A lunar day is the period of time it takes for the Earth’s Moon to complete one full rotation on its axis with respect to the Sun. Equivalently, it is the time it takes the Moon to make one complete orbit around the Earth and come back to the same phase. It is marked from a new moon to the next new moon.
On average, this synodic period lasts 29 days, 12 hours, 44 minutes and 3 seconds. Which just so happens to be what we call a synodic month here on Earth.
This is an average figure, since the speed of the Earth-Moon system around the Sun varies slightly over a year, due to the eccentricity of the orbit. The Moon’s own orbit also undergoes a number of periodic variations about its mean value, due to the gravitational perturbations of the Sun.
Types of Months used in Astronomy:
The following types of months are mainly of significance in astronomy, most of them (but not the distinction between sidereal and tropical months) first recognized in Babylonian lunar astronomy.
- The sidereal month is defined as the Moon’s orbital period in a non-rotating frame of reference (which on average is equal to its rotation period in the same frame). It is about 27.32166 days (27 days, 7 hours, 43 minutes, 11.6 seconds). The exact duration of the orbital period cannot be easily determined, because the ‘non-rotating frame of reference’ cannot be observed directly. However, it is approximately equal to the time it takes the Moon to pass twice a “fixed” star (different stars give different results because all have proper motions and are not really fixed in position).
- A synodic month is the most familiar lunar cycle, defined as the time interval between two consecutive occurrences of a particular phase (such as new moon or full moon) as seen by an observer on Earth. The mean length of the synodic month is 29.53059 days (29 days, 12 hours, 44 minutes, 2.8 seconds). Due to the eccentric orbit of the lunar orbit around Earth (and to a lesser degree, the Earth’s elliptical orbit around the Sun), the length of a synodic month can vary by up to seven hours.
- The tropical month is the average time for the Moon to pass twice through the same equinox point of the sky. It is 27.32158 days, very slightly shorter than the sidereal month (27.32166) days, because of precession of the equinoxes. Unlike the sidereal month, it can be measured precisely.
- An anomalistic month is the average time the Moon takes to go from perigee to perigee – the point in the Moon’s orbit when it is closest to Earth. An anomalistic month is about 27.55455 days on average.
- The draconic month or nodal month is the period in which the Moon returns to the same node of its orbit; the nodes are the two points where the Moon’s orbit crosses the plane of the Earth’s orbit. Its duration is about 27.21222 days on average.
A synodic month is longer than a sidereal month because the Earth-Moon system is orbiting the Sun in the same direction as the Moon is orbiting the Earth. Therefore, the Sun appears to move with respect to the stars, and it takes about 2.2 days longer for the Moon to return to the same apparent position with respect to the Sun.
An anomalistic month is longer than a sidereal month because the perigee moves in the same direction as the Moon is orbiting the Earth, one revolution in nine years. Therefore, the Moon takes a little longer to return to perigee than to return to the same star.
A draconic month is shorter than a sidereal month because the nodes move in the opposite direction as the Moon is orbiting the Earth, one revolution in 18 years. Therefore, the Moon returns to the same node slightly earlier than it returns to the same star.
Sources: Wikipedia, NASA Lunar Reconnaissance Orbiter.