Great Astronomers: Ptolemy
Great Astronomers in Modern English
by Sir Robert S. Ball, 1895 (paraphrased by Leslie Noelani Laurio)
To view the table of contents for the rest of this book, click here.
Claudius Ptolemy, 100 AD-168 AD
Created the elaborate geocentric Ptolemaic model of the universe.
The "P" in Ptolemy is silent, so the name is pronounced TOH leh mee.
The career of the man who gets the first chapter in this book is one of the most remarkable careers in the history of human learning. Perhaps other men may have done more for science, but no other discoverer's ideas and authority has influenced the minds of men for as long as his -- his opinions about how heavenly bodies move were the ones everyone believed for fourteen centuries! The theories he explained in his book "The Almagest" [online at archive.org] were accepted as true for ages. In all that time, nobody even made any notable additions to what he laid out, and none of his many errors were corrected. He was considered the authority in all things related to the heavens, and a lot of things on earth, too, since he was also an eager geographer.
These days, even a child knows more real truths about celestial movements than Ptolemy ever knew, but the fact that his concepts influenced human minds for sixty generations shows that his work must have been truly impressive. Let's look at this remarkable man and see if we can discover the secret of his astonishing success.
It's unfortunate that we don't know much about Ptolemy's personal life. He was a native of Egypt [although his name Ptolemaeus is Greek, and Claudius is Roman; Egypt may have been a Roman province]. Some have wondered if, because his name, Ptolemy, was the name of some pharaohs, he may have belonged to one of the royal families. But there's no evidence that he did; Ptolemy was a common name in Egypt at the time. We know when he lived because the earliest date he recorded in his notes of his observations was 127 A.D., and the latest date is 151 A.D. One of his observations says, 'on the parallel of Alexandria,' so we assume he lived near Alexandria -- and that is the extent of all we know about his personal life.
Ptolemy is undoubtedly the greatest figure in ancient astronomy. He collected the wisdom of all the philosophers who had lived before him and blended it with his own observations to come up with his theories. Even those of his speculations that turned out to be wrong actually seemed to match the observable facts of nature so closely that nobody disputed them. In our own day [1895], there are still some people who say that Ptolemy's doctrines not only seem true, but they actually are true.
Since the tools to discover accurate knowledge of physics and mechanics weren't available yet, the earliest science-philosophers had to rely on principles that they reasoned out with their imaginations to fit what they thought ought to be the case -- although later science often found that they were mistaken. For example, they knew that the most simple, symmetrical geometric figure is a circle. It was obvious that heavenly bodies weren't traveling in a straight line, so they naturally concluded that the heavenly bodies must be traveling in a perfect circle. They had no observational evidence to base this on, but it seemed rational since a circle was the only 'perfect' shape, whatever 'perfect' might have meant. They reasoned further that it was impossible for heavenly bodies to travel in anything other than perfect shapes [because the world was created by a perfect God]. Thus, Ptolemy and everyone who came after him for the next 1400 years concluded that all heavenly bodies traveled in some kind of circles.
Ptolemy came up with a brilliantly elaborate scheme to explain how the changes we observe from earth are caused by heavenly bodies traveling in a network of circles combined with other circles. His scheme seemed to explain so accurately the actual things that are observed in the sky using the logic of perfect circles that it's no wonder the entire world approved of his theory. Let's look at his famous scheme in detail.
Ptolemy begins by stating that the earth is a round ball. He uses the same proofs we use today, such as the sails of a ship appearing over the horizon before the ship because the curve of the sea hides the bottom part of the ship.
Ptolemy came up with another less obvious proof to demonstrate that the earth curves and is not flat. Travelers who visited the south reported that as they moved farther and farther south, the night sky gradually changed. Stars that are familiar to people in the northern hemisphere appear lower in the sky the more south you are. From England's point of view, the Great Bear constellation never sets as it rotates around the north pole. But seen from a latitude far enough south, it does set! At the same time, when constellations first appear to those in the northern hemisphere, they always rise from southern horizon. These things couldn't happen if the earth was flat. The stars wouldn't seem to move just by travelling south. It took a remarkably insightful mind to figure that out, and even today, we can't improve on his evidence.
Ptolemy came up with a variety of ways to demonstrate that the earth is round. Here's one that shows what a sharp mind Ptolemy had. If the earth were flat, sunset would happen at the same instant for everyone, no matter where they were on the earth's surface. But Ptolemy knew that the time of sunset changed as the observer's longitude changed. It's obvious to us -- everybody knows that sunset may have reached England while it's still noon in the western United States. But Ptolemy didn't have our advantages of fast communication and frequent travel. How could he possibly prove that the sun set earlier in his home of Alexandria, Egypt than it would in Libya a few hundred miles to the west? There was no telephone or telegraph wire for instant communication. Reliable, portable clocks hadn't been invented yet -- they still used sundials. But Ptolemy thought of a way to compare the times of sunset in two different places. It was known that the moon's light is merely reflected sunlight. A lunar eclipse happened when the position of the earth blocked the sun's light from reaching the moon. Such an event would happen at a specific instant in time no matter where you were watching it from, although the moon would appear at different parts of the sky depending on where you were on earth. So Ptolemy asked people from all over to record when they saw the lunar eclipse beginning -- early evening, late night, etc. He found that people west of Alexandria recorded earlier times -- the farther west they were, the earlier they saw the eclipse. And people east of Alexandria recorded it at later times. The event was happening instantaneously, yet people were recording it as appearing at different times! Imagine if there was a line of observers along the same latitude line, circling the globe, and each one rang a bell right at sunset. Those in the east would be ringing their bells earlier than those in the west, so a person could hear an eastern sunset bell ringing while it was still daylight for him! This proves without a doubt that sunset happens at different times all over the earth. But if the earth were flat, everyone would be ringing their bells at the same instant. When Ptolemy was able to prove that sunset happened at different times in various places, he proved conclusively that the earth was round and not flat.
