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During the course of a year, the sun's intrinsic motion causes it to trace out a fixed circle which bisects the celestial sphere. This circle is known as the ecliptic. The sun travels around the ecliptic from west to east (i.e., in the opposite direction
to the celestial sphere's diurnal rotation). Moreover, the ecliptic circle is inclined at a fixed angle of
to the celestial equator.
This angle actually represents the fixed inclination of the earth's axis of rotation to the normal to its orbital
plane.^{}
Figure 5:
The ecliptic circle. , , , , , , ,
and denote the north celestial pole, south celestial pole, north ecliptic pole, south
ecliptic pole, vernal equinox, autumnal equinox, summer solstice, and winter
solstice, respectively. is the celestial equator, the ecliptic, and the
celestial axis.

The vernal equinox, , is defined as the point at which the ecliptic crosses the celestial equator
from south to north (in the direction of the sun's ecliptic motion)see Fig. 5. Likewise, the autumnal equinox, , is the point at which the ecliptic crosses the
celestial equator from north to south. In addition, the summer solstice, , is the
point on the ecliptic which is furthest north of the celestial equator, whereas the
winter solstice, , is the point which is furthest south. It follows that the lines and
are perpendicular. Let be the normal to the plane of the ecliptic which passes through the earth, as shown in Fig. 5.
Here, is termed the northern ecliptic pole, and the southern ecliptic pole.
It is easily demonstrated that
where is a unit vector which is directed from the earth to the summer solstice, and a unit vector which is directed from the earth to the north ecliptic polesee Fig. 5. We can also write
Thus, , , and constitute another righthanded, mutually perpendicular, set of unit vectors.
Figure 6:
Ecliptic coordinates. is the earth, a celestial
object, and its projection onto the ecliptic plane, .

Next: Ecliptic Coordinates
Up: Spherical Astronomy
Previous: Celestial Coordinates
Richard Fitzpatrick
20100721