The Sun shines on Mars as it does on Earth. For at least a billion years, only dusty red rocks have cast shadows on the fourth planet from the Sun. Lately, however, the Sun has been lighting up something new on Mars, and it’s casting a shadow that slowly changes with the hours. It is a sundial.
In fact, there are now three sundials on Mars. Since 2004, each of the rovers sent to the planet by the National Aeronautics and Space Administration (NASA) has possessed a sundial—also known as a MarsDial—that I and a small team of other artists and astronomers designed to cast shadows across a plate of concentric gray circles and four colored squares. Scientists on Earth use the colors to calibrate how our robotic explorers “see.” Periodically, the cameras of the rover are pointed where the Sun should appear. If the Sun’s disk is perfectly centered in the photos, then the rover must be located and oriented exactly as thought. It’s a tiny example of the scientific method in action: a test of our ideas versus reality.
A sundial on a nuclear spacecraft, navigating by the Martian sky, may seem like an odd combination of old and new (and an equally strange way to begin a story of eclipses), but in a way, it’s not odd at all. We have depended on the Sun and its motion for as long as we have been human, so it’s only natural that we should use whatever it can tell us no matter what planet we happen to be on (at least within our own solar system).
On Earth and Mars, the motion of the Sun in the sky defines the cardinal directions and the lengths of both day and year. A Martian day (called a Sol) is only forty minutes longer than our own, while a Martian year is 88 percent longer, owing to its slower speed around the Sun and the greater distance to travel. Yet each planet’s axis is tilted, so Mars experiences its seasons just as we do on Earth, though those on Mars last comparably longer. Only our month, defined by the approximate time it takes our Moon to go through its phases, has no reasonable analog on the Red Planet, as that world has two moons, each with a different orbital period.
For thousands of years, on Earth at least, the proof that the calendars we made kept accurate track of these days, months, seasons, and years was that they were able to stay synchronized with the celestial cycles. Eclipses were a benchmark for checking whether we were right. Because eclipses are caused by the shadows the Sun casts on both Earth and Moon, eclipses should happen only when all three worlds line up. Lunar eclipses occur only at Full Moon, when Moon and Sun are on opposite sides of the Earth, visible to everyone on the shadowed side of Earth. A solar eclipse occurs two weeks (or half an orbit) later, when the Moon passes between Sun and Earth and its shadow falls somewhere on our planet. Only those fortunate enough to stand in the relatively small shadow get to see a solar eclipse.
Since it takes the Moon a month to orbit the Earth, it stands to reason that every month should see a lunar eclipse at Full Moon, and two weeks later a solar eclipse when the Moon is new. How I wish this were so. Sadly, the Moon’s orbit is tilted by five degrees to our own around the Sun. For the majority of New Moons, the Moon passes without notice slightly above or beneath the Sun, and two weeks later similarly misses the shadow that our planet projects out into space. Only when the alignment is exactly right do eclipses occur.
Let’s see how a person, without spacecraft or computers, without knowledge of planetary orbits or even of planets, would have figured this out. Science begins with observation. For most of human history, our lives depended on observing the cycles of the Sun. By noting where it rose each morning, our ancestors could measure the changing of the seasons, and thus determine when to hunt, plant, and harvest. The axial tilt of our planet is what gives us our seasons, and even a simple sundial, including those on Mars, reveals their passage. As winter turns to summer, the Sun rises farther to the north and climbs higher in the sky. Noontime shadows grow shorter each day, and then, as summer gives way to winter, the low southern Sun casts longer shadows once more.aa
All over the Earth there are ancient buildings, petroglyphs, and geographic alignments that our ancestors used to mark the passage of light and shadow over days, months, and years. The most famous of these is Stonehenge in southern England. Two concentric rings of massive standing stones with horizontal slabs stretched across their tops form its most prominent feature. These date to at least 2300 BCE,bb though other surrounding features are older. Radiocarbon dating of burnt wood reveals that people have been in the area since as far back as the eighth millennium BCE.
Outside these rings stands a large pointed boulder called the Heel Stone. Archaeological evidence indicates that a similar boulder was once set into the ground beside it. From the center of the stone rings toward the point between the Heel Stone and its missing twin, an observer 4,300 years ago would be looking precisely at the rising Sun at its northernmost point on the horizon on the longest day of the year: the summer solstice.
