Galileo s Physics. Relative Motion

Transcription

1 Theme 4 Part 1 Galileo In this unit, we'll meet Galileo, perhaps the first truly modern physical scientist, and learn of his principal contributions to our understanding of physics. We'll discuss the concepts of relative motion and inertia. We'll digress briefly to discuss the function and limitations of the human eye and learn why the telescope was so important for Galileo to make critical observations. We'll discuss four interesting astronomical discoveries that he made, but then a further two that were absolutely critical in supporting the correctness of the Copernican notion of a heliocentric solar system. Those discoveries were the orbiting moons of Jupiter and the full range of phases displayed by Venus. Galileo s Physics Galileo brought a new philosophy to physics: namely, that we should carry out experiments again and again to understand the true laws of nature, pure thought alone could not lead us to the correct interpretations. He studied dynamics (the relationships between forces and motions) and studied, for example, balls rolling on slopes and on flat planes. For the first time, he recognized the importance of friction, and tried to smooth the flat planes on which the balls were rolling to eliminate that effect. He recognized air resistance as well, and the effect it had on falling objects. It had long been believed that heavier objects would fall to the ground faster than light objects, but he demonstrated that not to be the case. There is a story, probably apocryphal, that he went to the Tower of Pisa and dropped from its summit a heavy metal ball and a lightweight cork ball demonstrating they both reached the ground at the same time. I've provided a link at the bottom that shows an equivalent experiment in which astronauts on the moon drop a geologist's hammer and a feather at the same time. As you can see, they reach the ground together: there's no air resistance on the Moon. Relative Motion Galileo introduced the very important concept of relative motion in what we now call the Galilean relativity principle. In other words, the behaviour of objects depends on your point of view. Look for example at the cartoon to the right, which shows a man on a ship dropping a heavy weight from the top of the mast. From his perspective, it drops straight down and lands at the foot of the mast, on the deck. From the point of view of a person on shore, however, it appears to follow a long curved path -- but nonetheless arrives on the deck at the foot of the mast. Is the weight falling straight down, or in a curved trajectory? Well, it depends. Are you the person on shore, or on board the ship? The motion is relative. So your frame of reference is what determines the apparent motion. The lesson of this in the astronomical context is that this means that, if we throw stones in the air and have them fall back down directly into our hands, that does not tell us that the Earth must be standing still. This was an ancient argument that had been used to say the Earth cannot be moving in an orbit around the sun. But Galileo's experiment showed that this was in fact not a valid argument.

2 (At the bottom of this page, I've provided a link to a very modern experiment of the same sort in which water-filled balloons are dropped from fast-moving cars. You might enjoy watching that.) Inertia Galileo also introduced the notion of inertia, the concept that an object in motion will tend to stay in that state of motion unless something acts to oppose it. This is demonstrated by the picture on the upper right. Secondly, that an object that's at rest, will tend to stay at rest, unless something acts to get it moving. His reasoning, by the way, was as shown in the cartoon on the left of this panel: balls rolling down a slope tend to pick up speed, balls rolling up a slope tend to lose speed, so he reasoned that a ball rolling across flat ground should just continue to move without slowing down or speeding up. This, of course, requires you to eliminate friction, something we mentioned before. Galileo got this wrong, however, in one important sense. He thought about the moon going around the Earth, and reasoned that it continued in its orbit around the Earth simply because of inertia. That was just a natural state of motion it would just continue to move in a circle. We'll see later, that that's not quite correct and Newton provided the full answer. The Human Eye We're going to leave Galileo for the moment to consider the human eye, the way it functions and some of its limitations. We'll return to Galileo when we talk about the use of the telescope and why that was so critical for his astronomical insights. As you know from everyday experience, light changes direction, or refracts, as it moves from one medium to another. This explains the apparently broken stem of the flower in the vase that we see on the left. The light moves through water, then through the glass, then into air, changing direction each time and distorting the image. We can use this, and nature can use this, to allow lenses to focus light, including the lens in your eye, which focuses incoming light to provide an image on the retina at the back of your eye. Here are the basic steps that explain our sense of vision. First of all, light enters the pupil of the eye where it's refracted and focussed, mainly by the lens of the eye, but also by other elements such as the cornea. This forms an image on the retina of the eye. As I'm sure you know, light carries energy, and the energy of the light landing on the retina has a chemical effect on the pigments in it or enzymes that are in the receptor cells in the retina. This causes an electrical signal to be sent along the optic nerve to the brain, and the brain does the rest. The Dynamic Range of the Eye Let's consider some important concepts that characterize our power of vision. The first of these is what a physicist might call dynamic range, the fact that we have vision under a huge variety of levels of illumination. Of course we see very easily in daytime, but we can also see at night under the moon's light, even though it's millions and

