The ecliptic coordinate system is a

celestial coordinate system Astronomical coordinate systems are organized arrangements for specifying positions of satellites, planets, stars, galaxies, and other celestial objects relative to physical reference points available to a situated observer (e.g. the true horizo ...

commonly used for representing the apparent positions,

orbit In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a ...

s, and

pole Pole may refer to: Astronomy * Celestial pole, the projection of the planet Earth's axis of rotation onto the celestial sphere; also applies to the axis of rotation of other planets *Pole star, a visible star that is approximately aligned with th ...

orientations of

Solar System The Solar System Capitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar ...

objects. Because most

planet A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a yo ...

s (except Mercury) and many small Solar System bodies have orbits with only slight

inclination Orbital inclination measures the tilt of an object's orbit around a celestial body. It is expressed as the angle between a reference plane and the orbital plane or axis of direction of the orbiting object. For a satellite orbiting the Earth ...

s to the

ecliptic The ecliptic or ecliptic plane is the orbital plane of the 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 again ...

, using it as the fundamental plane is convenient. The system's

origin Origin(s) or The Origin may refer to: Arts, entertainment, and media Comics and manga * ''Origin'' (comics), a Wolverine comic book mini-series published by Marvel Comics in 2002 * ''The Origin'' (Buffy comic), a 1999 ''Buffy the Vampire Sl ...

can be the center of either the

Sun The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...

Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...

, its primary direction is towards the vernal (March)

equinox 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 se ...

, and it has a right-hand convention. It may be implemented in

spherical A sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance from a given point in three-dimensional space.. That given point is the ...

rectangular coordinates A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in ...

Primary direction

The

celestial equator The celestial equator is the great circle of the imaginary celestial sphere on the same plane as the equator of Earth. This plane of reference bases the equatorial coordinate system. In other words, the celestial equator is an abstract project ...

and the

are slowly moving due to perturbing forces on the

, therefore the

orientation Orientation may refer to: Positioning in physical space * Map orientation, the relationship between directions on a map and compass directions * Orientation (housing), the position of a building with respect to the sun, a concept in building des ...

of the primary direction, their intersection at the

Northern Hemisphere The Northern Hemisphere is the half of Earth that is north of the Equator. For other planets in the Solar System, north is defined as being in the same celestial hemisphere relative to the invariable plane of the solar system as Earth's N ...

vernal

, is not quite fixed. A slow motion of Earth's axis,

precession Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In oth ...

, causes a slow, continuous turning of the coordinate system westward about the poles of the

, completing one circuit in about 26,000 years. Superimposed on this is a smaller motion of the

, and a small oscillation of the Earth's axis,

nutation Nutation () is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behaviour of a mechanism. In an appropriate reference frame ...

. In order to reference a coordinate system which can be considered as fixed in space, these motions require specification of the

of a particular date, known as an

epoch In chronology and periodization, an epoch or reference epoch is an instant in time chosen as the origin of a particular calendar era. The "epoch" serves as a reference point from which time is measured. The moment of epoch is usually decided by ...

, when giving a position in ecliptic coordinates. The three most commonly used are: ;Mean equinox of a standard epoch: (usually the J2000.0 epoch, but may include B1950.0, B1900.0, etc.) is a fixed standard direction, allowing positions established at various dates to be compared directly. ;Mean equinox of date: is the intersection of the

of "date" (that is, the ecliptic in its position at "date") with the ''mean'' equator (that is, the equator rotated by

to its position at "date", but free from the small periodic oscillations of

). Commonly used in planetary

calculation. ;True equinox of date: is the intersection of the

of "date" with the ''true'' equator (that is, the mean equator plus

). This is the actual intersection of the two planes at any particular moment, with all motions accounted for. A position in the ecliptic coordinate system is thus typically specified ''true equinox and ecliptic of date'', ''mean equinox and ecliptic of J2000.0'', or similar. Note that there is no "mean ecliptic", as the ecliptic is not subject to small periodic oscillations.

Spherical coordinates

;Ecliptic longitude :''Ecliptic longitude'' or ''celestial longitude'' (symbols: heliocentric , geocentric ) measures the angular distance of an object along the

from the primary direction. Like

right ascension Right ascension (abbreviated RA; symbol ) is the angular distance of a particular point measured eastward along the celestial equator from the Sun at the March equinox to the (hour circle of the) point in question above the earth. When paired w ...

in the

equatorial coordinate system 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 fu ...

, the primary direction (0° ecliptic longitude) points from the Earth towards the Sun at the vernal

of the Northern Hemisphere. Because it is a right-handed system, ecliptic longitude is measured positive eastwards in the fundamental plane (the ecliptic) from 0° to 360°. Because of

axial precession 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 partic ...

