Moon Facts

by Michael Watson, President
Michael.Watson@gowlingwlg.com

Since I learned, more than half a century ago, that the Moon’s distance from Earth varies significantly—resulting sometimes in total solar eclipses and other times in annular eclipses—I have been both fascinated and puzzled by the inconstancy of the second-most prominent body in our sky. Perhaps I should say, by the inconstancy of the orbital motion of that body. I have also been intrigued by obscure facts about the Earth–Moon system that make me realize how little I really understand about our home planet’s natural satellite. Please let me share a few of these facts and my interest in them.

What exactly does the Moon orbit? Any two bodies in space that are bound together can be said to be “in orbit.” But around what exactly are they in orbit? It’s common for us to speak of the Moon, which is only 1.23 percent the mass of Earth, as orbiting an Earth that follows a perfectly and smoothly elliptical orbit around the Sun, unaffected by the proximity of its Moon. But in a two-body system, such as Earth and the Moon, neither orbits around the other; rather, they both orbit—or revolve—around a common centre of mass. The location of that common orbital centre is the “barycentre” (from the Greek “barus,” meaning heavy). If Earth and the Moon were of equal mass (such as are some binary stars), the barycentre would lie halfway between them and they would have identical orbits around, and 180 degrees on either side of, that midpoint. Owing to Earth’s much greater mass than the Moon’s, however, the barycentre of the Earth–Moon system is actually located within our home planet, about 4,670 km from Earth’s centre, or about 1,707 km below Earth’s surface. This means that while the Moon appears to orbit Earth, both Earth and the Moon orbit around the barycentre, and Earth is sometimes described as “wobbling” around that common centre of mass once per month.

The Moon’s distance from Earth: This is a phenomenon that is quite widely known, I think. Throughout its 4-billion-year existence, the Moon has been constantly moving further away from Earth, as a consequence of tidal action slowing Earth’s rotation period, and the principle of conservation of angular momentum, by which Earth’s rotational angular momentum is gradually being transferred to the Moon’s orbit. Eventually Earth and the Moon would become tidally locked, with the same hemisphere of Earth facing the same hemisphere of the Moon. Current estimates suggest that this would occur about 50 billion years from now, and at that point Earth and the Moon would revolve around their barycentre in about 47 current Earth days, with the same hemisphere of each body perpetually facing the other. I say “would” rather than “will” because the Earth-Moon system will never reach that tidally locked stage. Why? Because in about 5 billion years the Sun will exhaust its supply of hydrogen, turn into a red giant, and expand in size dramatically and swallow Mercury, Venus, Earth (including the RASC’s head office) and the Moon.

Some terminology—“eclipses” and “occultations”: Before I consider the end of total solar eclipses in the next section, it’s worth noting here that the expression “eclipse of the Sun” is a misnomer. An eclipse occurs when one body falls into the shadow cast by another body, such as when the Moon passes through Earth’s (Sun) shadow. When one body passes in front of another body, either partially or totally obscuring or hiding the other body, the first body is said to “occult”—not to eclipse—the second body (“occult,” from the Latin “occultus,” meaning clandestine, hidden, secret).

Eclipses and occultations occur at the same time, when three bodies, one of which is light emitting such as our Sun, line up. Take the example of an eclipse of the Moon. Earth lies exactly, or almost exactly, between the Sun and the Moon. Earth casts its (Sun) shadow into space, and the Moon glides through the shadow to produce an eclipse, as seen from Earth. Now let’s place a hypothetical observer on the surface of the Moon. Looking toward the Sun, that observer would see the black disk of Earth either partially or totally obscuring, or occulting, the Sun.

The same effect, and terminology, apply to the situation where the Moon lies exactly, or almost exactly, between the Sun and Earth. As seen from Earth, the Moon either partially or totally occults the Sun. A hypothetical observer on the Moon, however, would see Moon’s shadow crossing Earth’s surface from west to east, in a partial eclipse of Earth.

So, we can see that each time the Sun, the Moon, and Earth line up, at least twice per year during the “eclipse seasons,” both an eclipse and an occultation are occurring, and the event is either an occultation or an eclipse, depending on one’s observing location and the direction in which the observer is looking.

Nonetheless, the convention was adopted long ago to use the term “eclipse” to denote the partial or total disappearance of the Sun when the Moon passes over it, so I’ll use that term in the rest of this column, even though it’s actually an occultation!

The end of total “eclipses” of the Sun: Most astronomers know that one of the most remarkable coincidences in nature is that in this epoch the Sun is approximately 400 times the diameter of the Moon, and also, on average, is about 400 times as far away from Earth as is the Moon. The result is that the Moon and the Sun appear to be approximately the same size as seen from the surface of Earth. Of course, owing to the elliptical orbits of the Earth–Moon system around the Sun, and of Earth and the Moon around their barycentre, sometimes the Sun appears a little larger and sometimes a little smaller in the sky than does the Moon.

