Epoch (astronomy): Difference between revisions - Wikipedia

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{{Short description|Moment in time used as a reference point in astronomy}}

In [[astronomy]], an '''epoch''' or '''reference epoch''' is a [[instant|moment]] in time used as a reference point for some time-varying astronomical quantity. It is useful for the [[celestial coordinates]] or [[orbital elements]] of a [[Astronomical object|celestial body]], as they are subject to [[Perturbation (astronomy)|perturbations]] and vary with time.{{sfn|Soop|1994|p=}} These time-varying astronomical quantities might include, for example, the [[mean longitude]] or [[mean anomaly]] of a body, the node of its orbit relative to a [[reference plane]], the direction of the [[apogee]] or [[Perihelion and aphelion|aphelion]] of its orbit, or the size of the [[major axis]] of its orbit.

The main use of astronomical quantities specified in this way is to calculate other relevant parameters of motion, in order to predict future positions and velocities. The applied tools of the disciplines of [[celestial mechanics]] or its subfield [[orbital mechanics]] (for predicting orbital paths and positions for bodies in motion under the gravitational effects of other bodies) can be used to generate an [[ephemeris]], a table of values giving the positions and velocities of astronomical objects in the sky at a given time or times.

Astronomical quantities can be specified in any of several ways, for example, as a [[polynomial]] function of the time- interval, with an epoch as a temporal point of origin (this is a common current way of using an epoch). Alternatively, the time-varying astronomical quantity can be expressed as a constant, equal to the measure that it had at the epoch, leaving its variation over time to be specified in some other way—for example, by a table, as was common during the 17th and 18th centuries.

The word ''epoch'' was often used in a different way in older astronomical literature, e.g. during the 18th century, in connection with astronomical tables. At that time, it was customary to denote as "epochs", not the standard date and time of origin for time-varying astronomical quantities, but rather the values at that date and time ''of those time-varying quantities themselves''.<ref>M Chapront-Touzé (ed.), ''Jean le Rond d'Alembert, Oeuvres Complètes: Ser.1, Vol.6'', Paris (CNRS) (2002), p.xxx, n.50.</ref> In accordance with that alternative historical usage, an expression such as 'correcting the epochs' would refer to the adjustment, usually by a small amount, of the values of the tabulated astronomical quantities applicable to a fixed standard date and time of reference (and not, as might be expected from current usage, to a change from one date and time of reference to a different date and time).

==Epoch versus equinox==

Astronomical data are often specified not only in their relation to an epoch or date of reference but also in their relations to other conditions of reference, such as coordinate systems specified by "[[equinox (celestial coordinates)|equinox]]", or "equinox and [[equator]]", or "equinox and [[ecliptic]]" ~~–~~– when these are needed for fully specifying astronomical data of the considered type.

===Date-references for coordinate systems===

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The equinox with equator/ecliptic of a given date defines which coordinate system is used.

Most standard coordinates in use today refer to 2000 '''TT''' (i.e. to 12h (noon) on the [[Terrestrial Time]] scale on January 1, 2000, see below), which occurred about 64 seconds sooner than noon [[UT1]] on the same date (see [[ΔT (timekeeping)|ΔT]]). Before about 1984, coordinate systems dated to 1950 or 1900 were commonly used.

There is a special meaning of the expression "equinox (and ecliptic/equator) '''of date'''". When coordinates are expressed as [[polynomial]]s in time relative to a reference frame defined in this way, that means the values obtained for the coordinates in respect of any interval t after the stated epoch, are in terms of the coordinate system of the same date as the obtained values themselves, i.e. the date of the coordinate system is equal to (epoch + t).{{efn|name=NumExp}}

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It can be seen that the date of the coordinate system need not be the same as the epoch of the astronomical quantities themselves. But in that case (apart from the "equinox of date" case described above), two dates will be associated with the data: one date is the epoch for the time-dependent expressions giving the values, and the other date is that of the coordinate system in which the values are expressed.