Since this appeared to be the case in every location where Ptolemy had been himself, and every place he could hear about from others, it seemed logical to him that the earth was not a flat surface surrounded by a limitless ocean, but a round ball. This led to a startling realization: there was nothing supporting this globe! Could it be simply poised in space? That's an unsettling thought for anyone who bases what "seems to be" on the evidence of their senses rather than on the evidence of intellectual understanding. Our ordinary experience tells us that things don't just hang in space without falling. No matter how many times or how many ways we might try to get a ball to hang in midair, it wouldn't stay there. However -- there is no such thing as up or down in open space. When we say that something falls down, we mean that it falls towards the center of the earth. But in space, there's no default direction for things to fall. If a stone falls in New Zealand, it wall fall towards earth -- but to those on the other side of the globe in England, it's actually falling upside down! It's falling up! Ptolemy reasoned that, if this was the case, and all directions on earth are neither up nor down, why should the earth need any support? With this reasoning, he concluded that the earth is a round ball floating freely in space and surrounded on all sides by glittering stars.
Ptolemy's recognition of this great truth marks a milestone in the development of human understanding. It's possible that other philosophers suspected that the earth was round, but we credit it to Ptolemy, not only because he discovered it, but because he explained it so well with clear, logical arguments. It's hard for us to even imagine what it was like not to know this truth, but we can imagine the intellectual shock it would be for someone who had assumed the earth was flat to suddenly be forced to accept that the earth was actually a round ball that amounted to nothing more than a mere speck in the immense vastness of the heavens.
The way the stars moved in the sky led Ptolemy to conclude that they were bright points of light attached to the inner side of a huge sphere surrounding the world with earth in the very center. As this sphere moved, the stars moved with it. This model only works if the earth is imagined in the center. The fact the stars appeared just as bright no matter where on earth a person stood proved that the earth must be tiny compared with how large the sphere must be. If that celestial sphere were a few yards in diameter, the earth must be the size of a grain of sand!
This was a tremendous revolution to human knowledge! It must have made Ptolemy famous overnight. But if he had taken it only one step further, he could have freed men's minds from the notion that the earth is the important central point in the universe. How can the daily movement of the sun, moon and stars be explained? The stars appearing in a fixed position with the same distance from year to year for ages seemed to Ptolemy to be because they were fixed in place on the spherical surface of the sky itself, and the sphere must revolve completely around the earth once a day. Assuming that the earth was stationary, this would explain the daily rising and setting of the sun and the regular movements of the other celestial bodies. It seems like a preposterous theory -- the earth is gigantic, but only a tiny speck compared with that celestial sphere. How could such an unthinkably large sphere move every day? As unlikely as this sounds, Ptolemy believed it, and even managed to convince other men that it was true.
Ptolemy was excellent at geometry. From a geometry perspective, he realized that the movements of the celestial bodies -- the moon, the stars, the rising and setting of the sun -- could have another explanation other than his giant sphere theory. If it was the earth turning once a day in the center rather than the giant sphere, that would still explain the movements of celestial bodies. This is easy to imagine. If you were standing on the earth and it was in the middle of the heavens, there would be stars above you and stars below you, beneath the horizon where you couldn't see them. As the earth turned, your perspective would change. The stars above your head would appear to move, and new stars would come into focus as others moved out of your field of vision. No matter you stood, you'd never see the half of the celestial bodies that were on the other side of the globe. So it would appear as if some stars were rising and others were setting. Whether it's the earth in the center turning once a day, or the giant sphere encompassing the heavens that turns, the effect is the same from the earth. Ptolemy knew enough about mathematics to understand that either of these two possibilities would work equally well to explain what he observed. For someone standing on the earth, there's really no way to know which is moving -- the earth, or the sky around it.
