The top animation shows the Moon's orbit as it would be seen looking down on Earth from high above the North Pole, and it shows the Moon's phases as they would be seen from most places in the northern hemisphere.
The bottom animation shows the Moon's orbit as it would be seen looking down on Earth from high above the South Pole, and it shows the Moon's phases as they would be seen from most places in the southern hemisphere.
To see how the same motion can appear to go either clockwise or anti-clockwise depending on where it is viewed from, experiment with the animation below of the rotating Earth. Try viewing it from above the north pole and from above the south pole. (Click the up and down arrow buttons.)
THE MOON'S CYCLES AND ASSOCIATED TERMINOLOGY
Real motion and apparent motion
The Moon has two real motions and one apparent motion:
1) It rotates (spins) around its own axis, which is the line through the centre of the Moon from its north pole to its south pole. The Moon's north and south poles point toward (approximately) the same directions in space as the Earth's north and south poles, and, like the Earth, the Moon rotates from west to east. The Earth's and the Moon's rotation both obey the "right-hand rule," which is followed by most of the major bodies of our solar system (the planets and their Moons). The right-hand rule defines the relationship between the direction that we call "north" and the direction of the body's spin. If you make a fist of your right hand with the thumb pointing upward, your fist represents the body, your raised thumb represents the direction the north pole points toward and your curled fingers point in the direction of the body's spin.
2) The Moon also revolves around the Earth, meaning it orbits or circles the Earth. The direction of its orbital motion is the same as the direction of its rotation and that is also the direction of the Earth's rotational and orbital motions. If you were viewing the solar system from a point high above the Earth's north pole, those motions would appear anti-clockwise from your point of view.
3) Additionally, to us on Earth, the Moon appears to continuously move across our sky from east to west. At moonrise it appears above our eastern horizon, at moonset it descends below our western horizon and halfway between the two it reaches upper transit when it crosses our meridian heading westward. This westward motion is not real motion; it is apparent motion -- an optical illusion caused by our planet's rotation on its axis from west to east. Beause the Moon's real orbital motion eastward is in the opposite direction to its apparent westward motion, but much slower, it has the effect of making the period from one upper transit of the Moon to the next longer than 24 hours. That period (called a tidal day) is, on average, about 24 hours, 50 minutes. Here is an animation showing this.
The Moon's rotation is locked rotation, meaning that its rotational period is the same as its orbital period. In other words, in the same time that it takes the Moon to complete a single, 360° revolution around the Earth it also completes a single, 360° rotation around its own axis. The result of this is that the same side of the Moon is always turned toward the Earth. The side that constantly faces us is called the Moon's near side; it is the only side we see from Earth. The opposite side, called the Moon's far side, has only been seen from spacecraft in lunar orbit.
A lunation is a cycle associated with the Moon's orbital motion around the Earth. It commences when the Moon is at some notional starting point (P) in its orbit and it ends when the Moon next returns to P. Astronomy recognises several candidates for P. Consequently, there are different kinds of lunation, each with its own starting point, and each one has a different length. The length depends on whether P is stationary or moving as seen from our observation point (Earth), and, if moving, its rate and direction of motion relative to the Moon's motion.
Because the Moon's orbit is eliptical, not circular, it does not move at a uniform speed. Its orbital motion is fastest at perigee (the point in its orbit where it is closest to Earth) and slowest at apogee (the point furthest from Earth). For that reason, no lunation has a constant period; they all vary in length. But we are able to speak of their mean length.
Of the above five lunations, two are of interest to us here. The sidereal lunation, for which P is a fixed star, is the best measure of the Moon's "true" orbital period, i.e. the time it takes the Moon to complete a single, 360° orbit of the Earth, which we measure by observing how long it takes the Moon to return to the same position in our sky relative to a fixed star. (Sidereal comes from sider, the Latin word for star.) The Moon's sidereal period is about 27.32 days. From this, we derive the mean (angular) speed of the Moon's orbital motion: about 13.176° per day (360°/27.32 days).
The Synodic Lunation
Because we are primarily focussed here on the Moon's phases, we will be mainly concerned with the synodic lunation, which is a full cycle of lunar phases. The Moon's synodic period, the time taken to complete such a cycle, is about 29.53 days. This animation shows why the Moon's synodic period is about 2.21 days longer than its sidereal period.
For the synodic lunation, P is the Sun, and to us on Earth, the Sun appears to make a full circuit of the sky over the course of a year. This apparent motion is eastward and its rate is just under 1° per day (360°/365.242 days). So, although the Moon's mean orbital velocity is about 13.176° per day, eastward, its speed relative to the Sun's apparent eastward motion (as seen from Earth), is only about 12.19° per day.
The cycle of the Moon's phases notionally begins at astronomical New Moon. At that time, the Sun and the Moon both occupy the same celestial longitude as seen from Earth. Hence the name "synodic," which comes from synodos, the Greek word for meeting, because the cycle begins when the Sun and Moon appear to meet at the same celestial longitude.