I have personally seen a similar alignment of Sun and structure much closer to home in Southern California. There, on the spring and fall equinoxes, the last rays of the setting Sun shine down a long passage to a doorway into which a crystal has been set. Through it the Sun’s light is refracted in a rainbow of color across a small vestibule and through a large room where it shines directly onto a square niche imbedded into a wall. It’s a magical sight that I have been lucky to see every spring and fall for the past decade—the fact that it’s also the living room in my own house in no way diminishes its power to delight me. I live in my own personal Stonehenge, by accident rather than by design, and in a country where many city streets were laid out by surveyors precisely along the cardinal directions, there is an excellent chance that you do, too.
One such alignment occurs in the heart of New York City, where the streets are arranged in a grid angled 29 degrees east of north. Twenty-one days before and after the summer solstice (typically on or around May 28 and July 12), the setting Sun shines perfectly down the canyon of streets on the island of Manhattan. It is a phenomenon the astronomer Neil deGrasse Tyson calls Manhattanhenge, and there are actually people who will brave evening rushhour commuters to dash out in traffic and photograph this alignment of city and Sun.
Whether Stonehenge was initially planned as an observatory, was an observatory by accident like the one in my house and New York City, or was never an observatory at all, the fact remains that it works as one today, and so, too, marks the movement of the Moon. It takes the Moon 29.5 days to complete one lunation (the time between two Full Moonscc). One of Stonehenge’s stone rings features 30 archways, one of which is half as wide as all the rest. Outside this ring are two more rings of holes in the ground, one with 29, the other with 30. Is either of these symbolic of the Moon’s 29.5-day lunation? With enough boulders and holes, almost any astronomical connection can be found, but it is intriguing nevertheless.
What is known with certainty is that cultures all over the world continue to mark time by the sunrise, including the Hopi in the American Southwest, whose ancestors, the Chacoans, built the “Great Houses” mentioned earlier. The alignment of the Great Houses appears to keep track of the same celestial cycles as the standing stones at Stonehenge.
For those who do not live someplace where the changing location of sunrise is obvious, the Sun provides another clue: it moves against the background stars with the seasons (and thus we see different stars at night in summer and fall). The path the Sun follows across these stars defines the plane of the Earth’s orbit and is called the ecliptic. It crosses twelve prominent constellations, and the Sun passes through approximately one of them every month. You’ve likely heard of these constellations: Libra, Scorpius, Sagittarius, and so on. Western astrology is based on the premise that your personality and fate are influenced by whichever one of these constellations the Sun was in front of on the day you were born. The prevalence of daily horoscopes says a lot about astrology’s popularity, if nothing about its accuracy.
Because of the Moon’s orbital tilt, the Moon spends half the month above the ecliptic and half below. Where the Moon crosses the ecliptic marks a node (Latin for “knot”). As viewed from the Earth, there are two nodes on either side of the celestial sphere that is our sky. Through one, the Moon passes upward through the ecliptic, and through the other it passes back down. When the Moon and the Sun both cross a node together, an eclipse takes place. Twice each year, the Sun is close to a node when the Moon goes sailing by, and thus twice each year we see solar and lunar eclipses somewhere on Earth.
FIGURE 2.1. Because the plane of the Moon’s orbit is tilted with respect to the orbit of the Earth around the Sun, eclipses are only possible when the “line of nodes,” the point at which the Moon crosses the Earth’s orbital plane, points toward the Sun. (Image by the author)
If the Sun and Moon were mere points of light, they would have to perfectly cross the node at precisely the same instant for an eclipse to occur. But the Moon and the Sun both span about half a degree on the sky. This produces a period of about 34 days, called an eclipse season, during which each body passes close enough to a node at Full or New Moon for an eclipse to take place, even if only partially.
The direction in which the Moon’s orbit tilts slowly changes over an 18.6-year period. The positions of the nodes therefore drift westward along the ecliptic, and so the Sun and Moon encounter them slightly more often than every six months. Lunar eclipses therefore happen either every five or six lunations (every 148 or 177 days), with a solar eclipse occurring two weeks before or after each one.
We see ancient knowledge of this pairing between lunar and solar eclipses in a narrative from the Pomo people, a Native American tribe in Northern California. Their explanation of eclipses involves the story of a bear that walks the Milky Way. When he comes upon the Sun, the Sun refuses to step out of the way. For his impertinence, the two wrestle, and the great bear bites the Sun: “Sun got bit [by] bear” is the meaning of the word the Pomo used to describe an eclipse. After his battle with the Sun, the bear comes upon the Sun’s sister, Moon. She, too, refuses to step aside, and again there is a great fight in the sky.
