The Antikythera Mechanism
Astrophysicist Dr. Laurance Doyle and Tusker Founding Guide, Eddie Frank have been teaming up on Astronomy trips since 1983. Their many celestial adventures include trips to solar eclipses around the planet. They are planning an exciting Solar Eclipse trip to Mexico in 2024. You can join this trip.
First brought up from the sea off the Greek island of Antikythera in the years 1900-1901 (in what may be considered the first ocean archaeology project), the mechanism was so covered with rust and calcium deposits that various forms of imaging (including x-rays) would have to be used over the span of decades to ascertain its exact purpose. But the time it took to decipher its workings was well worthwhile, for the Antikythera Mechanism turned out to actually be an analog computer designed and built to calculate the positions of astronomical objects! It could compute and display the seasonal positions of the stars in the night sky, the phases and positions of the moon, the positions of the planets at any given time, and predict both lunar and solar eclipses, among other things. The whole mechanism is 13.4 inches long, 7.1 inches wide, and 3.5 inches thick, and had 30 exquisitely-tooled bronze gears. Although the manufacture of the mechanism is amazing, just as impressive was the knowledge that the ancient designer needed in order to incorporate all the astronomical motions into one mechanism - that could be held in the hand.
So how did the mechanism work? The largest gear, for example, is about 5.5 inches across and has 223 triangular teeth. Why 223 gear teeth? Its discovery brought up many questions. We perhaps may start with the question, “Who might it have been designed for?” It was apparently designed to be used by someone who knew enough about astronomical knowledge for it to be useful, and who could at least read instructions, because instructions for its use are engraved all over the device. And there are labels for everything; on the faceplates of the gears are letters and symbols for planets and stars, cycles, risings, settings, and how to adjust for the seasons and where on the Earth the user is located. All this is thought to have enabled the possessor to work the mechanism even without a personal knowledge of the intricacies of the heavenly motions.
The actual Antikythera Mechanism appears to have been driven by a handle on the side. The front showed the phases of the Moon, a pointer that showed its motions through the signs of the zodiac, another pointer showing the motions of the Sun through the zodiac, a gear for the motions of the planets inside the Earth’s orbit (Mercury and Venus), and a gear for the motions of the outer planets (Mars, Jupiter, and Saturn), and a large four-spoked wheel for the setting of the date (seasons). On the back were a lunar-solar calendar, an epicycle turntable, and an eclipse cycle predictor. Epicycles are orbital circles that rotate around on circular tracks; sort of like riding a Ferris wheel at the fair—your seat makes one circle while the whole wheel rotates once (otherwise you would be upside down sometimes). This motion was needed to account for the sometimes apparent backward motion of some planets as we orbit past them (overtake them like a race car on the inner track). Epicycles were used to explain this motion instead of putting the Sun in the center of our planetary system and using elliptical orbits (which would come much later). One might add that the miniaturization of all these gears in the mechanism is not the least of its wonders.
On the eclipse calculating-side there is a gear with 1 Metonic period = 5 turns of spiral = 235 synodic months, or about 19 years. If you want to impress your friends you can call it the “Enneadecaeteris,” which is Greek for “19 years.” A synodic month is 29.5 days and is the time it takes the Moon to get back to the same phase again – full Moon to full Moon, for example. This is not the same as the sidereal month, which is 27.3 days long and is the time it takes the Moon to get back to the same position compared to the stars. The reason these are different is that by the time the Moon gets back to the same star position, the Earth has moved in its orbit around the Sun by another 2.2 days. The Metonic cycle was first noticed by Meton of Athens around 435 BC and is a fit between the synodic months and the year. If one counts 12 months according to the Moon each year, there would be 29.5 x 12 = 354 days to the year, or 11 days short of the real year. But what if you add in an extra month every now and then – say every couple of 12-month years? Let’s start with a 13-month year, then have two 12-month years, then another 13-month year, then another two 12-month years. After 19 years we’d have twelve 12-month years and seven 13-month years. It turns out that, to within a few hours, these 235 months (6940 days) then turn out to fit very closely to within 19 years (within a third of a day). So the lunar monthly cycle nearly fits within the yearly solar cycle every 19 years. This is the Metonic cycle and is found on a middle gear in the lunar-solar rear section of the Antikythera Mechanism.
Other gear-cycles that are found are the Callippic Cycle, a 76-year improvement on the Metonic cycle (note that 19 x 4 = 76). This cycle is a fine tuning to the Metonic cycle and consists of 27,756 days and is amazingly accurate to within about 11 minutes per year. Also there is a gear for the 4-year Olympiad cycle, which was the main calendar of ancient Greece. One could have used this gear, for example, to calculate that the year 2012 would have been the 697th Olympics if the games had been played continuously since their inception in 776 BC.