For example, [[orbital elements]], especially [[osculating elements]] for minor planets, are routinely given with reference to two dates: first, relative to a recent epoch for all of the elements: but some of the data are dependent on a chosen coordinate system, and then it is usual to specify the coordinate system of a standard epoch which often is not the same as the epoch of the data. An example is as follows: For [[minor planet]] (5145) [[5145 Pholus|Pholus]], orbital elements have been given including the following data:<ref>[http://scully.cfa.harvard.edu/~cgi/ReturnPrepEph?d=d&o=05145 Harvard Minor Planet Center, data for ''Pholus'']{{dead link|date=January 2018 |bot=InternetArchiveBot |fix-attempted=yes }}</ref>

Epoch 2010 Jan. 4.0 TT . . . = [[Julian day|JDT]] 2455200.5~~<br />~~

M 72.00071 . . . . . . . .(2000.0)~~<br />~~

n. 0.01076162 .. . . . Peri . 354.75938~~<br />~~

a 20.3181594 . . . . . Node . 119.42656~~<br />~~

e. 0.5715321 . . . . . Incl .. 24.66109

where the epoch is expressed in terms of Terrestrial Time, with an equivalent Julian date. Four of the elements are independent of any particular coordinate system: M is mean anomaly (deg), n: mean daily motion (deg/d), a: size of semi-major axis (AU), e: eccentricity (dimensionless). But the argument of perihelion, [[longitude of the ascending node]] and the inclination are all coordinate-dependent, and are specified relative to the reference frame of the equinox and ecliptic of another date "2000.0", otherwise known as J2000, i.e. January 1.5, 2000 (12h on January 1) or [[Julian day|JD]] 2451545.0.<ref>See [http://www.cfa.harvard.edu/iau/info/OrbElsExplanation.html Explanation of Orbital Elements].</ref>

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===Epochs and periods of validity===

In the particular set of coordinates exampled above, much of the elements has been omitted as unknown or undetermined; for example, the element n allows an approximate time-dependence of the element M to be calculated, but the other elements and n itself are treated as constant, which represents a temporary approximation (see [[Osculating elements]]).

Thus a particular coordinate system (equinox and equator/ecliptic of a particular date, such as J2000.0) could be used forever, but a set of osculating elements for a particular epoch may only be (approximately) valid for a rather limited time, because osculating elements such as those exampled above do not show the effect of future [[Perturbation (astronomy)|perturbations]] which will change the values of the elements.

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==Changing the standard equinox and epoch==

To calculate the visibility of a celestial object for an observer at a specific time and place on the Earth, the coordinates of the object are needed relative to a coordinate system of the current date. If coordinates relative to some other date are used, then that will cause errors in the results. The magnitude of those errors increases with the time difference between the date and time of observation and the date of the coordinate system used, because of the precession of the equinoxes. If the time difference is small, then fairly easy and small corrections for the precession may well suffice. If the time difference gets large, then fuller and more accurate corrections must be applied. For this reason, a star position read from a star atlas or catalog based on a sufficiently old equinox and equator cannot be used without corrections if reasonable accuracy is required.

Additionally, stars move relative to each other through space. Apparent motion across the sky relative to other stars is called [[proper motion]]. Most stars have very small proper motions, but a few have proper motions that accumulate to noticeable distances after a few tens of years. So, some stellar positions read from a star atlas or catalog for a sufficiently old epoch require proper motion corrections as well, for reasonable accuracy.

Due to precession and proper motion, star data become less useful as the age of the observations and their epoch, and the equinox and equator to which they are referred, get older. After a while, it is easier or better to switch to newer data, generally referred to as a newer epoch and equinox/equator, than to keep applying corrections to the older data.

==Specifying an epoch or equinox==

Epochs and equinoxes are moments in time, so they can be specified in the same way as moments that indicate things other than epochs and equinoxes. The following standard ways of specifying epochs and equinoxes seem the most popular:

* [[Julian day]]s, e.g., JD 2433282.4235 for January 0.9235, 1950 [[Terrestrial Time|TT]]

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==Besselian years==

A Besselian year is named after the German mathematician and astronomer [[Friedrich Bessel]] (1784–1846). ~~Meeus<ref>[[Jean Meeus~~{{harvnb|Meeus~~, J.]]: "Astronomical Algorithms", page 125. Willmann-Bell,~~ |1991~~</ref>~~|p=125}} defines the beginning of a Besselian year to be the moment at which the [[mean longitude]] of the Sun, including the effect of [[Aberration of light|aberration]] and measured from the mean equinox of the date, is exactly 280 degrees. This moment falls near the beginning of the corresponding [[Gregorian year]]. The definition depended on a particular theory of the orbit of the Earth around the Sun, that of Newcomb (1895), which is now obsolete; for that reason among others, the use of Besselian years has also become or is becoming obsolete.