Back at Stonehenge, there are 56 Aubrey holes in a giant ring around the standing stones. The British astronomer Fred Hoyle hypothesized that these pits could be used to keep track of when lunar and solar eclipses occur. The ancient people of Stonehenge could have periodically moved a series of four stones from one hole to another at different rates, one for the Moon, one for the Sun, and two that were always kept a half circle apart to represent the nodes. An eclipse was possible when the Moon and Sun stones fell on either the same node stone (a solar eclipse) or opposite node stones (a lunar eclipse). With little more than these measures, a person could keep track of the phases of the Moon and the times of eclipses under Britain’s cloudy skies and remain remarkably accurate for years.
The Mayans, too, were aware of eclipse seasons. One of the few remaining Mayan books, called the Dresden Codex after the city where it now resides, reveals multiple entries of the numbers 148 and 177 in the Mayan’s unusual base-20 counting system of bars and dots. While it could be a coincidence that these are the exact numbers of days between lunar eclipses, the Mayan artist/author/astronomer who composed each page went on to make their meaning clear. At the center of each tally, the unknown scribe placed an elaborate half-black and half-white figure portraying the Sun and Moon, including one where it is about to be eaten by an enormous snake.
There are numbers other than the intervals between eclipse seasons that appear in ancient manuscripts and reveal the awareness of the frequency with which they occur. Consider that total solar eclipses can only happen at New Moon (every 29.53 days), during eclipse seasons (on average, every 173.3 days), and when the Moon is nearest to the Earth in its noncircular orbit (every 27.3 days). How often does it take for each of these cycles of different lengths to come around again like hands on a clock? Every 6,585.3 days (18 years, 11 days, and 8 hours), the Moon will fully eclipse the Sun at the same node, at the same time of year, and with the Sun and Moon in nearly the same constellations as it did before. For no shorter period of time do all of these three cycles of differing lengths coincide.dd We call this the Saros cycle.
Eclipses separated by this amount of time are said to be of the same Saros, and each Saros is numbered. The first total solar eclipse I saw was of Saros 145 on August 11, 1999, in Hungary. The eclipse in the United States on August 21, 2017, is 18 years and 11 days later (if it were visible in Hungary it would be August 22) and therefore must be Saros 145 again.
The difference between the eclipse being visible in Europe in 1999 and being visible in North America 18 years and 11 days later is due entirely to the remaining 8 hours (0.3 days) in the Saros cycle. Between two eclipses of the same Saros, the extra 8 hours means the Earth will have rotated an extra third of its day, moving the eclipse a third of the way around the Earth to the west.
After 3 cycles of 18 years (called an Exeligmos), totality once again occurs at the same longitude on Earth. But now 33 extra days have passed, and the Sun is a little higher (or lower) in the sky, depending upon the season, which shifts the path of totality a little farther north or south (depending on whether the Moon is ascending or descending through the node). Over time, total eclipses of a single Saros will begin at one pole of the Earth, slowly leave tracks spiraling around the planet, cross the equator, and after 1,300 years “retire” the Saros as it produces its last eclipse at the other pole. The solar eclipse of August 21, 2017, is the sixth total eclipse of Saros 145. There will be 35 more before it is done with us in 2143.
To notice cycles that repeat on a timescale of decades hints at cooperation over generations requiring careful recordkeeping. The first unambiguous record of the Saros cycle comes from the Chaldeans, who in 626 BCE ruled an empire that contained the ancient city of Babylon and extended from the Mediterranean eastward to the Persian Gulf and from the Red Sea northward into modern Turkey. What we know of their astronomy comes largely from the writing of later Greek astronomers and from a handful of small clay tablets full of closely spaced cuneiform markings. These tablets were used to record the names of kings and the dates of their reigns.
Perhaps as long ago as the eighth century BCE, the Chaldeans kept daily astronomical diaries recording the positions of the Moon and planets relative to the stars. Their observations were so precise that recent analysis of these tablets reveals they had developed a rudimentary form of calculus to keep track of the planet Jupiter’s speed across the background stars. As far back as the seventh century BCE, these diaries also kept track of the weather as well as of economic and political events. I can imagine a Chaldean astrologer/astronomer making a note of everything he saw each day in hopes of identifying patterns that might indicate what phenomena bode well for the king and what occurrences bode ill.
