Epoch (astronomy)

In astronomy, an epoch is a moment in time used as a reference for the orbital elements of a celestial body. [cite book|last=Soop|first=E. M.|title=Handbook of Geostationary Orbits|publisher=Springer|date=1994|isbn=9780792330547] Typically, the epoch is either the moment an observation was made or the moment for which a prediction was calculated.

Epoch versus equinox

The difference between epoch and Equinox is that the equinox addresses changes in the coordinate system, while the epoch addresses changes in the position of the celestial body itself. The equinox defines (partly) which coordinate system is used. The epoch defines (completely) which moment observations or predictions are valid. A particular coordinate system (equinox) could be used forever, but a set of predictions for a particular date (epoch) will be (approximately) valid for only a limited time. Coordinates must specify the coordinate system used. The most common celestial coordinate systems are equatorial coordinates and ecliptic coordinates. These are relative to the vernal equinox position, which itself is determined by the orientations of the Earth's rotation axis and orbit around the Sun. These orientations vary (though slowly, e.g. due to precession), so there is an infinite number of such coordinate systems possible.

For example, the boundaries of the IAU constellations are specified relative to an equinox from near the beginning of the year 1875. To find out in which constellation a particular comet stands today, the current position of that comet must be expressed in the coordinate system of 1875 (epoch = now, equinox = 1875). That coordinate system can still be used today, while hardly any predictions made originally for 1875 (epoch = 1875) are still useful today.

Equinox of the date means that the equinox is the same as the epoch.

Changing the standard equinox and epoch

Calculation of celestial object visibility to an observer at a specific location on Earth requires the equatorial coordinates of the object, relative to the equinox of the date. If the coordinates relative to some other equinox are used, then that will cause errors in the results. The magnitude of those errors increases with the time difference compared to the equinox of the date, because of precession of the equinoxes. If the time difference is small, then fairly easy and small corrections for the precession suffice. If the time difference gets large, then tedious, complicated corrections must be applied. So, a stellar position read from a star atlas or catalog that is based on a sufficiently old equinox 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, for reasonable accuracy.

Due to precession and proper motion, star positions become less useful as their equinox and epoch get older. After a while, it is easier to switch to a newer epoch and equinox than keep applying corrections to data from the older epoch and equinox.

pecifing 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 most popular:

* Julian Day Numbers, e.g., JDN 2433282.4235 for 1950 January 0.9235 TT
* Besselian years, e.g., 1950.0 or B1950.0 for 1950 January 0.9235 TT
* Julian years, e.g., J2000.0 for 2000 January 1.5000 TT

All three of these are expressed in TT = Terrestrial Time.

Besselian and Julian years are not often used to specify an epoch, except for things that vary very slowly, such as star positions. For example, the Hipparcos catalog summary ["The Hipparcos and Tycho Catalogues", ESA SP-1200, Vol. 1, page XV. ESA, 1997] defines the 'catalog epoch' to be equal to J1991.25, which is in terms of Julian years.

Besselian years

A Besselian year is named after the German mathematician and astronomer Friedrich Bessel (1784 – 1846). Meeus [Meeus, J.: "Astronomical Algorithms", page 125. Willmann-Bell, 1991] defines the beginning of a Besselian year to be the moment at which the mean longitude of the Sun, including the effect of 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. Unfortunately, the orbit of the Earth around the Sun is not entirely fixed, so the length of the Besselian year according to this definition is not constant. This makes Besselian years somewhat difficult to work with.

Lieske [Lieske, J.H.: "Precession Matrix Based on IAU (1976) System of Astronomical Constants", page 282. Astronomy & Astrophysics, 73, 282-284 (1979)] says that a 'Besselian epoch' can be calculated from the Julian date according to

: B = 1900.0 + (Julian date − 2415020.31352) / 365.242198781

This relationship is included in the SOFA software library, [cite web|url=http://www.iau-sofa.rl.ac.uk/|title=SOFA Libraries Issue 2007-08-10 |date=2007-08-18|accessdate=2008-10-01] which implies endorsement by the IAU.

Lieske's definition is not consistent with the earlier definition in terms of the mean longitude of the Sun. When using Besselian years, specify which definition is being used.

To distinguish between calendar years and Besselian years, it became customary to add '.0' to the Besselian years. Since the switch to Julian years in the mid-1980s, it has become customary to prefix 'B' to Besselian years. So, '1950' is the calendar year 1950, and '1950.0' = 'B1950.0' is the beginning of Besselian year 1950.

* The IAU constellation boundaries are defined in the equatorial coordinate system relative to the equinox of B1875.0.
* The Henry Draper Catalog uses the equinox B1900.0.
* The classical star atlas Tabulae Caelestes used B1925.0 as its equinox.

