Kitabı oku: «Big Bang», sayfa 2
Figure 3 Having estimated the size of the Moon, it is relatively easy to work out the distance to the Moon. First, you will notice that you can just block out the Moon with a fingertip at arms length. Therefore, it becomes clear that the ratio of a fingernail’s height to an arm’s length is roughly the same as the ratio of the Moon’s diameter to its distance from the Earth. An arm’s length is roughly a hundred times longer than a fingernail, so the distance to the Moon is roughly a hundred times its diameter.
In the third century BC, Aristarchus built on Anaxagoras’ idea. If moonshine was reflected sunshine, he argued, then the half Moon must occur when the Sun, Moon and Earth formed a right-angled triangle, as shown in Figure 4. Aristarchus measured the angle between the lines connecting the Earth to the Sun and Moon, and then used trigonometry to work out the ratio between the Earth—Moon and Earth—Sun distances. He measured the angle to be 87°, which meant that the Sun was roughly 20 times farther away than the Moon, and our previous calculation has already given us the distance to the Moon. In fact, the correct angle is 89.85°, and the Sun is 400 times further away than the Moon, so Aristarchus had clearly struggled to measure this angle accurately. Once again, accuracy is not the point: the Greeks had come up with a valid method, which was the key breakthrough, and better measuring tools would take future scientists closer to the true answer.
Figure 4 Aristarchus argued that it was possible to estimate the distance to the Sun using the fact that the Earth, Moon and Sun form a right-angled triangle when the Moon is at its half phase. At half Moon he measured the angle shown in the diagram. Simple trigonometry and the known Earth-Moon distance can then be used to determine the Earth-Sun distance.
Finally, deducing the size of the Sun is obvious, because it is a well-established fact that the Moon fits almost perfectly over the Sun during a solar eclipse. Therefore, the ratio of the Sun’s diameter to the Sun’s distance from the Earth must be the same as the ratio of the Moon’s diameter to the Moon’s distance from the Earth, as shown in Figure 5. We already know the Moon’s diameter and its distance from the Earth, and we also know the Sun’s distance from the Earth, so the Sun’s diameter is easy to calculate. This method is identical to the one illustrated in Figure 3, whereby the distance to and height of our fingernail was used to measure the distance to the Moon, except that now the Moon has taken the place of our fingernail as an object of known size and distance.
The amazing achievements of Eratosthenes, Aristarchus and Anaxagoras illustrate the advances in scientific thinking that were taking place in ancient Greece, because their measurements of the universe relied on logic, mathematics, observation and measurement. But do the Greeks really deserve all the credit for laying the foundations of science? After all, what about the Babylonians, who were great practical astronomers, making thousands of detailed observations? It is generally agreed by philosophers and historians of science that the Babylonians were not true scientists, because they were still content with a universe guided by gods and explained with myths. In any case, collecting hundreds of measurements and listing endless stellar and planetary positions was trivial compared with genuine science, which has the glorious ambition of trying to explain such observations by understanding the underlying nature of the universe. As the French mathematician and philosopher of science Henri Poincaré rightly declared: ‘Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.’
Figure 5 It is possible to estimate the size of the Sun, once we know its distance. One approach is to use a total solar eclipse and our knowledge of the Moon’s distance and diameter. A total solar eclipse is visible only from a small patch on the Earth’s surface at any given time, because the Sun and the Moon appear almost the same size when viewed from the Earth. This diagram (not to scale) shows how an eclipse observer on the Earth is at the apex of two similar triangles. The first triangle stretches to the Moon, and the second triangle to the Sun. Knowing the distances to the Moon and to the Sun and knowing the diameter of the Moon is enough to deduce the diameter of the Sun.
If the Babylonians were not the first proto-scientists, then what about the Egyptians? The Great Pyramid of Cheops predates the Parthenon by two thousand years, and the Egyptians were certainly far in advance of the Greeks in terms of their development of weighing scales, cosmetics, inks, wooden locks, candles and many other inventions. These, however, are examples of technology, not science. Technology is a practical activity, as demonstrated by the Egyptian examples already given, which helped to facilitate death rituals, trading, beautification, writing, protection and illumination. In short, technology is all about making life (and death) more comfortable, while science is simply an effort to understand the world. Scientists are driven by curiosity, rather than comfort or utility.