If either explanation could work as well as the other, how could anyone know which was the correct one? Ptolemy used indirect lines of reasoning to think it through. One of them had to be true, but both had major problems to reconcile. Ptolemy was the one who recognized how vast the world was, and how small the earth was in comparison. If the huge celestial sphere was what rotated every twenty-four hours, then it would have to be moving unbelievably fast to account for how the stars seemed to move. It would be much simpler if it was the earth that rotated once a day. But wouldn't we be able to feel it moving? Ptolemy might have dismissed this by relying on logic more than senses. But there was an even bigger point. If the earth was turning fast enough to make a rotation every day, wouldn't that cause enough wind to blow mankind off the planet? Even if the air moved around along with the earth, what about things like birds? They might be fine as long as they were perched on a tree so that they could move along with the tree. But when the bird was flying, how would it be able to keep up with the speed of the earth's turning? The moment it left the tree to fly, the ground would slip away pretty quickly. When the bird landed, it might be a vast distance away from where it started. This concept still confuses people. There was once an interesting idea for travelling by hot air balloon. The idea was to go up in the balloon and hover while the earth rotated until the part you wanted to visit arrived under you. Then you would just lower the balloon and land! Ptolemy should have been smart enough to know that it didn't work quite that way. But it seemed to him that the air must lag behind if the earth was rotating. Now we know that he was mistaken. But he didn't have the advantage of physics discoveries that explain the laws of motion that we have today.
Although Ptolemy was diligent at studying heavenly bodies, he doesn't seem to have known much about the movement of earthly objects. Even some pretty simple experiments would have convinced a scientific philosopher less gifted than Ptolemy that if the earth moved, the air would have to move with it. For instance, if a rider is galloping on horseback and tosses a ball into the air, the ball lands back in his hand just as if he had been standing still when he threw the ball. The ball is part of the rider's forward motion. To someone watching from the sidelines, the ball would move in a curve, but to the rider, it would look as if it was moving up and down in a straight line. This clearly demonstrates that as the earth rotates, the atmosphere around it is moving along with it, so there would be no great gust of wind to blow mankind off the earth. But Ptolemy didn't realize this, so he concluded that the earth couldn't possibly be moving. Therefore, it must be the vast sphere around the earth that was moving, even though such a massive object spinning completely around in only a day is improbable. And that's how Ptolemy made it a foundational part of his theory that the earth was stationary, and suspended in the center of a sphere so massive that the earth positioned right in the middle was like a tiny point in comparison.
Since Ptolemy flatly rejected the concept that it was the earth that rotated, he had to accept some other rather erroneous ideas. It was obvious to him that each star needed the same amount of time to do a complete circuit of the heavens. He knew that the stars were extremely far away from the earth, although even in his wildest imaginings, he probably never dreamed they were as far away as we now know them to be. If the stars had been at varying distances from the earth, it didn't seem likely that they'd be able to complete their circuits at the same time. So Ptolemy reasoned that they must all be the same distance away from the earth -- in fact, stuck on the surface of the huge sphere. Although this might sound silly to us, it seemed to be confirmed by the fact that the individual stars in each constellation kept their positions within the constellation for centuries. It made sense that the stars must all be affixed to the surface of the sphere like jewels, although Ptolemy never explained what the sphere was made of or how the stars were stuck on.
For the era and knowledge available at that time, this isn't as absurd as it sounds. The stars actually do look like they're lying on the surface of a sphere with us in the center. It doesn't just look like this to the average non-technical star-gazer, but it looks like this to the most experienced scientist. He knows very well that the stars are all different distances away, some ten times as far or even a thousand times as far as others, but to his eye, they all look like they're on the surface of a sphere, and he can't help using that surface as a point of reference when measuring the distance of far-away stars. In fact, most of the accurate measurements made in the observatory relate to the positions of the stars as they appear to be projected on the giant celestial sphere over the earth -- and we owe that concept to the genius of Ptolemy.
Ptolemy used ingenious ways of showing that the earth must be at the center of the sphere. For example, if this wasn't the case, why do all the stars move with absolute uniformity? Such logic inspires our profound admiration for Ptolemy's genius, even though he was wrong about the earth being stationary. And he took this error even further. By showing that the earth was an isolated object suspended in the middle of space, it must be capable of movement. It would be possible for it to turn around, or even to move from one place to another. But if Ptolemy determined that the sphere was turning and the earth was not, then could the earth move from one place to another? Did it? He concluded that any kind of motion from the earth wouldn't be compatible with the theory he had already chosen. He decided that the earth lies at the very center of the celestial sphere, and the center doesn't change. If the earth moved, then it would no longer be in the center -- and that didn't make sense. If the earth was to move over somewhere else in the sphere, the stars would look different, too, and that never happened. Therefore, the earth must not be able to move around any more than it could rotate. Thus he was able to use philosophical logic to convince himself that what his senses perceived was correct [even though he was actually wrong].
It often happens that philosophers have conflict with ignorant people and their own ideas. But in Ptolemy's case, his scheme matched what seemed obvious to everyone, so his theory was accepted as absolute truth and was unchallenged for generations.
Up to this point, we've only been talking about the major motions of celestial bodies -- the 24-hour rotation. But Ptolemy had some equally remarkable theories about the monthly orbit of the moon, the yearly movement of the sun, and planets with movements that were irregular enough to be called 'wandering stars.'
Since Ptolemy was convinced that everything was moving in perfect circles, it seemed obvious to Ptolemy and all astronomers before him, that the path of the moon through the stars must be making a perfect circle around the earth every month. The sun, too, must be traveling in a circle, but a yearly circle rather than a monthly one. The constellations' change of position to mark the seasons seemed like confirmation of this, although the brightness of the sun obscured the stars during the day. The daily rotation of the huge celestial sphere, the monthly orbit of the moon, and the yearly cycle of the sun seemed to confirm that all celestial bodies moved in circles -- the perfect curve that manifested their perfection.