One pattern becomes obvious in what are now referred to as the Saros Cycle Texts. These are multiple tables of kings’ reigns and dates arranged in columns of 5 and 6 lunar months with columns precisely laid out 223 lunar months apart (223 months add up to 18 years). Though no mention is made of eclipses, modern calculations show almost perfect agreement with lunar eclipses visible in Babylon during that time. The fact that these dates were given with the names of known kings implies, of course, that the tablets were written after these eclipses would have come to pass.
What evidence is there that after noticing these cycles, ancient astronomers made the connections necessary to predict their future occurrence? Today we would refer to that as forming a hypothesis. If similar eclipses happen every 18 years, then once one sees the pattern, one should be able to predict the next.
The earliest account of someone predicting the exact time and place of a solar eclipse is from the Greek historian Herodotus. In his Histories, written around 450 BCE, he told of a five-year-long war between the Lydians and the Medes that had taken place a hundred years earlier in what is now central Turkey:
In this war they brought about a battle by night; and the engagement came about in the sixth year when they were still contending with each other at war on an equal basis, when it happened, as the battle was beginning, that day suddenly became night. (Thales the Milesian predicted to the Ionians this change [of day to night] would come about, setting beforehand the favorable period in which the ominous event did indeed happen.) When the Lydians and Medes saw it become night instead of day, they quit the battle and rather made haste on both sides that peace came about.
Historians and astronomers as early as Pliny the Elder in 77 CE have interpreted this “day turned to night” as a solar eclipse. Numerous attempts have been made to pinpoint exactly which eclipse this would have been. Unfortunately, the only solar eclipse that appears to match in both time and place (May 28, 585 BCE) was partial, and certainly not enough to have turned “day to night.” Nevertheless, Thales could have been aware of the Saros cycle, and if he had heard of its previous occurrence over Egypt and the Persian Gulf on May 18, 603 BCE, then he could easily have predicted the day the next would occur.
As a result, there are astronomers who would like to see the site of the ancient battle declared a World Astronomical Heritage Site to help preserve its place in the history of science. At the very least, whether Thales actually predicted a solar eclipse or the story is a complete myth, the fact that writers of the time believed it was possible to predict an eclipse means that these amazing spectacles were no longer considered the work of demons or gods, but had been placed firmly in the realm of natural phenomena.
Predicting eclipses was one of the central roles of Chinese court astrologers. Like their colleagues in Babylon, the Chinese astrologers were responsible for recording eclipses, and they noted virtually every one that could be seen in their region over a period of more than 3,000 years. Accurate prediction and observation of heavenly events was necessary for effective time-keeping and ceremony. If an eclipse occurred as predicted, it meant you understood the periods of the Sun, Moon, and Earth, and thus your calendar of months and years accurately reflected the seasons. An accurate calendar meant you could successfully identify the dates of holy days important to unite your people, praise your rulers, and appease the gods.
This tradition continues today, not just in China, but also in most other areas of the world. Holidays like Christmas that occur on the same date every year are essentially tied to the period of the Sun (or, more accurately, the period of the Earth around the Sun). But each of the three main monotheistic religions has holidays that float from date to date because they are tied to the period of the Moon. Ramadan is the ninth month of the Islamic calendar, where each month begins at the first sighting of the crescent New Moon after sunset. Passover, like Ramadan, is also tied to the Moon. It occurs on the 15th day of the Jewish month of Nisan, which begins at dusk with the New Moon. Since 15 days is almost equal to half of the lunar cycle, Passover occurs at the Full Moon, and to keep it in the spring it has become the first Full Moon after the spring equinox. In Christian tradition, the Last Supper of Jesus was a Passover Seder, after which followed the crucifixion and resurrection. So Easter is now set as the first Sunday after the first Full Moon after the spring equinox.
In our modern world we may no longer worship the Sun and the Moon, but our worldwide religions are still tied intimately to their motions. At the very least, each year individuals celebrate life’s victories and tragedies by the number of trips around the Sun they have made since their occurrence. Ours is a world enumerated, regimented, illuminated, and measured by astronomy.