Although scientists and technologists have very different goals, science and technology are frequently confused as being one and the same, probably because scientific discoveries often lead to technological breakthroughs. For example, scientists spent decades making discoveries about electricity, which technologists then used to invent light bulbs and many other devices. In ancient times, however, technology grew without the benefit of science, so the Egyptians could be successful technologists without having any grasp of science. When they brewed beer, they were interested in the technological methods and the results, but not why or how one material was being transformed into another. They had no inkling of the underlying chemical or biochemical mechanisms at work.
So, the Egyptians were technologists, not scientists, whereas Eratosthenes and his colleagues were scientists, not technologists. The intentions of the Greek scientists were identical to those described two thousand years later by Henri Poincaré:
The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living. Of course I do not here speak of that beauty that strikes the senses, the beauty of qualities and appearances; not that I undervalue such beauty, far from it, but it has nothing to do with science; I mean that profounder beauty which comes from the harmonious order of the parts, and which a pure intelligence can grasp.
In summary, the Greeks had shown how knowing the diameter of the Sun depends on knowing the distance to the Sun, which depends on knowing the distance to the Moon, which depends on knowing the diameter of the Moon, which depends on knowing the diameter of the Earth, and that was Eratosthenes’ great breakthrough. These distance and diameter stepping stones were made possible by exploiting a deep vertical well on the Tropic of Cancer, the Earth’s shadow cast upon the Moon, the fact that the Sun, Earth and Moon form a right angle at half Moon, and the observation that the Moon fits perfectly over the Sun during a solar eclipse. Throw in some assumptions, such as moonlight being nothing more than reflected sunlight, and a framework of scientific logic takes shape. This architecture of scientific logic has an inherent beauty which emerges from how various arguments fit together, how several measurements interlock with one another, and how different theories are suddenly introduced to add strength to the edifice.
Having completed their initial phase of measurement, the astronomers of ancient Greece were now ready to examine the motions of the Sun, Moon and planets. They were about to create a dynamic model of the universe in an attempt to discern the interplay between the various celestial bodies. It would be the next step on the road to a deeper understanding of the universe.
Circles within Circles
Our most distant ancestors studied the sky in detail, whether it was to predict changes in the weather, keep track of time or measure direction. Every day they watched the Sun cross the sky, and every night they watched the procession of stars that followed in its wake. The land on which they stood was firm and fixed, so it was only natural to assume that it was the heavenly bodies that moved relative to a static Earth, not vice versa. Consequently, the ancient astronomers developed a view of the world in which the Earth was a central static globe with the universe revolving around it.
Table 1
The measurements made by Eratosthenes, Aristarchus and Anaxagoras were inaccurate, so the table below corrects previously quoted figures by providing modern values for the various distances and diameters.
| Earth’s circumference | 40,100 km = 4.01 × 104 km |
| Earth’s diameter | 12,750 km = 1.275 × 104 km |
| Moon’s diameter | 3,480 km = 3.48 × 103 km |
| Sun’s diameter | 1,390,000 km = 1.39 × 106 km |
| Earth-Moon distance | 384,000 km = 3.84 × 105 km |
| Earth-Sun distance | 150,000,000 km = 1.50 × 108 km |
This table also serves as an introduction to exponential notation, a way of expressing very large numbers — and in cosmology there are some very, very large numbers:
| 101 means 10 | = 10 |
| 102 means 10 × 10 | =100 |
| 103 means 10 × 10 × 10 | =1,000 |
| 104 means 10 × 10 × 10 | =10,000 etc. |
The Earth’s circumference, for example, can be expressed as: 40,100 km = 4.01 × 10,000 km = 4.01 × 104km.
Exponential notation is an excellent way of concisely expressing numbers that would otherwise be full of zeros. Another way to think of 10N is as 1 followed by N zeros, so that 103 is 1 followed by three zeros, which is 1,000.
