Epoch (astronomy)
Encyclopedia
In astronomy
, an epoch is a moment in time used as a reference point for some time-varying astronomical quantity, such as celestial coordinates, or elliptical orbital elements
of a celestial body
, where these are (as usual) subject to perturbations
and vary with time. The time-varying astronomical quantities might include, for example, the mean longitude
or mean anomaly
of a body, or of the node of its orbit relative to a reference-plane, or of the direction of the apogee or aphelion of its orbit, or the size of the major axis of its orbit.
The main uses of astronomical quantities specified in this way include their use to calculate other parameters of relevant motions, e.g. in order to predict future positions and velocities. The applied tools of the mathematics 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 for example be used to generate an ephemeris
, which can be presented as a table of values giving 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, counted from an epoch as temporal point of origin. (This is a common current way of using an epoch.) Otherwise, the time-varying astronomical quantity can be expressed by a constant, equal to the measure that it had at the epoch, leaving the law of its variation according to time interval from the epoch to be specified in some other way—for example, by a table, as was common practice during the 17th and 18th centuries.
The word epoch was often used in an alternative 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. 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).
', or 'equinox and equator
', or 'equinox and ecliptic
' – when these are needed for fully specifying astronomical data of the considered type.
Celestial coordinate system
s most commonly used in astronomy are equatorial coordinates and ecliptic coordinates. These are defined relative to the (moving) vernal equinox position, which itself is determined by the orientations of the Earth
's rotation axis and orbit around the Sun
. Their orientations vary (though slowly, e.g. due to precession
), and there is an infinity
of such coordinate systems possible. Thus the coordinate systems most used in astronomy need their own date-reference because the coordinate systems of that type are themselves in motion, e.g. by the precession of the equinoxes
, nowadays often resolved into precessional components, separate precessions of the equator and of the ecliptic.
The epoch of the coordinate system need not be the same, and often in practice is not the same, as the epoch for the data themselves.
The difference between reference to an epoch alone, and a reference to a certain equinox
with equator or ecliptic, is therefore that the reference to the epoch contributes to specifying the date of the values of astronomical variables themselves; while the reference to an equinox along with equator/ecliptic, of a certain date, addresses the identification of, or changes in, the coordinate system in terms of which those astronomical variables are expressed. (Sometimes the word 'equinox' may be used alone, e.g. where it is obvious from the context to users of the data in which form the considered astronomical variables are expressed, in equatorial form or ecliptic form.)
The equinox with equator/ecliptic of a given date defines which coordinate system is used.
Most standard coordinates in use today refer to 2000 Jan 1.5 TT (i.e. to 12h on the Terrestrial Time
scale on 2000 Jan 1), which occurred about 64 seconds sooner than noon UT1 on the same date (see 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).
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) Pholus
, orbital elements have been given including the following data:
Epoch 2010 Jan. 4.0 TT . . . = JDT
2455200.5
M 72.00071 . . . . . . . .(2000.0)
n. 0.01076162 .. . . . Peri . 354.75938
a 20.3181594 . . . . . Node . 119.42656
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 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. 2000 Jan 1.5 (12h on January 1) or JD
2451545.0.
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 perturbations
which will change the values of the elements.
Nevertheless, the period of validity is a different matter in principle, and not the result of the use of an epoch to express the data. In other cases, e.g. the case of a complete analytical theory of the motion of some astronomical body, all of the elements will usually be given in the form of polynomials in interval of time from the epoch, and they will also be accompanied by trigonometrical terms of periodical perturbations
specified appropriately. In that case, their period of validity may stretch over several centuries or even millennia on either side of the stated epoch.
Some data and some epochs have a long period of use for other reasons. For example, the boundaries of the IAU
constellation
s are specified relative to an equinox from near the beginning of the year 1875. This is a matter of convention, but the convention is defined in terms of the equator and ecliptic as they were in 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 (equinox/equator of 1875). Thus that coordinate system can still be used today, even though most comet predictions made originally for 1875 (epoch = 1875) would no longer, because of the lack of information about their time-dependence and perturbations, be useful today.
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 a newer epoch and equinox/equator, than to keep applying corrections to the older data.
All three of these are expressed in TT = Terrestrial Time
.
