| Galileo Provides the Proof:
Galileo the Experimenter.
Galileo was a contemporary of Kepler. They lived very far apart, but were certainly aware of each other's work; however, they were quite different. Far from being a mystic, Galileo was an empiricist and the first great experimenter. He overthrew the longstanding notion, dominant since the time of Aristotle, that pure thought could give rise to a deep and correct understanding of physical laws.
For instance, Aristotle had argued that two bodies of very different mass (weight) should fall to the ground at different rates -- the heavy one should fall faster and get there first. This was, if you like, simply 'common sense,' and there seemed to be no need to test the hypothesis with controlled experiments. Galileo was able to demonstrate that such commonsensical ideas were often wrong. The story, perhaps apocryphal, is that he dropped balls off the Leaning Tower of Pisa to show this. Certainly he carried out experiments in which he rolled balls down slopes of different steepness, and generalized his findings to pure vertical motion.
Galileo's biggest breakthrough in the science of dynamics (forces and motions), however, came with his recognition of inertia. This word encapsulates a fundamental truth in physics: a body in any state of motion will continue in that state unless some external force acts to change it. (This law, restated more quantitatively, will be met again as Newton's First Law.)
In other words, a body at rest tends to stay at rest unless, for instance, you push on it, or something else affects it. Aristotle would have agreed with this. But a body in a state of motion - say, a ball rolling across a table - should keep on doing exactly that. Why, then, do we always see the ball come quickly to rest? Aristotle's reply would be simply that the ball's `natural state' is one of rest, so it automatically slows down. Galileo was the first to say, however, that the ball would keep on moving if not for various external forces which act on it -- air resistance, the friction with the tabletop, and so forth.
Despite these insights, Galileo had an imperfect understanding of inertia. He assumed, for instance, that the Moon moves in a near-circular orbit around the Earth because of a kind of inertia. Having been set going in this path, he thought, the Moon will 'just naturally' continue doing so. (Actually, the very fact that the Moon changes direction as it goes tells us that there must be a force acting -- the attractive gravitational pull of the Earth.)
Galileo's influence was very far-reaching, in more branches of science than just physics. He was the first of the great experimental scientists who were completely to overthrow the Aristotelian school. But it is to the more limited context of his astronomical discoveries that we will turn now.
The Concept of Relativity.The word relativity frightens many non-physicists, with its obvious connections with the intellectually challenging notions of Einstein's theories (topics we will encounter later in the course). But we are all familiar with the ordinary concept of relativity as first introduced by Galileo. In oversimplified terms, this is merely a statement that measurements of uniform, steady motion can only be made relative to some specific frame of reference, and motion in one frame will not appear the same in some other frame. What does this mean? Galileo presented his physical theories and speculations in the form of dialogues between various intelligent people representing different points of view. In one such dialogue, one of his characters points out that it is often not possible to measure motion in any absolute way. For instance, if you are below decks on a very smoothly-moving ship, you may erroneously believe that you are sitting becalmed; but once you come up on deck you see that you are indeed in motion across the water. Or consider the following experiment: climb the mast of the ship and drop a ball. As seen by someone on the ship, the ball will fall parallel to the mast and land right next to its base. But someone on the shore will see the ball fall in a curved path, with some `sideways' motion in the direction the ship is sailing plus some downward motion as it falls to the deck. Of course, the motion of the ship carries the mast forward as well, so the ball lands next to the base anyway! And you all know the everyday experience of being able to toss a ball up and down while on a fast-moving train, although from the point of view of a person beside the track the ball seems to be moving in a long 'sideways' curve. The real question is: who is to say who is actually in motion? It seems natural to say that the ship is obviously moving, and the people on the shore are at rest; but there is no inconsistency in the observed behaviour to say instead that the ship is at rest and everything else -- the sea, the shore, the people on shore -- are moving `backwards' relative to the ship. Nothing tells you which frame of reference is `better.' In fact, if the person on the ship were isolated from the surroundings (say, immersed in a thick fog) and if the ship were travelling very smoothly (so that bumps and jolts don't give away the situation), there is no simple experiment you can carry out on board which will reveal the fact that the ship is moving at some constant, steady speed. Galileo's point in discussing relativity in this way is simply to point out that our apparently smooth ride on the Earth, with no strong winds blowing in our faces, is no evidence for an Earth at rest, as had long been argued. If the Earth is moving smoothly (no `bumpy ride') through space, and if it carries everything (us, the air, etc.) along with it, then it is no surprise that we cannot detect our motion through empty space. Moreover, if the Earth were ever somehow set into motion, then its passage through space might well be frictionless and continue forever, because of the inertia of the motion. Galileo argued that the Earth would not simply coast to a halt, as an Aristotelian might have expected. With discussions of this sort, Galileo laid the ground for a new way of looking at the universe, one in which we are moving smoothly and quietly through space, in orbit around the sun which, he believed, was the true centre of the planetary system. But such remarks, even if persuasively presented, are not sufficient. Galileo sought and found experimental proof that Copernicus's heliocentric model was correct. To do so, however, he needed a new tool: the telescope.