And yet, even the simplest observations show that some planets move irregularly in a path that doesn't look perfectly circular. But Ptolemy's genius mind had an answer for that, too. He devised an elaborate scheme of perfect circles within perfect circles to account for the wandering aspect of those planets, providing a way to account for these 'imperfect' movements with perfect circles.
In order to follow his train of logic, let's explain a few things first. Let's take two planets as an example -- Venus and Mars, since these two illustrate the peculiarities of inner planets and outer planets very well. Even the simplest observation shows that Venus doesn't orbit around the sky in the same way as the sun and the moon. You can see this for yourself. Look at the evening star [Venus] when it's at its brightest -- in the west just after sunset. It doesn't work its way eastward among the stars like the sun or the moon. Week after week, we find that Venus is slowly moving closer to the sun until it's lost in the sun's beams. Then it emerges on the other side of the sun, and it's no longer an evening star, but a morning star! It seems like Venus is accompanying the sun in its yearly orbit, but then it seems to cross in front of the sun, and then it appears to lag behind the sun.
This can't be a simple perfect circular orbit. Venus's path must be somehow connected with the orbit of the sun, and Ptolemy came up with an ingenious way of explaining it. Imagine there's a long pole extending from the earth to the sun, as shown in Figure 1 below. As the sun moves, this pole will move around. Imagine Venus is making a small orbit around point "P" as the pole revolves around with the sun's movement. This would explain the irregularities in Venus's orbit. As Venus revolves around point "P," an observer on earth will sometimes see Venus on one side of the sun, and sometimes on the other side, but always somewhere near the sun. At some times in its orbit, it will appear in the evening, and at other times it will appear in the morning. In this way Ptolemy accounted for the odd path of Venus while still maintaining his theory of perfectly uniform circular orbits.
Ptolemy used the same method to explain the sporadic movement of Mercury, the rarely seen planet. First Mercury appears close to one side of the sun, then close to the other side. Ptolemy theorized that its orbit, like Venus's, was also centered around a point on an imaginary pole from the earth to the sun, although Mercury made a smaller circle than Venus. Today, we know it makes a smaller circle because it's closer to the sun than Venus.
Explaining the movements of an outer planet like Mars could also be done by imagining a circle revolving on an imaginary point that was rotating in a circle [a circle within a circle]. But the changes Mars makes are so different from Venus that further schemes had to be imagined. Mars circles around the entire heaven [it appears so from our perspective because its circle is outside of the earth]. So, in one sense, its orbit resembles that of the sun or the moon. But anyone who watches Mars closely will see that it has some wild irregularities as it moves. Generally speaking, it moves from west to east among the stars -- but someone watching closely will notice that it sometimes seems to slow down, and even stop. A few days later, it reverses and seems to be moving in the opposite direction, from east to west! It starts slowly, but picks up speed. Then it slows down again and then seems still. Then it reverses again and resumes its original movement west to east. It continues moving from west to east until it repeats the process of slowing down and reversing. How could that be consistent with a perfectly circular orbit? Ptolemy's geometrical genius gave him a solution for this problem.
Figure 2 shows his explanation. The earth is still in the center with the sun making a perfect circle around it. The orbit of Mars is on the exterior side of the sun. Ptolemy's explanation had an imaginary planet at a point marked "M." This planet orbited the earth along a circular path he called the "deferent." Point M is making a perfect circle around earth along the deferent, and Mars is orbiting in a perfect circle around point M. This circle rotating around a planet making a bigger circle would explain why Mars seemed to slow down and reverse. In the diagram, Mars would appear to someone watching from earth as if it were moving from west to east. But when it reaches point "R," it would appear to someone on earth as if was moving from east to west. Yet, the entire time, it hasn't actually reversed -- it's still traveling in the direction of the arrow around point M. Meanwhile, the whole thing -- planet M with Mars orbiting around it -- is moving in the opposite direction. That could explain why Mars seemed to slow down and reverse to an observer on earth.
The other planets Ptolemy was aware of -- Jupiter and Saturn -- had movements similar to Mars. They each made a perfectly circular orbit around a point that was orbiting around the earth in a larger perfect circle.
It seems strange to us that Ptolemy didn't go just one step further. He could have simplified his whole system. He could have put the sun at the center of Venus's circle and made Venus's orbit large enough to go around it. The other planets, too, could have had the sun as their center, and the whole thing, the sun with all the planets orbits circling around it, could have been circling around the earth. Maybe he never thought of this. Or maybe he saw difficulties with that theory. The one who finally took that next step was Tycho Brahe almost 1500 years later. Tycho reasoned that all the planets were orbiting around the sun in perfect circles, and the whole system was making a giant circle around the earth. Once that step was taken, only one more step was needed to realize the truth about the solar system's structure, with the sun, rather than the earth, at the very center. And that step was taken by the Polish astronomer, Copernicus.
[View an animated illustration of Ptolemy's model of the solar system on YouTube.]