Besselian years, used mostly for star positions, can be encountered in older catalogs but are now becoming obsolete. The Hipparcos
catalog summary, for example, defines the 'catalog epoch' as J1991.25 (one quarter-year after the start of calendar year 1991).
(1784–1846). Meeus 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. 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.
Lieske says that a 'Besselian epoch' can be calculated from the Julian date according to
This relationship is included in the SOFA software library
.
Lieske's definition is not exactly 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.
According to Meeus, and also according to the formula given above,
, 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 12h on 1 January 2000, and J1900 refers to the instant of 12h (midday) on 0 January 1900, equal to 31 Dec 1899. 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
.
In addition, an epoch optionally prefixed by 'J' and designated as a year with decimals (2000 +x), where x is positive or negative and quoted to 1 or 2 decimal places, has come to mean a date that is an interval of x Julian years of 365.25 days away from the epoch J2000 = JD 2451545.0 (TT), still corresponding (in spite of the use of the prefix 'J' or word 'Julian') to the Gregorian calendar
date of 2000 Jan 1 at 12h TT (about 64 seconds before noon UTC on the same calendar day). (See also Julian year (astronomy)
.) Like the Besselian epoch, an arbitrary Julian epoch is therefore related to the Julian date by
The IAU decided at their General Assembly of 1976 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.) There have been some indications that the epoch J2000 is (at least currently) intended to have a longer period of usage than to mid-century.
Different astronomers or groups of astronomers used to define epochs to suit themselves, but nowadays standard epochs are generally defined by international agreement 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, he/she then uses 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", defined by international agreement, is that of 2000 January 1.5 (or January 1 at 12h on a defined time scale usually TT) and is precisely defined to be
.
In ordinary usage, the civil day
is reckoned by the midnight
epoch, that is, the civil day begins at midnight. In older astronomical usage, it was usual, until 1 January 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
at noon.
In traditional cultures and in antiquity other epochs were used. In ancient Egypt days were reckoned from sunrise to sunrise, following a 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 just before dawn.
In cultures following a 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. This practice was followed in the Jewish
and Islamic calendar
s and in Medieval Western Europe in reckoning the dates of religious festivals.
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
, an epoch is a moment in time used as a reference point for some time-varying astronomical quantity, such as celestial coordinates, or elliptical orbital elements
Orbital elements
Orbital elements are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are generally considered in classical two-body systems, where a Kepler orbit is used...
of a celestial body
Celestial Body
Celestial Body is a Croatian film directed by Lukas Nola. It was released in 2000....
, where these are (as usual) subject to perturbations
Perturbation (astronomy)
Perturbation is a term used in astronomy in connection with descriptions of the complex motion of a massive body which is subject to appreciable gravitational effects from more than one other massive body....
and vary with time. The time-varying astronomical quantities might include, for example, the mean longitude
Mean longitude
In astrodynamics or celestial dynamics, mean longitude is the longitude at which an orbiting body could be found if its orbit were circular, and free of perturbations, and if its inclination were zero. Both the mean longitude and the true longitude of the body in such an orbit would change at a...
or mean anomaly
Mean anomaly
In celestial mechanics, the mean anomaly is a parameter relating position and time for a body moving in a Kepler orbit. It is based on the fact that equal areas are swept at the focus in equal intervals of time....
of a body, or of the node of its orbit relative to a reference-plane, or of the direction of the apogee or aphelion of its orbit, or the size of the major axis of its orbit.
The main uses of astronomical quantities specified in this way include their use to calculate other parameters of relevant motions, e.g. in order to predict future positions and velocities. The applied tools of the mathematics disciplines of celestial mechanics
Celestial mechanics
Celestial mechanics is the branch of astronomy that deals with the motions of celestial objects. The field applies principles of physics, historically classical mechanics, to astronomical objects such as stars and planets to produce ephemeris data. Orbital mechanics is a subfield which focuses on...
or its subfield orbital mechanics (for predicting orbital paths and positions for bodies in motion under the gravitational effects of other bodies) can for example be used to generate an ephemeris
Ephemeris
An ephemeris is a table of values that gives the positions of astronomical objects in the sky at a given time or times. Different kinds of ephemerides are used for astronomy and astrology...