Galileo's Need for a Telescope: The Inadequacies of the Human Eye.As we saw earlier, the Ptolemaic and Copernican models of the solar system made distinctly different predictions about the way Venus should appear from the Earth -- the phases would not be the same. In Ptolemy's model, Venus is always between the Earth and the Sun and should never be seen fully lit up; in Copernicus's model, Venus goes around to the far side of the sun and can be almost fully lit up from our point of view. (This is shown on page 75 of your textbook.) The problem is that this effect was, before Galileo, completely undetectable because, to the unaided human eye, Venus always looks like just a point of light. To understand that, let's spend a little time considering the nature and function of the eye. With reference to a sketch in the class, I reminded you how the eye works. Light is focussed by the lens to form an upside-down image (which the brain interprets correctly) on the retina, the light-sensitive layer at the back of the eye. (See page 174 of the text.) Some of the other features or capabilities of the eye include: Accommodation: The lens of the eye can be changed in shape by the ring of muscles which surround it, a capability which allows us to focus on both nearby and remote objects. This is called accommodation; it is automatic and unconscious, but diminishes with age as the lens becomes less flexible, which is why people sometimes develop a need for bifocal or reading glasses -- as I myself have lately learned! Rods and Cones: The retina contains the structures which detect incoming light. There are two kinds, named for their shapes. The rods are sensitive simply to the presence or absence of light, and give us black-and-white vision. The cones are sensitive to various colours of light, thanks to the mix of different pigments they contain. The interesting thing is that the cones need a fairly bright level of light before they work at all well; the rods are more sensitive at low light levels. This is why you see things as mere shades of grey in dim light, as when you get up at night before you turn on the lights. By the way, this also partly explains why most stars seem to be just shades of white: they are too faint to stimulate the colour receptors in the eye. There are a few exceptions. Betelgeuse and Antares, which are quite bright, look reddish to the eye, for instance, and the planet Mars is also bright enough to show its characteristic red colour. But although there are very many red stars, most of them are so faint that they merely look dim and colourless (whitish). Some of the more familiar stars, like Sirius, are very bright -- certainly bright enough to stimulate the colour receptors! -- but nevertheless look white to the eye. The reason is quite prosaic: these stars are simply not particularly colourful. (They are truly white.) We will explore the reasons for the observed differences in stellar colours later on; it has an important astrophysical interpretation. Resolution: The colour sensitivities are interesting, but another aspect is more central to the discussion of Galileo's contributions. The retina of the eye has a granularity which limits its ability to resolve or discern detail. Here is a simple analogy. Suppose that you suspected that your car was leaking oil. You could park it over a huge funnel-shaped hole, and then discover in the morning that some oil had accumulated in the bottom of the hole. This would confirm that there is a leak, but would not tell you where it is. Is it from the engine block? A rear axle? You have detected the leak, but not resolved its position. Indeed, if there were two separate leaks, you would have no way of knowing! A better experiment would have been to park the car over a big sheet of white paper. In the morning, you would find a stain under the source of the oil leak (or two stains, if there is more than one leak). The extra information is useful: you have worked out some of the details of how the oil leaks are distributed. Now suppose your eye was like the funnel -- that is, suppose it only registered whether light was falling on it or not. (By the way, eyes as primitive as this can be found in some simple animals. This may sound pointless, but such light detectors could still be beneficial. For instance, by turning your head around, you would be able to tell the rough direction of the sun, and you would be able to tell if a dark shadow -- perhaps from a predator -- fell onto you. But you would not be able to discern details, or read an informative neon sign that says ``Rosie's Bar and Grill.'') Of course, our eyes do very much better than this simple model. We can see many details -- the letters and words you are reading on this page, for instance -- although not as many fine details as a hawk would. But the graininess of the retina means that a very small image, such as the image of the planet Venus formed by the lens of your eye, lies completely within one resolution element, one of the patches of light-sensitive material making up the retina. In other words, we know Venus is there, because the lit-up retinal patch registers that light is hitting it, but we do not see any finer details at all -- things like the crescent shape of Venus, for example. We notice only a point of light. Given the limits of the physiology of the eye, there is an inescapable limit to how much detail your unaided eye can detect, no matter how hard you stare or how bright the source. To make any progress, then, we need a means of magnifying the image of Venus so that the same picture, in expanded form, is spread out over a large part of the retina. The many millions of retinal cells in your eye will then be able to distinguish the top and bottom of the image, see subtle structure and shapes, and so on. Galileo had the good fortune to learn of the invention of the telescope, exactly the device needed. Although it is often said that he invented the telescope, this is not correct, but he had the initiative to build one for his own use, having heard reports of its construction, and gradually improved on its capabilities. This was essential for the success of his arguments in favour of the Copernican model.