Exponential notation is also used for writing very small numbers:
| 10-1 means 1 ÷ 10 | =0.1 |
| 10-2 means 1 ÷ (10 × 10) | = 0.01 |
| 10-3 means 1 ÷ (10 × 10 × 10) | = 0.001 |
| 10-4 means 1 ÷ (10 × 10 × 10 × 10) | = 0.0001 etc. |
In reality, it is of course the Earth that moves around the Sun, and not the Sun moving around the Earth, but nobody considered this possibility until Philolaus of Croton entered the debate. A pupil of the Pythagorean school in the fifth century BC, he was the first to suggest that the Earth orbited the Sun, not vice versa. In the following century, Heracleides of Pontus built on Philolaus’ ideas, even though his friends thought he was crazy, nicknaming him Paradoxolog, ‘the maker of paradoxes’. And the final touches to this vision of the universe were added by Aristarchus, who was born in 310 BC, the same year that Heracleides died.
Although Aristarchus contributed to measuring the distance to the Sun, this was a minor accomplishment compared with his stunningly accurate overview of the universe. He was trying to dislodge the instinctive (though incorrect) picture of the universe, in which the Earth is at the centre of everything, as shown in Figure 6(a). In contrast, Aristarchus’ less obvious (though correct) picture has the Earth dashing around a more dominant Sun, as shown in Figure 6(b). Aristarchus was also right when he stated that the Earth spins on its own axis every 24 hours, which explained why each day we face towards the Sun and each night we face away from it.
Aristarchus was a highly respected philosopher, and his ideas on astronomy were well known. Indeed, his belief in a Sun-centred universe was documented by Archimedes, who wrote: ‘He hypothesises that the fixed stars and the Sun remain unmoved; that the Earth is borne around the Sun on the circumference of a circle.’ Yet philosophers completely abandoned this largely accurate vision of the Solar System, and the idea of a Sun-centred world disappeared for the next fifteen hundred years. The ancient Greeks were supposed to be smart, so why did they reject Aristarchus’ insightful world-view and stick to an Earth-centred universe?
Figure 6 Diagram (a) shows the classical and incorrect Earth-centred model of the universe, in which the Moon, Sun and other planets orbit the Earth. Even the thousands of stars orbit the Earth. Diagram (b) shows Aristarchus’ Sun-centred view of the universe, with only the Moon orbiting the Earth. In this case, the stars form a static backdrop to the universe.
Egocentric attitudes may have been a contributory factor behind the dominance of the geocentric world-view, but there were other reasons for preferring an Earth-centred universe to Aristarchus’ Sun-centred universe. One basic problem with the Sun-centred world-view was that it appeared to be simply ridiculous. It just seemed so utterly obvious that the Sun revolved round a static Earth, and not the other way round. In short, a Sun-centred universe ran counter to. Good scientists, however, should not be swayed by common sense, because it sometimes has little to do with the underlying scientific truth. Albert Einstein condemned common sense, declaring it to be ‘the collection of prejudices acquired by age eighteen’.
Another reason why the Greeks rejected Aristarchus’ Solar System was its apparent failure to stand up to scientific scrutiny. Aristarchus had built a model of the universe that was supposed to match reality, but it was not clear that his model was accurate. Did the Earth really orbit the Sun? Critics pointed to three apparent flaws in Aristarchus’ Sun-centred model.
First, the Greeks expected that if the Earth moved then we would feel a constant wind blowing against us, and we would be swept off our feet as the ground raced from under us. However, we feel no such constant wind, and neither is the ground tugged away, so the Greeks concluded that the Earth must be stationary. Of course, the Earth does move, and the reason that we are oblivious to our fantastic velocity through space is that everything on the Earth moves with it, including us, the atmosphere and the ground. The Greeks failed to appreciate this argument.