, which can be presented as a table of values giving 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
Polynomial
In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...
function of the time-interval, counted from an epoch as temporal point of origin. (This is a common current way of using an epoch.) Otherwise, the time-varying astronomical quantity can be expressed by a constant, equal to the measure that it had at the epoch, leaving the law of its variation according to time interval from the epoch to be specified in some other way—for example, by a table, as was common practice during the 17th and 18th centuries.
The word epoch was often used in an alternative 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. 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 'equinoxEquinox (celestial coordinates)
-Overview:In astronomy, equinox is a moment in time at which the vernal point, celestial equator, and other such elements are taken to be used in the definition of a celestial coordinate system. The position at other equinoxes can be computed by taking into account precession, nutation and...
', or 'equinox and equator
Equator
An equator is the intersection of a sphere's surface with the plane perpendicular to the sphere's axis of rotation and containing the sphere's center of mass....
', or 'equinox and ecliptic
Ecliptic
The ecliptic is the plane of the earth's orbit around the sun. In more accurate terms, it is the intersection of the celestial sphere with the ecliptic plane, which is the geometric plane containing the mean orbit of the Earth around the Sun...
' – when these are needed for fully specifying astronomical data of the considered type.
Date-references for coordinate systems
When the data are dependent for their values on a particular coordinate system, the date of that coordinate system needs to be specified directly or indirectly.Celestial coordinate system
Coordinate system
In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of a point or other geometric element. The order of the coordinates is significant and they are sometimes identified by their position in an ordered tuple and sometimes by...
s most commonly used in astronomy are equatorial coordinates and ecliptic coordinates. These are defined relative to the (moving) vernal equinox position, which itself is determined by the orientations of the Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
's rotation axis and orbit around the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
. Their orientations vary (though slowly, e.g. due to precession
Precession
Precession is a change in the orientation of the rotation axis of a rotating body. It can be defined as a change in direction of the rotation axis in which the second Euler angle is constant...
), and there is an infinity
Infinity
Infinity is a concept in many fields, most predominantly mathematics and physics, that refers to a quantity without bound or end. People have developed various ideas throughout history about the nature of infinity...
of such coordinate systems possible. Thus the coordinate systems most used in astronomy need their own date-reference because the coordinate systems of that type are themselves in motion, e.g. by the precession of the equinoxes
Precession of the equinoxes
In astronomy, axial precession is a gravity-induced, slow and continuous change in the orientation of an astronomical body's rotational axis. In particular, it refers to the gradual shift in the orientation of Earth's axis of rotation, which, like a wobbling top, traces out a pair of cones joined...
, nowadays often resolved into precessional components, separate precessions of the equator and of the ecliptic.
The epoch of the coordinate system need not be the same, and often in practice is not the same, as the epoch for the data themselves.
The difference between reference to an epoch alone, and a reference to a certain equinox
Equinox (celestial coordinates)
-Overview:In astronomy, equinox is a moment in time at which the vernal point, celestial equator, and other such elements are taken to be used in the definition of a celestial coordinate system. The position at other equinoxes can be computed by taking into account precession, nutation and...
with equator or ecliptic, is therefore that the reference to the epoch contributes to specifying the date of the values of astronomical variables themselves; while the reference to an equinox along with equator/ecliptic, of a certain date, addresses the identification of, or changes in, the coordinate system in terms of which those astronomical variables are expressed. (Sometimes the word 'equinox' may be used alone, e.g. where it is obvious from the context to users of the data in which form the considered astronomical variables are expressed, in equatorial form or ecliptic form.)
The equinox with equator/ecliptic of a given date defines which coordinate system is used.
Most standard coordinates in use today refer to 2000 Jan 1.5 TT (i.e. to 12h on the Terrestrial Time
Terrestrial Time
Terrestrial Time is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of the Earth....
scale on 2000 Jan 1), which occurred about 64 seconds sooner than noon UT1 on the same date (see 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
Polynomial
In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...
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).
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
Orbital elements
Orbital elements are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are generally considered in classical two-body systems, where a Kepler orbit is used...
, 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
Minor planet
An asteroid group or minor-planet group is a population of minor planets that have a share broadly similar orbits. Members are generally unrelated to each other, unlike in an asteroid family, which often results from the break-up of a single asteroid...
(5145) Pholus
5145 Pholus
5145 Pholus is a centaur in an eccentric orbit, with a perihelion less than Saturn's and aphelion greater than Neptune's. Pholus has not come within one astronomical unit of a planet since 764 BC, and will not until 5290. It is believed that Pholus originated as a Kuiper belt object.It was...