3 millions of times fainter in absolute illumination than during the day. One of the ways we achieve this is by having an expanding pupil as shown in the pictures here: in dim light, the pupil opens wide; in bright light, it shrinks down. But you can see from the comparison of these two pictures, that this could only explain a small fraction of the total accommodation of the eye to these different levels of illumination. Much more important is the replenishment of the pigments at the back of the eye and how sensitive the retina becomes as a result. This is in fact part of what we call becoming dark-adapted. When you go out at night, it takes time before you can get used to the low level of illumination. Accommodation by the Eye A second feature is what we call accommodation, the ability to focus our eyes on things in the foreground or the background. Hold your finger up in front of your face and focus your eyes on it, then look at the wall in the distance. Your eye automatically adjusts. This is done by muscles around the lens stretching and flattening it appropriately to focus different objects on the retina. We lose this ability as we age, which is why older people need reading glasses to look at nearby things such as print. The Persistence of Vision The third feature is persistence of vision which is best exemplified perhaps by a flip book of the sort shown on the left here, or by an actual movie strip, as shown on the right. (Indeed this is the very first movie ever made, "The Kiss.") If pictures that are very subtly different are shown to your eyes in quick succession, one sees this as a continuous unbroken sequence of events, and that is what allows us to watch movies and television in a continuous flow like real life. (At the bottom of the page, I ve provided you with a link to a very interesting television commercial that makes that point as it goes from a series of static images into what looks like smooth continuous motion.) Colour Vision Let's now turn to the very interesting question of colour vision. To discriminate colours, we need to have at least two different kinds of receptors with different enzymes having different sensitivities so that, for example, we can distinguish, say, red light coming in from blue light coming in to the eye. As it happens, our retinas contain cells called rods and cones, and in effect we have four different receptors --the rods on the one hand, and three different kinds of cones, similar in appearance but containing three different enzymes. A picture of the rods and cones is shown on the right, and on the bottom you see their arrangement on the retina of the eye. Light comes in here from the right, stimulates the rods and cones, and gives rise to signals that pass out through the nerves to the brain down the optic nerve. Let's consider the rods and cones separately. The rods are the most sensitive, but they respond merely to the presence or absence of light. With the rods, one sees merely shades of black or grey or white, levels of illumination. The cones are less sensitive than the rods, but they respond to colour. And as I said, there are three kinds, with

4 different enzymes that are broadly sensitive to red light, green light, and blue light. The remarks that I just made lead to one implication and one puzzle. The implication is this: when it's dark, there isn't enough light to stimulate the cones of the eye, so we don't see colour at all! -- everything look shades of black and white at night, as I'm sure you've experienced yourself. That means, for example, in the astronomical context, that stars in general look colorless: they're not bright enough to stimulate the receptors. You might have noticed, though, subtle redness of sufficiently bright stars, like Betelgeuse or Antares, or the planet Mars. The puzzle is that if our cones are sensitive to red, green, and blue, then why do some things look yellow or orange or purple or other colours? The answer is complex and we'll touch on it only briefly here. Imagine shining red and green light into your eye. You might think that the red light would stimulate only the red cones, and the green light only the green cones. But that's not the case. Those cones have a range of sensitivities. And the light of different colours can stimulate the various cones to different degrees. The net effect is that red and green together on the eye stimulate the cones in such a way that we perceive yellow. Green and blue stimulate the cones in such a way that we perceive teal: and red and blue produce magenta. All three in appropriate balance (red, green, and blue) give a sensation of white light. This is demonstrated very nicely in a clip that I provided a link to in the middle of the page. And in fact this is how old colour televisions work: electrons from the back of the television (through the electron gun ) are aimed at the screen to stimulate small spots of red, green, or blue illumination in appropriate balance. Together, these give rise to the full palate of colours that we want to create on the television screen. The Resolution of the Human Eye Those aspects of vision are all very interesting. But now we come to a critical issue that was important for Galileo and the study of the Solar System. That is, the resolution of detail. How much detail can your eye discern, and what determines that? Look at the picture on the left here. Do you know who this is? You probably do, but it's easier if you look at the picture on the right. That's the same person, but seen in finer detail and more easily recognizable. One of the ways of getting better resolution, therefore, is to have finer grain in the detector. Think of a digital camera, for example, which has an electronic detector at the back called a CCD. These cameras are sold on the basis of how many pixels (or picture elements) they contain. The camera I have at present has 12 megapixels (twelve million pixels) to paint the picture at the back. In your eye, there's actually 125 million rods and cones, which sounds like a very, very fine-grained detector. In fact they're clumped in groups, so there are not really quite as many as that. So if you want to be eagle-eyed and have very, very fine ability to pick out details, it helps to have a fine-grained detector at the back of the eye. But the size of the image also matters. If you have lumps

