Why the Moon changes phase and how eclipses occur

Lunar eclipses

What is an eclipse?

An eclipse requires an alignment of three celestial bodies: the Sun, the Earth and the Moon.

Lunar eclipses are occultations of the Moon by the Earth's shadow, whereas solar eclipses are occultations of the Sun by the Moon's shadow. These celestial coincidences are frequently observed, at least one of each (lunar eclipse and solar eclipse) every 6 months.

The phases of the Moon

The Moon appears to us in different phases, that is, with different illuminations of the lunar sphere. This is due to the rotation of the Moon around the Earth and to the constantly moving relative positions of the Sun, the Earth and the Moon. Since the Moon only reflects the light of the Sun, the only visible part of the Moon is the one facing both the Earth and the Sun.

Lunar periodicity and syzygies

The periodicity of the phases of the Moon is 29.5 days, that is, one lunation or synodic lunar month. This duration should not be confused with the sidereal lunar month (27.32 days), which corresponds to the return of the Moon to the same position relative to the stars, nor with the anomalistic month (27.55 days), which measures the return of the Moon to its perigee. These three periods differ because the Earth moves along its orbit while the Moon revolves around it, and because the lunar orbit itself is elliptical and undergoes precession.

Eclipses take place at syzygies, that is, at the moment when there is a near alignment between the Sun, the Earth and the Moon. Two configurations are distinguished:

• the new Moon, when the Moon is between the Sun and the Earth: the illuminated side is turned toward the Sun, and the face visible from the Earth is in shadow;
• the full Moon, when the Earth is between the Sun and the Moon: the visible face of the Moon is then entirely illuminated.

A solar eclipse therefore takes place at the new Moon, and a lunar eclipse takes place at the full Moon. However, a perfect alignment is not enough: the Moon must also be sufficiently close to the line of nodes, that is, to the intersection between the plane of its orbit and the plane of the ecliptic. Outside these windows, the Moon passes above or below the Sun (at new Moon) or the Earth's shadow (at full Moon), without any eclipse occurring.

Syzygies are therefore not systematically ecliptic. Since the Moon returns to the same relative position with respect to the Sun every 29.5 days, but the line of nodes moves slowly, eclipses are grouped into eclipse seasons of about 34.5 days, separated by intervals of five to six months. Between two successive eclipses of the same type (Sun or Moon), one lunation generally elapses, that is, about 29.5 days, which explains why solar and lunar eclipses often alternate about fifteen days apart.

A happy coincidence makes the solar eclipse spectacular

The coincidence of apparent sizes

The ratio between the diameter of the Sun (1,400,000 km) and the diameter of the Moon (3,500 km) is ≈1/400th; the ratio between the distance of the Sun (149,600,000 km) and the distance of the Moon (384,000 km) is ≈1/400th. Since the Sun is 400 times larger and 400 times farther away than the Moon, their apparent sizes in the sky are almost identical (≈0.5° or ≈30 arc minutes). In reality, the apparent size of the Moon varies between 29.3' and 33.5' and the apparent size of the Sun varies between 31.5' and 32.5'.

Consequences and future evolution

This temporal coincidence is the basis of the mythological interpretations of certain civilizations, since the Moon sometimes perfectly masks the Sun.

Today, a total solar eclipse arouses the passion of crowds. Some amateurs are called "eclipse chasers"; they track eclipses all around the world. However, this coincidence will disappear; in hundreds of millions of years there will be only annular eclipses, because the Moon is moving away from the Earth by 4 cm per year.

Periods of revolution of the Moon

Sidereal period

The sidereal period of revolution of the Moon is measured relative to the stars. It is the time required for the Moon to return to the same position relative to a star, as seen from the Earth. This sidereal period of revolution is 27.321582 days, or about 27 days 7 hours 43 minutes.

For comparison, the sidereal period of the Earth, measured relative to the stars, is about 23h 56min, or 0.99726968 day. It is shorter than the synodic period (relative to the Sun) by about 4 minutes, because in 24 h the Earth has advanced along its orbit around the Sun by 1/365th, which corresponds to about 4 minutes.

Synodic period

The synodic period of revolution of the Moon is measured relative to the Sun. It is the time required for the Moon to return to the same position relative to the Sun, as seen from the Earth. This period is 29.530589 days, or about 29 days 12 hours 44 minutes.

It is longer than the sidereal period because, during one month, the Earth has advanced along its orbit around the Sun: the Moon therefore needs about 2 extra days to catch up to the same position relative to the Sun.

It is this synodic period of 29.5 days that paces the phases of the Moon and explains why solar eclipses and lunar eclipses follow one another with an interval of about 15 days.

The plane of the ecliptic and the nodes

Inclination of the lunar orbit

Although the synodic period of revolution is 29.5 days, eclipses do not occur every month. The Moon passes above or below the Sun, because the plane of the Moon's orbit around the Earth and the plane of the Earth's orbit around the Sun (ecliptic) do not coincide: they form an angle of about 5.145°.

If the Moon moved around the Earth in the same plane as the Earth around the Sun, that is, on the plane of the ecliptic, there would be a lunar eclipse at every full moon and a solar eclipse at every new moon, every 29.5 days, each separated by 15 days.

In fact, alignments of the three bodies can occur only if the Moon is very close to the plane of the ecliptic. This is why this plane was named after the eclipse.

The nodes of the lunar orbit

The place where the Moon passes above the plane of the ecliptic is called the ascending node. Conversely, the place where the Moon passes below the plane of the ecliptic is called the descending node.

To witness a total or partial eclipse, the Moon must be on the line of nodes: it is the only place where the alignment of the three bodies is perfect. There are therefore between four and six eclipses in the year, at least two of the Sun and at least two of the Moon.

Syzygies and eclipse seasons

In summary, eclipses occur during syzygies (alignment of the three bodies) close to the line of nodes. Around the passage of the nodes, there is a period of 35 days during which an eclipse can occur. In 34.5 days, it is possible to observe two solar eclipses or two lunar eclipses, because the lunation lasts 29.5 days. Eclipses are therefore spaced by about one month or by five to six months.

Influence of the Earth-Moon distance

The Earth-Moon distance varies between 363,104 km and 405,696 km. The farther the Moon is from the Earth at the time of the syzygy, the more partial the eclipse. The interval between two total solar eclipses of the same season (for example from one summer to the next) is generally 12 lunations, or 354.4 days (1 year - 11 days). Thus, we were able to witness a total eclipse in Mongolia on August 1, 2008, then a total eclipse in China on July 22, 2009, and finally a total eclipse in Polynesia on July 11, 2010.

Alignment conditions

Plane of the apparent orbits of the Moon and the Sun, as seen from the Earth. If the Moon moved around the Earth in the same plane as the Earth around the Sun, i.e. on the plane of the ecliptic, there would be a lunar eclipse at every full moon and a solar eclipse at every new moon, every 29.5 days, each separated by 15 days.

The eclipse period lasts 34.5 days; there are therefore 2 or 3 eclipses during this period. There are also 1.5 or 6 months between two consecutive solar or lunar eclipses. The alignments of the three bodies can occur only if the Moon is very close to the plane of the ecliptic; this is why this plane was named after the eclipse.