, orbital elements have been given including the following data:
Epoch 2010 Jan. 4.0 TT . . . = JDT
Julian day
Julian day is used in the Julian date system of time measurement for scientific use by the astronomy community, presenting the interval of time in days and fractions of a day since January 1, 4713 BC Greenwich noon...
2455200.5
M 72.00071 . . . . . . . .(2000.0)
n. 0.01076162 .. . . . Peri . 354.75938
a 20.3181594 . . . . . Node . 119.42656
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 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. 2000 Jan 1.5 (12h on January 1) or JD
Julian day
Julian day is used in the Julian date system of time measurement for scientific use by the astronomy community, presenting the interval of time in days and fractions of a day since January 1, 4713 BC Greenwich noon...
2451545.0.
Epochs and periods of validity
In the particular set of coordinates exampled above, much of the time-dependence 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 perturbations
Perturbation (astronomy)
Perturbation is a term used in astronomy in connection with descriptions of the complex motion of a massive body which is subject to appreciable gravitational effects from more than one other massive body....
which will change the values of the elements.
Nevertheless, the period of validity is a different matter in principle, and not the result of the use of an epoch to express the data. In other cases, e.g. the case of a complete analytical theory of the motion of some astronomical body, all of the elements will usually be given in the form of polynomials in interval of time from the epoch, and they will also be accompanied by trigonometrical terms of periodical perturbations
Perturbation (astronomy)
Perturbation is a term used in astronomy in connection with descriptions of the complex motion of a massive body which is subject to appreciable gravitational effects from more than one other massive body....
specified appropriately. In that case, their period of validity may stretch over several centuries or even millennia on either side of the stated epoch.
Some data and some epochs have a long period of use for other reasons. For example, the boundaries of the IAU
International Astronomical Union
The International Astronomical Union IAU is a collection of professional astronomers, at the Ph.D. level and beyond, active in professional research and education in astronomy...
constellation
Constellation
In modern astronomy, a constellation is an internationally defined area of the celestial sphere. These areas are grouped around asterisms, patterns formed by prominent stars within apparent proximity to one another on Earth's night sky....
s are specified relative to an equinox from near the beginning of the year 1875. This is a matter of convention, but the convention is defined in terms of the equator and ecliptic as they were in 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 (equinox/equator of 1875). Thus that coordinate system can still be used today, even though most comet predictions made originally for 1875 (epoch = 1875) would no longer, because of the lack of information about their time-dependence and perturbations, be useful today.
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 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 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
Proper motion
The proper motion of a star is its angular change in position over time as seen from the center of mass of the solar system. It is measured in seconds of arc per year, arcsec/yr, where 3600 arcseconds equal one degree. This contrasts with radial velocity, which is the time rate of change in...
. 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 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 most popular:- Julian DayJulian dayJulian day is used in the Julian date system of time measurement for scientific use by the astronomy community, presenting the interval of time in days and fractions of a day since January 1, 4713 BC Greenwich noon...
s, e.g., JD 2433282.4235 for 1950 January 0.9235 TTTerrestrial TimeTerrestrial Time is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of the Earth.... - Besselian years (see below), e.g., 1950.0 or B1950.0 for 1950 January 0.9235 TT
- Julian yearsJulian year (astronomy)In astronomy, a Julian year is a unit of measurement of time defined as exactly 365.25 days of 86 400 SI seconds each, totaling 31 557 600 seconds. The Julian year is the average length of the year in the Julian calendar used in Western societies in previous centuries, and for which the unit is...
, e.g., J2000.0 for 2000 January 1.5000 TT
All three of these are expressed in TT = Terrestrial Time
Terrestrial Time
Terrestrial Time is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of the Earth....
.
Besselian years, used mostly for star positions, can be encountered in older catalogs but are now becoming obsolete. The Hipparcos
Hipparcos
Hipparcos was a scientific mission of the European Space Agency , launched in 1989 and operated between 1989 and 1993. It was the first space experiment devoted to precision astrometry, the accurate measurement of the positions of celestial objects on the sky...
catalog summary, for example, defines the 'catalog epoch' as J1991.25 (one quarter-year after the start of calendar year 1991).
