The Moon’s Orbital Period and Movement

The Moon orbits the Earth approximately every 29.5 days while undergoing a cycle of waxing and waning. The orbital period of the moon (i.e. the period of time taken for the moon to orbit the earth while changing its phase) is referred to as one lunar (synodic) month.

Because the Earth rotates from West to East on its own axis, when viewed from the Earth, the moon appears to rise in the East and set in the West in the same way as the Sun. However, as this occurs, the Moon is actually moving gradually from West to East by a little each day, and the time at which the Moon rises becomes later every day. This is due to the fact that the moon orbits the Earth with an average orbital period of approximately 29.5 days (or more precisely 29.530589 days) while the earth orbits the Sun over a period of 365 days.

A simple calculation tells us that dividing the Moon’s orbit of 360 degrees by 29.5 days gives 11.8; meaning that the Moon shifts from West to East by approximately 12 degrees per day. The Earth must spin that much more on its own axis, and this means that the time at which the Moon rises becomes later by the equivalent of those 12 degrees each day.
The rate of rotation of the Earth on its own axis is 360 degrees every 24 hours, meaning that 12 degrees equates to approximately 50 minutes (24 hours × 12/360 degrees = 0.8 hours = approx. 50 mins); meaning that the Moon rises around 50 minutes later each day.

Observing the Moon From Earth

Fifteen days after the beginning of a lunar cycle, the Moon (rising approximately 50 minutes later each day and moving towards the East) is exactly 12 hours later in terms of time, and has shifted by 180 degrees from West to East.

For example, if we were to observe the position and phase (state of waxing and waning) of the Moon at the same time (e.g. midnight) every day and to sketch and summarize in one picture how the moon appeared over the course of 15 days, it would like something like the picture on the left. The waxing First Quarter Moon seen in the western sky on the day of commencing observation would change to appear as a full moon in the southern sky eight days later, and eventually as a waning Third Quarter Moon on the opposite side, in the eastern sky (a difference of 180 degrees) 15 days after commencing observation.

Lunar Phases (Waxing and Waning)

How about the moon’s phases of waxing and waning? The reason why the moon appears to wax and wane is that, over the course of one lunar cycle (lunar month), only the part of the Moon that is illuminated by the Sun reflects the Sun’s light and shines down on Earth.
When the Moon is in exactly the same direction as the Sun, we cannot see any part of it illuminated. We call this point in time a New Moon, because it is the start of a new lunar cycle. From there, the Moon begins its orbit around the Earth, and the angle of its position relative to the Earth changes. First, the Sun’s rays begin to illuminate the Moon’s right-hand edge, producing a Crescent Moon in which a large part of the left side of the Moon appears to be missing. As the Moon continues on its orbit, it passes through the phases of First Quarter Moon (a half moon where the left side is not visible), Full Moon and Third Quarter Moon (a half moon where the right side is not visible), before eventually completing its cycle and returning to the New Moon phase. Incidentally, in Japanese, a crescent moon (in is literally called a “three day moon,” because it appears on the third day after the New Moon; and the night of the Full Moon is sometimes referred to as “fifteenth night,” because it falls on the fifteenth day after the New Moon.
The plane of the Moon’s orbit is slanted by a mere 5.1 degrees relative to the plane of the Earth’s orbit around the Sun (referred to as “the ecliptic”), but it is not a problem to think that the Moon moves on almost the same ecliptic plane, as with the other planets of the Solar System. We call the the angle of the Moon (relative to the direction of the the Sun) as it moves within this ecliptic plane “the difference in ecliptic longitude.” At New Moon, we say that the difference in ecliptic longitude is zero. At First Quarter Moon we say that it is 90 degrees, at Full Moon we say that it is 180 degrees, and at Third Quarter Moon we say that it is 270 degrees.

Click image to enlarge

Actual Periods of Lunar Cycles

Image taken from the National Astronomical Observatory of Japan (NAOJ) Koyomi Wiki website
Image taken from the National Astronomical Observatory of Japan (NAOJ) Koyomi Wiki website

The average period of a lunar cycle of waxing and waning is approximately 29.5 days, but in reality, the actual period fluctuates in a complex manner between around 29.3 and 29.8 days. This is the reason why lunar calendars (which are based on the period of the Moon’s lunar cycle) have long months of 30 days and short months of 29 days.

Incidentally, lunar calendars have 354.36 days to a year (29.53 days × 12 = 354.36): 10.64 fewer days than our standard calendar, which has 365 days. This meant that in the past it was necessary to make adjustments with intercalary leap days, and leap months around once every three years.

What is Moon Phase?

Moon phase is the amount of time that has passed since the New Moon, expressed in units of days. At the instant of the New Moon it is 0.0, and it increases by 1.0 for each day that passes after the New Moon. The First Quarter Moon appears around age 7, with the Full Moon appearing around age 15, and the Third Quarter Moon appearing around age 22. When this figure nears around 30, it means that the Moon is approaching the beginning of a new cycle (i.e. the next New Moon.) The reason why there are sometimes numbers after the decimal point is that Moon Phase is typically represented in terms of the Moon’s age at noon on any given day. When we calculate the age of the current Moon at noon, counting from the instant of the New Moon, we will always get an answer that is a mixed number containing a fraction of less than 24 hours (one day).
Moon phase is almost synonymously linked with the phases of the moon. However, because the Moon follows an elliptical orbit around the Earth (due to the influence of the Sun) which rotates over a period of approximately 8.85 years, the Moon moves faster when it is nearer to the Earth, and moves slowly when it is further away. As a result of this, the speed of the Moon’s cycle of waxing and waning is not fixed. For example, the Moon’s age at Full Moon is not fixed at 15 days, but in fact fluctuates between values of 13.8 and 15.8 for each lunar cycle.
The Chushingura incident (a famous story in Japan, in which a band of forty-seven ronin-masterless samurai-avenged the death of their master) is said to have taken place during the early hours of December 14 in the old Japanese calendar (around 03:00 on December 15). It is said that the reason why the ronin chose to carry out their attack at this precise time and date (which was planned carefully in advance) was that it was almost a Full Moon, when the ronin would be able to tell friend from foe at night by the light of the Moon; and that the samurai guarding the mansion of the target, Kira Yoshinaka, would be full of sake drunk at a New Year’s poetry party held the night before, making it a favorable time for the ronin to attack.