5 of light, photons, coming in that arrive at well-separated spots on the retina, landing on different pixels, then you can tell that they're coming from two separate objects. But two photons that arrive very closely side by side can't be distinguished: the details are unresolved. So the image has to be big enough to light up an area on the retina. So there's the fundamental, astronomical limit of the human eye. Something like Saturn is just a point of light at the back of your eye, seen as a dot: its image on the retina is too small. If you want to see the details of Saturn as shown here (the beautiful ring structure), you have to do one of two things. Either move closer to the target, so that it looks bigger. That means the image is going to be spread over a larger area on the retina. But since that's not possible in practice, you can use a telescope to magnify the image, produce a larger image at the back of your eye so some of the details can be resolved. Galileo s Use of the Telescope So here we are back to Galileo at last. He was the first to use the telescope for astronomical purposes, although he didn't in fact invent it, as is sometimes commonly thought. Here's a picture of a couple of his early telescopes from the Galileo Museum in Florence. Using the telescope, Galileo made four very interesting discoveries, but they weren't definitive about the nature of the Solar System. Let's consider them in turn. First we'll discuss the features on the Moon; secondly, sunspots and their motions; third, the apparent "extensions" of Saturn; and fourth, stars in the Milky Way. The Moon On the right, we see a modern photograph of the Moon at first quarter phase. On the left, we see one of Galileo's books with his own drawings of the Moon. (Remember in those days, there was no ability to take photographs. These sketches were all done by hand as he gazed through the telescope.) Galileo saw features that he interpreted in various ways, as we will see. Galileo interpreted the dark regions on the moon as being seas, like the Mediterranean. The Latin word for sea is Mare and the plural is Maria. We still use that terminology these days, although of course, we know that they are not seas at all. The moon is airless and has no running water on the surface. You can see, in the figure on the right, the Sea of Tranquility where the Apollo 11 astronauts landed, and the Sea of Serenity, and so on. In the picture at the lower left, we see what Galileo correctly interpreted to be mountains sticking up from the plain. Here they're illuminated from the Sun coming in from the right-hand side. And you can see the shadows of the mountains being cast. So Galileo realized that the Moon was like the Earth, with rocky surfaces and mountains and so on. This had an important psychological implication, and that is that the Moon was in some sense imperfect, not an absolutely perfect spherical body out there like a jewel in the heavens. Galileo was able to take this one step farther. Look at the picture on the left, which is a detail from the picture we saw on the previous

6 panel. The arrows indicate two lit-up points which are in fact the peaks of mountains that are still just getting the last rays of the setting Sun. The diagram on the right makes the point. At the top of the diagram, you see the Sun's rays coming in, skimming along the horizon, and just illuminating the peak of the mountain labelled with the letter M. At the bottom of that figure, you see some simple geometrical representation, and from that and the known size of the moon and its distance, Galileo was, was able to crudely estimate the heights of the mountains, which are comparable to those in Italy. So these are no different than what we see on the Earth. The Behaviour of Sunspots Galileo also studied the sunspots on the surface of the Sun, and discovered that they move. They appear to travel once around the Sun, approximately every 25 days or so. You can see this for yourself by following the link at the bottom of this page. This has an important implication. It means that the sun can clearly spin on its axis without flying to pieces. One can conclude therefore that the Earth can do the same thing. (You will remember that there was an early ancient argument that said the Earth cannot be spinning because it would fly to pieces. But if the Sun clearly can, then presumably, so can we.) The Appearance of Saturn Galileo also look at Saturn and discovered that it seemed to have some structure. A couple of his sketches are shown at the top of the page; and in the middle of the page, you see how these sketches are embedded in the text of one of his books. At the bottom of the page, we see a modern picture showing the very clear ring-like structure, but Galileo's telescope was not powerful enough to allow him to see this sort of detail, and he could only speculate about the nature of the structure he was observing. Interestingly, Saturn orbits around the Sun in a plane that is not the same as that of the Earth's orbit around the Sun. So we see the rings from different aspects at different times. Occasionally, they seem to vanish completely, as shown in the figure at the top here, taken by the Hubble Space Telescope. This implies that the rings are very thin. Galileo had the experience of noting the disappearance of the structure that he had once seen, and wondered if he could have faith in his own ability as an observer. (Remember again, he had no photographs. All he could rely on were his earlier drawings.) So this led to a crisis of confidence. The Resolution of the Milky Way Galileo's fourth discovery was that the Milky Way could be resolved into individual stars in large numbers. On the left, you see the Milky Way, approximately as it appears to the eye: a band of light across the sky. On the right, a modern photograph, showing that it breaks up into myriads of stars, almost uncountable numbers of stars. Of course, Galileo didn't see a picture as dramatic as this, but nonetheless, he realized that the Milky Way contained many, many, many individual stars. This has an important implication as well: it means that the Sun may be far from unique. There may be millions of stars out there