But what do these millennia of observations, these innumerable cycles of Moon and Sun, traveling nodes, recurring eclipses, and repeating Saros reveal about our universe? If we derive our notions of direction and time from the Sun and stars, then what do the Sun and stars tell us about our place in space and time among them? And how do we know they are correct?
Stand in the Piazza San Marco at the heart of Venice, and you will see a giant model of the heavens in beautiful gold and lapis blue counting the hours from the Torre dell’Orologio. This spectacular clock dates from the 1490s and shows a golden Earth at the center of its massive wheel. Around it spins the Moon, its half-blue and half-gold sphere slowly rotating with the lunar phases over a period of 29.5 days. Farther out, an ornate golden Sun glides across the 12 constellations of the zodiac, in keeping with its actual position among the stars. Only in the very last ring are 24 giant roman numerals arrayed, revealing the time of day by their alignment with the Sun. During the Middle Ages, clocks like these could be found all over Europe, although few as grand. For those who were no longer attuned to the patterns of the sky, they served as a direct visual reminder in the heart of each community that there was, astrologically speaking, a comforting order to life. The other thing these clocks provided was a model of the universe that reassuringly places us at its center. Around us the Moon, Sun, and planets (in that order) move against the background stars. For the natural philosophers concerned with understanding the nature of reality (who would one day be known as scientists), eclipses were a means to an end. They were a tool to use in order to understand if our model of the universe was correct.
The Greek philosopher Aristotle saw that during a lunar eclipse, the shadow the Earth projected on the Moon was always curved. From this he reasoned that the Earth must be round (2,000 years before Columbus). Since we do not feel the Earth move under our feet (nor are we blown off the Earth like a rider’s hat on horseback), he reasoned that we alone must be stationary. The Moon, Sun, planets, and stars must orbit the Earth in perfectly uniform circles—because the circle is the most perfect shape, and the only logical place for the center of the universe to be is at the center of these circles. This geocentric (or Earth-centered) model of the universe explained a lot, and in many ways it was a very good scientific theory. It explained what most people could see on a daily basis and tied together a variety of phenomena. It even did an excellent job of predicting what people would see in the future. Go to any planetarium, and you can see the universe circle around you on the surface of a giant celestial sphere, just as it appears in reality. It works, but that doesn’t change the fact that it is wrong (although a 2014 survey by the National Science Foundation revealed that one in four Americans was not aware of that).
Even during Aristotle’s day, astronomers noticed that the planets didn’t seem to move across the background stars in a simple way. We can see this most easily when watching the motion of Mars from night to night. Every twenty-six months, Mars completes a loop-the-loop across the background stars: seemingly stopping, moving backward, then stopping and moving forward again. Each of the planets performs a similar type of retrograde motion at some point in its orbit. Yet Aristotle and others refused to reject a good idea for unfortunate observations: the heavens were perfect, and so were circles. Their solution was to add complicated layers of overlapping circles to each planet’s orbit causing them to spiral along in their paths through the heavens.
In the second century CE, the mathematical astronomer Claudius Ptolemaeus (better known as Ptolemy) of ancient Alexandria, in Egypt, took the geocentric model and, using the ancient eclipse observations of the Babylonians, made detailed calculations for predicting the positions of the Moon, Sun, and planets within this complex geocentric system. His Almagest, published in 150 CE, was the definitive word on what every astronomer needed to know up to the time of Galileo. Think about that for a moment: for 1,500 years, this was the most widely used astronomy textbook in the history of the Western world. Everyone used it because it worked (mostly), and so over the centuries it became unheard of to question the correctness of Ptolemy or of Aristotle before him. Add to their infallibility the fact that the new Christian church had adopted their Earth-centered universe as proof of our special status in God’s creation, and eventually, any questioning of their astronomy took on the burden of heresy. Without the freedom to question anyone’s conclusions, new discoveries die, and a single astronomy text can hold sway for over a millennium.
But there were those who rejected this philosophy. They believed that no matter how elegant the hypothesis, it is the experiment that determines what is right. Almost forgotten in the West today is the work of the tenth-century Islamic mathematician and scientist Ibn al-Haytham. From him we have one of the earliest statements of what today we recognize as the scientific method:
The seeker after the truth is not one who studies the writings of the ancients and, following his natural disposition, puts his trust in them, but rather the one who suspects his faith in them and questions what he gathers from them, the one who submits to argument and demonstration, and not to the sayings of a human being whose nature is fraught with all kinds of imperfection and deficiency. Thus the duty of the man who investigates the writings of scientists, if learning the truth is his goal, is to make himself an enemy of all that he reads, and, applying his mind to the core and margins of its content, attack it from every side. He should also suspect himself as he performs his critical examination of it, so that he may avoid falling into either prejudice or leniency.
