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Wikipedia dicit:

Concerning the lunar month of approximately 29.53 days as viewed from Earth, the lunar phase or Moon phase is the shape of the Moon’s directly sunlit portion, which can be expressed quantitatively using areas or angles, or described qualitatively using the terminology of the four major phases (new moon, first quarter, full moon, last quarter) and four minor phases (waxing crescent, waxing gibbous, waning gibbous, and waning crescent).

The lunar phases gradually change over a synodic month (c. 29.53 days) as the orbital positions of the Moon around Earth, and Earth around the Sun, shift. The visible side of the Moon is variously sunlit, depending on the position of the Moon in its orbit, with the sunlit portion varying from 0% (at new moon) to 100% (at full moon).

Each of the four major lunar phases is approximately 7.4 days±19 hours (6.58–8.24 days), the variation being due to the elliptical shape of the Moon’s orbit.

There are four principal (primary, or major) lunar phases: the new moon, first quarter, full moon, and last quarter (also known as third or final quarter), when the Moon’s ecliptic longitude is at an angle to the Sun (as viewed from the center of the Earth) of 0°, 90°, 180°, and 270° respectively. Each of these phases appears at slightly different times at different locations on Earth, and tabulated times are therefore always geocentric (calculated for the Earth’s center).

Between the principal phases are intermediate phases, during which the Moon’s apparent shape is either crescent or gibbous. On average, the intermediate phases last one-quarter of a synodic month, or 7.38 days.

The term waxing is used for an intermediate phase when the Moon’s apparent shape is thickening, from new to a full moon; and waning when the shape is thinning. The duration from full moon to new moon (or new moon to full moon) varies from approximately 13 days 22+1⁄2 hours to about 15 days 14+1⁄2 hours.

A new moon appears highest on the summer solstice and lowest on the winter solstice. A first quarter moon appears highest on the spring equinox and lowest on the autumn equinox. A full moon appears highest on the winter solstice and lowest on the summer solstice. A last quarter moon appears highest on the autumn equinox and lowest on the spring equinox.

Credit: NASA Goddard