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The phenomenon of libration, discovered by Galileo Galilei in 1635, makes it possible to observe about 59% of the lunar surface. The fact is that the Moon rotates around the Earth with a variable angular velocity due to the eccentricity of the lunar orbit (it moves faster near the perigee, slower near the apogee), while the rotation of the satellite around its own axis is uniform. This makes it possible to see the western and eastern edges of the far side of the Moon from the Earth (optical libration in longitude). In addition, due to the inclination of the Moon's axis of rotation to the plane of its orbit, from the Earth one can see the northern and southern edges of the far side of the Moon (optical libration in latitude).

Although the Moon rotates around its axis, it always faces the Earth with the same side, that is, the Moon's revolution around the Earth and rotation around its own axis are synchronized. This synchronization is caused by the friction of the tides produced by the Earth in the shell of the Moon[40]. According to the laws of mechanics, the Moon is oriented in the Earth's gravitational field so that the semi-major axis of the lunar ellipsoid is directed towards the Earth.

Since the Moon does not glow itself, but only reflects sunlight, only the part of the lunar surface illuminated by the Sun is visible from the Earth (in the phases of the Moon close to the new moon, that is, at the beginning of the first quarter and at the end of the last quarter, with a very narrow crescent, you can observe " the ashen light of the moon" - weak illumination of it by the rays of the sun reflected from the earth). The Moon revolves in an orbit around the Earth, and thereby the angle between the Earth, the Moon and the Sun changes; we observe this phenomenon as a cycle of lunar phases. The period of time between successive new moons averages 29.5 days (709 hours) and is called the synodic month. The fact that the duration of the synodic month is longer than the sidereal one is explained by the movement of the Earth around the Sun: when the Moon makes a complete revolution around the Earth relative to the stars, the Earth by this time has already passed 1/13 of its orbit, and so that the Moon again finds itself between the Earth and the Sun, She needs an extra two days.

The GRAIL program for studying the gravitational field and the internal structure of the Moon, as well as reconstructing its thermal history, established that the Moon has an internal solid and external metal parts of the core (consisting of iron and siderophile elements). The very weak magnetic field of the Moon is formed due to residual magnetism in lunar rocks, as well as tidal forces acting on the core

It is believed that the source of the magnetic field of the planets is tectonic activity. For example, for the Earth, the field is created by the movement of molten metal in the core, for Mars, by the consequences of past activity.
"Luna-1" in 1959 established the absence of a uniform magnetic field on the Moon[38]:24. The results of research by scientists at the Massachusetts Institute of Technology confirm the hypothesis that it had a liquid core. This fits into the most popular hypothesis of the origin of the Moon - the collision of the Earth about 4.5 billion years ago with a cosmic body the size of Mars “knocked out” a huge piece of molten matter from the Earth, which later turned into the Moon. Experimentally, it was possible to prove that at an early stage of its existence, the Moon had a magnetic field similar to that of the Earth

around the Earth in an elliptical orbit with a period of 27.32166 days - this is the so-called sidereal month (that is, the movement is measured relative to the stars);
rotation of the plane of the lunar orbit: its nodes (the points of intersection of the orbit with the ecliptic) are shifted to the west, making a complete revolution in 18.6 years. This movement is precessional;
rotation of the major axis of the lunar orbit (lines of apsides) with a period of 8.8 years (occurs in the opposite direction than the movement of the nodes indicated above, that is, the longitude of the perigee increases);
periodic change in the inclination of the lunar orbit with respect to the ecliptic from 4°59' to 5°19';
periodic change in the size of the lunar orbit: perigee - from 356.41 to 369.96 thousand km, apogee - from 404.18 to 406.74 thousand km;
the gradual removal of the Moon from the Earth due to tidal acceleration (by 38 mm per year) [12] [13], so its orbit is a slowly unwinding spiral

In the first approximation, we can assume that the Moon moves in an elliptical orbit with an eccentricity of 0.0549 and a geocentric orbit semi-major axis of 384,399 km (while the semi-major axis in the system relative to the center of mass of the Earth-Moon system is 379,730 km). The actual motion of the Moon is quite complex, and many factors must be taken into account in calculating it, for example, the oblateness of the Earth and the strong influence of the Sun, which attracts the Moon 2.2 times stronger than the Earth [comm. 2]. More precisely, the movement of the Moon around the Earth can be represented as a combination of several movements

Modern science can calculate the motion of the moon and verify these calculations with even greater accuracy. Using laser ranging methods, the distance to the Moon is measured with an error of several centimeters [10]. Not only measurements, but also theoretical predictions of the position of the Moon have such accuracy; for such calculations, expressions with tens of thousands of terms are used, and there is no limit to their number if even higher accuracy is required.

Since ancient times, people have tried to describe and explain the movement of the moon. Over time, more and more accurate theories appeared.
The basis of modern calculations is Brown's theory. Created at the turn of the 19th-20th centuries, it described the movement of the moon with the accuracy of the measuring instruments of that time. At the same time, more than 1400 terms (coefficients and arguments for trigonometric functions) were used in the calculation.

The Moon is the only natural satellite of the Earth. The closest satellite of the planet to the Sun, since the planets closest to the Sun (Mercury and Venus) do not have them. The second brightest [comm. 1] an object in the earth's sky after the Sun and the fifth largest natural satellite of a planet in the solar system. The average distance between the centers of the Earth and the Moon is 384,467 km (0.00257 AU, ~30 Earth diameters).
The apparent stellar magnitude of the full moon in the earth's sky is −12.71m[5]. The illumination created by the full Moon near the surface of the Earth in clear weather is 0.25-1 lux.
The Moon appeared about 4.5 billion years ago, a little later than the Earth. The most popular hypothesis is that the Moon was formed from fragments left after the “Giant Collision” between the Earth and Theia, a planet similar in size to Mars.
To date, the Moon is the only extraterrestrial astronomical object visited by man.