The phases of the Moon characterize the aspect of the
Moon for a terrestrial observer. The Moon may be either between the Sun
and the Earth, or at the opposite side of the Sun relatively to Earth.
Then, the Moon may be illuminated very differently for an observer on Earth.
The appearence of the Moon is continuouly varying under a cycle of 29 days and an half approximately, corresponding to the period of synodic rotation of the Moon, named lunation.
By convention, the lunation begins at the New Moon (NL) date where the geocentric longitudes of the Moon and the Sun are the same. At this moment, the Moon is between the Sun and the Earth and so, is invisible for an observer on Earth, except in the case of a total solar eclipse.
The age of the Moon is the elapsed time since the last New Moon; the day of the Moon is an integer number associated to the days of a lunation by numbering them successively, the day "one" being the day when the New Moon occurs.
The Full Moon occurs when the geocentric longitudes of the Moon and the Sun differ by 180° (then, the Earth is between the Sun and the Earth and an observer on Earth sees the Moon completely illuminated during the night).
Full Moon and New Moon are named syzygys. The lunar eclipses occur always near the Full Moon, since the solar ones occur near the New Moon.
The quadratures correspond to the epochs when the geocentric longitudes of the Moon and the Sun differ by 90 or 270°. The First Quarter (PQ) occurs between the New Moon and the Full Moon; the Last Quarter (DQ) occurs between the Full Moon and the New Moon.
The figure below shows for what positions of Moon, Earth and Sun the phases are observable from Earth.
The figures below show the aspect of the Moon depending on its phases for an observer of the Northern hemisphere on Earth looking in the direction of the South.
The Moon is not visible, too close to the Sun (1)
visible on the evening (3)
The Moon is completely illuminated and visible all night (5)
Gibbous Moon (6)
visible in the morning (7)
preceeding the next New Moon (8)
Credit : J.E. Arlot/IMCCE
Click here in order to get the dates of the phases of the Moon