7 comparable to our own sun, and this has implications for the potential for life elsewhere, and so on. Galileo made two critical discoveries that supported the Copernican model of the Solar System. We'll consider them in turn. The first is that Jupiter has moons that orbit it, and secondly, that Venus displays a full range of phases from new through crescent to full and back again. The Moons of Jupiter Here's a page from one of Galileo's notebooks. He discovered one night that Jupiter appeared to have some dots of light near it, which he assumed were background stars. Jupiter, of course, moves across the starry background in its orbit, and he was surprised to discover that these dots of light seemed to keep up with it, but not always in the same orientation. They appeared to be moving with it but also in orbit around it. They are indeed moons of Jupiter, and he discovered that there were four bright moons. (Jupiter, in fact, has many more moons than that. But the four bright ones, now known as the Galilean satellites, are conspicuous.) The implication of this is that the moons can keep up with Jupiter even as it moves, and that implies that our Moon can keep up with us if we happen to be moving around the Sun. You'll remember that there was an early argument that the Earth could not be moving because the Moon would get left behind. This discovery of the behaviour of Jupiter clearly invalidates that counter argument. Here are some modern images of moons in the Solar System. On the top right, the four Galilean satellites of Jupiter: Io, Europa, Ganymede, and Callisto. On the bottom left, a montage of a variety of moons, including the Earth's moon on the upper left, with the Earth itself on the lower right for scale. You can see the four moons of Jupiter are comparable in size to our own Moon. The largest moon in the Solar System is Titan. It's a moon of Saturn and is shown in the middle of this figure. On the bottom right, finally, we see two of the moons of Jupiter projected against its face: on the left, the moon Io; on the right, the moon Europa. The Phases of Venus To understand the importance of Galileo's critical observations of Venus, let's think back to the Ptolemaic model, shown here in the diagram. In Ptolemy's system, Venus always lay between the Earth and the Sun, moving back and forth on an epicycle so that it was sometimes a little ahead of the Sun, sometimes a little behind. Because Venus is always between us and the Sun, we should never see the fully lit up face of Venus, just crescents of various sizes. On the other hand, if Copernicus is right, Venus should travel from our point of view around to the far side of the Sun, at which time we should see Venus looking first smaller, but secondly, fully lit up. This is a very different prediction from what Ptolemy's model suggested, and was amenable to discovery through telescopic observations. Of course, the behaviour of Venus has to be monitored for a considerable time to notice this behaviour. It's moving in its orbit around the Sun and we in ours. So it will take time for these effects

8 to accumulate and change. You can test this yourself, though very quickly, by using your Stellarium night-sky simulation software. Turn it on, find the planet Venus and zoom in on it to see what its appearance is now, and then speed up the passage of time to see how that will change as the days and weeks and months pass. I've captured this sort of behaviour on a video clip that's available through a link shown here in the middle of this panel, but you can see the final effect in the series of still photographs at the bottom, where we see that Venus goes from quite a small full phase, to quite a large, thin crescent. The implication is that Venus is indeed travelling around to the far side of the Sun and orbits the Sun. Copernicus was right. Just to finish, here's a picture of the full Venus. You see it's covered with cloud, and it's very difficult to discern the surface. This photograph was not taken from the Earth, by the way, but by a space probe. Galileo s Fate The story of Galileo has a sad ending, and is well known. He was charged by the Roman Catholic Church with heresy for expressing the view that the Earth was not the divine centre of the Solar System, found guilty, and sentenced to house arrest -- a fairly mild sentence, given that at that time people were sometimes executed for expressing heretical views. He spent the last years of his life under house arrest in Florence, but at a time when he was already quite elderly and losing his vision. Still, it must have been very uncomfortable for him to be so constrained. Here's a picture from Florence showing the Tuscany fields in the background and a wonderful quote from Galileo, who insisted, by the way, on having a great wine cellar. Galileo said, "Wine is light held together by moisture." Here's a final picture from the Galileo Museum in Florence showing Galileo's right index finger pointing heavenward, saved as a relic. Summary In this unit, we considered Galileo's important contributions to physics, and then considered the function and limitations of the human eye in explaining why Galileo needed the astronomical telescope to make the important discoveries that would confirm our understanding of the Copernican Solar System. We began by describing four astronomically interesting discoveries that he made, but then followed with two critically important discoveries that were essential to support the Copernican model: namely, the orbiting moons of Jupiter, and the full range of phases displayed by Venus.