Lunar cycle
The lunar cycle is the repeating change in the Moon's visible shape as it moves around Earth. A full cycle from one new moon to the next takes about 29.5 days and is called a synodic month.
The four major phases are new moon, first quarter, full moon, and last quarter. Astronomically, they occur when the Moon's ecliptic longitude differs from the Sun's longitude by about 0, 90, 180, and 270 degrees. Published phase times are usually geocentric, calculated for Earth's center, so local observing conditions can differ slightly.
At new moon, the Moon is near the Sun in the sky and its illuminated side mostly faces away from Earth. As the Moon moves eastward along its orbit, more of the bright side becomes visible: this is the waxing half of the cycle. Light increases through waxing crescent, first quarter, and waxing gibbous to full moon, when the Moon is opposite the Sun and rises around sunset.
After full moon, the illuminated part shrinks. This waning half passes through waning gibbous, last quarter, and waning crescent before returning to new moon. The exact phase is not caused by Earth's shadow; it is the viewing angle between the Sun, Earth, and Moon. Earth's shadow creates a lunar eclipse only during especially precise alignment.
Intermediate phases are the crescent and gibbous phases between the four major points. On average each intermediate phase lasts about a quarter of a synodic month, roughly 7.4 days, but the Moon's elliptical orbit makes that rhythm not perfectly even.
A sidereal month, the Moon's circuit relative to the stars, lasts about 27.3 days. The phase cycle is longer because Earth is also moving around the Sun; the Moon has to travel a little farther before the Sun-Earth-Moon geometry repeats.
The Moon almost always shows Earth the same face because its rotation period is synchronized with its orbital period. Even so, a small wobble called libration lets us see slightly more than half of the lunar surface over time.
The appearance of the Moon's phase also depends on the observer's latitude. A crescent that looks upright in one region may be tilted in another, and between the Northern and Southern Hemispheres the view is effectively rotated.
Thin crescents can show earthshine: a faint glow on the Moon's dark part caused by sunlight reflected from Earth back onto the lunar surface. Near full moon the Moon is brightest, but surface shadows are short; near the quarters, longer shadows make craters and mountain ridges easier to observe.
Moonrise and moonset shift later each day because the Moon moves along its orbit while Earth rotates. The interval is not fixed, but it is often close to 50 minutes. Distance changes during the month too, so some full moons look slightly larger near perigee and slightly smaller near apogee.
Eclipses do not happen every month because the Moon's orbital plane is tilted about five degrees relative to Earth's orbital plane, the ecliptic. A solar eclipse requires new moon near a lunar node, and a lunar eclipse requires full moon near one of those nodes.
Moon phases have also been used for timekeeping. Pure lunar calendars follow lunations directly, while lunisolar calendars add corrections because twelve lunar months are about ten or eleven days shorter than a solar year.