[View a brief documentary about a scale model of the solar system set up in a desert on YouTube.]
by Sir Robert S. Ball, 1895 (paraphrased by Leslie Noelani Laurio)
To view the table of contents for the rest of this book, click here.
Claudius Ptolemy, 100 AD-168 AD
Created the elaborate geocentric Ptolemaic model of the universe.
The "P" in Ptolemy is silent, so the name is pronounced TOH leh mee.
The career of the man who gets the first chapter in this book is one of the most remarkable careers in the history of human learning. Perhaps other men may have done more for science, but no other discoverer's ideas and authority has influenced the minds of men for as long as his -- his opinions about how heavenly bodies move were the ones everyone believed for fourteen centuries! The theories he explained in his book "The Almagest" [online at archive.org] were accepted as true for ages. In all that time, nobody even made any notable additions to what he laid out, and none of his many errors were corrected. He was considered the authority in all things related to the heavens, and a lot of things on earth, too, since he was also an eager geographer.
These days, even a child knows more real truths about celestial movements than Ptolemy ever knew, but the fact that his concepts influenced human minds for sixty generations shows that his work must have been truly impressive. Let's look at this remarkable man and see if we can discover the secret of his astonishing success.
It's unfortunate that we don't know much about Ptolemy's personal life. He was a native of Egypt [although his name Ptolemaeus is Greek, and Claudius is Roman; Egypt may have been a Roman province]. Some have wondered if, because his name, Ptolemy, was the name of some pharaohs, he may have belonged to one of the royal families. But there's no evidence that he did; Ptolemy was a common name in Egypt at the time. We know when he lived because the earliest date he recorded in his notes of his observations was 127 A.D., and the latest date is 151 A.D. One of his observations says, 'on the parallel of Alexandria,' so we assume he lived near Alexandria -- and that is the extent of all we know about his personal life.
Ptolemy is undoubtedly the greatest figure in ancient astronomy. He collected the wisdom of all the philosophers who had lived before him and blended it with his own observations to come up with his theories. Even those of his speculations that turned out to be wrong actually seemed to match the observable facts of nature so closely that nobody disputed them. In our own day [1895], there are still some people who say that Ptolemy's doctrines not only seem true, but they actually are true.
Since the tools to discover accurate knowledge of physics and mechanics weren't available yet, the earliest science-philosophers had to rely on principles that they reasoned out with their imaginations to fit what they thought ought to be the case -- although later science often found that they were mistaken. For example, they knew that the most simple, symmetrical geometric figure is a circle. It was obvious that heavenly bodies weren't traveling in a straight line, so they naturally concluded that the heavenly bodies must be traveling in a perfect circle. They had no observational evidence to base this on, but it seemed rational since a circle was the only 'perfect' shape, whatever 'perfect' might have meant. They reasoned further that it was impossible for heavenly bodies to travel in anything other than perfect shapes [because the world was created by a perfect God]. Thus, Ptolemy and everyone who came after him for the next 1400 years concluded that all heavenly bodies traveled in some kind of circles.
Ptolemy came up with a brilliantly elaborate scheme to explain how the changes we observe from earth are caused by heavenly bodies traveling in a network of circles combined with other circles. His scheme seemed to explain so accurately the actual things that are observed in the sky using the logic of perfect circles that it's no wonder the entire world approved of his theory. Let's look at his famous scheme in detail.
Ptolemy begins by stating that the earth is a round ball. He uses the same proofs we use today, such as the sails of a ship appearing over the horizon before the ship because the curve of the sea hides the bottom part of the ship.
Ptolemy came up with another less obvious proof to demonstrate that the earth curves and is not flat. Travelers who visited the south reported that as they moved farther and farther south, the night sky gradually changed. Stars that are familiar to people in the northern hemisphere appear lower in the sky the more south you are. From England's point of view, the Great Bear constellation never sets as it rotates around the north pole. But seen from a latitude far enough south, it does set! At the same time, when constellations first appear to those in the northern hemisphere, they always rise from southern horizon. These things couldn't happen if the earth was flat. The stars wouldn't seem to move just by travelling south. It took a remarkably insightful mind to figure that out, and even today, we can't improve on his evidence.
Ptolemy came up with a variety of ways to demonstrate that the earth is round. Here's one that shows what a sharp mind Ptolemy had. If the earth were flat, sunset would happen at the same instant for everyone, no matter where they were on the earth's surface. But Ptolemy knew that the time of sunset changed as the observer's longitude changed. It's obvious to us -- everybody knows that sunset may have reached England while it's still noon in the western United States. But Ptolemy didn't have our advantages of fast communication and frequent travel. How could he possibly prove that the sun set earlier in his home of Alexandria, Egypt than it would in Libya a few hundred miles to the west? There was no telephone or telegraph wire for instant communication. Reliable, portable clocks hadn't been invented yet -- they still used sundials. But Ptolemy thought of a way to compare the times of sunset in two different places. It was known that the moon's light is merely reflected sunlight. A lunar eclipse happened when the position of the earth blocked the sun's light from reaching the moon. Such an event would happen at a specific instant in time no matter where you were watching it from, although the moon would appear at different parts of the sky depending on where you were on earth. So Ptolemy asked people from all over to record when they saw the lunar eclipse beginning -- early evening, late night, etc. He found that people west of Alexandria recorded earlier times -- the farther west they were, the earlier they saw the eclipse. And people east of Alexandria recorded it at later times. The event was happening instantaneously, yet people were recording it as appearing at different times! Imagine if there was a line of observers along the same latitude line, circling the globe, and each one rang a bell right at sunset. Those in the east would be ringing their bells earlier than those in the west, so a person could hear an eastern sunset bell ringing while it was still daylight for him! This proves without a doubt that sunset happens at different times all over the earth. But if the earth were flat, everyone would be ringing their bells at the same instant. When Ptolemy was able to prove that sunset happened at different times in various places, he proved conclusively that the earth was round and not flat.
