Humanity’s need to track the Moon’s changing phases and motions is ancient. Mammoth hunters used the Moon as a timekeeper, carving crescent-shaped notches into bone and tusk. Sumerian astronomers recorded the Moon’s motion on clay tablets more than 3,000 years ago.
But as reliable and trustworthy as the Moon may seem, its dance around Earth and the Sun is also full of nuances and variations — expressions of the complexity and beauty of the laws of physics. Observing these subtle movements and unlocking their secrets was key to understanding our place in the cosmos.
Today, appreciating the many motions of the Moon connects us to one of the driving forces of science across the centuries, one that has led us from the pseudoscience of astrology to the complexities of landing on the Moon.
All the “Moonths”
As Earth orbits the Sun, the Sun appears from our perspective to follow an imaginary line called the ecliptic that circles the celestial sphere. The Moon and planets all travel near the ecliptic, within 6° of it. The 12 traditional constellations that lie along this line are called the zodiac.
While the Sun takes 365¼ days to complete one trip around the ecliptic and return to the same position, the Moon zips around this imaginary circle in just under 30 days.
It’s a delight to watch a thin crescent rise in the west shortly after sunset. Our natural satellite then progresses through its phases until it rises as a Full Moon in the east, opposite the setting Sun in the west. The Moon continues on its journey until it rejoins the Sun as a New Moon. This period of time, from one New Moon to the next, is called a synodic month and takes 29 days, 12 hours, 44 minutes, and 2.8 seconds to complete. This synodic lunar cycle was used for a millennium to make our calendars.
There are other ways to measure the Moon’s cycle. The Moon appears to move eastward approximately 13° a day along the ecliptic, leading to the next defined lunar cycle: a sidereal month. It lasts 27 days, 7 hours, 43 minutes, and 11.5 seconds, which is the time it takes our satellite to make one complete orbit around Earth. From our perspective, a sidereal month is measured when the Moon completes one circuit around the ecliptic, returning to the same point from where it began in reference to the fixed stars.
A draconic month (also called a nodal month) is yet another way to measure the Moon’s motion. Ancient observers realized that the Moon does not track the ecliptic perfectly. This is because the Moon’s orbit is inclined 5.1° to the ecliptic, causing it to appear above or below the plane. There are two exceptions per month when the Moon crosses the ecliptic, at points called lunar nodes. An ascending node occurs when the Moon crosses the ecliptic from south to north, and a descending node occurs when the Moon moves across the ecliptic from north to south. This cyclical motion requires 27 days, 5 hours, 5 minutes, and 36 seconds, slightly shorter than a sidereal month.
Solar and lunar eclipses can only happen when the Moon crosses these nodes. Some cultures — for example, in Chinese mythology — believed a dragon lurked along the nodes, waiting to swallow the Sun or the Moon, hence the name draconic.
These are only a few ways to differentiate lunar months, but the Moon provides more ways to measure time and seasons.
A cosmic ballet
The Moon always shows us the same face because its rotation and orbit are tidally locked. In the early solar system, a Mars-sized object, called Theia, collided with the infant Earth to eventually form the Moon. (This is known as the Giant Impact Hypothesis.) As the Moon coalesced, Earth’s gravity slowed the lunar spin until its rotation matched its orbit around Earth, thus denying us a view of what is now the farside. But even this motion has a twist. Because the Moon’s orbital motion is elliptical it appears to rock back and forth like a pendulum, a motion called libration. This wobble allows us to see slightly more than half the lunar surface. The changes this apparent motion causes are best observed with a telescope.
The Moon’s motion along the ecliptic provides an interesting counterpoint to the Sun’s annual progress. Each year, as Earth completes a single orbit around the Sun, the Moon orbits our globe about 13 times. From our viewpoint, it’s easy to imagine the Moon tracing out the Sun’s path along the ecliptic. For example, the Sun slides into the constellation Sagittarius on the winter solstice. A Full Moon near the winter solstice, known as the Long Night Moon, will appear directly across the sky in Gemini. In six months, this is where the Sun will appear. And as the Sun sets in the southwest on the winter solstice, the Moon will rise in the northeast where the Sun rises on the summer solstice. This pas de deux between the Sun and the Moon continues throughout the year and is fascinating to watch.
Navigation advances technology
Intellectual curiosity is not the only force that has pushed us to refine our understanding of the world. In the 15th and 16th centuries, navigation techniques became paramount to Europeans like Amerigo Vespucci who explored the Americas and searched for wealth to exploit.