Ibn al-Haytham, known in the West as Alhazen, was born in Basra in 965 CE in what is now Iraq. At a time when learning in Europe was stifled, with even the learning of the ancient Greeks suppressed, the acquisition of knowledge was considered an Islamic virtue. Early in life Alhazen turned his mind to the study of religion, but he was dismayed by its many contradictions and the conflicts it engendered. Believing that these disagreements lay in human interpretation and misunderstanding, he turned his eyes instead to mathematics. In the world of numbers, no matter what your beliefs, no matter where you were from, mathematics always worked. The fact that he thought mathematics could be used to describe God’s creation was a revolutionary idea: one that would come to be called physics.
Alhazen’s skills became known beyond Basra when he claimed to have calculated how to damn the Nile River that flooded each year, an event causing massive destruction and death. Unfortunately, when the powerful caliph of Egypt had Alhazen brought to him and he was shown the mighty river firsthand, Alhazen realized he was wrong. This was a difficult spot to be in with a caliph, who, though a patron of the sciences, was also a supremely dangerous man. What could he possibly do?
In the end Alhazen did the only logical thing: he pretended to go insane. The caliph had him confined to a house where he stayed for the next ten years, and he was freed only upon the caliph’s death. Although his body was imprisoned, Alhazen’s mind was free to work on the mathematical exploration of the world around him: specifically, the questions of sight and the nature of the bright Egyptian light pouring in through the windows of his home.
In The Book of Optics, written during his time of home confinement, Alhazen used his experiments to “dispel the prevailing confusion” of how we see (and what we see) by rejecting the writings of authority and instead beginning with what was actually known and observed. From that starting place he used mathematics and logical induction to develop laws of optics and vision that could actually be tested. He refuted the prevailing claim (by Ptolemy and others) that we see by our eyes sending out some “flux” that interacts with the world and then reflects back to our eyes. If the eye was going to depend on receiving information from its surroundings, why not save a step and just propose that objects emitted or reflected light, and the eye was merely the organ by which we received that light? Experimentally it makes sense, since it is easily demonstrable that the eye can be hurt by looking at incredibly bright sources, like the Sun (the perennial fear during eclipses).
During one solar eclipse, a hole in Alhazen’s window shade projected the crescent image of the partially covered Sun into his darkened room. Experimenting with candles and pinholes, he discovered how to calculate the sizes and positions of the images they projected onto screens, thereby inventing the camera obscura. We use this technique today when we build a box with a pinhole in one end and a screen at the other and use it to safely project the image of a partial eclipse. Although modern physics students around the world still use his methods of drawing light rays, most of us in the West aren’t very familiar with Alhazen—or of the role that other early Islamic scholars played in Europe’s rise out of its intellectual Dark Ages. But we can see this influence every night when we look at the sky. Our bright stars are still known by their Arabic names: Aldeberan, Altair, Alcor, Alberio. Our words “altitude” and “azimuth” (which determine the position of stars in the sky) are Arabic in origin as well and are represented by Arabic numerals, including the very concept of zero. The manipulation of these new numbers gave us “algebra,” which is also Arabic.
The Latin translation of Alhazen’s Optics was read widely in the West. But while initially European scholars would credit Alhazen’s discoveries in their own research, credit for developing the method that achieved those results was not granted to him. As a result, when we think of the modern scientific method and its role in discovery, it is Johannes Kepler, who lived six hundred years after Alhazen, who most often comes to mind. Kepler was well aware of Alhazen’s work and was fortunate to be living in a time when brave thinkers dared to finally question the universe of Aristotle and Ptolemy (and by extension the church). Alhazen had recognized that Ptolemy’s universe of crystal spheres spinning within spheres, turning with uniform circular motions, was too complex to work in reality: “The undoubted truth is that there exist for the planetary motions true and constant configurations from which no impossibilities or contradictions follow,” wrote Alhazen. “They are not the same as the configurations asserted by Ptolemy; and Ptolemy neither grasped them nor did his understanding get to imagine what they truly are.”