Since this appeared to be the case in every location where Ptolemy had been himself, and every place he could hear about from others, it seemed logical to him that the earth was not a flat surface surrounded by a limitless ocean, but a round ball. This led to a startling realization: there was nothing supporting this globe! Could it be simply poised in space? That's an unsettling thought for anyone who bases what "seems to be" on the evidence of their senses rather than on the evidence of intellectual understanding. Our ordinary experience tells us that things don't just hang in space without falling. No matter how many times or how many ways we might try to get a ball to hang in midair, it wouldn't stay there. However -- there is no such thing as up or down in open space. When we say that something falls down, we mean that it falls towards the center of the earth. But in space, there's no default direction for things to fall. If a stone falls in New Zealand, it wall fall towards earth -- but to those on the other side of the globe in England, it's actually falling upside down! It's falling up! Ptolemy reasoned that, if this was the case, and all directions on earth are neither up nor down, why should the earth need any support? With this reasoning, he concluded that the earth is a round ball floating freely in space and surrounded on all sides by glittering stars.
Ptolemy's recognition of this great truth marks a milestone in the development of human understanding. It's possible that other philosophers suspected that the earth was round, but we credit it to Ptolemy, not only because he discovered it, but because he explained it so well with clear, logical arguments. It's hard for us to even imagine what it was like not to know this truth, but we can imagine the intellectual shock it would be for someone who had assumed the earth was flat to suddenly be forced to accept that the earth was actually a round ball that amounted to nothing more than a mere speck in the immense vastness of the heavens.
The way the stars moved in the sky led Ptolemy to conclude that they were bright points of light attached to the inner side of a huge sphere surrounding the world with earth in the very center. As this sphere moved, the stars moved with it. This model only works if the earth is imagined in the center. The fact the stars appeared just as bright no matter where on earth a person stood proved that the earth must be tiny compared with how large the sphere must be. If that celestial sphere were a few yards in diameter, the earth must be the size of a grain of sand!
This was a tremendous revolution to human knowledge! It must have made Ptolemy famous overnight. But if he had taken it only one step further, he could have freed men's minds from the notion that the earth is the important central point in the universe. How can the daily movement of the sun, moon and stars be explained? The stars appearing in a fixed position with the same distance from year to year for ages seemed to Ptolemy to be because they were fixed in place on the spherical surface of the sky itself, and the sphere must revolve completely around the earth once a day. Assuming that the earth was stationary, this would explain the daily rising and setting of the sun and the regular movements of the other celestial bodies. It seems like a preposterous theory -- the earth is gigantic, but only a tiny speck compared with that celestial sphere. How could such an unthinkably large sphere move every day? As unlikely as this sounds, Ptolemy believed it, and even managed to convince other men that it was true.
Ptolemy was excellent at geometry. From a geometry perspective, he realized that the movements of the celestial bodies -- the moon, the stars, the rising and setting of the sun -- could have another explanation other than his giant sphere theory. If it was the earth turning once a day in the center rather than the giant sphere, that would still explain the movements of celestial bodies. This is easy to imagine. If you were standing on the earth and it was in the middle of the heavens, there would be stars above you and stars below you, beneath the horizon where you couldn't see them. As the earth turned, your perspective would change. The stars above your head would appear to move, and new stars would come into focus as others moved out of your field of vision. No matter you stood, you'd never see the half of the celestial bodies that were on the other side of the globe. So it would appear as if some stars were rising and others were setting. Whether it's the earth in the center turning once a day, or the giant sphere encompassing the heavens that turns, the effect is the same from the earth. Ptolemy knew enough about mathematics to understand that either of these two possibilities would work equally well to explain what he observed. For someone standing on the earth, there's really no way to know which is moving -- the earth, or the sky around it.