{{harvnb|Lieske|1979|p=282}} says that a "Besselian epoch" can be calculated from the Julian date according to

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* B1950.0 = JDE 2433282.4235 = 1950 January 0.9235 TT

==Julian ~~dates~~years and J2000{{anchor|J2000}}==

A Julian year is an interval with the length of a mean year in the [[Julian calendar]], i.e. 365.25 days. This interval measure does not itself define any epoch: the [[Gregorian calendar]] is in general use for dating. But, standard conventional epochs which are not Besselian epochs have been often designated nowadays with a prefix "J", and the calendar date to which they refer is widely known, although not always the same date in the year: thus "J2000" refers to the instant of 12 noon (midday) on January 1, 2000, and J1900 refers to the instant of 12 noon on [[January 0]], 1900, equal to December 31, 1899.<ref>See [http://naif.jpl.nasa.gov/pub/naif/toolkit_docs/FORTRAN/spicelib/j1900.html NASA Jet Propulsion Laboratory 'spice' toolkit documentation, function J1900].</ref> It is also usual now to specify on what time scale the time of day is expressed in that epoch-designation, e.g. often [[Terrestrial Time]].

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The IAU decided at their General Assembly of 1976{{sfn|Aoki|Soma|Kinoshita|Inoue|1983|pp=263–267}} that the new standard equinox of J2000.0 should be used starting in 1984. Before that, the equinox of B1950.0 seems to have been the standard.{{Citation needed|date=April 2012}}

Different astronomers or groups of astronomers used to define individually, but today standard epochs are generally defined by international ~~agreement~~agreements through the [[IAU]], so astronomers worldwide can collaborate more effectively. It is inefficient and error-prone if data or observations of one group have to be translated in non-standard ways so that other groups could compare the data with information from other sources. An example of how this works: if a star's position is measured by someone today, they then use a standard transformation to obtain the position expressed in terms of the standard reference frame of J2000, and it is often then this J2000 position which is shared with others.

On the other hand, there has also been an astronomical tradition of retaining observations in just the form in which they were made, so that others can later correct the reductions to standard if that proves desirable, as has sometimes occurred.

The currently- used standard epoch "J2000" is defined by international agreement to be equivalent to:

# The [[Gregorian date]] January 1, 2000, at 12:00 TT ([[Terrestrial Time]]).

# The [[Julian date]] 2451545.0 TT ([[Terrestrial Time]]).{{sfn|Seidelmann|2006|p=8}}

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== Epoch of the day ==

Over shorter timescales, there are a variety of practices for defining when each day begins. In ordinary usage, the [[Civil time|civil day]] is reckoned by the [[midnight]] epoch, that is, the civil day begins at midnight. But in older astronomical usage, it was usual, until January 1, 1925, to reckon by a [[noon]] epoch, 12 hours after the start of the civil day of the same denomination, so that the day began when the mean sun crossed the [[meridian (astronomy)|meridian]] at noon.{{sfn|Wilson|1925|pp=~~1-2~~1–2}} This is still reflected in the definition of J2000, which started at noon, Terrestrial Time.

In traditional cultures and in antiquity other epochs were used. In [[ancient Egypt]], days were reckoned from sunrise to sunrise, following a morning epoch. This may be related to the fact that the Egyptians regulated their year by the [[heliacal rising]] of the star [[Sirius]], a phenomenon which occurs in the morning just before dawn.{{sfn|Neugebauer|2004|p=1067}}

In some cultures following a [[lunar calendar|lunar]] or [[lunisolar calendar]], in which the beginning of the month is determined by the appearance of the New Moon in the evening, the beginning of the day was reckoned from sunset to sunset, following an evening epoch, e.g. the [[Hebrew calendar|Jewish]] and [[Islamic calendar]]s{{sfn|Neugebauer|2004|pp=~~1067-1069~~1067–1069}} and in Medieval Western Europe in reckoning the dates of religious festivals,<ref>[[Bede]], ''The Reckoning of Time'', 5, trans. Faith Wallis, (Liverpool: Liverpool University Press, 2004), pp. ~~22-24~~22–24. {{ISBN|0-85323-693-3}}</ref> while in others a morning epoch was followed, e.g. the [[Hindu calendar|Hindu]] and [[Buddhist calendar]]s.

