| Greek Cosmology:
Reasons to Consider a Heliocentric Model.
Let us quickly recap.
Thanks to -
we know the size of the Earth;
thanks to -
who studied the Earth's shadow during lunar eclipses, we know that the Earth is probably only a few times bigger than the Moon;
and thanks to -
we know that the Sun is much farther away than the Moon - say, 100 times or more (even given the imprecision of his determinations).
This leads inescapably to the conclusion that the Sun is much bigger and more imposing than the Earth, so a thoughtful person might have seriously entertained the possibility that the Sun is the center of things (a heliocentric model). The great legacy of Greek astronomy, however, was the geocentric model which we will now explore. A little later on, though, I will offer
that presumably motivated their thinking -- some of which seem moderately compelling! It would be quite wrong, from our secure modern perspective, to conclude that they were unintelligent, foolish, or lacking in insight and imagination.
The Fundamental Postulates of Greek Cosmology.We have learned of various successes, and touched upon other parallel and often flawed lines of thought. These were not carried out in complete isolation: the thinkers of the time were continuously striving to merge all such speculations to develop a cosmological model, a visualisation of how the Solar System might `work.' Many such models were develped through the centuries, and indeed some of them incorporated the notion of a sun-centered planetary system; but the best known is that of Ptolemy, which dates from about 140 AD. Unfortunately, it became the dominant model, and its unquestioning acceptance stifled real astronomical progress for a very long time. The Ptolemaic model starts with the following "self-evident" propositions: the Earth is at rest at the centre of the cosmos everything else orbits around us the orbits are perfect circles, as these are the most ideal forms in nature (as is demonstrated by the form of the sun and moon) the sun, the moon, and the various planets move in circles which are independent of each other and of the stars (which is why these objects drift across the field of remote background stars) the circular motions are carried out at uniform speed
Problems with the Greek Cosmology.As nice as this model sounds, a little observation and consideration reveals some gaping holes in it which then need to be plugged. For instance: 1 Non-uniform motions: The motions of the sun and moon are not uniform: their speeds across the field of background stars are not constant. This is fairly easily worked out for the moon, because you can see the stars in the sky near it; but you may find it hard to imagine how you would work out what stars are "behind the sun" at any given time in order to gauge its drift rate across the background. You will have to take my word that there is in fact a fairly simple way of accomplishing this. (Really it boils down to watching the rate at which the pattern of constellations visible at night changes from month to month, in the night sky -- that is, in the direction opposite to the Sun.) Anyway, the puzzling result is that the sun sometimes moves relatively quickly across the stars (in January, for instance) and at other times more slowly. The Greeks had to face the challenge of devising a mechanism which could make the motions speed up and slow down, preferably while keeping circles as the basis of everything. ( The modern understanding: the Earth does not orbit the sun at constant speed; neither does the Moon orbit the Earth at constant speed! The apparent motion of the sun across the field of remote stars is caused by our changing perspective as we orbit around it. Our orbit is not a perfect circle centred on the sun, and we move faster when we are close to the sun in January than when we are farther away from it, say in August. We will see why later.) 2 The behaviour of Mercury and Venus: The Greeks assumed that all the known planets move in circles centered on the Earth. Moreover, they realized that these motions are completely independent for at least some of the planets. Consider Mars, for instance. It is sometimes invisible in the daytime sky because it is on the same side of the Earth as the Sun itself is. At other times, Mars and the Sun are on opposite sides of the sky, so that Mars is brightly visible at midnight. Jupiter and Saturn are similarly free to wander. (In the fall of 2000, for example, Jupiter and Saturn were both brilliantly visible and near each other in the night sky, but they need not be -- they move around quite independently.) Mercury and Venus, by contrast, are never seen very far from the sun in the sky, and never overhead at midnight, the way Mars can be. The motions of these two planets are apparently constrained by the sun in some mysterious fashion. The Greeks had to build into their model a little extra feature to keep those two objects under control. In essence, they insisted that Mercury and Venus move in circles centred on the Earth but that they be independent of the sun only to an extent. There is a simple analogy. Suppose you are at a park and notice, a long way off, a person wandering back and forth, perhaps looking at some flower beds. Suppose you also notice a dog in that direction, a dog which is sometimes directly between you and the person and sometimes a bit off to one side; but as you observe this person, the dog never strays far from your line of sight, no matter how long you wait and watch. You might logically conclude that the dog is with that person, and perhaps even attached to the person by a thin leash which you cannot see from a distance. It would seem very strange to conclude instead that the dog is, say, exactly halfway between you and that person, and that some mysterious influence is keeping the three of you more-or-less lined up, so that when the walker moves a long way to the right, so does the dog! But this is, in essence, what the Greeks assumed for Venus and Mercury. (See page 75 of your text.) ( The modern understanding: Venus and Mercury orbit the sun itself in close proximity, held by the `leash' of gravity. Since they are always near the Sun, we can sometimes see one (or both) of these planets in the evening or morning sky, depending on where they are in their orbits. At times, Venus is 'to the right' of the Sun and rises before it in the dawn sky: it is called the "Morning Star." As the weeks and months pass, it moves around behind the Sun, and we lose sight of it for a time. Later, it reappears 'to the left' of the Sun and become visible in the evening sky, still above the horizon for a time after the Sun has set. In the fall of 2004, for example, you can see the conspicuous "Morning Star" in the south-eastern sky before sunrise. Of course, Mars and all the other planets also feel the 'leash' of the Sun's gravity -- Mercury and Venus are not unique in this respect! -- but their orbits are outside that of the Earth. It is therefore possible for the Earth to be positioned between the Sun and a planet like Mars. We then see it overhead at midnight. 