On the eclipse prediction side of the back of the Antikythera Mechanism was a gear for calculating the Exeligmos period, which is 669 synodic months long (that is, 54 years and 33 days long, which are three “Saros” cycles). The Exeligmos or “Saros” cycles families of eclipses that can be predicted to occur because of the alignment of the Earth, Moon, and Sun. When the Moon moves between the Earth and the Sun we have a solar eclipse, and when the Earth moves in between the Moon and the Sun we have a lunar eclipse. In a solar eclipse the Moon casts its shadow on a portion of the Earth; in a lunar eclipse the Moon moves into the Earth’s shadow, but turns red because the light from the Earth’s atmosphere at the sunrise and sunset points is bent (refracted) onto the face of the darkened Moon.
So why is there a 669 (synodic) month cycle? Why don’t we have a solar eclipse every month? This is because the Moon’s orbit is tilted to the Earth’s orbit. Think of having two hoola-hoops around your waste, with one tilted to the other by about 5 degrees. You are holding them both where they come together at your sides (these we’ll call “nodes.”) Notice that if you were to send a marble through the hoola-hoops they would never line up except then they crossed at where your hands are holding the hoola-hoops together – at the nodes. If you face a light, one marble would never block the light from the other marble. But now let’s send a marble around inside each hoola-hoop again and this time turn sideways so that one of our hands is closer to the light. Now, because the marbles will cross each other at the nodes sometimes, and the node is lined up with the light, one can now get one marble blocking the light from the other – an “eclipse.”
So what is happening with the Moon during the Exeligmos Cycle is that the nodes of the lunar orbit are rotating (backwards from the direction of the Moon’s motion, it turns out) about every 18.6 years. Remember our 223-toothed gear? 18.6 years is 223.2 months. Note that the nodes of the Moon’s orbit lining up is not enough for an eclipse; one also needs the Moon to be there in its orbit so that the Sun, Moon, and Earth line up. But the Antikythera Mechanism apparently even took this into account. It also had the ability to correct, for example, for the slower motion of the Moon when it is farthest from the Earth and the faster motion of the Moon when it is nearest the Earth. This is an example of what was later to become known as “Kepler’s Second Law” discovered in 1609 by Johannes Kepler, the Austrian astronomer. By the way, if you don’t get all these cycles, don’t be discouraged. The purpose of this article is to impress you with the sophistication of the Antikythera Mechanism.
OK, one last point: who could have built this mechanism so far in advance of what we thought the ancient Greeks were capable of? There was an ancient Greek scientist named “Ctesibius of Alexandria”; who was probably the first Director of the ancient Library of Alexandria. He is considered the father of hydraulics, for example, and invented a water clock whose accuracy would not be exceeded until the 17th Century. One of his students was Hero of Alexandria who invented a steam-powered device called an “aeolipile.” Hero also invented the first coin-operated vending machine and used to stage automated plays where everything moved automatically by “programmed” coiled ropes—the ropes were all set to unravel at given times, pulling on various props to make then move in a given way. Boats would sail across waves, with dolphins leaping and tell a whole story for about ten minutes automatically. Could Hero have built the Antikythera Mechanism? Possibly, but one needed detailed astronomical knowledge as well as mechanical skills. The ancient Greek astronomer, Hipparchus of Nicaea, comes to mind, but he is about a century too early for the date of the Antikythera Mechanism. The first person to suggest the Earth orbited the Sun, Aristarchus of Samos, also comes to thought but, again, he also is much too early. However, Archimedes of Syracuse mentioned the work of Aristarchus in his book, The Sand Reckoner. He is also known to have worked with Ctesibius in Alexandria, as well, before moving to Syracuse. So Archimedes, the brilliant engineer from the 2nd Century BC, might apparently have had access to the astronomical knowledge to “program” the gears, and certainly had the mechanical ability to construct the Antikythera Mechanism. It would mean that the Antikythera Mechanism would have to be even somewhat older than previous thought. So do we have the handiwork of Archimedes himself on display today in the National Archaeological Museum of Athens? We know that Archimedes pioneered the use of gears to lift weights and automate things, and he worked with Ctesibius in Alexandria. His Dad, Phidias, was a well-known astronomer, and the mathematician Pappas of Alexandria, working in the 4th Century AD, mentioned Archimedes having written a treatise about the subject of “Sphere Making,” a likely a reference to the Celestial Sphere.
So if you can get to Greece to see it, the Antikythera Mechanism, as encrusted and rusted as it is, would well be worth the trip. A reconstruction is on display next to it, and reconstructions are also on display in Bozeman (Montana), New York City, Kassel (Germany), and Paris. And if you spot any iPads in any old silent movies be sure to let me know.
