The Heavens Above: A Popular Handbook of Astronomy

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

This libration is due to the fact that the axis of the moon is not quite perpendicular to the plane of her orbit. The deviation from the perpendicular is six degrees and a half. As the axis of the moon, like that of the earth, maintains the same direction, the poles of the moon will be turned alternately six degrees and a half toward and from the earth.

(2) Libration in Longitude.—This libration enables us to see alternately a little farther around on the eastern and western limbs of the moon.

Fig. 119.

It is due to the fact that the moon's axial motion is uniform, while her orbital motion is not. At perigee her orbital motion will be in advance of her axial motion, while at apogee the axial motion will be in advance of the orbital. In Fig. 119, E represents the earth, M the moon, the large arrow the direction of the moon's motion in her orbit, and the small arrow the direction of her motion of rotation. When the moon is at M, the line AB, drawn perpendicular to EM, represents the circle which divides the visible from the invisible portion of the moon. While the moon is passing from M to M', the moon performs less than a quarter of a rotation, so that AB is no longer perpendicular to EM'. An observer on the earth can now see somewhat beyond A on the western limb of the moon, and not quite up to B on the eastern limb. While the moon is passing from M' to M'', her axial motion again overtakes her orbital motion, so that the line AB again becomes perpendicular to the line joining the centre of the moon to the centre of the earth. Exactly the same side is now turned towards the earth as when the moon was at M. While the moon passes from M'' to M''', her axial motion gets in advance of her orbital motion, so that AB is again inclined to the line joining the centres of the earth and moon. A portion of the eastern limb of the moon beyond B is now brought into view to the earth, and a portion of the western limb at A is carried out of view. While the moon is passing from M''' to M, the orbital motion again overtakes the axial motion, and AB is again perpendicular to ME.

(3) Parallactic Libration.—While an observer at the centre of the earth would get the same view of the moon, whether she were on the eastern horizon, in the zenith, or on the western horizon, an observer on the surface of the earth does not get exactly the same view in these three cases. When the moon is on the eastern horizon, an observer on the surface of the earth would see a little farther around on the western limb of the moon than when she is in the zenith, and not quite so far around on the eastern limb. On the contrary, when the moon is on the western horizon, an observer on the surface of the earth sees a little farther around on the eastern limb of the moon than when she is in the zenith, and not quite so far around on her western limb.

Fig. 120.

This will be evident from Fig. 120. E is the centre of the earth, and O a point on its surface. AB is a line drawn through the centre of the moon, perpendicular to a line joining the centres of the moon and the earth. This line marks off the part of the moon turned towards the centre of the earth, and remains essentially the same during the day. CD is a line drawn through the centre of the moon perpendicular to a line joining the centre of the moon and the point of observation. This line marks off the part of the moon turned towards O. When the moon is in the zenith, CD coincides with AB; but, when the moon is on the horizon, CD is inclined to AB. When the moon is on the eastern horizon, an observer at O sees a little beyond B, and not quite to A; and, when she is on the western horizon, he sees a little beyond A, and not quite to B. B is on the western limb of the moon, and A on her eastern limb.