The second problematic point was that a moving Earth was incompatible with the Greek understanding of gravity. As mentioned earlier, the traditional view was that everything tended to move towards the centre of the universe, and the Earth was already at the centre, so it did not move. This theory made perfect sense, because it explained that apples fell from trees and headed towards the centre of the Earth because they were being attracted to the centre of the universe. But if the Sun were at the centre of the universe, then why would objects fall towards the Earth? Instead, apples should not fall down from trees, but should be sucked up towards the Sun — indeed, everything on Earth should fall towards the Sun. Today we have a clearer understanding of gravity, which makes a Sun-centred Solar System much more sensible. The modern theory of gravity describes how objects close to the massive Earth are attracted to the Earth, and in turn the planets are held in orbit by the attraction of the even more massive Sun. Once again, however, this explanation was beyond the limited scientific framework of the Greeks.
The third reason why philosophers rejected Aristarchus’ Sun-centred universe was the apparent lack of any shift in the positions of the stars. If the Earth were travelling huge distances around the Sun, then we would see the universe from different positions during the course of the year. Our changing vantage point should mean a changing perspective on the universe, and the stars should move relative to one another, which is known as stellar parallax. You can see parallax in action at a local level by simply holding one finger in the air just a few centimetres in front of your face. Close your left eye and use your right eye to line your finger up with a nearby object, perhaps the edge of a window. Next, close your right eye and open your left one, and you will see that your finger has shifted to the right relative to the edge of the window. Switch between your eyes quickly and your finger will jump to and fro. So shifting your vantage point from one eye to the other, a distance of just a few centimetres, moves the apparent position of your finger relative to another object. This is illustrated in Figure 7(a).
The distance from the Earth to the Sun is 150 million km, so if the Earth orbited the Sun then it would be 300 million km away from its original position after six months. The Greeks found it impossible to detect any shift in the positions of the stars relative to one another over the course of the year, despite the enormous shift in Earthly perspective that would happen if we orbited the Sun. Once more, the evidence seemed to point to the conclusion that the Earth did not move and was at the centre of the universe. Of course, the Earth does orbit the Sun, and stellar parallax does exist, but it was imperceptible to the Greeks because the stars are so very far away. You can see how distance reduces the parallax effect by repeating the winking experiment, this time fully extending your arm so that your finger is almost a metre away. Again, use your right eye to line up your finger with the edge of the window. This time, when you switch to your left eye the parallax shift should be much less significant than before because your finger is farther away, as illustrated in Figure 7(b). In summary, the Earth does move, but the parallax shift rapidly reduces with distance and the stars are very far away, so stellar parallax could not be detected with primitive equipment.
Figure 7 Parallax is the apparent shift in the position of an object due to a change in an observer’s vantage point. Diagram (a) shows how a marker finger lines up with the left window edge when viewed with the right eye, but shifts when viewed with the other eye. Diagram (b) shows that the parallax shift caused by switching between eyes is significantly reduced if the marker finger is more distant. Because the Earth orbits the Sun, our vantage point changes, so if one star is used as a marker then it should shift relative to more distant stars over the course of a year. Diagram (c) shows how the marker star lines up with two different background stars depending on the position of the Earth. However, if diagram (c) were drawn to scale, then the stars would be over 1 km off the top of the page! Therefore the parallax shift would be minuscule and imperceptible to the ancient Greeks. The Greeks assumed that the stars were much closer, so to them a lack of parallax shift implied a static Earth.
At the time, the evidence against Aristarchus’ Sun-centred model of the universe seemed overwhelming, so it is quite understandable why all his philosopher friends stayed loyal to the Earth-centred model. Their traditional model was perfectly sensible, rational and self-consistent. They were content with their vision of the universe and their place within it. However, there was one outstanding problem. Sure enough, the Sun, Moon and stars all seemed to march obediently around the Earth, but there were five heavenly bodies that dawdled across the heavens in a rather haphazard manner. Occasionally, some of them even dared to stop momentarily before temporarily reversing their motion in a volte-face known as retrograde motion. These wandering rebels were the five other known planets: Mercury, Venus, Mars, Jupiter and Saturn. Indeed, the word ‘planet’ derives from the Greek planetes, meaning ‘wanderer’. Similarly, the Babylonian word for planet was bibbu, literally ‘wild sheep’ — because the planets seemed to stray all over the place. And the ancient Egyptians called Mars sekded-ef em khetkhet, meaning ‘one who travels backwards’.
