The Heavens Above: A Popular Handbook of Astronomy

by J. A. Gillet; W. J. Rolfe

Distance, Size, and Motions.

87. The Distance of the Moon.—The moon is the nearest of the heavenly bodies. Its distance from the centre of the earth is only about sixty times the radius of the earth, or, in round numbers, two hundred and forty thousand miles.

The ordinary method of finding the distance of one of the nearer heavenly bodies is first to ascertain its horizontal parallax. This enables us to form a right-angled triangle, the lengths of whose sides are easily computed, and the length of whose hypothenuse is the distance of the body from the centre of the earth.

Fig. 101.

Horizontal parallax has already been defined (32) as the displacement of a heavenly body when on the horizon, caused by its being seen from the surface, instead of the centre, of the earth. This displacement is due to the fact that the body is seen in a different direction from the surface of the earth from that in which it would be seen from the centre. Horizontal parallax might be defined as the difference in the directions in which a body on the horizon would be seen from the surface and from the centre of the earth. Thus, in Fig. 101, C is the centre of the earth, A a point on the surface, and B a body on the horizon of A. AB is the direction in which the body would be seen from A, and CB the direction in which it would be seen from C. The difference of these directions, or the angle ABC, is the parallax of the body.

The triangle BAC is right-angled at A; the side AC is the radius of the earth, and the hypothenuse is the distance of the body from the centre of the earth. When the parallax ABC is known, the length of CB can easily by found by trigonometrical computation.

We have seen (32) that the parallax of a heavenly body grows less and less as the body passes from the horizon towards the zenith. The parallax of a body and its altitude are, however, so related, that, when we know the parallax at any altitude, we can readily compute the horizontal parallax.

The usual method of finding the parallax of one of the nearer heavenly bodies is first to find its parallax when on the meridian, as seen from two places on the earth which differ considerably in latitude: then to calculate what would be the parallax of the body as seen from one of these places and the centre of the earth: and then finally to calculate what would be the parallax were the body on the horizon.