Communications network – any network that functions primarily to communicate with spacecraft rather than performing astronomy

Data – astrophysical data not associated with any single catalog or observing program

Celestial object – acronyms for natural objects in space and for adjectives applied to objects in space

Instrumentation – telescope and other spacecraft equipment, particularly detectors such as imagers and spectrometers

Meeting – meetings that are not named after organizations

Observing program – astronomical programs, often surveys, performed by one or more individuals; may include the groups that perform surveys

Organization – any large private organization, government organization, or company

Person – individual people

Publication – magazines, scientific journals, and similar astronomy-related publications

Software – software excluding catalogued data (which is categorized as "catalog") and scientific images

Spacecraft – any spacecraft except space telescopes

Telescope – ground-based and space telescopes; organizations that operate telescopes (for example, the National Optical Astronomy Observatory (NOAO)) are listed under "organization"

TDB

TDB may refer to:

The Daily Beast, a news site

Barycentric Dynamical Time (Temps Dynamique Barycentrique), time standard

The Daily Buzz

The Division Bell, a Pink Floyd album

Trivial Database, database engine

UNCTAD's Trade and Development Board

Trade Development Bank, a former Geneva-based bank, now defunct

Trade and Development Bank, a multilateral African development financial institution

Term (time)

A term is a period of duration, time or occurrence, in relation to an event. To differentiate an interval or duration, common phrases are used to distinguish the observance of length are near-term or short-term, medium-term or mid-term and long-term.

It is also used as part of a calendar year, especially one of the three parts of an academic term and working year in the United Kingdom: Michaelmas term, Hilary term / Lent term or Trinity term / Easter term, the equivalent to the American semester. In America there is a midterm election held in the middle of the four-year presidential term, there are also academic midterm exams.

In economics, it is the period required for economic agents to reallocate resources, and generally reestablish equilibrium. The actual length of this period, usually numbered in years or decades, varies widely depending on circumstantial context. During the long term, all factors are variable.

In finance or financial operations of borrowing and investing, what is considered long-term is usually above 3 years, with medium-term usually between 1 and 3 years and short-term usually under 1 year. It is also used in some countries to indicate a fixed term investment such as a term deposit.

In law, the term of a contract is the duration for which it is to remain in effect (not to be confused with the meaning of "term" that denotes any provision of a contract). A fixed-term contract is one concluded for a pre-defined time.

Terrestrial Time

Terrestrial Time (TT) is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of Earth.

For example, the Astronomical Almanac uses TT for its tables of positions (ephemerides) of the Sun, Moon and planets as seen from Earth. In this role, TT continues Terrestrial Dynamical Time (TDT or TD), which in turn succeeded ephemeris time (ET). TT shares the original purpose for which ET was designed, to be free of the irregularities in the rotation of Earth.

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, and real clocks can only approximate it.

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). Because of the historical difference between TAI and ET when TT was introduced, TT is approximately 32.184 s ahead of TAI.

Theoretical astronomy

Theoretical astronomy is the use of the analytical models of physics and chemistry to describe astronomical objects and astronomical phenomena.

Ptolemy's Almagest, although a brilliant treatise on theoretical astronomy combined with a practical handbook for computation, nevertheless includes many compromises to reconcile discordant observations. Theoretical astronomy is usually assumed to have begun with Johannes Kepler (1571–1630), and Kepler's laws. It is co-equal with observation. The general history of astronomy deals with the history of the descriptive and theoretical astronomy of the Solar System, from the late sixteenth century to the end of the nineteenth century. The major categories of works on the history of modern astronomy include general histories, national and institutional histories, instrumentation, descriptive astronomy, theoretical astronomy, positional astronomy, and astrophysics. Astronomy was early to adopt computational techniques to model stellar and galactic formation and celestial mechanics. From the point of view of theoretical astronomy, not only must the mathematical expression be reasonably accurate but it should preferably exist in a form which is amenable to further mathematical analysis when used in specific problems. Most of theoretical astronomy uses Newtonian theory of gravitation, considering that the effects of general relativity are weak for most celestial objects. The obvious fact is that theoretical astronomy cannot (and does not try to) predict the position, size and temperature of every star in the heavens. Theoretical astronomy by and large has concentrated upon analyzing the apparently complex but periodic motions of celestial objects.