From our modern Earth-orbits-Sun perspective, it is easy enough to understand the behaviour of these heavenly vagabonds. In reality, the planets orbit the Sun in a steady manner, but we view them from a moving platform, the Earth, which is why their motion appears to be irregular. In particular, the retrograde motions exhibited by Mars, Saturn and Jupiter are easy to explain. Figure 8(a) shows a stripped-down Solar System containing just the Sun, Earth and Mars. Earth orbits the Sun more quickly than Mars, and as we catch up to Mars and pass it, our line of sight to Mars shifts back and forth. However, from the old Earth-centred perspective, in which we sit at the centre of the universe and everything revolves around us, the orbit of Mars was a riddle. It appeared that Mars, as shown in Figure 8(b), looped the loop in a most peculiar manner as it orbited the Earth. Saturn and Jupiter displayed similar retrograde motions, which the Greeks also put down to looping orbits.
These loopy planetary orbits were hugely problematic for the ancient Greeks, because all the orbits were supposed to be circular according to Plato and his pupil Aristotle. They declared that the circle, with its simplicity, beauty and lack of beginning or end, was the perfect shape, and since the heavens were the realm of perfection then celestial bodies had to travel in circles. Several astronomers and mathematicians looked into the problem and, over the course of several centuries, they developed a cunning solution — a way to describe looping planetary orbits in terms of combinations of circles, which was in keeping with Plato and Aristotle’s edict of circular perfection. The solution became associated with the name of one astronomer, Ptolemy, who lived in Alexandria in the second century AD.
Figure 8 Planets such as Mars, Jupiter and Saturn exhibit so-called retrograde motion when viewed from Earth. Diagram (a) shows a stripped-down Solar System with just the Earth and Mars orbiting (anticlockwise) around the Sun. From position 1, we would see Mars move increasingly ahead of us, which continues as we observe Mars from position 2. But Mars pauses at position 3, and by position 4 is now moving to the right, and even further to the right when Earth arrives at position 5. There it pauses once more, before resuming its original direction of travel, as seen from positions 6 and 7. Of course, Mars is continually moving anticlockwise around the Sun, but it appears to us that Mars is zigzagging because of the relative motions of the Earth and Mars. Retrograde motion makes perfect sense in a Sun-centred model of the universe.
Diagram (b) shows how believers in an Earth-centred model perceived the orbit of Mars. The zigzag of Mars was interpreted as an actual looping orbit. In other words, traditionalists believed that the static Earth sat at the centre of the universe, while Mars looped its way around the Earth.
Ptolemy’s world-view started with the widely held assumption that the Earth is at the centre of the universe and stationary, otherwise ‘all the animals and all the separate weights would be left behind floating on the air’. Next, he explained the orbits of the Sun and Moon in terms of simple circles. Then, in order to explain retrograde motions, he developed a theory of circles within circles, as illustrated in Figure 9. To generate a path with periodic retrograde motion, such as the one followed by Mars, Ptolemy proposed starting with a single circle (known as the deferent), with a rod attached to the circle so that it pivoted. The planet then occupied a position at the end of this pivoted rod. If the main deferent circle remained fixed and the rod rotated around its pivot, then the planet would follow a circular path with a short radius (known as the epicycle), as shown in Figure 9(a). Alternatively, if the main deferent circle rotated and the rod remained fixed, then the planet would follow a circular path with a larger radius, as shown in Figure 9(b). However, if the rod rotated around its pivot and at the same time the pivot rotated with the main deferent circle, then the planet’s path would be a composite of its motion around the two circles, which mimics a retrograde loop, as shown in Figure 9(c).
