Ecliptic coordinate system

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The ecliptic coordinate system is a celestial coordinate system that uses the ecliptic for its fundamental plane. The ecliptic is the path that the sun appears to follow across the sky over the course of a year. It is also the projection of the Earth's orbital plane onto the celestial sphere. The latitudinal angle is called the ecliptic latitude (denoted β), and the longitudinal angle is called the ecliptic longitude (denoted λ). Like right ascension in the equatorial coordinate system, the zeropoint of the ecliptic longitude is the vernal equinox.

Such a coordinate system can be useful for charting solar system objects. Each of the planets (except Pluto) orbits the sun in roughly the same plane, so they always appear to be somewhere near the ecliptic (i.e., they always have small ecliptic latitudes).

This section originates from Jason Harris' Astroinfo which comes along with KStars, a Desktop Planetarium for Linux/KDE. See http://edu.kde.org/kstars/index.phtml

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Conversion from ecliptic to equatorial coordinates

Where (declination, right ascension,in degrees ) = (δ, α), and A=23.439 281° is the Earth's axial tilt,

sinδ = sinA sinλ cosβ + cosA sinβ

cosα = cosλ cosβ / cosδ

Note that both α and λ stay on the same side of 180°. When using a calculator to perform cos-1, this requires α = 360° - cos-1[ cosλ cosβ / cosδ ] when λ>180°.

Also: 15° of right ascension equal 1 hour and 1° of right ascension equals 4 minutes

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Conversion from equatorial to ecliptic coordinates

In the same notation as above,

sinβ = cosA sinδ - sinα cosδ sinA

cosλ = cosα cosδ / cosβ

Note that both α and λ stay on the same side of 180°. When using a calculator to perform cos-1, this requires λ = 360° - cos-1[ cosα cosδ / cosβ ] when α>180°.ca:Coordenades eclíptiques de:Ekliptikales Koordinatensystem fr:Système de coordonnées écliptiques ko:황도좌표 ja:黄道座標 vi:Hệ tọa độ hoàng đạo

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