How a Telescope Works.Since I am an observational astronomer myself, rather than a theorist, I spend a lot of time using telescopes, and will have a fair bit to say about them in due course. For now, though, I invite you to look at the top figure on page 177 of your text, to see how a simple refracting telescope works. (Refraction is the change in direction of light as it passes from one medium, like air, into another, like glass. The telescope shown on page 178 is a reflecting telescope, which means that it uses mirrors. We will consider the differences later.) Now imagine turning the telescope towards an object like Venus. The light rays from the target are focussed in such a way that they converge to form a perfect little image, floating in the air in ghostly fashion in the middle of the tube of the telescope, as shown in the figure. (If you were to hold a white piece of paper in the right location, you could actually project the image ov Venus onto the surface.) But the incoming rays of light don't stop there: they continue on their way down the telescope tube. To all intents and purposes, it is just as though a tiny luminescent Venus had taken up residence inside the telescope tube and started to glow away. If such a thing did happen, how would you examine this tiny object? The answer is that you would imitate a jeweller examining the inner workings of a fine watch. That is, you would get out a good magnifying glass and hold it close to the mini-Venus (or whatever it is that you are studying) to allow you to see the details. In fact, the purpose of the `eyepiece' is to allow us to see the details of the tiny ghostly image we have created from the light captured by the large objective lens of the telescope. (Incidentally, if you find that the image is insufficiently magnified, you can increase it by a simple exchange of eyepieces. But there is no point in magnifying the image without limit, since the details we can see get blurred out by the swirling turbulence in the Earth's atmosphere through which we are looking, and at some stage there is no further gain.) The net effect of the appropriate combination of lenses is just what Galileo needed. When he put his eye to his own simple telescope, he saw a magnified image which seemed to cover a very large part of the field of view. This enlarged image of Venus now covered many of the ``resolution elements'' in his eye, as I discussed above, allowing Galileo to see details never before visible to human beings. (By the way, one of the ways in which he persuaded the authorities of the usefulness of the telescope was to point out that you could use such a device to detect and recognize ships at sea long before they reached port. This is important commercially and for military purposes.) Incidentally, most simple astronomical telescopes of the kind I have just described will invert the image, as it did for Galileo. This is not important or even obvious when you glance at the stars and planets, but if you use such a telescope to watch people in the distance, or ships at sea, they will look upside-down to you (although, confusingly, the actual image is now right-side-up on your retina!). Telescopes and binoculars intended for terrestrial use are designed with extra lenses or mirrors to re-invert the image. In astronomy, we usually don't bother. Let us just recap the critical point. For what Galileo was doing, magnification was the key. He had to be able to see details like the phases of Venus to test the Copernican model directly. In day-to-day life, this is also important. Bird-watchers need to see details of plumage to identify avian species, and race-goers want to see what is happening when the horses are on the far side of the track. Consequently, when the average person thinks of a telescope, she tends to think of its ability to "bring objects closer" by magnifiying the images. Understandably, then, most people believe that professional astronomers build telescopes as large as possible to provide enormous magnification. In general, this is a mistaken belief. In certain specialized contexts, magnifying the image is undeniably still important - for instance, in informal 'backyard viewing' of planets and clusters of stars. But in general, research telescopes are built as large as possible simply so that they will collect lots of light and allow us to study very faint objects. That was not an issue for Galileo - Venus is plenty bright enough! But until the image was magnified, none of the critical details could be discerned.
