3. Inclination of the ecliptic to the equator.
As is well known, the celestial sphere is imagined to be spanned by an imaginary line called the celestial equator, which is in the same plane as the earth’s equator, and as it were, a vast concentric circle. The points in the celestial sphere opposite the north and south terrestrial poles are called the north and south celestial poles, and the celestial equator is midway between these. Owing to the special form of the earth the north celestial pole is visible to us in the northern hemisphere, and marked very nearly by the pole-star, its height above the horizon being equal to the latitude of the place where the observer stands. Owing to the daily rotation of the earth the whole celestial sphere seems to revolve daily on the axis of the north and south celestial poles, carrying the sun, moon and stars with it. To this the apparent daily course of the sun and moon is due. Their course seems to us oblique, as we are north of the equator.
If the earth’s axis were set vertically to the plane of its orbit round the sun, then it would follow that the plane of the equator would pass through the centre of the sun, and that the line drawn by the sun in its apparent revolution against the background of the celestial sphere would be in the same plane. That is, the sun would seem to move round a circle in the heavens in the same plane as the earth’s equator, or round the celestial equator. But the earth’s axis is inclined at 23½° to the plane of its orbit, and therefore the apparent path traced by the sun in the celestial sphere, which is the same path as the earth would really follow to an observer on the surface of the sun, is inclined at 23½° to the celestial equator. This is the ecliptic, and is really the line of the plane of the earth’s orbit extended to cut the celestial sphere.