Dynamical time scale

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Deviation of day length from SI based day Deviation of day length from SI day.svg
Deviation of day length from SI based day

In time standards, dynamical time is the independent variable of the equations of celestial mechanics. This is in contrast to time scales such as mean solar time which are based on how far the earth has turned. Since Earth's rotation is not constant, using a time scale based on it for calculating the positions of heavenly objects gives errors. Dynamical time can be 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). [1] [2]

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. [3] 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, [1] 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[ further explanation needed ] in their original definitions.[ citation needed ] 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. [4] 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), [5] 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.

See also

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International Atomic Time is a high-precision atomic coordinate time standard based on the notional passage of proper time on Earth's geoid. TAI is a weighted average of the time kept by over 450 atomic clocks in over 80 national laboratories worldwide. It is a continuous scale of time, without leap seconds, and it is the principal realisation of Terrestrial Time. It is the basis for Coordinated Universal Time (UTC), which is used for civil timekeeping all over the Earth's surface and which has leap seconds.

<span class="mw-page-title-main">Astronomical unit</span> Mean distance between Earth and the Sun

The astronomical unit is a unit of length, roughly the distance from Earth to the Sun and equal to 150 million kilometres or 8.3 light-minutes. The actual distance from Earth to the Sun varies by about 3% as Earth orbits the Sun, from a maximum (aphelion) to a minimum (perihelion) and back again once each year. The astronomical unit was originally conceived as the average of Earth's aphelion and perihelion; however, since 2012 it has been defined as exactly 149597870700 m.

Δ<i>T</i> (timekeeping) Measure of variation of solar time from atomic time

In precise timekeeping, ΔT is a measure of the cumulative effect of the departure of the Earth's rotation period from the fixed-length day of International Atomic Time. Formally, ΔT is the time difference ΔT = TT − UT between Universal Time and Terrestrial Time. The value of ΔT for the start of 1902 was approximately zero; for 2002 it was about 64 seconds. So Earth's rotations over that century took about 64 seconds longer than would be required for days of atomic time. As well as this long-term drift in the length of the day there are short-term fluctuations in the length of day which are dealt with separately.

The term ephemeris time can in principle refer to time in association with any ephemeris. In practice it has been used more specifically to refer to:

  1. a former standard astronomical time scale adopted in 1952 by the IAU, and superseded during the 1970s. This time scale was proposed in 1948, to overcome the disadvantages of irregularly fluctuating mean solar time. The intent was to define a uniform time based on Newtonian theory. 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.
  2. 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 from, the TCB time scale currently adopted as a standard by the IAU.
<span class="mw-page-title-main">Second</span> SI unit of time

The second is the unit of time in the International System of Units (SI), historically defined as 1⁄86400 of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds each.

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, which 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.

<span class="mw-page-title-main">Time standard</span> Specification for measuring time

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.

Universal Time is a time standard based on Earth's rotation. While originally it was mean solar time at 0° longitude, precise measurements of the Sun are difficult. Therefore, UT1 is computed from a measure of the Earth's angle with respect to the International Celestial Reference Frame (ICRF), called the Earth Rotation Angle. UT1 is the same everywhere on Earth. UT1 is required to follow the relationship

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 is now 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, and overall will remain at less than 2 milliseconds for several millennia.

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. 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 is the time coordinate for the Barycentric Celestial Reference System (BCRS).

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. 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. The TCG is the time coordinate for the Geocentric Celestial Reference System (GCRS).

The astronomical system of units, formerly called the IAU (1976) System of Astronomical Constants, is a system of measurement developed for use in astronomy. It was adopted by the International Astronomical Union (IAU) in 1976 via Resolution No. 1, and has been significantly updated in 1994 and 2009.

<span class="mw-page-title-main">William Markowitz</span> American astronomer

William Markowitz was an American astronomer, principally known for his work on the standardization of time.

Newcomb's Tables of the Sun is a work by the American astronomer and mathematician Simon Newcomb, published in volume VI of the serial publication Astronomical Papers Prepared for the Use of the American Ephemeris and Nautical Almanac. The work contains Newcomb's mathematical development of the position of the Earth in the Solar System, which is constructed from classical celestial mechanics as well as centuries of astronomical measurements. The bulk of the work, however, is a collection of tabulated precomputed values that provide the position of the sun at any point in time.

An astronomical constant is any of several physical constants 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. 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.

Theoretical astronomy is the use of analytical and computational models based on principles from physics and chemistry to describe and explain astronomical objects and astronomical phenomena. Theorists in astronomy endeavor to create theoretical models and from the results predict observational consequences of those models. The observation of a phenomenon predicted by a model allows astronomers to select between several alternate or conflicting models as the one best able to describe the phenomena.

<span class="mw-page-title-main">Coordinate time</span> Time scale

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. The time specified by the time coordinate is referred to as coordinate time to distinguish it from proper time.

<span class="mw-page-title-main">Unit of time</span> Measurement unit for time

A unit of time is any particular time interval, used as a standard way of measuring or expressing duration. The base unit of time in the International System of Units (SI) and by extension most of the Western world, is the second, defined as about 9 billion oscillations of the caesium atom. The exact modern SI definition is "[The second] is defined by taking the fixed numerical value of the cesium frequency, ΔνCs, the unperturbed ground-state hyperfine transition frequency of the cesium 133 atom, to be 9 192 631 770 when expressed in the unit Hz, which is equal to s−1."

A tropical year or solar year is the time that the Sun takes to return to the same position in the sky of a celestial body of the Solar System such as the Earth, completing a full cycle of seasons; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice. It is the type of year used by tropical solar calendars. The solar year is one type of astronomical year and particular orbital period. Another type is the sidereal year, which is the time it takes Earth to complete one full orbit around the Sun as measured with respect to the fixed stars, resulting in a duration of 20 minutes longer than the tropical year, because of the precession of the equinoxes.

<span class="mw-page-title-main">Coordinated Universal Time</span> Primary time standard

Coordinated Universal Time or UTC is the primary time standard by which the world regulates clocks and time. It is within about 1 second of mean solar time at 0° longitude and is not adjusted for daylight saving time. It is effectively a successor to Greenwich Mean Time (GMT).

References

  1. 1 2 B. Guinot, P. K. Seidelmann (April 1988). "Time scales - Their history, definition and interpretation". Astronomy and Astrophysics. 194 (1–2): 304–308. Bibcode:1988A&A...194..304G. at p.304
  2. ↑ P.K.Seidelmann, ed. (1992). Explanatory Supplement to the Astronomical Almanac. CA: University Science Books. 41. ISBN   0-935702-68-7.
  3. ↑ W Markowitz, 'Variations in the Rotation of the Earth, Results Obtained with the Dual-Rate Moon Camera and Photographic Zenith Tubes', Astron J v64 (1959) 106-113.
  4. ↑ See S Klioner et al., "Units of relativistic time scales and associated quantities", IAU Symposium 261 (2009).
  5. ↑ IAU 2000 resolutions, at Resolution B1.9.
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