(Celestial longitude is how we measure east-west separation of solar system objects in our sky. It is used here in the same sense as ecliptic longitude, which is the correct astronomical term.)
At New Moon, the Moon is on the Earth-Sun line between the Sun and the Earth. Because the Moon is then at the same celestial longitude as the Sun, the Moon is said to be at conjunction at that time and that astronomical event is called a lunar conjunction.
A little over two weeks later, at Full Moon, the Moon is again on the (extended) Earth-Sun line, but on the opposite side of Earth from the Sun, so that the three bodies lie on that line in the order Sun, Earth, Moon. This means that the Moon is at the opposite celestial longitude to the Sun as seen from Earth. Therefore the Moon is said to be at opposition at that time and that astronomical event is called a lunar opposition.
The terms lunar conjunction and lunar opposition refer to the Moon's longitudinal position relative to that of the Sun, i.e. it is in conjunction with or in opposition to the Sun. At both of those times, the three bodies, Sun, Earth and Moon are in syzygy, meaning that they are aligned with one another so that on diagrams such as these, you can draw a single straight line joining the centres of all three of them. At New Moon the three bodies are aligned on the line of syzygy in the order Sun, Moon, Earth, and at Full Moon they lie on the line of syzygy in the order Sun, Earth Moon.
At New Moon, lunar elongation is 0° and at Full Moon it is 180°. As shown graphically in the above animations, lunar elongation is the angle Sun-Earth-Moon, i.e. the angle at the vertex of the Earth-Sun line and the Earth-Moon line. It is an angular measure of the east-west separation in our sky between the Sun and the Moon as seen from Earth.
More generally in astronomy, elongation refers to the angle body-Earth-parent, where body and parent are a solar sytem body revolving around a parent body, usually a planet and the Sun.
Unlike the Sun, the Moon does not emit light of its own. Moonshine is sunlight that is reflected from the surface of the Moon's near side towards the Earth. It is important to remember that exactly half of the Moon's surface is lit by the Sun at all times (except during a lunar eclipse, when the Moon passes through the Earth's shadow). Like the Earth, the Moon always has a sunlit side and a night side. The changes in illumination of the Moon that we see from Earth are changes in the amount of the Moon's near side that is lit. This occurs because, as the Moon orbits the Earth, different parts of it face the Sun, so, as on Earth, the sunlit side keeps moving around the Moon's surface and the amount of the Moon's near side that it covers is continuously changing, ranging from none of it to all of it. This directly affects the shape of our view of of the Moon from Earth. Those different shapes are called lunar phases.
Phases of the Moon
At New Moon, when lunar elongation is 0°, only the Moon's far side is lit up by the Sun; its near side is turned fully away from the Sun, so none of that side is visible to us at that time.
During the first half of the lunation (between New Moon and Full Moon), while lunar elongation increases from 0° to 180°, increasingly more of the Moon's near side becomes illuminated and the sunlit portion that we see grows. During this half of the lunation the Moon is said to be waxing. This is an old English word for growing. It is allied to the German word wachsen.
Halfway through the synodic lunation, when lunar elongation is 180°, the Moon's near side is turned fully toward the Sun and all of that side is lit up by the Sun, so we see a Full Moon.
During the second half of the lunation (between Full Moon and New Moon), while lunar elongation decreases from 180° to 0°, less and less of the Moon's near side is illuminated and the sunlit portion that we see diminishes. During this half of the lunation the Moon is said to be waning, meaning shrinking in size and brightness.
In summary, the general principle is that the amount of the Moon's near side that is illuminated depends on the size of the angle Sun-Earth-Moon, i.e. the angle where the Earth-Sun line meets the Earth-Moon line. The value of that angle ranges from 0° at New Moon, when none of the Moon's near side is illuminated, to 180° at Full Moon, when all of the Moon's near side is illuminated. In between those two values, the smaller the angle, the less of the Moon's near side is illuminated and the greater the angle, the more of the Moon's near side is illuminated.
Here are the names of the Moon's phases in the order that they occur during the synodic cycle, and the lunar elongation angles corresponding to each phase.
First half of lunation
Sun-Earth-Moon geometry for each of the Moon's eight phases
Below are eight pairs of images, which are visual depictions of the Sun-Earth-Moon geometry for each of the Moon's eight phases, with an explanation alongside each pair. Remember that in each pair of images, the first one shows things from a northern hemisphere point of view, in which the Moon's orbital motion appears to go anti-clockwise, and the second one shows things from a southern hemisphere point of view, in which the Moon's orbital motion appears to go clockwise. (The same also applies to the Sun's apparent annual motion.)