3 The changing apparent sizes of the sun and moon: There is pretty clear evidence which proves that the sun and moon can't be moving in perfect circles: namely, the changeable nature of solar eclipses. When we see a solar eclipse, it is sometimes total, with the moon completely blocking out the sun; at other times, it is annular, which means that the moon does not fully cover the sun and we see a ring, or annulus, of light around the dark central silhouette of the moon. (We saw an annular eclipse here in Kingston in May of 1994.) The pictures on page 46 of your text show the dramatic difference between total and annular eclipses. What this must mean, of course, is that the sun and moon do not always look the same size from our point of view. When there is an annular eclipse, the sun must look a bit bigger, or else the moon looks a little smaller, so that the whole sun is too big to be blocked off. If we rule out the possibility that the moon and sun themselves change in size, we must conclude that they are not at a constant distance away from us. In other words, the Sun and Moon can't be moving in perfect circles which are centred on the Earth. At least one of them, and possibly both, must be moving in an orbit which causes the distance from the Earth to vary. ( The modern understanding: the orbits are not circles, but rather ellipses, so it is indeed true that our distance from the Sun, and the moon's distance from the Earth, vary from time to time.) 4 The retrograde motion of the outer planets: The outer planets -- most noticeably Mars -- display "retrograde loops." That is, as we watch them night after night drifting across the field of stars, they unaccountably slow down, come to a stop, start moving backwards, again stop, and then start moving forwards again (over the space of several weeks, typically). This really poses a puzzle: what imaginable mechanism can cause the planets to come to a grinding halt -- or rather one without the grinding of brakes and gears! -- and then start up again? ( The modern understanding: this one is very easily understood in the modern heliocentric model; see the diagrams on pages 49-51 of your text. There is a simple analogy which can help us. First, imagine yourself standing still beside Highway 401, watching a car in the "slow lane" go past you at 100 km/h. You see it move smoothly from right to left, passing the trees, houses, and hills in the background. Now imagine yourself moving as an impatient driver, in a car passing that one at a speed of 120 km/h in the outside or "fast" lane. As you pass the other car and look out at it, it appears, from your perspective, actually to be moving backwards with respect to the remote objects. Of course it is not doing anything of the sort. A comparable phenomenon happens in the Solar System. The Earth moves faster in its orbit than Mars does, for reasons we will discover later. Thus we "overtake Mars on the inside" as we move around the sun, and our changing perspective gives the illusion of Mars temporarily coming to rest and reversing its direction of motion. (See the figure on page 51 in particular.) The critical factors are that we are on an orbit which is closer to the Sun than that of Mars (and of the other outer planets); and we are travelling faster than Mars, so that we overtake it. (If we were travelling much more slowly, so that Mars overtook us, we would not see retrograde loops.) Of these criticisms, perhaps the most difficult was that of retrograde motion. How could the cosmological model be taken seriously if it could not plug these holes?
The Ptolemaic Model: Problems Fixed (?)As you can appreciate, Ptolemy's model had to be made rather contrived to keep all the desired features (Earth-centred; motion at uniform speed in circles; etc) but also to account for the problems described above. What he wound up with had the following features: there were "circles within circles." Each planet was assumed to move on a small circle called an epicycle, which itself moves around a bigger circle called a deferent . This gives the motion a "loop-the-loop" effect (rather like what a Spirograph produces, if you are familiar with those devices) which explains the retrograde motion and the variable speeds. To understand the geometry, see the figure on page 68 of the text. even this did not work well enough, however. Ptolemy also had to suppose that the center of each deferent did not lie on the Earth, but rather a little off to one side. (Notice that this in fact represents an abandonment of the notion of circles exactly centered on the Earth.) and even that wasn't enough: Ptolemy had to introduce a line joining the centre of the epicycle to the equant, a point opposite the centre of the deferent from the Earth. (These details are meant for interest and to demonstrate the complexity which they were willing to build in, but I am not really concerned that you learn the material at this level of detail!) Ptolemy determined that the epicycle would have to move around the deferent in such a way that this line should move at constant speed (like the hand of a clock) around the equant. finally, Ptolemy had to hypothesise that, for some unknown reason, the epicycles of Mercury and Venus were always lined up with the direction of the sun. This kept those two planets always near the sun from our perspective.
