As the Moon revolves around the Earth, the angle from which we see the part of it illuminated by the Sun changes as well. This is what’s behind the cycle of lunar phases, which always succeed one another in the same order:
At the new moon, our satellite can be found in the same direction as the Sun. We don’t see the Moon at that moment (except during a solar eclipse), because its “night” side is turned towards the Earth;
At the first quarter, we see a half moon illuminated on the right
At the full moon, our satellite is found opposite to the Sun in the sky. The Moon is lit full face, and we see its complete disc;
At the last quarter, we see a half moon illuminated on the left
The Moon appears as a crescent at the start and at the end of its cycle, before the first quarter or after the last quarter. The Moon is referred to as gibbous (humpbacked) when it’s less than full but more than half illuminated. It will be waxing gibbous until the moment of the full moon, then waning gibbous until the last quarter.
Astronomical definition of the lunar phases
By definition, the primary phases of the Moon listed above are the moments when the difference between the ecliptic longitude of the Moon and that of the Sun equals precisely 0 degrees (new moon), 90 degrees (first quarter), 180 degrees (full moon) and 270 degrees (last quarter).
These times are indicated in the tables of the phases of the Moon. Due to geometric considerations, they do not necessarily coincide with the moments when the illuminated fraction of the visible face of the Moon is exactly 0 percent, 50 percent or 100 percent.
The lunar phases correspond to precise instants; they therefore have no “duration,” strictly speaking. Nevertheless, the visual aspect of a phase can last a number of hours. For example, to the naked eye the Moon may look “full” for two or three consecutive days.
Duration of the lunar cycle
The Moon takes an average of 27 days, 7 hours, 43 minutes and 12 seconds to complete one orbit around the Earth; that’s its sidereal period. But because the Earth-Moon couple also moves around the Sun during that time, the duration of the lunar cycle – the lunation or synodic period – is therefore extended: 29 days, 12 hours, 44 minutes and 3 seconds, on average.
In the end, the interval between two successive new moons ranges from 29 days, 6 hours and 34 minutes to 29 days, 19 hours and 58 minutes. Different gravitational disturbances (tidal forces, the equatorial bulge of the Earth, the attraction of planets like Jupiter, and so on) continually modify the Moon’s orbit. Its trajectory is therefore much more complex than it appears, and calculating it is one of the most difficult problems to solve in celestial mechanics.