Although this description of circles and pivots conveys the central idea of Ptolemy’s model, it was actually far more complicated. To start with, Ptolemy thought of his model in three dimensions and constructed it from crystal spheres, but for simplicity we will continue to think in terms of two-dimensional circles. Also, in order to accurately explain the retrogrades of different planets, Ptolemy had to carefully tune the radius of the deferent and the radius of the epicycle for each planet, and select the speed at which each rotated. For even greater accuracy he introduced two other variable elements. The eccentric defined a point to the side of the Earth which acted as a slightly displaced centre for the deferent circle, while the equant defined another point close to the Earth, whose influence contributed to the variable speed of the planet. It is hard to imagine this increasingly complicated explanation for planetary orbits, but essentially it consisted of nothing more than circles on top of more circles within yet more circles.
Figure 9 The Ptolemaic model of the universe explained the loopy orbits of planets such as Mars using combinations of circles. Diagram (a) shows the main circle, called the deferent, and a pivoted rod with a planet on the end. If the deferent does not rotate, but the rod does rotate, then the planet follows the smaller, bold circle mapped out by the end of the rod, which is called an epicycle.
Diagram (b) shows what happens if the pivoted rod remains fixed and the deferent is allowed to rotate. The planet follows a circle with a large radius.
Diagram (c) shows what happens when both the rod rotates around its pivot, and the pivot rotates with the deferent. This time the epicycle is superimposed on the deferent, and the planet’s orbit is the combination of two circular paths, which results in the loopy retrograde orbit associated with a planet such as Mars. The radii of the deferent and epicycle can be adjusted and both speeds of rotation can be tuned to mimic the path of any planet.
The best analogy for Ptolemy’s model of the universe is to be found in a fairground. The Moon follows a simple path, a bit like a horse on a rather tame merry-go-round for young children. But the path of Mars is more like a wild waltzer ride, which locks the rider in a cradle that pivots at the end of a long rotating arm. The rider follows a circular path while spinning in the cradle, but at the same time he is following another, much larger, circular path at the end of the long arm that holds the cradle. Sometimes the two motions combine, giving rise to an even greater forward speed, while sometimes the cradle is moving backwards relative to the arm and the speed is slowed or even reversed. In Ptolemaic terminology, the cradle spins around an epicycle and the long arm traces out the deferent.
The Ptolemaic Earth-centred model of the universe was constructed to comply with the beliefs that everything revolves around the Earth and that all celestial objects follow circular paths. This resulted in a horribly complex model, replete with epicycles heaped upon deferents, upon equants, upon eccentrics. In The Sleepwalkers, Arthur Koestler’s history of early astronomy, the Ptolemaic model is described as ‘the product of tired philosophy and decadent science’. But despite being fundamentally wrong, the Ptolemaic system satisfied one of the basic requirements of a scientific model, which is that it predicted the position and movement of every planet to a higher degree of accuracy than any previous model. Even Aristarchus’ Sun-centred model of the universe, which happens to be basically correct, could not predict the motion of the planets with such precision. So, all in all, it is not surprising that Ptolemy’s model endured while Aristarchus’ disappeared. Table 2 summarises the key strengths and weaknesses of the two models, as understood by the ancient Greeks, and it serves only to reinforce the apparent superiority of the Earth-centred model.
Ptolemy’s Earth-centred model was enshrined in his Hè megalè syntaxis (‘The Great Collection’), written in about AD 150, which became the most authoritative text on astronomy for centuries to come. In fact, every astronomer in Europe for the next millennium was influenced by the Syntaxis, and none of them seriously questioned its Earth-centred picture of the universe. Syntaxis reached an even wider audience in AD 827, when it was translated into Arabic and retitled the Almagest (‘The Greatest’). So, during the lull in scholasticism during the European Middle Ages, Ptolemy’s ideas were kept alive and studied by the great Islamic scholars in the Middle East. During the golden age of the Islamic empire, Arab astronomers invented many new astronomical instruments, made significant celestial observations and built several major observatories, such as the al-Shammasiyyah observatory in Baghdad, but they never doubted Ptolemy’s Earth-centred universe with its planetary orbits defined by circles within circles within circles.