Did the Greeks Seriously Believe This Model? Occam's Razor.The model is so contrived, with circles embedded within circles, that it is worth wondering whether it was ever meant to be taken seriously, or if instead it simply provided a convenient way of visualising and calculating the motions within the Solar System. There is no clear-cut answer to this: no one is certain just how the model was thought of by its various proponents. In recent centuries, science - and Physics in particular - has developed a philosophy in which the tenet of Occam's Razor is applied. Basically, this is a statement that, if you have a choice of explanations, you adopt the one which is simplest provided it is still consistent with all the observations. You resist the need to adopt another more complex model until forced to do so by some inexplicable observations. (The name, by the way, comes from William of Occam, who lived in the 1300s. In other sciences, it is sometimes called by other names, such as the `Principle of Parsimony.') You may remember that Occam's Razor is referred to several times in the movie Contact, and indeed it is, or should be, part of every scientist's approach to his or her work. Here is a fanciful example. Suppose I develop a theory which says that all objects fall with the same acceleration under the influence of gravity (ignoring air resistance) except those which are painted in alternate stripes of cyan and magenta, with a uniform sprinkling of green polka-dots and yellow crosses. Is this theory worth consideration? Should it appear in every Physics textbook? Please note that my pet theory correctly explains every experiment ever carried out on falling objects, so in a very real sense it is perfectly successful! (I think I am safe in assuming that no one has ever tested the behaviour of an object with the special paint job I described!) But although the theory 'works', you should be quick to reject it. It is unappealing because the added condition is so clearly unnecessary. If and when someone tests it - which seems unlikely! - we could amend the law to take into the special behaviour of objects of the sort described (and then try to understand the mechanism which makes this happen). It is worth adding that Physicists, and other scientists, also have a real liking for scientific theories and laws which are, in a word, elegant (or even beautiful ) in their simplicity and clarity. There are, unfortunately, some branches of science in which we do not find such laws. Nature seems to be deeply complex and muddy in some areas of study, such as in the deep inner workings of the fundamental particles which make up all matter, or in the new science of chaotic behaviour. But in many fields, there is a powerful urge to look for 'elegant' theories. Of course, there may be a subtle trap in our modern predisposition for simplicity (in the sense implied by Occam's Razor). The great physicist Richard Feynman pointed out, for instance, that the very simplest situation would be for there to be nothing whatsoever, and Nature is at least more complicated than that! Just because we find simple laws aesthetically pleasing does not mean that Nature will always pamper us by providing them, however passionately we hope and search for them. But it is clear, at least in retrospect, that the Ptolemaic model is anything but elegant, with all its add-ons and dubious fixes. Where the Greeks failed -- at least in modern terms, which it is of course an unfair test! -- was in not recognizing that a simple stroke, that of shifting the model to a heliocentric cosmology, would have admitted a much simpler explanation of the observed motions, and in particular the retrograde motions. This would have appealed to modern adherents of Occam's Razor. The real question, of course, is whether they might have been able to test their cosmological theory.