The problem was knowing your exact position on the globe. It had long been known that the difference in time between two locations on Earth was a measure of the east-west distance between these locations — in other words, their longitude. But, as no seaworthy clocks had yet been invented, seamen turned to the skies. Sailors had used stars such as Polaris to determine how far north or south they had sailed to find their latitude for decades. Now the race was on to find a celestial method to measure longitude.
One idea occurred to Galileo Galilei in 1609 when he discovered four moons orbiting the giant planet Jupiter in 1609. As Galileo watched these little moons whip around Jupiter, he realized they could serve as a grand celestial clock, ticking steadily for all observers. Almanacs could be created listing when moons would appear and disappear behind Jupiter for a reference location. Observing the difference in the local time of these events versus the times in the almanac would yield the difference in longitude. Unfortunately, using a handheld telescope on the deck of a rolling ship proved nearly impossible. Something bigger was needed: the Moon.
The lunar-distance method, suggested in the 16th century, proved to be more accurate. The idea is to use the Moon’s motion as a clock: It moves quickly through the sky, roughly its own width every hour. All you needed was an instrument to measure the angle between the Moon and a reference star, an almanac with precise calculations of that angle for given times, and the mathematical ability to solve a spherical triangle! It sounds straightforward, but minds like Isaac Newton’s were needed to explain the dynamics of the Sun-Earth-Moon system.
Newton’s headache
To measure the angular separation of celestial objects, sailors had been using a device called the quadrant since the 15th century. But navigational equipment improved rapidly throughout the 17th century, culminating in the 18th-century development of the sextant. This device delivered higher precision by incorporating a micrometer to make fine angular measurements. Detailed star charts were also being created. The real problem was understanding the Moon’s motion well enough to produce accurate almanacs.
With his first law of planetary motion, Johannes Kepler showed that planets and their satellites move in elliptical orbits. This helped to explain many observational problems. Decades later, Newton developed his laws of motion and the theory of universal gravity. In the 1690s, Newton used his work to explain variations in the Moon’s motions.
Newton understood that both the Sun and Earth pull on the Moon. The outcome of this tug-of-war varies depending on the changing positions of all three objects, making it extremely difficult to determine the Moon’s exact position at any given moment. Now known as the three-body problem, it caused Newton no end of grief. Newton told Edmund Halley that the problem kept him up at night and gave him headaches. Newton was able to make sense of the two-body problem, but was unable to completely solve the three-body problem.
However, he did establish the groundwork for understanding the laws of motion and universal gravitation. By taking into account the gravitational influence of other planets and even the shape of Earth, astronomers have been able to refine the motion and position of the Moon with great precision.
Round and round
How would the Moon’s motion look from a vantage point high above the solar system? Many popular astronomy books have diagrams from this perspective. If the diagram were animated, the Moon might appear to trace a spiral as it circled Earth and also moved around the Sun.
But these diagrams are rarely made to scale. In truth, the Moon does not form a spiral — Earth’s orbital speed around the Sun is much faster than the Moon’s motion around Earth. As Earth speeds along at about 18 miles (30 kilometers) per second, the Moon looks a bit like a faithful dog trying to keep up with its master, at its side and then alternately falling behind and pulling ahead.
Looking from above, we might intuitively think of this motion as resembling a sine wave crisscrossing Earth’s path. But even this image isn’t quite correct!
In truth, the Moon is pulled by the Sun’s gravity with a force that is more than twice as strong as Earth’s pull on the Moon. As a result, the speed of the Moon around Earth is so much slower than its motion around the Sun that its path never curves away from the Sun. The Moon’s path does crisscross Earth’s path twice a month, but this wobble is slight — not enough to resemble a wave.
This view of the Sun-Earth-Moon system provides a better idea of the push-pull effect created by gravity. It’s easy to understand Newton’s throbbing head.
From this perspective, the Moon appears to actually orbit the Sun, with its orbit almost imperceptibly disturbed by Earth’s pull. Some (including science-fiction author Isaac Asimov) have even argued that the Moon should be considered a planet, coequal with Earth — two bodies traveling together around the Sun.
But when considering the Earth-Moon relationship, the reality is that the two bodies orbit a common center of gravity called the barycenter. As this point is located inside Earth — roughly 1,000 miles (1,700 km) below its surface — most consider the Moon to be Earth’s satellite.
Astronomers have been challenged by the Moon’s complex motions for centuries. This story only touches on a few of them. For most of us, however, the beauty of the ever-changing Moon is a sight that will always be amazing and intriguing.