If either explanation could work as well as the other, how could anyone know which was the correct one? Ptolemy used indirect lines of reasoning to think it through. One of them had to be true, but both had major problems to reconcile. Ptolemy was the one who recognized how vast the world was, and how small the earth was in comparison. If the huge celestial sphere was what rotated every twenty-four hours, then it would have to be moving unbelievably fast to account for how the stars seemed to move. It would be much simpler if it was the earth that rotated once a day. But wouldn't we be able to feel it moving? Ptolemy might have dismissed this by relying on logic more than senses. But there was an even bigger point. If the earth was turning fast enough to make a rotation every day, wouldn't that cause enough wind to blow mankind off the planet? Even if the air moved around along with the earth, what about things like birds? They might be fine as long as they were perched on a tree so that they could move along with the tree. But when the bird was flying, how would it be able to keep up with the speed of the earth's turning? The moment it left the tree to fly, the ground would slip away pretty quickly. When the bird landed, it might be a vast distance away from where it started. This concept still confuses people. There was once an interesting idea for travelling by hot air balloon. The idea was to go up in the balloon and hover while the earth rotated until the part you wanted to visit arrived under you. Then you would just lower the balloon and land! Ptolemy should have been smart enough to know that it didn't work quite that way. But it seemed to him that the air must lag behind if the earth was rotating. Now we know that he was mistaken. But he didn't have the advantage of physics discoveries that explain the laws of motion that we have today.
Although Ptolemy was diligent at studying heavenly bodies, he doesn't seem to have known much about the movement of earthly objects. Even some pretty simple experiments would have convinced a scientific philosopher less gifted than Ptolemy that if the earth moved, the air would have to move with it. For instance, if a rider is galloping on horseback and tosses a ball into the air, the ball lands back in his hand just as if he had been standing still when he threw the ball. The ball is part of the rider's forward motion. To someone watching from the sidelines, the ball would move in a curve, but to the rider, it would look as if it was moving up and down in a straight line. This clearly demonstrates that as the earth rotates, the atmosphere around it is moving along with it, so there would be no great gust of wind to blow mankind off the earth. But Ptolemy didn't realize this, so he concluded that the earth couldn't possibly be moving. Therefore, it must be the vast sphere around the earth that was moving, even though such a massive object spinning completely around in only a day is improbable. And that's how Ptolemy made it a foundational part of his theory that the earth was stationary, and suspended in the center of a sphere so massive that the earth positioned right in the middle was like a tiny point in comparison.
Since Ptolemy flatly rejected the concept that it was the earth that rotated, he had to accept some other rather erroneous ideas. It was obvious to him that each star needed the same amount of time to do a complete circuit of the heavens. He knew that the stars were extremely far away from the earth, although even in his wildest imaginings, he probably never dreamed they were as far away as we now know them to be. If the stars had been at varying distances from the earth, it didn't seem likely that they'd be able to complete their circuits at the same time. So Ptolemy reasoned that they must all be the same distance away from the earth -- in fact, stuck on the surface of the huge sphere. Although this might sound silly to us, it seemed to be confirmed by the fact that the individual stars in each constellation kept their positions within the constellation for centuries. It made sense that the stars must all be affixed to the surface of the sphere like jewels, although Ptolemy never explained what the sphere was made of or how the stars were stuck on.
For the era and knowledge available at that time, this isn't as absurd as it sounds. The stars actually do look like they're lying on the surface of a sphere with us in the center. It doesn't just look like this to the average non-technical star-gazer, but it looks like this to the most experienced scientist. He knows very well that the stars are all different distances away, some ten times as far or even a thousand times as far as others, but to his eye, they all look like they're on the surface of a sphere, and he can't help using that surface as a point of reference when measuring the distance of far-away stars. In fact, most of the accurate measurements made in the observatory relate to the positions of the stars as they appear to be projected on the giant celestial sphere over the earth -- and we owe that concept to the genius of Ptolemy.
Ptolemy used ingenious ways of showing that the earth must be at the center of the sphere. For example, if this wasn't the case, why do all the stars move with absolute uniformity? Such logic inspires our profound admiration for Ptolemy's genius, even though he was wrong about the earth being stationary. And he took this error even further. By showing that the earth was an isolated object suspended in the middle of space, it must be capable of movement. It would be possible for it to turn around, or even to move from one place to another. But if Ptolemy determined that the sphere was turning and the earth was not, then could the earth move from one place to another? Did it? He concluded that any kind of motion from the earth wouldn't be compatible with the theory he had already chosen. He decided that the earth lies at the very center of the celestial sphere, and the center doesn't change. If the earth moved, then it would no longer be in the center -- and that didn't make sense. If the earth was to move over somewhere else in the sphere, the stars would look different, too, and that never happened. Therefore, the earth must not be able to move around any more than it could rotate. Thus he was able to use philosophical logic to convince himself that what his senses perceived was correct [even though he was actually wrong].
It often happens that philosophers have conflict with ignorant people and their own ideas. But in Ptolemy's case, his scheme matched what seemed obvious to everyone, so his theory was accepted as absolute truth and was unchallenged for generations.
Up to this point, we've only been talking about the major motions of celestial bodies -- the 24-hour rotation. But Ptolemy had some equally remarkable theories about the monthly orbit of the moon, the yearly movement of the sun, and planets with movements that were irregular enough to be called 'wandering stars.'
Since Ptolemy was convinced that everything was moving in perfect circles, it seemed obvious to Ptolemy and all astronomers before him, that the path of the moon through the stars must be making a perfect circle around the earth every month. The sun, too, must be traveling in a circle, but a yearly circle rather than a monthly one. The constellations' change of position to mark the seasons seemed like confirmation of this, although the brightness of the sun obscured the stars during the day. The daily rotation of the huge celestial sphere, the monthly orbit of the moon, and the yearly cycle of the sun seemed to confirm that all celestial bodies moved in circles -- the perfect curve that manifested their perfection.