Built Before its Time
Imagine you are watching an old, silent movie with Charlie Chaplin starring. He walks down a street, wiggles his mustache, opens up his bag, and pulls out an iPad. “Wait!” you might say. “That wasn’t invented for another 90 years!” Well, then you might have an idea how surprised archaeologists were to find a complicated clockwork mechanism off the coast of the Greek island of Antikythera in a shipwreck that sunk in the First Century BC. It was thought that such a sophisticated mechanism could not have been built until Renaissance clock-makers in Europe began to build much more complicated time pieces in the 14th Century. Yet, here was an ancient artifact, found among classic Greek wine amphoras, millennia-old marble statues, and oxidized bronze figures from 2,000 years ago which should not have been able to be built for another 14 centuries.
First brought up from the sea off the Greek island of Antikythera in the years 1900-1901 (in what may be considered the first ocean archaeology project), the mechanism was so covered with rust and calcium deposits that various forms of imaging (including x-rays) would have to be used over the span of decades to ascertain its exact purpose. But the time it took to decipher its workings was well worthwhile, for the Antikythera Mechanism turned out to actually be an analog computer designed and built to calculate the positions of astronomical objects! It could compute and display the seasonal positions of the stars in the night sky, the phases and positions of the moon, the positions of the planets at any given time, and predict both lunar and solar eclipses, among other things. The whole mechanism is 13.4 inches long, 7.1 inches wide, and 3.5 inches thick, and had 30 exquisitely-tooled bronze gears. Although the manufacture of the mechanism is amazing, just as impressive was the knowledge that the ancient designer needed in order to incorporate all the astronomical motions into one mechanism - that could be held in the hand.
So how did the mechanism work? The largest gear, for example, is about 5.5 inches across and has 223 triangular teeth. Why 223 gear teeth? Its discovery brought up many questions. We perhaps may start with the question, “Who might it have been designed for?” It was apparently designed to be used by someone who knew enough about astronomical knowledge for it to be useful, and who could at least read instructions, because instructions for its use are engraved all over the device. And there are labels for everything; on the faceplates of the gears are letters and symbols for planets and stars, cycles, risings, settings, and how to adjust for the seasons and where on the Earth the user is located. All this is thought to have enabled the possessor to work the mechanism even without a personal knowledge of the intricacies of the heavenly motions.
The actual Antikythera Mechanism appears to have been driven by a handle on the side. The front showed the phases of the Moon, a pointer that showed its motions through the signs of the zodiac, another pointer showing the motions of the Sun through the zodiac, a gear for the motions of the planets inside the Earth’s orbit (Mercury and Venus), and a gear for the motions of the outer planets (Mars, Jupiter, and Saturn), and a large four-spoked wheel for the setting of the date (seasons). On the back were a lunar-solar calendar, an epicycle turntable, and an eclipse cycle predictor. Epicycles are orbital circles that rotate around on circular tracks; sort of like riding a Ferris wheel at the fair—your seat makes one circle while the whole wheel rotates once (otherwise you would be upside down sometimes). This motion was needed to account for the sometimes apparent backward motion of some planets as we orbit past them (overtake them like a race car on the inner track). Epicycles were used to explain this motion instead of putting the Sun in the center of our planetary system and using elliptical orbits (which would come much later). One might add that the miniaturization of all these gears in the mechanism is not the least of its wonders.
On the eclipse calculating-side there is a gear with 1 Metonic period = 5 turns of spiral = 235 synodic months, or about 19 years. If you want to impress your friends you can call it the “Enneadecaeteris,” which is Greek for “19 years.” A synodic month is 29.5 days and is the time it takes the Moon to get back to the same phase again – full Moon to full Moon, for example. This is not the same as the sidereal month, which is 27.3 days long and is the time it takes the Moon to get back to the same position compared to the stars. The reason these are different is that by the time the Moon gets back to the same star position, the Earth has moved in its orbit around the Sun by another 2.2 days. The Metonic cycle was first noticed by Meton of Athens around 435 BC and is a fit between the synodic months and the year. If one counts 12 months according to the Moon each year, there would be 29.5 x 12 = 354 days to the year, or 11 days short of the real year. But what if you add in an extra month every now and then – say every couple of 12-month years? Let’s start with a 13-month year, then have two 12-month years, then another 13-month year, then another two 12-month years. After 19 years we’d have twelve 12-month years and seven 13-month years. It turns out that, to within a few hours, these 235 months (6940 days) then turn out to fit very closely to within 19 years (within a third of a day). So the lunar monthly cycle nearly fits within the yearly solar cycle every 19 years. This is the Metonic cycle and is found on a middle gear in the lunar-solar rear section of the Antikythera Mechanism.
Other gear-cycles that are found are the Callippic Cycle, a 76-year improvement on the Metonic cycle (note that 19 x 4 = 76). This cycle is a fine tuning to the Metonic cycle and consists of 27,756 days and is amazingly accurate to within about 11 minutes per year. Also there is a gear for the 4-year Olympiad cycle, which was the main calendar of ancient Greece. One could have used this gear, for example, to calculate that the year 2012 would have been the 697th Olympics if the games had been played continuously since their inception in 776 BC.