Besselian years
A Besselian year is named after the German mathematician and astronomer Friedrich BesselFriedrich Bessel
-References:* John Frederick William Herschel, A brief notice of the life, researches, and discoveries of Friedrich Wilhelm Bessel, London: Barclay, 1847 -External links:...
(1784–1846). Meeus defines the beginning of a Besselian year to be the moment at which the mean longitude
Mean longitude
In astrodynamics or celestial dynamics, mean longitude is the longitude at which an orbiting body could be found if its orbit were circular, and free of perturbations, and if its inclination were zero. Both the mean longitude and the true longitude of the body in such an orbit would change at a...
of the Sun, including the effect of aberration
Aberration
An aberration is something that deviates from the normal way.Aberration may refer to:In optics and physics:*Optical aberration, an imperfection in image formation by an optical system...
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.
Lieske 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
SOFA (Astronomy)
The SOFA software libraries are a collection of subroutines that implement official IAU algorithms for astronomical computations.As of February 2009 they are available in both Fortran and C source code format....
.
Lieske's definition is not exactly 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
Julian years and J2000
A Julian year is an interval with the length of a mean year in the Julian calendarJulian calendar
The Julian calendar began in 45 BC as a reform of the Roman calendar by Julius Caesar. It was chosen after consultation with the astronomer Sosigenes of Alexandria and was probably designed to approximate the tropical year .The Julian calendar has a regular year of 365 days divided into 12 months...
, i.e. 365.25 days. This interval measure does not itself define any epoch: the Gregorian calendar
Gregorian calendar
The Gregorian calendar, also known as the Western calendar, or Christian calendar, is the internationally accepted civil calendar. It was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582, a papal bull known by its opening words Inter...
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 12h on 1 January 2000, and J1900 refers to the instant of 12h (midday) on 0 January 1900, equal to 31 Dec 1899. 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
Terrestrial Time
Terrestrial Time is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of the Earth....
.
In addition, an epoch optionally prefixed by 'J' and designated as a year with decimals (2000 +x), where x is positive or negative and quoted to 1 or 2 decimal places, has come to mean a date that is an interval of x Julian years of 365.25 days away from the epoch J2000 = JD 2451545.0 (TT), still corresponding (in spite of the use of the prefix 'J' or word 'Julian') to the Gregorian calendar
Gregorian calendar
The Gregorian calendar, also known as the Western calendar, or Christian calendar, is the internationally accepted civil calendar. It was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582, a papal bull known by its opening words Inter...
date of 2000 Jan 1 at 12h TT (about 64 seconds before noon UTC on the same calendar day). (See also Julian year (astronomy)
Julian year (astronomy)
In astronomy, a Julian year is a unit of measurement of time defined as exactly 365.25 days of 86 400 SI seconds each, totaling 31 557 600 seconds. The Julian year is the average length of the year in the Julian calendar used in Western societies in previous centuries, and for which the unit is...
.) Like the Besselian epoch, an arbitrary Julian epoch is therefore related to the Julian date by
- J = 2000.0 + (Julian date − 2451545.0)/365.25 .
The IAU decided at their General Assembly of 1976 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.) There have been some indications that the epoch J2000 is (at least currently) intended to have a longer period of usage than to mid-century.
Different astronomers or groups of astronomers used to define epochs to suit themselves, but nowadays standard epochs are generally defined by international agreement through the IAU
IAU
IAU may refer to:*International Astronomical Union*International American University*International American University College of Medicine*International Association of Universities*International Association of Ultrarunners...
, 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, he/she then uses 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", defined by international agreement, is that of 2000 January 1.5 (or January 1 at 12h on a defined time scale usually TT) and is precisely defined to be
- The Julian date 2451545.0 TT (Terrestrial TimeTerrestrial TimeTerrestrial Time is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of the Earth....
), or January 1, 2000, noon TT. - This is equivalent to January 1, 2000, 11:59:27.816 TAI (International Atomic TimeInternational Atomic TimeInternational Atomic Time is a high-precision atomic coordinate time standard based on the notional passage of proper time on Earth's geoid...
) or - January 1, 2000, 11:58:55.816 UTC (Coordinated Universal TimeCoordinated Universal TimeCoordinated Universal Time is the primary time standard by which the world regulates clocks and time. It is one of several closely related successors to Greenwich Mean Time. Computer servers, online services and other entities that rely on having a universally accepted time use UTC for that purpose...
