Equinox (celestial coordinates)

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In astronomy, an equinox is either of two places on the celestial sphere at which the ecliptic intersects the celestial equator. [1] [2] [3] Although there are two such intersections, the equinox associated with the Sun's ascending node is used as the conventional origin of celestial coordinate systems and referred to simply as "the equinox". In contrast to the common usage of spring/vernal and autumnal equinoxes, the celestial coordinate system equinox is a direction in space rather than a moment in time.

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In a cycle of about 25,800 years, the equinox moves westward with respect to the celestial sphere because of perturbing forces; therefore, in order to define a coordinate system, it is necessary to specify the date for which the equinox is chosen. This date should not be confused with the epoch. Astronomical objects show real movements such as orbital and proper motions, and the epoch defines the date for which the position of an object applies. Therefore, a complete specification of the coordinates for an astronomical object requires both the date of the equinox and of the epoch. [4]

The currently used standard equinox and epoch is J2000.0, which is January 1, 2000 at 12:00 TT. The prefix "J" indicates that it is a Julian epoch. The previous standard equinox and epoch was B1950.0, with the prefix "B" indicating it was a Besselian epoch. Before 1984 Besselian equinoxes and epochs were used. Since that time Julian equinoxes and epochs have been used. [5]

Motion of the equinox

The precession of the equinox Equinox path.png
The precession of the equinox

The equinox moves, in the sense that as time progresses it is in a different location with respect to the distant stars. Consequently, star catalogs over the years, even over the course of a few decades, will list different ephemerides. [6] This is due to precession and nutation, both of which can be modeled, as well as other minor perturbing forces which can only be determined by observation and are thus tabulated in astronomical almanacs.

Precession

Precession of the equinox was first noted by Hipparchus in 129 BC, when noting the location of Spica with respect to the equinox and comparing it to the location observed by Timocharis in 273 BC. [7] It is a long term motion with a period of 25,800 years.

Nutation

Nutation is the oscillation of the ecliptic plane. It was first observed by James Bradley as a variation in the declination of stars. Bradley published this discovery in 1748. Because he did not have an accurate enough clock, Bradley was unaware of the effect of nutation on the motion of the equinox along the celestial equator, although that is in the present day the more significant aspect of nutation. [8] The period of oscillation of the nutation is 18.6 years.

Equinoxes and epochs

Besselian equinoxes and epochs

A Besselian epoch, named after German mathematician and astronomer Friedrich Bessel (1784–1846), is an epoch that is based on a Besselian year of 365.242198781 days, which is a tropical year measured at the point where the Sun's longitude is exactly 280°. Since 1984, Besselian equinoxes and epochs have been superseded by Julian equinoxes and epochs. The current standard equinox and epoch is J2000.0, which is a Julian epoch.

Besselian epochs are calculated according to:

B = 1900.0  + (Julian date   2415020.31352) / 365.242198781

The previous standard equinox and epoch were B1950.0, a Besselian epoch.

Since the right ascension and declination of stars are constantly changing due to precession, astronomers always specify these with reference to a particular equinox. Historically used Besselian equinoxes include B1875.0, B1900.0, B1925.0 and B1950.0. The official constellation boundaries were defined in 1930 using B1875.0.

Julian equinoxes and epochs

A Julian epoch is an epoch that is based on Julian years of exactly 365.25 days. Since 1984, Julian epochs are used in preference to the earlier Besselian epochs.

Julian epochs are calculated according to:

J = 2000.0 + (Julian date 2451545.0)/365.25

The standard equinox and epoch currently in use are J2000.0, which corresponds to January 1, 2000, 12:00 Terrestrial Time.

J2000.0

The J2000.0 epoch is precisely 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 or January 1, 2000, 11:58:55.816 UTC.

Since the right ascension and declination of stars are constantly changing due to precession, (and, for relatively nearby stars due to proper motion), astronomers always specify these with reference to a particular epoch. The earlier epoch that was in standard use was the B1950.0 epoch.

When the mean equator and equinox of J2000 are used to define a celestial reference frame, that frame may also be denoted J2000 coordinates or simply J2000. This is different from the International Celestial Reference System (ICRS): the mean equator and equinox at J2000.0 are distinct from and of lower precision than ICRS, but agree with ICRS to the limited precision of the former. Use of the "mean" locations means that nutation is averaged out or omitted. This means that the Earth's rotational North pole does not point quite at the J2000 celestial pole at the epoch J2000.0; the true pole of epoch nutates away from the mean one. The same differences pertain to the equinox. [9]

The "J" in the prefix indicates that it is a Julian equinox or epoch rather than a Besselian equinox or epoch.