==See also==

* [[Astrometry]]

* [[Epoch (reference date)]]

* [[Ephemeris time]]

* [[Epoch]]

* [[International Celestial Reference System]]

* [[International Celestial Reference ~~Frame~~System and its realizations]]

* [[Time in astronomy]]

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{{notelist|refs=

{{efn|name=NumExp|Examples of this usage are seen in: {{harvnb|Simon|Bretagnon|Chapront|Chapront-Touze|1994|pp=~~663-683~~663–683}} }}

{{efn|name=clock24|This article uses a 24-hour clock, so 11:59:27.816 is equivalent to 11:59:27.816 a.m.}}

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===Sources===

*{{cite journal |~~last~~last1=Aoki|~~first~~first1=S. |first2=M.|last2=Soma |first3=H.|last3=Kinoshita |first4=K.|last4=Inoue |date=December 1983|title=Conversion matrix of epoch B 1950.0 FK 4-based positions of stars to epoch J 2000.0 positions in accordance with the new IAU resolutions|journal=Astronomy and Astrophysics |volume=128 |issue=3 |pages=263–267 |issn=0004-6361 |bibcode=1983A&A...128..263A}}

*{{cite journal|last=Lieske|first= J.H.|title=Precession Matrix Based on IAU (1976) System of Astronomical Constants|pppages= ~~282-284~~282–284|journal= Astronomy & Astrophysics|volume=73|issue=3|date=1979|bibcode=1979A&A....73..282L}}

*{{cite book|last=Meeus|first=Jean |authorlink=Jean Meeus|title=Astronomical Algorithms|url=https://archive.org/details/astronomicalalgorithmsjeanmeeus1991|year=1991|publisher=Willmann-Bell|isbn=978-0-943396-35-4}}

*{{cite book|last=Neugebauer|first=O. |title=A History of Ancient Mathematical Astronomy|url=https://books.google.com/books?id=vO5FCVIxz2YC&pg=PA1067|date= 2004|publisher=Springer |isbn=978-3-540-06995-9}}

*{{cite book~~|ref=harv~~|editor-last=Seidelmann|editor-first=P. Kenneth|title=Explanatory Supplement to the Astronomical Almanac|url=https://books.google.com/books?id=uJ4JhGJANb4C|year=2006|publisher=University Science Books|location=Sausalito, CA|isbn=978-1-891389-45-0}}

*{{cite journal

|last1=Simon|first1= J. L.

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|last6=Laskar|first6= J

|title=Numerical expressions for precession formulae and mean elements for the Moon and the planets.

|journal=Astronomy and Astrophysics|volume= 282|pppages=~~663-683~~663–683|date=1994|bibcode= 1994A&A...282..663S}}

*{{cite book|last=Soop|first=E.M. |title=Handbook of Geostationary Orbits|url=https://books.google.com/books?id=hqhZKjLaYZUC|year=1994|publisher=Springer |isbn=978-0-7923-3054-7}}

*{{cite journal|first=H. C.|last= Wilson|bibcode=1925PA.....33....1W |title=Change of astronomical time|journal=Popular Astronomy|volume=33|date=1925|pppages= ~~1-2~~1–2}}

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==External links==

* [http://aa.usno.navy.mil/faq/docs/TT.html What is Terrestrial Time?] -{{Webarchive|url=https://web.archive.org/web/20060806040555/http://aa.usno.navy.mil/faq/docs/TT.html |date=August 6, 2006 }} – U.S. Naval Observatory

* [http://aa.usno.navy.mil/faq/docs/ICRS_doc.html International Celestial Reference System, or ICRS] -{{Webarchive|url=https://web.archive.org/web/20060805073908/http://aa.usno.navy.mil/faq/docs/ICRS_doc.html |date=August 5, 2006 }} – U.S. Naval Observatory

* [http://www.iers.org/MainDisp.csl?pid=46-25776 IERS Conventions 2003 (defines ICRS and other related standards)] {{Webarchive|url=https://web.archive.org/web/20131213022556/http://www.iers.org/MainDisp.csl?pid=46-25776 |date=December 13, 2013 }}

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