Galileo's Principal Astronomical Discoveries: The First Four.When Galileo turned his telescope to the skies, he made six important discoveries. Four of these are only peripherally relevant to the question of proving the correctness of the Copernican model (but are nevertheless interesting in their own right). These four discoveries were as follows: 1 He discovered features on the moon. These included large dark areas, which he took to be seas, or maria ("mare", pronounced "mah-ray", is the Latin for "sea", as in the word "marine"; maria is simply the plural form). He also recognized, from the straggly nature of the terminator (the line which separates the lit-up part of the moon from the dark region), that the surface of the moon was rugged, even mountainous. (See the photograph on page 74 of the text.) He was even able to deduce the heights of some of the mountains on the moon by noting that bright spots of light near the tip of the half-full moon were probably sunlit mountain peaks just reaching up high enough to be illuminated, and concluded that they were comparable in size to the mountains of Europe. 2 He discovered sunspots on the sun, and from their motions deduced that the sun rotates on its own axis about once every 25 days or so. 3 He discovered that Saturn was not round, but rather bulged out on two sides into extensions, or `ansae.' (Imagine the shadow of the head of a person with very big ears.) His telescope was of such poor quality, however, that he could not actually tell that the ansae were rings around the planet. (See the photographs on page 359.) 4 He looked at the Milky Way, which to the eye looks like a band of diffuse white light in the sky, and discovered that he could resolve it into myriads of stars. (See the photograph on page 13.) It is interesting to reflect that you could now make all these observations yourself, plus the two more critical findings I will describe a bit later, with nothing more than a pair of binoculars or a small telescope. What is important, of course, is the set of implications that Galileo drew from the various observations, implications which quite literally overthrew the then-current notions of our place in the universe.
The Significance of These Four Observations.Galileo's discovery of features on the moon was a philosophically important one because it laid to rest the notion that all heavenly bodies had to be `perfect' -- by which was meant featureless, perfectly smooth and spherical, of ideal crystalline regularity. In modern thinking, of course, there is nothing wrong or imperfect about having mountains, but the religious thinking of the day assumed that the moon was rather like a giant jewel in the sky, as befits its heavenly location and by contrast to Earth, the realm of disease, evil, and human frailty. The discovery of sunspots carried the same sort of implication: even the dazzling sun was not free of flaws. The fact that it rotated was also significant, since it demonstrated that a large body could spin on its own axis without breaking apart, an argument that had been used to attack the Copernican notion of a rotating Earth. Of course, this did not prove that the Earth rotated, but it demonstrated that it could. [By the way, it has sometimes been suggested that Galileo's observing of sunspots led to his blindness late in his life. In fact, the available records seem to suggest that this was not the cause - the symptoms reported in his accumulated papers and contemporary accounts suggest that his vision was failing for other reasons, as is not uncommon in older people, and in any event the telescope which he used in his solar observations was very small and inefficient, and probably did not do any significant damage. Still, I would counsel you never to look directly at the sun with binoculars or any other aid - it could prove very dangerous!] The discovery of the ansae of Saturn has no particular significance for the Ptolemy-Copernicus argument, but there is an interesting sidelight to it, one which tells us something about Saturn's rings. Some years after his first observations, Galileo looked again at Saturn and saw no ansae! The reason was that the Earth and Saturn orbit in slightly different planes, and from time to time we find ourselves looking at the rings exactly edge-on. They are so thin that they then seem to disappear completely, just as a long-playing record can scarcely be seen if looked at exactly edge-on from some distance away. Galileo was very concerned about this, though, because it caused him to doubt his own skills as an observer and interpreter. (Remember that in those days there was no photography, no way of recording an image except by sketching it.) The resolution of the Milky Way into stars was significant in that it vastly expanded the number of stars known to be in the heavens. In the year 1600 Giordano Bruno was burned at the stake by the Catholic church for (among other things) arguing that there might be a multiplicity of other worlds. The finding of thousands or millions of stars made our position seem somewhat less special and central, and challenged the religious orthodoxy.
Two Critical Astronomical Discoveries.As noted, two observations made by Galileo had a more direct impact on the question of the correctness of the Copernican model. They were the following: He looked at Jupiter, and found that it had four bright star-like companions, objects which he indeed first thought to be background stars. Galileo knew, however, that the planets move across the field of stars, and reasoned that Jupiter should steadily leave the bright objects behind. Instead, as the days passed, he saw that they moved along with Jupiter. However, they did not always stay in the same positions: one night, he might see a pair of them to the left of Jupiter and another pair to the right; a few days later he might see one to the left, and three to the right; and occasionally one or the other of them might not be visible at all. He deduced, correctly, that these obects were orbiting Jupiter. They are moons, which we now call the Galilean satellites. In fact, the Galilean satellites are comparable in size to our own moon. (Moreover, they all move in the same plane: that is, the moons around Jupiter are like a smaller version of the solar system, where we see the planets orbiting the sun in a flattened plane. The plane in which the Galilean satellites move is also closely aligned to that of the Solar System itself. Eventually we will make sense of all this!) In the lecture, I showed Galileo's own sketches of the changing positions and visibility of the moons. He deduced, correctly, that the occasional disappearances were attributable to the fact that they sometimes move behind Jupiter from our point of view, or orbit through its shadow so that they are not illuminated, or are in front of Jupiter and don't show up against the bright face of the planet. Galileo also studied Venus, and was able to tell that it went through phases all the way from a thin crescent to being nearly fully lit up, just as shown diagramatically on page 75 of the text. Moreover, the planet changed considerably in size as it did so: it looked smaller when it was fully lit up, but bigger 'from top to bottom' when it was a crescent. These effects are detectable over the span of just a few months as Venus rounds the far side of the sun (looking small but fully lit up) and then approaches us in its orbit (getting larger in apparent size but changing steadily to a thin crescent in form). In fact, at this writing, in mid-October 2004, Venus is particularly well placed for observing, prominent in the Eastern sky in the early morning hours.