According to Meeus, and also according to the formula given above,

* B1900.0 = JDE 2415020.3135 = 1900 January 0.8135 TT
* B1950.0 = JDE 2433282.4235 = 1950 January 0.9235 TT

B1900.0

B1950.0

Julian years

A Julian year, named after Julius Caesar (100 BC — 44 BC), is a year of exactly 365.25 days. Julian year 2000 began on 2000 January 1 at exactly 12:00 TT. The beginning of Julian years are indicated with prefix 'J' and suffix '.0', for example 'J2000.0' for the beginning of Julian year 2000. Because Julian years have a fixed length, their beginning is far easier to calculate than that of Besselian years.

The IAU decided at their General Assembly of 1976 [cite journal|last=Aoki|first=S.|coauthors=M. Soma, H. Kinoshita, K. 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 |url=http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1983A%26A...128..263A|accessdate=2008-10-01] 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.) If the past is a good guide, then we may expect to switch to J2050.0 in the mid-2030s.

Julian epochs are calculated according to:

: J = 2000.0 + (Julian date − 2451545.0)/365.25

J2000.0

In astronomy, an epoch is a specific moment in time for which celestial coordinates or orbital elements are specified, and from which other orbital parametrics are thereafter calculated in order to predict future position. The applied tools of the mathematics disciplines of Celestial mechanics or its subfield Orbital mechanics (both predict orbital paths and positions) about a center of gravity are used to generate an ephemeris (plural: "ephemerides"; from the Greek word "ephemeros" = daily) which is a table of values that gives the positions of astronomical objects in the sky at a given time or times, or a formula to calculate such given the proper time offset from the epoch. Such calculations generally result in an elliptical path on a plane defined by some point on the orbit, and the two focii of the ellipse. Viewing from another orbiting body, following its own trace and orbit, creates shifts in three dimensions in the spherical trigonometry used to calculate relative positions. Over time, inexactitudes and other errors accumulate, creating more and greater errors of prediction, so ephemeris factors need recalculated from time to time, and that requires a new epoch to be defined. Different astronomers or groups of astronomers used to define epochs to suit themselves, but these days of speedy communications, the epochs are generally defined in an international agreement, so astronomers world wide can collaborate more effectively. It was inefficient and error prone to translate data observed by one group so other groups could compare information. An example of how this works: if a star's position is measured by someone today, he/she then obtains the change that occurred in the reference frame position since J2000 and corrects the star's position appropriately, yielding the position of the star relative to the reference frame of J2000. It is this J2000 position which is shared with others.

Therefore, the current epoch, defined by international agreement, is called J2000.0 and is precisely defined to be
# The Julian date 2451545.0 TT (Terrestrial Time), or January 1, 2000, noon TT.
# This is equivalent to January 1, 2000, 11:59:27.816 TAI (International Atomic Time) or
# January 1, 2000, 11:58:55.816 UTC (Coordinated Universal Time).

Epoch of the Day

In addition to its usual application concerning a reference point for long term astronomical calculations, the term Epoch has also been used to refer to the time of the beginning of the day. In ordinary usage, the civil day is reckoned by the midnight epoch, that is, the civil day begins at midnight. In modern astronomical usage, it was common until 1925 to reckon by the noon epoch, in which the day begins when the mean sun crosses the meridian at noon.

In traditional cultures and in antiquity other epochs were used. In ancient Egypt days were reckoned from sunrise to sunrise, following the morning epoch. It has been suggested that 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 before dawn. [Otto Neugebauer, "A History of Ancient Mathematical Astronomy", (New York: Springer, 1975), p. 1067. ISBN 0-387-06995-X]

In cultures following a lunar or lunisolar calendar, in which the beginning of the month is determined by the the appearance of the New Moon in the evening, the beginning of the day was reckoned from sunset to siunset, following the evening epoch. This practice was followed in the Jewish and Islamic calendars [Otto Neugebauer, "A History of Ancient Mathematical Astronomy", (New York: Springer, 1975), pp. 1067-1069. ISBN 0-387-06995-X] and in Medieval Western Europe in reckoning the dates of religious festivals. [Bede, "The Reckoning of Time", 5, trans. Faith Wallis, (Liverpool: Liverpool University Press, 2004), pp. 22-24. ISBN 0-85323-693-3]

ee also

* International Celestial Reference System
* International Celestial Reference Frame
* Astrometry

References

External links

*cite journal|last=Standish|first=E. M., Jr.|date=November 1982|title=Conversion of positions and proper motions from B1950.0 to the IAU system at J2000.0|journal=Astronomy and Astrophysics|volume=115|issue=1|pages=20-22|url=http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1982A%26A...115...20S
* [http://aa.usno.navy.mil/faq/docs/TT.html What is Terrestrial Time?] - U.S. Naval Observatory
* [http://aa.usno.navy.mil/faq/docs/ICRS_doc.html International Celestial Reference System, or ICRS] - U.S. Naval Observatory
* [http://www.iers.org/MainDisp.csl?pid=46-25776 IERS Conventions 2003 (defines ICRS and other related standards)]