Equinox of Date

There is a special meaning of the expression "equinox (and ecliptic/equator) of date". This reference frame is defined by the positions of the ecliptic and the celestial equator as of the date/epoch on which the position of something else (typically a solar system object) is being specified. [10]

Other equinoxes and their corresponding epochs

Other equinoxes and epochs that have been used include:

Epochs and equinoxes for orbital elements are usually given in Terrestrial Time, in several different formats, including:

Sidereal time and the equation of the equinoxes

Sidereal time is the hour angle of the equinox. However, there are two types: if the mean equinox is used (that which only includes precession), it is called mean sidereal time; if the true equinox is used (the actual location of the equinox at a given instant), it is called apparent sidereal time. The difference between these two is known as the equation of the equinoxes, and is tabulated in the Astronomical Almanac . [12]

A related concept is known as the equation of the origins, which is the arc length between the Celestial Intermediate Origin and the equinox. Alternatively, the equation of the origins is the difference between the Earth Rotation Angle and the apparent sidereal time at Greenwich.

Diminishing role of the equinox in astronomy

In modern astronomy the ecliptic and the equinox are diminishing in importance as required, or even convenient, reference concepts. (The equinox remains important in ordinary civil use, in defining the seasons, however.) This is for several reasons. One important reason is that it is difficult to be precise what the ecliptic is, and there is even some confusion in the literature about it. [13] Should it be centered on the Earth's center of mass, or on the Earth-Moon barycenter?

Also with the introduction of the International Celestial Reference Frame, all objects near and far are put fundamentally in relationship to a large frame based on very distant fixed radio sources, and the choice of the origin is arbitrary and defined for the convenience of the problem at hand. There are no significant problems in astronomy where the ecliptic and the equinox need to be defined. [14]

Related Research Articles

<span class="mw-page-title-main">Declination</span> Astronomical coordinate analogous to latitude

In astronomy, declination is one of the two angles that locate a point on the celestial sphere in the equatorial coordinate system, the other being hour angle. The declination angle is measured north (positive) or south (negative) of the celestial equator, along the hour circle passing through the point in question.

<span class="mw-page-title-main">Ecliptic</span> Apparent path of the Sun on the celestial sphere

The ecliptic or ecliptic plane is the orbital plane of Earth around the Sun. From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic against the background of stars. The ecliptic is an important reference plane and is the basis of the ecliptic coordinate system.

A solar equinox is a moment in time when the Sun crosses the Earth's equator, which is to say, appears directly above the equator, rather than north or south of the equator. On the day of the equinox, the Sun appears to rise "due east" and set "due west". This occurs twice each year, around 20 March and 23 September.

<span class="mw-page-title-main">Right ascension</span> Astronomical equivalent of longitude

Right ascension is the angular distance of a particular point measured eastward along the celestial equator from the Sun at the March equinox to the point in question above the Earth. When paired with declination, these astronomical coordinates specify the location of a point on the celestial sphere in the equatorial coordinate system.

<span class="mw-page-title-main">Year</span> Time of one planets orbit around a star

A year is the time taken for astronomical objects to complete one orbit. For example, a year on Earth is the time taken for Earth to revolve around the Sun. Generally, a year is taken to mean a calendar year, but the word is also used for periods loosely associated with the calendar or astronomical year, such as the seasonal year, the fiscal year, the academic year, etc. The term can also be used in reference to any long period or cycle, such as the Great Year.

<span class="mw-page-title-main">Zodiac</span> Area of the sky divided into twelve signs

The zodiac is a belt-shaped region of the sky that extends approximately 8° north and south of the ecliptic, the apparent path of the Sun across the celestial sphere over the course of the year. Also within this zodiac belt appear the Moon and the brightest planets, along their orbital planes. The zodiac is divided along the ecliptic into 12 equal parts ("signs"), each occupying 30° of celestial longitude. These signs roughly correspond to the astronomical constellations with the following modern names: Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, and Pisces.

<span class="mw-page-title-main">Equatorial coordinate system</span> Celestial coordinate system used to specify the positions of celestial objects

The equatorial coordinate system is a celestial coordinate system widely used to specify the positions of celestial objects. It may be implemented in spherical or rectangular coordinates, both defined by an origin at the centre of Earth, a fundamental plane consisting of the projection of Earth's equator onto the celestial sphere, a primary direction towards the March equinox, and a right-handed convention.

<span class="mw-page-title-main">Ecliptic coordinate system</span> Celestial coordinate system used to describe Solar System objects

In astronomy, the ecliptic coordinate system is a celestial coordinate system commonly used for representing the apparent positions, orbits, and pole orientations of Solar System objects. Because most planets and many small Solar System bodies have orbits with only slight inclinations to the ecliptic, using it as the fundamental plane is convenient. The system's origin can be the center of either the Sun or Earth, its primary direction is towards the March equinox, and it has a right-hand convention. It may be implemented in spherical or rectangular coordinates.

