The Moon has been since the early times the natural way to count regurarly the time and so the basis of many of the oldest calendars, prior to the adoption of a solar calendar. The 30day month is an approximation of the lunar cycle.
Not by chance in many cultures the term month derives from Moon, as the current English noun month and the same in other Germanic languages derives just from Moon and even the Ancient Greek μήνας (mēnas), means month. Indo-European root moon evolved via Latin into the terms measure and menstrual. With more accurate calendars the lunar months was observed to not fit easily into the year, which causes the usage of lunisolar calendars difficult. With the time the solar calendars, no longer relate to the phase of the Moon and being based only on the motion of the Sun on the sky, replaced the lunar calendars.
The Moon has three major movements: rotation around its axis, revolution around the earth and revolution around the sun together with the Earth as satellite.
The Rotation of the Moon around its axis has the same direction of the Earth’s rotation, from west to east with an angular velocity of 13 ° per day, which correspond to 53 minutes. For this reason every day the Moon rises later than the day before about 53 minutes.
The Moon makes a complete orbit around the Earth with respect to the fixed stars in about 27.3 days (its sidereal period). However, while the Moon is orbiting the Earth, the Earth is progressing in its orbit around the Sun at the same time, so it takes slightly longer for the Moon to show the same phase to Earth, which is about 29.5 days (its synodic period). The synodic period or lunation is the temporal interval that the Moon, relative to the Sun as observed from Earth, needs to return to the same illumination phase, so this is the complete period of the Moon's phases. Because of perturbations in the orbits of the Earth and Moon, the actual time may range from about 29.18 to about 29.93 days.
The rotation period of the Moon is exactly equal to its orbital period around the Earth, so an observer always sees the same face of the Moon from the Earth. This is called synchronous rotation: the Moon rotates about its axis in the same time it takes to orbit the Earth.
The lunar phases describe the quantity of the lunar surface illuminated by the Sun, as seen from the Earth during its motions.
There are four basic phases and four intermediate phases:
New Moon (sigizia, conjunction, new moon phase)
First quarter (quadrature)
Full Moon (sigizia, opposition, during the full moon)
Last quarter (quadrature)
The term "quarter" refers to the position of the Moon orbit around the Earth, from these two positions is visible from the Earth half hemisphere. At the new moon, the Moon is interposed between the Earth and the Sun, so the side facing Earth is not illuminated. The Moon rises in the morning and sets in the evening. When it is aligned with the Earth, the Sun is covered and there is a solar eclipse. In the quadratures or quarters (first quarter and last quarter), the Earth-Moon has a 90 ° angle with the Earth-Sun. In the first quarter rises at noon and sets at midnight last quarter rises at midnight and sets at noon. At full moon the Earth is between the Sun and Moon, and so Moon is fully illuminated. The Moon rises and sets in the evening to morning. If it is aligned behind the shadow of the Earth, iy happens has a lunar eclipse.