Libration of the Moon

Libration of the Moon 

the apparent periodic pendulum-like oscillations of the moon at its center, as a result of which the spots on the lunar disk seen by an observer on the earth appear to shift slightly first in one direction and then in the other. Optical (geometric) libration and physical libration are distinguished.

Optical libration in longitude occurs because the moon revolves about the earth nonuniformly while it rotates about its axis at a constant angular velocity. Figure 1 depicts an elliptic lunar orbit;

Figure 1. Libration in longitude

T is the earth (at the focus of the ellipse). When the moon is at position A (perigee), let some point a on its surface be visible at the center of the disk. After a quarter of a month, the moon will be at point B and will have turned about its axis one-fourth of a revolution, that is, 90°. The point a observed from the earth will no longer be visible at the center of the disk but will have shifted to the east. At position C (apogee), the point a again coincides with the center of the disk. At the end of the third quarter, the point a will lie to the west of the center at position D. The largest libration in longitude is 7°45″.

Figure 2. Libration in latitude

Libration in latitude is explained by the fact that the moon’s axis of rotation is inclined at an angle of 83°19″ to the plane of the moon’s orbit and approximately maintains its direction in space in the course of one revolution. It is evident from Figure 2 that the moon’s south pole P″ and north pole P are alternately visible on the side of the moon turned toward the earth T. Libration in latitude reaches 6°41’.

There is also diurnal, or parallactic, libration. This is a consequence of the earth’s diurnal rotation, as a result of which the observer on the earth views the moon in different directions. The diurnal libration can reach 1°. It is possible to see up to 59 percent of the moon’s surface from the earth because of the combined result of libration in latitude, libration in longitude, and diurnal libration. The remaining 41 percent of the surface of the moon can be observed only by means of space probes.

Physical libration is due to the moon’s being a triaxial ellipsoid whose semimajor axis as a consequence of optical libration periodically deviates by several degrees from the precise orientation to the center of the earth. A force couple, created as a result of the earth’s attraction, is applied to the moon and rocks it at its center of mass by an angle of up to 2′. Exact measurement of these oscillations makes it possible to determine the moments of inertia of the moon as a function of its figure and the distribution of masses in its body.

REFERENCES

Iakovkin, A. A. “Vrashchenie i figura Luny.” Uch. zap. Kazanskogo gos. un-ta im. V. I. Ul’ianova-Lenina, 1939, vol. 99, book 2; 1945, vol. 105, book 1.
Bel’kovich, I. V. “Fizicheskaia libratsiia Luny.” Uch. zap. Kazanskogo gos. un-ta im. V. I. Ul’ianova-Lenina, 1949, vol. 109, book 2.