The apparent motion of theSun along the ecliptic (red) as seen on the inside of thecelestial sphere. Ecliptic coordinates appear in (red). Thecelestial equator (blue) and theequatorial coordinates (blue), being inclined to the ecliptic, appear to wobble as the Sun advances.
Thecelestial equator and theecliptic are slowly moving due toperturbing forces on theEarth, therefore theorientation of the primary direction, their intersection at theMarch 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 theecliptic, completing one circuit in about 26,000 years. Superimposed on this is a smaller motion of theecliptic, 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 theequinox of a particular date, known as anepoch, when giving a position in ecliptic coordinates. The three most commonly used are:
Mean equinox of a standard epoch
(usually theJ2000.0 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 theecliptic of "date" (that is, the ecliptic in its position at "date") with themean equator (that is, the equator rotated byprecession to its position at "date", but free from the small periodic oscillations ofnutation). Commonly used in planetaryorbit calculation.
True equinox of date
is the intersection of theecliptic of "date" with thetrue equator (that is, the mean equator plusnutation). 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 specifiedtrue 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 orcelestial longitude (symbols: heliocentricl, geocentricλ) measures the angular distance of an object along theecliptic from the primary direction. Likeright ascension in theequatorial coordinate system, the primary direction (0° ecliptic longitude) points from the Earth towards the Sun at theMarch 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 ofaxial precession, the ecliptic longitude of most "fixed stars" (referred to the equinox of date) increases by about 50.3arcseconds per year, or 83.8arcminutes 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 orcelestial latitude (symbols: heliocentricb, geocentricβ), measures the angular distance of an object from theecliptic towards the north (positive) or south (negative)ecliptic pole. For example, thenorth 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: heliocentricr, geocentricΔ). Different distance units are used for different objects. Within theSolar System,astronomical units are used, and for objects near theEarth,Earth radii orkilometers are used.
From antiquity through the 18th century, ecliptic longitude was commonly measured using twelvezodiacal signs, each of 30° longitude, a practice that continues in modernastrology. The signs approximately corresponded to theconstellations 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 signLeo. Since Leo begins 120° from the March equinox, the longitude in modern form is139° 55′ 58″.[9]
In China, ecliptic longitude is measured using 24 Solar terms, each of 15° longitude, and are used byChinese lunisolar calendars to stay synchronized with the seasons, which is crucial for agrarian societies.
Heliocentric ecliptic coordinates. Theorigin is theSun's center, theplane of reference is theecliptic plane, and the primary direction (thex-axis) is the Marchequinox. Aright-handed rule specifies ay-axis 90° to the east on the fundamental plane. Thez-axis points toward the northecliptic pole. The reference frame is relatively stationary, aligned with the March equinox.
Arectangular variant of ecliptic coordinates is often used inorbital calculations and simulations. It has itsorigin at the center of theSun (or at thebarycenter of theSolar System), itsfundamental plane on theecliptic plane, and thex-axis toward the Marchequinox. The coordinates have aright-handed convention, that is, if one extends their right thumb upward, it simulates thez-axis, their extended index finger thex-axis, and the curl of the other fingers points generally in the direction of they-axis.[10]
These rectangular coordinates are related to the corresponding spherical coordinates by
