Ecliptic coordinate system


The ecliptic coordinate system is a celestial coordinate system commonly used for representing the apparent positions and orbits 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 vernal equinox, and it has a right-hand convention. It may be implemented in spherical or rectangular coordinates.
. Ecliptic longitude is measured along the ecliptic from the vernal equinox. Ecliptic latitude is measured perpendicular to the ecliptic. A full globe is shown here, although high-latitude coordinates are seldom seen except for certain comets and asteroids.

Primary direction

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 Northern Hemisphere vernal 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.
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: 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" with the mean equator. Commonly used in planetary orbit calculation.
;True equinox of date: is the intersection of the ecliptic of "date" with the true equator. 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 latitude
;Distance

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 is 19.933° east of the start of the sign Leo. Since Leo begins 120° from the vernal equinox, 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 orbital calculations and simulations. It has its origin at the center of the Sun, its fundamental plane on the ecliptic plane, and the -axis toward the vernal equinox. 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

Conversion between celestial coordinate systems

Converting Cartesian vectors

Conversion from ecliptic coordinates to equatorial coordinates

Conversion from equatorial coordinates to ecliptic coordinates

where is the obliquity of the ecliptic.