Could The Ptolemaic Model Have Been Tested?As we have seen, the Ptolemaic model is very contrived. Just as serious a failing, from a modern perspective, is that there is no physics in it. That is, the model describes how the planets move, but says nothing about why. There are, however, two testable predictions, one of which we have already considered. 1 Stellar Parallax: We have already considered the first test. If we should discover that the nearby stars appear to shift with respect to the background stars, we will have incontrovertible proof that the Earth itself moves through space. Once you admit that, and recognize that it is with respect to the Sun that we move, it is no great extension to admit that the other planets probably do so as well. (It might still be the case, however, that the Earth orbits the sun but everything else orbits us!) 2 The Phases and Changing Size of Venus: In an earlier discussion I pointed out that the most compelling argument in favour of the proposition that is that we see the pattern of phases which we do. If, instead, the moon was farther away than the sun, then it would always look "full" (or nearly so) instead of showing slender crescents and so forth. A similar argument holds here for the planet Venus (and for Mercury, which is much harder to observe, thanks to its close proximity to the Sun). The figure on page 75 of your text makes the point clear. If Ptolemy is right, Venus is always between us and the sun, and we should never see its face fully lit up -- we should mostly be seeing its unlit dark side. But if Venus ever goes around the far side of the sun, then we should see its face fully lit up (looking rather like a full moon). This represents another critical test for the Ptolemaic model. Unfortunately, to detect this effect requires a telescope, so no answer was possible for about 1500 more years; but the prediction was a clearcut one. A closely related point is that Venus should change conspicuously in apparent size as well. In the Ptolemaic model, Venus was thought to change only a little in its distance from the Earth as it moved on its epicyclic path. In the heliocentric model, however, its distance from us changes enormously as it moves around and around the sun. As shown in the figure on page 75 of your text, Venus should look small and full when on the far side of the sun, and bigger but a thin crescent when on the near side. Once again, however, this proposition was untestable until the invention of the telescope.
In Defence of the Ancients: Reasons to Consider a Geocentric Model.Let me offer a few thoughts in defence of the development of what now seems a very strange and contrived model of the solar system: It is quite unfair to judge the thinking of millennia ago by the standards of today, especially since (as I have noted) we have no real idea of just how seriously this model was meant to be taken. Let us instead admire the intelligence and imagination which went into this elaborate construction, and acknowledge the many successes which were enjoyed and which we have considered. Given the steadiness of the Earth under our feet, the stillness of the atmosphere, and so forth, it is certainly forgiveable that the ancients assumed that the Earth was at rest in the cosmos. To conclude otherwise, as some bold thinkers did, was in fact very daring. Finally, let us not forget the plain fact that the moon changes only a little -- indeed, almost imperceptibly -- in apparent size as the months pass. Given that, the Greeks were certainly completely justified in concluding that the moon orbits the Earth; its orbit is not centered on the sun. If you knew this, and then turned your attention to the planets (objects for which no simple distance estimates could be made), it would be logical to assume that the other moving bodies are likewise orbiting the Earth. To assume otherwise requires that we replace one centre of motion (which they took to be the Earth) with two. This is really a rather profound change. (Of course, we now know that the Solar System has many centers of motion! The planets orbit the sun, and various moons orbit the different planets.) With respect to this last point, it is fascinating to speculate what the Greeks might have concluded if the Earth had had no moon. The (near) constancy in the apparent size of the Sun is explicable in either a geocentric or a heliocentric model, but the fact that the Moon obviously orbits us perhaps encouraged the generalisation -- we are at the center! -- which was so misleading. Previous chapter:Next chapter
0: Physics 015: The Course Notes, Fall 2004 1: Opening Remarks: Setting the Scene. 2: The Science of Astronomy: 3: The Importance of Scale: A First Conservation Law. 4: The Dominance of Gravity. 5: Looking Up: 6: The Seasons: 7: The Spin of the Earth: Another Conservation Law. 8: The Earth: Shape, Size, and State of Rotation. 9: The Moon: Shape, Size, Nature. 10: The Relative Distances and Sizes of the Sun and Moon: 11: Further Considerations: Planets and Stars. 12: The Moving Earth: 13: Stellar Parallax: The Astronomical Chicken 14: Greek Cosmology: 15: Stonehenge: 16: The Pyramids: 17: Copernicus Suggests a Heliocentric Cosmology: 18: Tycho Brahe, the Master Observer: 19: Kepler the Mystic. 20: Galileo Provides the Proof: 21: Light: Introductory Remarks. 22: Light as a Wave: 23: Light as Particles. 24: Full Spectrum of Light: 25: Interpreting the Emitted Light: 26: Kirchhoff's Laws and Stellar Spectra. 27: Understanding Kirchhoff's Laws. 28: The Doppler Effect: 29: Astronomical Telescopes: 30: The Great Observatories: 31: Making the Most of Optical Astronomy: 32: Adaptive Optics: Beating the Sky. 33: Radio Astronomy: 34: Observing at Other Wavelengths: 35: Isaac Newton's Physics: 36: Newtonian Gravity Explains It All: 37: Weight: 38: The Success of Newtonian Gravity: 39: The Ultimate Failure of Newtonian Gravity: 40: Tsunamis and Tides: 41: The Organization of the Solar System: 42: Solar System Formation: 43: The Age of the Solar System: 44: Planetary Structure: The Earth. 45: Solar System Leftovers: 46: The Vulnerability of the Earth: 47: Venus: 48: Mars: 49: The Search for Martian Life: 50: Physics 015 - Parallel Readings.
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(Monday, 17 May, 2021.)