The axis of a sphere is the diameter on which it rotates. The poles of a sphere are the ends of its axis. Thus, supposing the spheres of Figs. 1 and 2 to rotate on the diameter PP', this line would be called the axis of the sphere, and the points P and P' the poles of the sphere. A great circle, MM', situated half way between the poles of a sphere, is called the equator of the sphere.
Every great circle of a sphere has two poles. These are the two points on the surface of the sphere which lie 90° away from the circle. The poles of a sphere are the poles of its equator.
Fig. 2.
2. The Celestial Sphere.—The heavens appear to have the form of a sphere, whose centre is at the eye of the observer; and all the stars seem to lie on the surface of this sphere. This form of the heavens is a mere matter of perspective. The stars are really at very unequal distances from us; but they are all seen projected upon the celestial sphere in the direction in which they happen to lie. Thus, suppose an observer situated at C (Fig. 3), stars situated at a, b, d, e, f, and g, would be projected upon the sphere at A, B, D, E, F, and G, and would appear to lie on the surface of the heavens.
Fig. 3.
3. The Horizon.—Only half of the celestial sphere is visible at a time. The plane that separates the visible from the invisible portion is called the horizon. This plane is tangent to the earth at the point of observation, and extends indefinitely into space in every direction. In Fig. 4, E represents the earth, O the point of observation, and SN the horizon. The points on the celestial sphere directly above and below the observer are the poles of the horizon. They are called respectively the zenith and the nadir. No two observers in different parts of the earth have the same horizon; and as a person moves over the earth he carries his horizon with him.
Fig. 4.