The Significance of Galileo's Observations of Jupiter and Venus.The discovery of the moons of Jupiter was a strong (but not completely compelling) argument in favour of the Copernican model because it showed that there could be more than one "centre of revolution" in the solar system. Whether you believed in the Ptolemaic or the Copernican model, we all agree that the moon orbits around the Earth; to many people, this seemed to suggest that everything else must do so as well, since it seemed `logical' that there should be only one such central location -- clearly the Earth. Now, however, Jupiter was demonstrably providing an exception to this rule. There was more to it than that, however. The argument had been made that the Earth could not be orbiting the sun because the moon would `fall behind' and get lost! It was thought that the moon would simply not be able to keep up with us. Of course, everyone agreed that Jupiter was in motion, whether it orbited the Sun or the Earth, so now we had a convincing demonstration that its moons could keep up with it. While this does not prove the Copernican model correct, it does allow one to reject one of the apparently strong objections to it. The really critical observation, however, was that of the phases of Venus. The behaviour demonstrated conclusively that Venus orbits the Sun, especially when one looks not just at the phases but also at the very dramatic changes in the apparent size of Venus. In short Ptolemy was wrong, and Copernicus was right!
The End of the Galileo Story.Galileo's observations were clearcut in their support of the Copernican model of the Solar System, but were thought dangerously heretical by the religious authority of his day. The textbook describes how he published two books, about 20 years apart, which challenged the religious orthodoxy. Not described in there is his relationship with various archbishops and popes, friendships that first helped to protect him but of which he was eventually judged to have taken inappropriate advantage. For more information, see Koestler's `The Sleepwalkers ' or one of the scholarly works on Galileo by Stillman Drake, an historian of science at the University of Toronto. Galileo's second book, the Dialogue, is the one that got him into the most serious trouble. It featured discussions among three fictional people: an intelligent moderator; a credulous defender of the religious view (who was, rather insultingly, named Simplicio); and a persuasive spokesman presenting the evidence for Galileo's model. On the basis of this publication, Galileo was tried for heresy and found guilty. His sentence, however, was relatively light: he was confined to house arrest for the rest of his life. As he was already quite elderly and nearly blind, the hardship was minimal compared to the penalties often imposed in those days (but perhaps still very onerous, since Galileo was denied visitors and many ordinary freedoms). There is an unproven (and unprovable!) story that as he was withdrawing from the trial at which he was forced to recant his views, he muttered under his breath ``..and yet it still moves'' (i.e. he was persisting in his claim that the Earth does move around the sun, despite his disavowal of this tenet). As noted in the text, by the way, the Catholic Church `retried' Galileo posthumously in the 1990s as a gesture meant to eliminate any perceived residual hostility between science and religion.
Where Are We Now? The Need for Some Real Physics.Thanks to Galileo, we now have all the evidence we need for the correctness of the Copernican model: we know for certain that the Earth is not the centre of all motions. Thanks to Kepler's laws, we know the shapes and relative sizes of the orbits of the planets around the sun, plus how long it takes the planets to trace out these paths. We do not yet know the correct size of the Solar System - we have only a `scale model' of it - but we know exactly how it behaves. Why, then, do we feel dissatisfied? The problem is that our understanding is purely phenomenological. That is, we know how the solar system behaves, but not why it does so. The sought-after explanation came from the remarkable mind of Isaac Newton. In a very real sense, it was he who brought physics -- or classical physics, to be more precise, as opposed to later developments in quantum and atomic (modern) physics -- to its first maturity. This remarkable scientist will be the subject of a somewhat later section of the course. First, though, inspired by Galileo's first use of an astronomical telescope, we will turn our attention to light -- what it is, and what we can learn from it. 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.)