<span class="mw-page-title-main">Sidereal time</span> Timekeeping system on Earth relative to the celestial sphere

Sidereal time is a system of timekeeping used especially by astronomers. Using sidereal time and the celestial coordinate system, it is easy to locate the positions of celestial objects in the night sky. Sidereal time is a "time scale that is based on Earth's rate of rotation measured relative to the fixed stars".

A sidereal year, also called a sidereal orbital period, is the time that Earth or another planetary body takes to orbit the Sun once with respect to the fixed stars.

<span class="mw-page-title-main">Axial precession</span> Change of rotational axis in an astronomical body

In astronomy, axial precession is a gravity-induced, slow, and continuous change in the orientation of an astronomical body's rotational axis. In the absence of precession, the astronomical body's orbit would show axial parallelism. In particular, axial precession can refer to the gradual shift in the orientation of Earth's axis of rotation in a cycle of approximately 26,000 years. This is similar to the precession of a spinning top, with the axis tracing out a pair of cones joined at their apices. The term "precession" typically refers only to this largest part of the motion; other changes in the alignment of Earth's axis—nutation and polar motion—are much smaller in magnitude.

<span class="mw-page-title-main">First point of Aries</span> Point on the celestial sphere

The first point of Aries, also known as the cusp of Aries, is the location of the March equinox, used as a reference point in celestial coordinate systems. In diagrams using such coordinate systems, it is often indicated with the symbol ♈︎. Named for the constellation of Aries, it is one of the two points on the celestial sphere at which the celestial equator crosses the ecliptic, the other being the first point of Libra, located exactly 180° from it. Due to precession of the equinoxes since the positions were originally named in antiquity, the position of the Sun when at the March equinox is now in Pisces; when it is at the September equinox, it is in Virgo.

In astronomy, an epoch or reference epoch is a 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 celestial body, as they are subject to perturbations and vary with time. 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 aphelion of its orbit, or the size of the major axis of its orbit.

In astronomy, a Julian year is a unit of measurement of time defined as exactly 365.25 days of 86400 SI seconds each. The length of the Julian year is the average length of the year in the Julian calendar that was used in Western societies until the adoption of the Gregorian Calendar, and from which the unit is named. Nevertheless, because astronomical Julian years are measuring duration rather than designating dates, this Julian year does not correspond to years in the Julian calendar or any other calendar. Nor does it correspond to the many other ways of defining a year.

<span class="mw-page-title-main">Spherical astronomy</span> Branch of astronomy about the celestial sphere

Spherical astronomy, or positional astronomy, is a branch of observational astronomy used to locate astronomical objects on the celestial sphere, as seen at a particular date, time, and location on Earth. It relies on the mathematical methods of spherical trigonometry and the measurements of astrometry.

<span class="mw-page-title-main">Orbit of the Moon</span> The Moons circuit around Earth

The Moon orbits Earth in the prograde direction and completes one revolution relative to the Vernal Equinox and the stars in about 27.32 days and one revolution relative to the Sun in about 29.53 days. Earth and the Moon orbit about their barycentre, which lies about 4,670 km (2,900 mi) from Earth's centre, forming a satellite system called the Earth–Moon system. On average, the distance to the Moon is about 385,000 km (239,000 mi) from Earth's centre, which corresponds to about 60 Earth radii or 1.282 light-seconds.

<span class="mw-page-title-main">Earth-centered inertial</span> Coordinate frames

Earth-centered inertial (ECI) coordinate frames have their origins at the center of mass of Earth and are fixed with respect to the stars. "I" in "ECI" stands for inertial, in contrast to the "Earth-centered – Earth-fixed" (ECEF) frames, which remains fixed with respect to Earth's surface in its rotation, and then rotates with respect to stars.

A tropical year or solar year is the time that the Sun takes to return to the same position in the sky – as viewed from the Earth or another celestial body of the Solar System – thus completing a full cycle of astronomical seasons. For example, it is the time from vernal equinox to the next vernal equinox, or from summer solstice to the next summer solstice. It is the type of year used by tropical solar calendars.

<span class="mw-page-title-main">Lunar month</span> Time between successive new moons

In lunar calendars, a lunar month is the time between two successive syzygies of the same type: new moons or full moons. The precise definition varies, especially for the beginning of the month.

Astronomical nutation is a phenomenon which causes the orientation of the axis of rotation of a spinning astronomical object to vary over time. It is caused by the gravitational forces of other nearby bodies acting upon the spinning object. Although they are caused by the same effect operating over different timescales, astronomers usually make a distinction between precession, which is a steady long-term change in the axis of rotation, and nutation, which is the combined effect of similar shorter-term variations.

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