).
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 dayDay
A day is a unit of time, commonly defined as an interval equal to 24 hours. It also can mean that portion of the full day during which a location is illuminated by the light of the sun...
.
In ordinary usage, the civil day
Civil time
In modern usage, civil time refers to statutory time scales designated by civilian authorities, or to local time indicated by clocks. Modern civil time is generally standard time in a time zone at a fixed offset from Coordinated Universal Time or from Greenwich Mean Time , possibly adjusted by...
is reckoned by the midnight
Midnight
Midnight is the transition time period from one day to the next: the moment when the date changes. In the Roman time system, midnight was halfway between sunset and sunrise, varying according to the seasons....
epoch, that is, the civil day begins at midnight. In older astronomical usage, it was usual, until 1 January 1925, to reckon by a noon
Noon
Noon is usually defined as 12 o'clock in the daytime. The word noon is also used informally to mean midday regarding the location of the sun not the middle of a persons day. Although this is a time around the middle of the day when people in many countries take a lunch break...
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
Meridian (astronomy)
This article is about the astronomical concept. For other uses of the word, see Meridian.In the sky, a meridian is an imaginary great circle on the celestial sphere. It passes through the north point on the horizon, through the celestial pole, up to the zenith, through the south point on the...
at noon.
In traditional cultures and in antiquity other epochs were used. In ancient Egypt days were reckoned from sunrise to sunrise, following a morning epoch. It has been suggested that this may be related to the fact that the Egyptians regulated their year by the heliacal rising
Heliacal rising
The heliacal rising of a star occurs when it first becomes visible above the eastern horizon for a brief moment just before sunrise, after a period of time when it had not been visible....
of the star Sirius
Sirius
Sirius is the brightest star in the night sky. With a visual apparent magnitude of −1.46, it is almost twice as bright as Canopus, the next brightest star. The name "Sirius" is derived from the Ancient Greek: Seirios . The star has the Bayer designation Alpha Canis Majoris...
, a phenomenon which occurs in the morning just before dawn.
In cultures following a lunar
Lunar calendar
A lunar calendar is a calendar that is based on cycles of the lunar phase. A common purely lunar calendar is the Islamic calendar or Hijri calendar. A feature of the Islamic calendar is that a year is always 12 months, so the months are not linked with the seasons and drift each solar year by 11 to...
or lunisolar calendar
Lunisolar calendar
A lunisolar calendar is a calendar in many cultures whose date indicates both the moon phase and the time of the solar year. If the solar year is defined as a tropical year then a lunisolar calendar will give an indication of the season; if it is taken as a sidereal year then the calendar will...
, 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. This practice was followed in the Jewish
Hebrew calendar
The Hebrew calendar , or Jewish calendar, is a lunisolar calendar used today predominantly for Jewish religious observances. It determines the dates for Jewish holidays and the appropriate public reading of Torah portions, yahrzeits , and daily Psalm reading, among many ceremonial uses...
and Islamic calendar
Islamic calendar
The Hijri calendar , also known as the Muslim calendar or Islamic calendar , is a lunar calendar consisting of 12 lunar months in a year of 354 or 355 days. It is used to date events in many Muslim countries , and used by Muslims everywhere to determine the proper day on which to celebrate Islamic...
s and in Medieval Western Europe in reckoning the dates of religious festivals.
See also
- International Celestial Reference SystemInternational Celestial Reference SystemThe International Celestial Reference System is the current standard celestial reference system adopted by the International Astronomical Union . Its origin is at the barycenter of the solar system, with axes that are intended to be "fixed" with respect to space...
- International Celestial Reference FrameInternational Celestial Reference FrameThe International Celestial Reference Frame is a quasi-inertial reference frame centered at the barycenter of the Solar System, defined by the measured positions of 212 extragalactic sources . Although relativity implies that there is no true inertial frame, the extragalactic sources used to...
- AstrometryAstrometryAstrometry is the branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies. The information obtained by astrometric measurements provides information on the kinematics and physical origin of our Solar System and our Galaxy, the Milky...
External links
- What is Terrestrial Time? - U.S. Naval Observatory
- International Celestial Reference System, or ICRS - U.S. Naval Observatory
- IERS Conventions 2003 (defines ICRS and other related standards)