Coordinates for the solar system
Ecliptic coordinates use the plane of the Earth's orbit, the ecliptic, as their reference. Ecliptic (or celestial) longitude λ is measured eastward along the ecliptic from the vernal equinox, from 0° to 360°. Ecliptic latitude β is the angle north or south of the ecliptic, from +90° to −90°.
Because the planets orbit close to the ecliptic plane, their latitudes stay small and their motion is almost entirely a change in longitude. This makes the ecliptic system the natural one for the solar system. Planetary theories such as VSOP87 give their results directly as ecliptic longitude, latitude and distance.
Heliocentric and geocentric
The same plane can be viewed from two centres. Heliocentric coordinates, written L, B and R, describe a planet as seen from the Sun. They are what the 3D view on AstroAlgos draws. Geocentric coordinates, λ and β, describe the planet as seen from the Earth. The difference can be large: a planet at opposition has the same heliocentric longitude as the Earth, but a geocentric longitude 180° from the Sun.
Longitudes also define the planetary events of the almanacs. A conjunction happens when two bodies have the same geocentric longitude, and an opposition when a planet is 180° from the Sun in longitude.
The Sun's longitude and the seasons
Seen from the Earth, the Sun always has a latitude close to 0° and moves about 1° per day in longitude. The seasons are defined by its longitude:
| Sun's longitude | Event | Approximate date |
|---|---|---|
| 0° | March equinox | 20 March |
| 90° | June solstice | 21 June |
| 180° | September equinox | 22–23 September |
| 270° | December solstice | 21–22 December |
Latitudes of the Moon and planets
- The Moon's orbit is inclined about 5.1° to the ecliptic, so its latitude varies between about +5.3° and −5.3°. Eclipses are only possible when the Moon is near a node, at a latitude close to 0°.
- The major planets have orbital inclinations of less than 3.4°, except Mercury (7.0°). Seen from the Earth, Venus can nevertheless reach a latitude of more than 8° near inferior conjunction, because it is then close to us.
- Pluto (17°) and many asteroids and comets have much larger inclinations and wander far from the ecliptic.
- Stars have fixed latitudes but their longitudes increase by about 50″ per year because of precession. Regulus, in Leo, is the bright star closest to the ecliptic, less than half a degree away.
Converting to equatorial coordinates
With the obliquity ε ≈ 23.44°, the inverse rotation gives right ascension and declination from λ and β:
tan α = (sin λ cos ε − tan β sin ε) / cos λsin δ = sin β cos ε + cos β sin ε sin λPollux, at λ = 113.215630° and β = +6.684170°, returns to α = 7h 45m 18.946s and δ = +28° 01′ 34.26″, the values of Meeus' example 13.a. For apparent positions, use the true obliquity of the date, which includes nutation.
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Frequently asked questions
What is ecliptic longitude?
The angle measured eastward along the ecliptic from the vernal equinox, from 0° to 360°. The Sun's ecliptic longitude is 0° at the March equinox and increases by about 1° per day.
Why do the planets have small ecliptic latitudes?
Because the solar system formed from a flat disk, and all the major planets orbit within a few degrees of the plane of the Earth's orbit.
Is ecliptic longitude the same as a zodiac sign?
The tropical zodiac is built on it: each sign is a 30° sector of ecliptic longitude, starting at the vernal equinox. The constellations of the same names are no longer aligned with the signs, because of precession.