Time

Time is the indefinite continued progress of existence and events that occur in apparently irreversible succession from the past, through the present, to the future. Time is a component quantity of various measurements used to sequence events, to compare the duration of events or the intervals between them, and to quantify rates of change of quantities in material reality or in the conscious experience. Time is often referred to as a fourth dimension, along with three spatial dimensions.Time has long been an important subject of study in religion, philosophy, and science, but defining it in a manner applicable to all fields without circularity has consistently eluded scholars.

Nevertheless, diverse fields such as business, industry, sports, the sciences, and the performing arts all incorporate some notion of time into their respective measuring systems.Time in physics is unambiguously operationally defined as "what a clock reads". See Units of Time. Time is one of the seven fundamental physical quantities in both the International System of Units and International System of Quantities. Time is used to define other quantities – such as velocity – so defining time in terms of such quantities would result in circularity of definition. An operational definition of time, wherein one says that observing a certain number of repetitions of one or another standard cyclical event (such as the passage of a free-swinging pendulum) constitutes one standard unit such as the second, is highly useful in the conduct of both advanced experiments and everyday affairs of life. The operational definition leaves aside the question whether there is something called time, apart from the counting activity just mentioned, that flows and that can be measured. Investigations of a single continuum called spacetime bring questions about space into questions about time, questions that have their roots in the works of early students of natural philosophy.

Temporal measurement has occupied scientists and technologists, and was a prime motivation in navigation and astronomy. Periodic events and periodic motion have long served as standards for units of time. Examples include the apparent motion of the sun across the sky, the phases of the moon, the swing of a pendulum, and the beat of a heart. Currently, the international unit of time, the second, is defined by measuring the electronic transition frequency of caesium atoms (see below). Time is also of significant social importance, having economic value ("time is money") as well as personal value, due to an awareness of the limited time in each day and in human life spans.

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 standard can be a time scale, specifying a method for measuring divisions of time. A standard for civil time can specify both time intervals and time-of-day.

Standardized time measurements are made using a clock to count periods of some period changes, which may be either the changes of a natural phenomenon or of an artificial machine.

Historically, time standards were often based on the Earth's rotational period. From the late 18 century to the 19th century it was assumed that the Earth's daily rotational rate was constant. Astronomical observations of several kinds, including eclipse records, studied in the 19th century, raised suspicions that the rate at which Earth rotates is gradually slowing and also shows small-scale irregularities, and this was confirmed in the early twentieth century. Time standards based on Earth rotation were replaced (or initially supplemented) for astronomical use from 1952 onwards by an ephemeris time standard based on the Earth's orbital period and in practice on the motion of the Moon. The invention in 1955 of the caesium atomic clock has led to the replacement of older and purely astronomical time standards, for most practical purposes, by newer time standards based wholly or partly on atomic time.

Various types of second and day are used as the basic time interval for most time scales. Other intervals of time (minutes, hours, and years) are usually defined in terms of these two.

Universal Time

Universal Time (UT) is a time standard based on Earth's rotation. It is a modern continuation of Greenwich Mean Time (GMT), i.e., the mean solar time on the Prime Meridian at Greenwich, England. In fact, the expression "Universal Time" is ambiguous (when accuracy of better than a few seconds is required), as there are several versions of it, the most commonly used being Coordinated Universal Time (UTC) and UT1 (see § Versions). All of these versions of UT, except for UTC, are based on Earth's rotation relative to distant celestial objects (stars and quasars), but with a scaling factor and other adjustments to make them closer to solar time. UTC is based on International Atomic Time, with leap seconds added to keep it within 0.9 second of UT1.

International standards
Obsolete standards
Time in physics
Horology
Calendar
Archaeology and geology
Astronomical chronology
Other units of time
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