Ecliptic coordinate system
In
![](http://upload.wikimedia.org/wikipedia/commons/thumb/5/50/Ecliptic_grid_globe.png/220px-Ecliptic_grid_globe.png)
Primary direction
![](http://upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Ecliptic_vs_equator_small.gif/220px-Ecliptic_vs_equator_small.gif)
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]
Spherical coordinates
Spherical | Rectangular | |||
---|---|---|---|---|
Longitude | Latitude | Distance | ||
Geocentric | λ | β | Δ | |
Heliocentric | l | b | r | x, y, z[note 1] |
|
- Ecliptic longitude
- Ecliptic longitude or celestial longitude (symbols: heliocentric l, geocentric λ) measures the angular distance of an object along the 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 north ecliptic polehas 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 kilometersare 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
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
See also
- Celestial coordinate system
- Ecliptic
- Ecliptic pole, where the ecliptic latitude is ±90°
- Equinox
Notes and references
- Bibcode:1985MPBu...12...13C.
- ^ Nautical Almanac Office, U.S. Naval Observatory; H.M. Nautical Almanac Office, Royal Greenwich Observatory (1961). Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac. H.M. Stationery Office, London (reprint 1974). pp. 24–27.
- ^ Explanatory Supplement (1961), pp. 20, 28
- ^
U.S. Naval Observatory, Nautical Almanac Office (1992). P. Kenneth Seidelmann (ed.). Explanatory Supplement to the Astronomical Almanac. University Science Books, Mill Valley, CA (reprint 2005). pp. 11–13. ISBN 1-891389-45-9.
- ^
Meeus, Jean (1991). Astronomical Algorithms. Willmann-Bell, Inc., Richmond, VA. p. 137. ISBN 0-943396-35-2.
- ^ Explanatory Supplement (1961), sec. 1G
- (PDF) from the original on 2012-03-25.
- ^ J.H. Lieske et al. (1977), "Expressions for the Precession Quantities Based upon the IAU (1976) System of Astronomical Constants". Astronomy & Astrophysics 58, pp. 1-16
- ^ Leadbetter, Charles (1742). A Compleat System of Astronomy. J. Wilcox, London. p. 94.; numerous examples of this notation appear throughout the book.
- ^ Explanatory Supplement (1961), pp. 20, 27
- ^ Explanatory Supplement (1992), pp. 555-558
External links
- The Ecliptic: the Sun's Annual Path on the Celestial Sphere Durham University Department of Physics
- Equatorial ↔ Ecliptic coordinate converter
- MEASURING THE SKY A Quick Guide to the Celestial Sphere James B. Kaler, University of Illinois