I don't really understand how it's drawn on sketches of the celestial sphere. At first I thought it goes through east and west, but it does not. How do you know where to draw it?
Example from Roy and Clarke, Astronomy: Principles and Practice:
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The ecliptic is the plane of the Earth's orbit around the Sun. From the Earth's point of view, the Sun appears to migrate along the ecliptic, eastward one cycle per year. The ecliptic and equator intersect at the equinoxes. The Sun appears to cross the equator northward at the vernal equinox (♈) around March 20 and southward at the autumnal equinox (♎) around September 22.
Equatorial coordinates are linked to the equinoxes; ♈ is at right ascension 0h, and ♎ is at RA 12h. Where these points appear in the sky depends on the local sidereal time:
Once you've determined where on the celestial equator to mark ♈ and ♎, then you can draw the ecliptic through them as another great circle 23.4° oblique to the equator. The ecliptic runs north of the equator east of ♈, and south of the equator east of ♎, in the sense that eastward is counterclockwise as seen from the north celestial pole.
The ecliptic is the mean apparent path of the Sun throughout the year. Thus it is the plane of the Earth's orbit. The ecliptic crosses the celestial equator from south to north at the vernal equinox.