The apparent diameter of the Sun as seen from Earth varies about 3.4 percent during the year, from 31.46 arcminutes at aphelion between July 3 and 6 (depending on the year), to 32.53 arcminutes at perihelion between January 2 and 5 (again depending on the year). The changes in the Moon’s apparent angular diameter as seen from Earth are much greater. According to the celebrated Belgian astronomical mathematician, Jean Meeus (Mathematical Astronomy Morsels, 1997, p. 15), the extreme distances between the centres of the Moon and Earth in the 1,000 years between 1500 and 2500 CE are 406,720 km on 2266 January 7 and 356,371 km on 2257 January 1. At these extremes, the Moon’s diameter as seen from Earth varies from 29.38 arcminutes to 33.52 arcminutes, a difference of 14.1%. In most years, the difference in the Moon’s distance is a little smaller. In 2025, for example, the extremes will be 406,692 km on November 20 (Moon diameter 29.38′) and 356,961 km on December 4 (Moon diameter 33.47′), for a difference of 13.9 percent.

These varying apparent sizes of the Sun and Moon as seen from Earth determine the type of solar eclipse that occurs at new Moon during the two eclipse seasons every year. When the Moon passes centrally across the disk of the Sun, as seen from inside a path that crosses from west to east across Earth, the result will be either an annular or a total eclipse of the Sun, depending on the apparent angular sizes of the Sun and the Moon at the time of the eclipse.

At some future point, the Moon will have moved so far from Earth that even at its closest perigee, it will be so distant and will appear too small ever to be able to cover the Sun’s photosphere completely. The result will be only annular and partial “eclipses” (i.e. occultations) of the Sun by the Moon, and no total eclipses, from that point on. When will that be? No one knows for sure, because current thinking is that the rate by which the Moon retreats from Earth has always varied, that the current rate of ~3.8 cm per year is anomalously high, and that the rate is likely to continue increasing. But Jean Meeus has estimated that this may occur in about 1.2 billion years, so there is still the opportunity for all celestial observers alive today to see some total solar eclipses during their lifetimes!

The Perigee Moon: That brings me to the subject of what has—annoyingly to me—come to be referred to as a “supermoon” or “Super Moon.” This term was coined and first used in Dell Horoscope magazine by astrologer Richard Nolle in 1979. He decided to define it as “a new or full Moon which occurs with the Moon at or near (within 90 percent of) its closest approach to Earth in a given orbit (perigee).” In the decades since, it has been used to describe only a full Moon at or near perigee, because at perigee, the new Moon is unobservable except from within the path of totality of a total solar eclipse.

What is “super” about such a Moon? Well, supposedly its size as seen from Earth. But as we have seen, the difference between the apparent angular size of the Moon between apogee and perigee is only about 14 percent, or one-seventh of its diameter. How noticeable is that? Well-known American astrophysicist and astronomy popularizer, Neil deGrasse Tyson, has said that “a ‘supermoon’ is just a 16-inch pizza pretending to be special next to a 15-inch one,” and “the very concept of a supermoon is an embarrassment to everything else we call super.” With the average difference between the size of a perigee and an apogee Moon being ~14 percent, the more accurate metaphor is a 16-inch pizza compared to a 14-inch one, so let’s use that.

The silliness and futility of the term “supermoon” to this amateur astronomer—and the way in which it misleads the public—goes further than merely the 16- to 14-inch pizza analogy, for two reasons. First, in order to make the pizza comparison, a valid comparison to the appearance of the Moon in the sky, our 16- and 14-inch pizzas would have to be observed from about 42 metres away, or about the distance between the goal line and midfield of a football field or soccer pitch. Could anyone readily, or at all, discern the difference between two pizzas of those sizes at that distance, even if they were side by side?

Second, on average, extreme apogee and perigee full Moons occur about six months apart. So discerning the difference in appearance between an apogee full Moon and a perigee “supermoon” would be like looking at a 14-inch pizza from a distance of 42 metres, and then six months later looking at a 16-inch pizza from the same distance, and trying to compare how the 16-pizza looks now to how you remember the 14-inch pizza appearing half a year earlier. That’s why in my own view—I suspect that many of my fellow RASC members may disagree—this concept of a “supermoon” is misleading hype to the non-astronomical public and should not be used by astronomers generally, and the RASC in particular. Let’s use the terms “apogee Moon” and “perigee Moon,” and use the opportunity of these full Moons to teach something really useful and interesting about Earth’s natural satellite.