Because the Moon orbits the Earth eastwards, the mean period between one moonrise and the next is about 50 minutes longer than 24 hours. Therefore, during the first half of the synodic lunation, the east-west separation between the Sun and the Moon in our sky increases from 0° to 180°. During all of this period, the Moon is east of the Sun in our sky, so lunar elongation is said to be eastern elongation and the lunar elongation angle shown in the images is prefixed by "E". During this time, the Moon is also waxing (i.e. the portion of its near side that is illuminated is growing), as is also shown in the images.
At the halfway point in this cycle of phases, when lunar elongation reaches 180°, meaning that the Moon is opposite the Sun in our sky, it is Full Moon and immediately thereafter, as the Moon crosses around to the other side of our planet, it is now to the west of the Sun in our sky for all of the second half of the synodic lunation, so lunar elongation is now said to be western elongation and the lunar elongation angle shown in the images is prefixed by "W". As the Moon now progresses towards the completion of its orbit, the east-west separation between the Sun and the Moon in our sky now decreases from 180° to 0°. During this time, the Moon is also waning (i.e. the portion of its near side that is illuminated is decreasing), as is also shown in the images.
When lunar elongation has reduced to 0°, it is New Moon again and the synodic lunation starts all over again.
Technically, the four cardinal phases - New Moon, First Quarter, Full Moon and Third Quarter - last only for an instant, because the Moon never stops moving. To the naked eye however, for at least a day or so before and after each of the four cardinal phases, the Moon's appearance is indistinguishable from its appearance at the exact moment of that phase.
The intermediate phases between the cardinal ones - Waxing Crescent, Waxing Gibbous, Waning Gibbous and Waning Crescent, are each about a week long. The mean length of the full synodic lunation is about 29.53 days.
How soon after New Moon can the young waxing crescent first be seen?
There are many factors affecting this, some of them unpredictable because they are local atmospheric and light conditions. Also, the skill of the observer is a factor. Among the less obvious astronomical factors are the latitude of the observer (20° to 30° is best), the Moon's altitude at sunset, which should be at least 10° and the difference between the Sun's and Moon's azimuths when they set. The main astronomical factors are the time difference between sunset and moonset (the longer the better), the age of the Moon and its elongation. Lunar elongation is not just a function of the Moon's age. If the Moon is close to perigee at or soon after New Moon, it will be moving faster than its mean orbital speed, so lunar elongation will grow more quickly. For first visibility, elongation should be at least 9°. This is a bare minimum; on other advice, it should be 12°. In general, it is uncommon to see a Moon younger than 24 hours and never younger than 15 hours. There have been reports of sightings of an 18-hour-old Moon, but they are rare.
The Moon as a clock
Lunar elongation also governs the times of day and night during which the Moon is "up" (i.e. above our horizon).
At New Moon, when lunar elongation is 0°, the Moon is up all day. It rises around sunrise, transits the observer's meridian around noon and sets around sunset, but it is not visible in the sky for the reason explained above.
During all of the first half of the synodic lunation, when the lunar elongation angle is increasing, the Moon is to the east of the Sun in our sky. It rises after sunrise and sets after sunset. At first it is not far behind the Sun, but as the east-west separation between the Sun and the Moon grows, the Moon gets further and further behind the Sun. It rises each day about 50 minutes later than it did yesterday. At First Quarter, when lunar elongation is 90° E, it rises around noon, transits the observer's meridian around sunset and sets around midnight. During the Waxing Gibbous phase, it rises later and later each afternoon, until, when nearly full, it rises shortly before sunset.
At Full Moon, when lunar elongation is 180°, the Moon is up all night. It rises around sunset, transits the observer's meridian around midnight and sets around sunrise.
During all of the second half of the synodic lunation, when the lunar elongation angle is decreasing, the Moon is to the west of the Sun in our sky. It rises before sunrise and sets before sunset. At first it is very far ahead of the Sun (by around 11 hours), but the east-west separation between the Sun and the Moon is now decreasing because the Moon rises each day about 50 minutes later than it did yesterday. During the Waning Gibbous phase, it rises later each night until, at Third Quarter, when lunar elongation is 90° W, it rises around midnight, transits the observer's meridian around sunrise and sets around noon. Nearly a week later, during the last days of the lunation, it rises only a short time before sunrise and is up almost all day.
As you grow in your understanding of how the Moon's elongation governs not only its phases but also the times that it rises and sets, you will be able to use it like a clock.
Finding the Sun's position from the Moon
There is a rule of thumb to tell which side of the Moon is facing the Sun. It is expressed in an ancient saying that the Sun never sees the imperfection of the Moon. This is what it means: During the following six phases, one side of the Moon is a perfect semi-circle, the other is not. The side that is a perfect semi-circle is the side that the Sun 'sees,' so to speak. The opposite side, which we might call the imperfect side, does not face the Sun. As seen from Earth, that side:
On the Moon, daytime and night-time both last about 14.765 Earth days -- half of the Moon's mean synodic period.