And yet, even the simplest observations show that some planets move irregularly in a path that doesn't look perfectly circular. But Ptolemy's genius mind had an answer for that, too. He devised an elaborate scheme of perfect circles within perfect circles to account for the wandering aspect of those planets, providing a way to account for these 'imperfect' movements with perfect circles.
In order to follow his train of logic, let's explain a few things first. Let's take two planets as an example -- Venus and Mars, since these two illustrate the peculiarities of inner planets and outer planets very well. Even the simplest observation shows that Venus doesn't orbit around the sky in the same way as the sun and the moon. You can see this for yourself. Look at the evening star [Venus] when it's at its brightest -- in the west just after sunset. It doesn't work its way eastward among the stars like the sun or the moon. Week after week, we find that Venus is slowly moving closer to the sun until it's lost in the sun's beams. Then it emerges on the other side of the sun, and it's no longer an evening star, but a morning star! It seems like Venus is accompanying the sun in its yearly orbit, but then it seems to cross in front of the sun, and then it appears to lag behind the sun.
This can't be a simple perfect circular orbit. Venus's path must be somehow connected with the orbit of the sun, and Ptolemy came up with an ingenious way of explaining it. Imagine there's a long pole extending from the earth to the sun, as shown in Figure 1 below. As the sun moves, this pole will move around. Imagine Venus is making a small orbit around point "P" as the pole revolves around with the sun's movement. This would explain the irregularities in Venus's orbit. As Venus revolves around point "P," an observer on earth will sometimes see Venus on one side of the sun, and sometimes on the other side, but always somewhere near the sun. At some times in its orbit, it will appear in the evening, and at other times it will appear in the morning. In this way Ptolemy accounted for the odd path of Venus while still maintaining his theory of perfectly uniform circular orbits.
Ptolemy used the same method to explain the sporadic movement of Mercury, the rarely seen planet. First Mercury appears close to one side of the sun, then close to the other side. Ptolemy theorized that its orbit, like Venus's, was also centered around a point on an imaginary pole from the earth to the sun, although Mercury made a smaller circle than Venus. Today, we know it makes a smaller circle because it's closer to the sun than Venus.
Explaining the movements of an outer planet like Mars could also be done by imagining a circle revolving on an imaginary point that was rotating in a circle [a circle within a circle]. But the changes Mars makes are so different from Venus that further schemes had to be imagined. Mars circles around the entire heaven [it appears so from our perspective because its circle is outside of the earth]. So, in one sense, its orbit resembles that of the sun or the moon. But anyone who watches Mars closely will see that it has some wild irregularities as it moves. Generally speaking, it moves from west to east among the stars -- but someone watching closely will notice that it sometimes seems to slow down, and even stop. A few days later, it reverses and seems to be moving in the opposite direction, from east to west! It starts slowly, but picks up speed. Then it slows down again and then seems still. Then it reverses again and resumes its original movement west to east. It continues moving from west to east until it repeats the process of slowing down and reversing. How could that be consistent with a perfectly circular orbit? Ptolemy's geometrical genius gave him a solution for this problem.
Figure 2 shows his explanation. The earth is still in the center with the sun making a perfect circle around it. The orbit of Mars is on the exterior side of the sun. Ptolemy's explanation had an imaginary planet at a point marked "M." This planet orbited the earth along a circular path he called the "deferent." Point M is making a perfect circle around earth along the deferent, and Mars is orbiting in a perfect circle around point M. This circle rotating around a planet making a bigger circle would explain why Mars seemed to slow down and reverse. In the diagram, Mars would appear to someone watching from earth as if it were moving from west to east. But when it reaches point "R," it would appear to someone on earth as if was moving from east to west. Yet, the entire time, it hasn't actually reversed -- it's still traveling in the direction of the arrow around point M. Meanwhile, the whole thing -- planet M with Mars orbiting around it -- is moving in the opposite direction. That could explain why Mars seemed to slow down and reverse to an observer on earth.
The other planets Ptolemy was aware of -- Jupiter and Saturn -- had movements similar to Mars. They each made a perfectly circular orbit around a point that was orbiting around the earth in a larger perfect circle.
It seems strange to us that Ptolemy didn't go just one step further. He could have simplified his whole system. He could have put the sun at the center of Venus's circle and made Venus's orbit large enough to go around it. The other planets, too, could have had the sun as their center, and the whole thing, the sun with all the planets orbits circling around it, could have been circling around the earth. Maybe he never thought of this. Or maybe he saw difficulties with that theory. The one who finally took that next step was Tycho Brahe almost 1500 years later. Tycho reasoned that all the planets were orbiting around the sun in perfect circles, and the whole system was making a giant circle around the earth. Once that step was taken, only one more step was needed to realize the truth about the solar system's structure, with the sun, rather than the earth, at the very center. And that step was taken by the Polish astronomer, Copernicus.
[View an animated illustration of Ptolemy's model of the solar system on YouTube.]
[View a brief documentary about a scale model of the solar system set up in a desert on YouTube.]
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