Who Uses Moon Phase, and How?

There are some convenient clocks and watches that are equipped with a Moon Phase Display, which displays the phases of the Moon on their dial. But who uses them, and in what way?
The ocean tides are determined by the forces exerted on the Earth by the Moon and Sun. The ocean facing the Moon and Sun are pulled towards them by gravitational forces, resulting in high tides; while the oceans on the opposite side also experience high tides due to centrifugal forces. Moreover, it is said that the Moon has roughly twice the tidal force of the Sun, and that the majority of differences in the changing of the tides can be understood by looking at the positional relationships of the Moon and Sun; or, in other words, by studying the phases of the Moon (i.e. differences in ecliptic longitude).
The difference (range) in water levels between high and low tide is greatest around the days of the New Moon (age 1) and the Full Moon (age 15). These times are referred to as spring tides, when the Moon, Sun and Earth are aligned in a straight line (a state known as syzygy) and the lunar and solar tidal forces are combined. By contrast, the range of water levels between high and low tide is smallest around the time of the First Quarter Moon (age 8) and the Third Quarter Moon (age 23), when the Moon and Sun are positioned perpendicular to one another, and the lunar and solar tidal forces cancel each other out. These times are referred to as neap tides.
The tidal cycle follows this pattern: New Moon spring tide → medium tide (intermediate range of water levels between high and low tide) → First Quarter Moon neap tide (narrow range of water levels between high and low tide) → “long tide” 1 to 2 days after the First Quarter Moon (when the tides are at their most calm) → “young tide” the following day (when a difference in water level at high and low tide begins to be seen) → medium tide → Full Moon spring tide. The same cycle is repeated until the next New Moon spring tide; meaning that this tidal cycle is repeated twice over the course of a Moon Phase calendar month (29.5 days). In addition to this, theoretically speaking, it is high tide when the Moon is positioned directly overhead, and low tide approximately six hours later, when the moon dips down towards the horizon.
Typically, it is said that the tides move the most around spring tide, particularly around two hours after high tide and low tide, and that the most fish can be caught around these times.

In this way, moon phase has been used by many people who worked at sea, or lived on the coast since long ago. The fact that there still reports of the tides in newspapers and on the news even today is for this reason.

Small and Large Moons

Image taken from the National Astronomical Observatory of Japan (NAOJ) Koyomi Wiki website
Image taken from the National Astronomical Observatory of Japan (NAOJ) Koyomi Wiki website

Because of the elliptical shape of the Moon’s orbit, the distance between the Moon and the Earth and the apparent size of the Moon in the sky change depending on where along the orbital path the Full Moon occurs.

The term “Super Moon” refers to a New Moon or Full Moon occurring when the Moon is at the point on its orbit where it is in closest proximity to the Earth. In comparison to when the Moon is furthest away from the Earth and appears smallest, a Super Moon is approximately 50,000km nearer to the earth, 14% larger in apparent size, and 30% brighter.

Why Can’t See the Other Side of the Moon?

Why is it that we can only ever see the same side of the Moon when we observe it?
This is because the moon rotates once on its own axis for every orbit it makes around the Earth. In other words, the period of the Moon’s orbit is the same as its period of rotation (on its own axis).

For example, when the Moon has travelled to a relative position of 45 degrees along its orbit, it will also have rotated by 45 degrees on its axis; which means that the front face of the Moon is always facing towards the Earth.
The reason why this occurs is that the Moon’s center of gravity is biased fairly heavily towards its surface (rather than its physical center). The gravitational forces between the Earth and the Moon as it moves along its orbit pull the side of the Moon on which its center of gravity is located such that it is always facing towards the Earth. The same kind of principle as in a self-righting tumble doll is at work on the Moon.

Lunar Observation and Exploration

The Moon has flat, dark-looking areas called maria (or “seas”) and heavily-cratered, bright-looking areas called highlands. Since long ago, the way in which the patterns and terrain shapes of the dark seas on the visible surface of the moon have been regarded and interpreted has varied between countries and regions. In Japan, they were said to resemble a rabbit, holding a mallet and making mochi rice cakes. In Europe it was likened to a crab, and in Arabia to a roaring Lion. These various interpretations are interesting, as they reflect the national character of each nation and region.
The seas cover 17% of the total surface of the Moon, but approximately 30% of the visible side, and we now know that they cover only 2% of the far side. The Japanese lunar orbiter SELENE (Selenological and Engineering Explorer; better known in Japan as Kaguya) has acquired various regional lunar surface data,including data on the other side of the Moon. From the analysis of this data, the differing underground structures of the near and far sides of the Moon and the history of their formation is gradually becoming clearer to us. In the future we may be able to unravel many mysteries, such as the question of how the Earth and Moon were created.

Click image to enlarge

References

・National Astronomical Observatory of Japan (NAOJ) Koyomi Wiki
・Chugakujuken Rika no Tamatebako