But what that truth was, even Alhazen had no idea. Six centuries later, the heliocentric model of the solar system proposed by Nicolaus Copernicus and championed by a new generation of experiment-minded scientists, like Kepler and Galileo, proved vastly simpler than Ptolemy’s complex cycles upon cycles. If all the planets, including the Earth, went around the Sun, then the retrograde motion of Mars was simply an optical illusion created by the faster-moving Earth passing the slower moving Mars. But what determined the order of the planets, their spacing and speed? Kepler thought he’d discovered the solution by hypothesizing that the size and spacing between each planet’s orbit was determined by the shapes of five perfect Pythagorean solids. He instantly became famous as the first person to read the celestial blueprints of God.
Yet, just like Alhazen before him, Kepler believed that the ultimate arbiter of what was true was what was seen. Sadly, when applied to Mars, what he saw was not what he had predicted. His model was exceptionally beautiful, but its predictions were unquestionably wrong. The statesman and scientist Benjamin Franklin once wrote, “In going on with these Experiments, how many pretty systems do we build, which we soon find ourselves oblig’d to destroy!” How painful it must have been for Kepler to discard what had made him so well known. Though it took him another decade of work to finally arrive at the truth, his act of intellectual honesty has become one of the defining examples of the scientific method.
What Kepler finally found were three laws of planetary motion that, although constructed specifically for the orbit of Mars, are now known to apply to all the planets around the Sun, to the Moon as it proceeds around the Earth, and to every star in orbit around any galaxy in space. They are:
1. All planets orbit the Sun in an ellipse, with the Sun located off center at one focus (a circle is just a special case of an ellipse).
The Moon orbits the Earth in an ellipse. This is why we occasionally have so-called supermoons, Full Moons that occur when the Moon is at its closest point to Earth. This is also why a solar eclipse two weeks before or after a supermoon is an annular eclipse, when the Moon is at its most distant point from the Earth and too small to fully cover the disk of the Sun.
2. A planet travels around its orbit at a rate that will always sweep out equal areas of space in equal amounts of time.
In other words, planets speed up when they are closest to the Sun, and slow down when they are farther away.
3. The time it takes the planet to complete one orbit around the Sun is related to the average distance between the planet and the Sun.
The constant that relates them is a product of nothing more than their mass. As a result, wherever we see two or more objects in orbit around one another, we can measure their combined mass. This single law has led to the discovery of everything from supermassive black holes at the centers of galaxies to the presence of mysterious dark matter that is the overwhelming component of the universe.
But what is the proof that these laws are correct?
Every single spacecraft that human beings have sent into space has worked because of precisely calculated orbits obeying every one of Kepler’s laws. The proof of these laws is evident in every photo returned from distant Pluto to our nearby Moon. Were it not for Kepler, there would not currently be three rovers on the Red Planet that Kepler studied most intently, each carrying its own tiny sundial to calibrate its cameras. And just like the ancient clock back in Venice, each MarsDial bears a small heliocentric solar system on its face, with a representation of the Sun at its center, surrounded by the elliptical orbits of Earth and Mars.
On August 19, 2013, NASA controllers had one of those rovers turn its cameras toward the Sun. Although they had performed this maneuver many times before, on this day, at precisely the moment predicted by Kepler’s laws, a tiny notch in the Sun appeared. Just a small one at first, but as the rover continued to snap images, an irregular blob began to appear against the glare of the Sun’s disk. Eventually, the strange silhouette stood out perfectly against the surrounding Sun: the silhouette of Phobos, a moon of Mars. After 5,000 years of marveling at solar eclipses on Earth, of deducing their cycles, predicting their appearances, and revising our hypotheses for why they occur, at that instant our robotic emissaries stood in the shadow of a Martian moon and beheld an eclipse on an alien world.
a Mars, by chance, currently has the same axial tilt as the Earth and so its seasons are similar to Earth’S, though more extreme due to the size and shape of its orbit.
b BCE means Before the Common Era, equivalent to BC.
c This is slightly longer than the Moon’s orbit around the Earth relative to the stars (27.3 days), since the Earth’s motion around the Sun causes the Moon to have to go a little bit farther each month to once more align with the Sun.
d This number, 6,585.3 days, is exactly 223 lunations, 38 eclipse seasons, and 239 orbits of the Moon.