The
celestial equator and the
ecliptic are slowly moving due to
perturbing forces on the
Earth, therefore the
orientation of the primary direction, their intersection at the
March equinox, is not quite fixed. A slow motion of Earth's axis,
precession, causes a slow, continuous turning of the coordinate system westward about the poles of the
ecliptic, completing one circuit in about 26,000 years. Superimposed on this is a smaller motion of the
ecliptic, and a small oscillation of the Earth's axis,
nutation.[3][4]
In order to reference a coordinate system which can be considered as fixed in space, these motions require specification of the
equinox of a particular date, known as an
epoch, 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
ecliptic of "date" (that is, the ecliptic in its position at "date") with the mean equator (that is, the equator rotated by
precession to its position at "date", but free from the small periodic oscillations of
nutation). Commonly used in planetary
orbit calculation.
True equinox of date
is the intersection of the
ecliptic of "date" with the true equator (that is, the mean equator plus
nutation). 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.[5]
Ecliptic longitude or celestial longitude (symbols: heliocentric l, geocentric λ) measures the angular distance of an object along the
ecliptic from the primary direction. Like
right ascension in the
equatorial coordinate system, the primary direction (0° ecliptic longitude) points from the Earth towards the Sun at the
March equinox. 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, the ecliptic longitude of most "fixed stars" (referred to the equinox of date) increases by about 50.3
arcseconds per year, or 83.8
arcminutes per century, the speed of general precession.[7][8] 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 b, geocentric β), measures the angular distance of an object from the
ecliptic towards the north (positive) or south (negative)
ecliptic pole. 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 r, geocentric Δ). Different distance units are used for different objects. Within the
Solar System,
astronomical units are used, and for objects near the
Earth,
Earth radii or
kilometers 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. The signs approximately corresponded to the
constellations crossed by the ecliptic. Longitudes were specified in signs, degrees, minutes, and seconds. For example, a longitude of ♌ 19° 55′ 58″ is 19.933° east of the start of the sign
Leo. Since Leo begins 120° from the March equinox, the longitude in modern form is 139° 55′ 58″.[9]
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
orbital calculations and simulations. It has its
origin at the center of the
Sun (or at the
barycenter of the
Solar System), its
fundamental plane on the
ecliptic plane, and the x-axis toward the March
equinox. The coordinates have a
right-handed convention, that is, if one extends their right thumb upward, it simulates the z-axis, their extended index finger the x-axis, and the curl of the other fingers points generally in the direction of the y-axis.[10]
These rectangular coordinates are related to the corresponding spherical coordinates by