On the eclipse prediction side of the back of the Antikythera Mechanism was a gear for calculating the Exeligmos period, which is 669 synodic months long (that is, 54 years and 33 days long, which are three “Saros” cycles). The Exeligmos or “Saros” cycles families of eclipses that can be predicted to occur because of the alignment of the Earth, Moon, and Sun. When the Moon moves between the Earth and the Sun we have a solar eclipse, and when the Earth moves in between the Moon and the Sun we have a lunar eclipse. In a solar eclipse the Moon casts its shadow on a portion of the Earth; in a lunar eclipse the Moon moves into the Earth’s shadow, but turns red because the light from the Earth’s atmosphere at the sunrise and sunset points is bent (refracted) onto the face of the darkened Moon.
So why is there a 669 (synodic) month cycle? Why don’t we have a solar eclipse every month? This is because the Moon’s orbit is tilted to the Earth’s orbit. Think of having two hoola-hoops around your waste, with one tilted to the other by about 5 degrees. You are holding them both where they come together at your sides (these we’ll call “nodes.”) Notice that if you were to send a marble through the hoola-hoops they would never line up except then they crossed at where your hands are holding the hoola-hoops together – at the nodes. If you face a light, one marble would never block the light from the other marble. But now let’s send a marble around inside each hoola-hoop again and this time turn sideways so that one of our hands is closer to the light. Now, because the marbles will cross each other at the nodes sometimes, and the node is lined up with the light, one can now get one marble blocking the light from the other – an “eclipse.”
So what is happening with the Moon during the Exeligmos Cycle is that the nodes of the lunar orbit are rotating (backwards from the direction of the Moon’s motion, it turns out) about every 18.6 years. Remember our 223-toothed gear? 18.6 years is 223.2 months. Note that the nodes of the Moon’s orbit lining up is not enough for an eclipse; one also needs the Moon to be there in its orbit so that the Sun, Moon, and Earth line up. But the Antikythera Mechanism apparently even took this into account. It also had the ability to correct, for example, for the slower motion of the Moon when it is farthest from the Earth and the faster motion of the Moon when it is nearest the Earth. This is an example of what was later to become known as “Kepler’s Second Law” discovered in 1609 by Johannes Kepler, the Austrian astronomer. By the way, if you don’t get all these cycles, don’t be discouraged. The purpose of this article is to impress you with the sophistication of the Antikythera Mechanism.
OK, one last point: who could have built this mechanism so far in advance of what we thought the ancient Greeks were capable of? There was an ancient Greek scientist named “Ctesibius of Alexandria”; who was probably the first Director of the ancient Library of Alexandria. He is considered the father of hydraulics, for example, and invented a water clock whose accuracy would not be exceeded until the 17th Century. One of his students was Hero of Alexandria who invented a steam-powered device called an “aeolipile.” Hero also invented the first coin-operated vending machine and used to stage automated plays where everything moved automatically by “programmed” coiled ropes—the ropes were all set to unravel at given times, pulling on various props to make then move in a given way. Boats would sail across waves, with dolphins leaping and tell a whole story for about ten minutes automatically. Could Hero have built the Antikythera Mechanism? Possibly, but one needed detailed astronomical knowledge as well as mechanical skills. The ancient Greek astronomer, Hipparchus of Nicaea, comes to mind, but he is about a century too early for the date of the Antikythera Mechanism. The first person to suggest the Earth orbited the Sun, Aristarchus of Samos, also comes to thought but, again, he also is much too early. However, Archimedes of Syracuse mentioned the work of Aristarchus in his book, The Sand Reckoner. He is also known to have worked with Ctesibius in Alexandria, as well, before moving to Syracuse. So Archimedes, the brilliant engineer from the 2nd Century BC, might apparently have had access to the astronomical knowledge to “program” the gears, and certainly had the mechanical ability to construct the Antikythera Mechanism. It would mean that the Antikythera Mechanism would have to be even somewhat older than previous thought. So do we have the handiwork of Archimedes himself on display today in the National Archaeological Museum of Athens? We know that Archimedes pioneered the use of gears to lift weights and automate things, and he worked with Ctesibius in Alexandria. His Dad, Phidias, was a well-known astronomer, and the mathematician Pappas of Alexandria, working in the 4th Century AD, mentioned Archimedes having written a treatise about the subject of “Sphere Making,” a likely a reference to the Celestial Sphere.
So if you can get to Greece to see it, the Antikythera Mechanism, as encrusted and rusted as it is, would well be worth the trip. A reconstruction is on display next to it, and reconstructions are also on display in Bozeman (Montana), New York City, Kassel (Germany), and Paris. And if you spot any iPads in any old silent movies be sure to let me know.