, the ecliptic longitude of most "fixed stars" (referred to the equinox of date) increases by about 50.3

arcsecond A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of one degree. Since one degree is of a turn (or complete rotation), one minute of arc is of a turn. The n ...

s per year, or 83.8

arcminute A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of one degree. Since one degree is of a turn (or complete rotation), one minute of arc is of a turn. The n ...

s per century, the speed of general precession. However, for stars near the ecliptic poles, the rate of change of ecliptic longitude is dominated by the slight movement of the ecliptic (that is, of the plane of the earth's orbit), so the rate of change may be anything from minus infinity to plus infinity depending on the exact position of the star. ;Ecliptic latitude :''Ecliptic latitude'' or ''celestial latitude'' (symbols: heliocentric , geocentric ), measures the angular distance of an object from the

towards the north (positive) or south (negative)

ecliptic pole An orbital pole is either point at the ends of an imaginary line segment that runs through the center of an orbit (of a revolving body like a planet, moon or satellite) and is perpendicular to the orbital plane. Projected onto the celestial sph ...

. For example, the north ecliptic pole has a celestial latitude of +90°. Ecliptic latitude for "fixed stars" is not affected by precession. ;Distance :''Distance'' is also necessary for a complete spherical position (symbols: heliocentric , geocentric ). Different distance units are used for different objects. Within the

astronomical unit The astronomical unit (symbol: au, or or AU) is a unit of length, roughly the distance from Earth to the Sun and approximately equal to or 8.3 light-minutes. The actual distance from Earth to the Sun varies by about 3% as Earth orbits ...

s are used, and for objects near the

Earth radii Earth radius (denoted as ''R''🜨 or R_E) is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid, the radius ranges from a maximum of nearly (equatorial radius, deno ...

kilometer The kilometre ( SI symbol: km; or ), spelt kilometer in American English, is a unit of length in the International System of Units (SI), equal to one thousand metres ( kilo- being the SI prefix for ). It is now the measurement unit used for e ...

s are used.

Historical use

From antiquity through the 18th century, ecliptic longitude was commonly measured using twelve zodiacal signs, each of 30° longitude, a practice that continues in modern

astrology Astrology is a range of divinatory practices, recognized as pseudoscientific since the 18th century, that claim to discern information about human affairs and terrestrial events by studying the apparent positions of celestial objects. Di ...

. The signs approximately corresponded to the

constellation A constellation is an area on the celestial sphere in which a group of visible stars forms a perceived pattern or outline, typically representing an animal, mythological subject, or inanimate object. The origins of the earliest constellation ...

s crossed by the ecliptic. Longitudes were specified in signs, degrees, minutes, and seconds. For example, a longitude of is 19.933° east of the start of the sign Leo. Since Leo begins 120° from the vernal

, the longitude in modern form is . In China, ecliptic longitude is measured using 24 Solar terms, each of 15° longitude, and are used by Chinese lunisolar calendars to stay synchronized with the seasons, which is crucial for agrarian societies.

Rectangular coordinates

A rectangular variant of ecliptic coordinates is often used in

al calculations and simulations. It has its

at the center of the

(or at the barycenter of the

), its fundamental plane on the

plane, and the -axis toward the vernal

. The coordinates have a right-handed convention, that is, if one extends their right thumb upward, it simulates the -axis, their extended index finger the -axis, and the curl of the other fingers points generally in the direction of the -axis. These rectangular coordinates are related to the corresponding spherical coordinates by :

\begin
x &= r \cos b \cos l \\
y &= r \cos b \sin l \\
z &= r \sin b \end

Conversion between celestial coordinate systems

Converting Cartesian vectors

Conversion from ecliptic coordinates to equatorial coordinates

\begin
  x_\text \\
  y_\text \\
  z_\text \\
 \end
 =
 \begin
  1 & 0 & 0 \\
  0 & \cos \varepsilon & -\sin \varepsilon \\
  0 & \sin \varepsilon &  \cos \varepsilon \\
 \end
 \begin
  x_\text \\
  y_\text \\
  z_\text \\
 \end

''Explanatory Supplement'' (1992), pp. 555-558

Conversion from equatorial coordinates to ecliptic coordinates

\begin
  x_\text \\
  y_\text \\
  z_\text \\
 \end
 =
 \begin
  1 & 0 & 0 \\
  0 & \cos \varepsilon & \sin \varepsilon \\
  0 & -\sin \varepsilon & \cos \varepsilon \\
 \end
 \begin
  x_\text \\
  y_\text \\
  z_\text \\
 \end

where is the

obliquity of the ecliptic In astronomy, axial tilt, also known as obliquity, is the angle between an object's rotational axis and its orbital axis, which is the line perpendicular to its orbital plane; equivalently, it is the angle between its equatorial plane and orbit ...

Notes and references

External links

The Ecliptic: the Sun's Annual Path on the Celestial Sphere
Durham University Department of Physics
Equatorial ↔ Ecliptic coordinate converter

James B. Kaler, University of Illinois {{Portal bar, Astronomy, Stars, Spaceflight, Outer space, Solar System Astronomical coordinate systems