| The Science of Astronomy:
Why Should We Be Interested in Astronomy At All?
Consider the words of Socrates, in conversation with Glaucon, as reported by Plato in The Republic, around 400 BC:
"Socrates: Shall we set down astronomy among the subjects of study?
Glaucon: I think so, to know something about the seasons, the months, and the years is of use for military purposes, as well as for agriculture and for navigation.
Socrates: It amuses me to see how afraid you are, lest the common herd of people should accuse you of recommending useless studies.
Socrates' point is a good one: there is no real need to justify our desire to learn about the universe by appealing to various practical applications, no matter how valid they may be. Being curious about the universe is justification enough! I recognize, however, that many of you probably think of astronomy as being devoid of any obvious practical use, but in fact (as Glaucon said) there are quite sensible reasons for needing or wanting to know some fundamental astronomy. In class, I described some of the motivation, past and present, for studying this science. Broadly speaking, I divided these aspects into ancient and modern, and made the following points:
Judging the seasons: In ancient times, and even in prehistory (i.e. before people kept written records at all), astronomical knowledge would have been important for the prediction of the changing seasons. This may surprise you, given that it is so easy to judge when fall is on the way in Canada: the days get noticeably shorter, the weather gets considerably cooler, and so on. But early civilizations sprang up in more equatorial regions, such as the Tigris and Euphrates valleys in Mesapotamia, and in these latitudes there are not such pronounced seasonal differences. In fact, the most conspicuous variation (other than the daily rising and setting of the sun) would have been the obvious changes in the phases of the moon as it goes from new to full and back to new again every month. This explains why many early calendars were based on the lunar cycle rather than a yearly one. Still, it would be very important to know when yet another full year had passed. For instance, in the Nile valley one would like to have some forewarning of the coming flooding of the river, so that one could plan irrigation, planting, and so forth. Obviously one could simply `keep count', like a prisoner in a jail cell scratching off the days on the wall, and recognize that after 365 days or so another year has finished. But a look at the sky saves you this trouble: the constellations themselves are a clear sign of where we are in the yearly cycle.
Why is this so? The answer, of course, comes from the fact that we are in orbit around the sun. Look at Figure 2.14, on page 35 of your text to see how this works. In June, we cannot see the constellation Gemini, since the sun lies between us and it. But in December we have moved around to the other side of the sun, and we see Gemini in the night sky (and also Orion, which is in nearly the same direction but which is not shown in the figure). This is why Orion is, for Canadians, a winter constellation, perhaps the best-known one of all. So you don't really need to notice our snowy surroundings to remind us that we are again in the dead of winter -- just look at the night sky!
The importance of the moon: Mention of the conspicuous changes in the appearance of the moon (its phases ) should remind you of another excellent reason for the ancients to be interested in astronomical phenomena. Knowing when the moon will be full, for instance, allows one to judge whether it is feasible to go out hunting or to harvest grain late into the evening. The beautiful full moon of late September is still called the "Harvest Moon" for this reason, and (I imagine) benefits farmers just as it always did. The October full moon is known as the "Hunters' Moon."
Using the stars for navigation: Many ancient civilizations encouraged enthusiastic exploration. You may know, for instance, that Phoenician sailors (from present-day Lebanon) reached Scotland and Scandinavia in sailboats. It is possible, of course, to make such voyages while sticking closely to the coastlines, so that one never gets lost; but a bolder approach is to strike out into the open sea, relying on the stars overhead to keep one oriented. Imagine what would happen if there were no stars, so that the sky was a uniform inky blackness at night. If you were out in the open sea, how would you know which way to travel? Nowadays, we can use radio beacons, or inertial navigation systems which contain gyroscopes, or even old-fashioned magnetic compasses - although these are not very reliable, especially in the far north. But for the ancients, the stars provided a brilliant and conspicuous reference frame.
The best-known application of this is the use of the North Star as a signpost. Since the Earth spins once a day, the whole pattern of stars moves across the sky at night, just as the sun does during the day. By chance, however, the North Star lies almost directly above the Earth's North Pole, so its motion is minimal and it is, to a very good approximation, always in the same place in the sky. (See Figures 2.12 and 2.13 on pp 34-35 of your text (Figs 2.13 and 2.14, pp 47-48 of the second edition.)
To understand this, visualise yourself standing at the North Pole itself, as if poised on the top of a very large beach ball which is slowly turning sideways (like a merry-go-round). Any star directly above your head will stay there no matter how far the ball turns. You just have to look straight up to see it! Stars which lie in other directions will appear to move sideways, parallel to your horizon - sometimes they will be in front of you, sometimes behind you, and so on, depending on the time of day. People at other latitudes (i.e. not right on top of the ball) will not see the North Star directly overhead, of course, but a bit of thought will reveal that they can always see it at the same location in the nighttime sky: to find it, they merely look North. Think, for instance, of people who live near the equator: for them, the North Star is always low on the northern horizon, and can be seen at any hour of the night. (The figures on pages 99-101 of your text show the effects which I have been describing. You should also explore the simulations and exercises which are available on the CD which accompanied your textbook, to develop a clear understanding.)
If you ever get lost in the woods, therefore, and need to walk out to civilization, you need merely find the North Star to figure out your directions. Unfortunately this is not very useful for people who live in the southern hemisphere, since there is no single conspicuous star directly above the South Pole of the Earth. But if you learned to recognize the southern constellations, you would be able to recognize the patch of sky which lies directly over the South Pole - the place where a bright star would be located if we lived in a universe designed for our convenence! (See Figure 2.13 on page 35.)
For timekeeping: just as your modern watch is set to record the passage of one full day in accordance with the regular reappearance of the sun, so too the stars at night, wheeling overhead, mark off the passage of the hours. It is possible, for instance, to develop the ability to tell the time by the stars, using the `handle' of the Big Dipper as the `hand' of a giant clock in the sky. (Look again at Figure 2.13 on page 35.) It is interesting to note, by the way, that the first clocks were built to run `clockwise' because that is the direction in which the shadow on a sundial moves in the Northern hemisphere as the sun crosses the sky during the day.
The religious significance: for reasons which we will explore a little later, most of which will be obvious to you, the heavens commonly had religious associations in many civilizations.
In Modern Times:
For navigation: To know where one is on the Earth, one usually relies on maps which are carefully drawn to meticulous scale, often through the use of images taken by satellites. Fundamentally, all such map-making is with reference to the stars. We know, for instance, that Vancouver is west of Kingston on the basis of the fact that when the sun (or the moon, or any star) is overhead in Kingston it is still seen low in the Eastern sky from Vancouver, and will not reach the zenith (the overhead point) there until several hours later, thanks to the turning of the Earth. Of course, it would be possible to make maps completely without reference to external objects like the stars. (If we were permanently enshrouded in a deep fog, we could still pace out the geographical features on our planet's surface and construct a map!) But historically and in present practice astronomy has a fundamental importance for navigation and positional work. Perhaps you know that there exists a network of artificial satellites, the so-called Global Positioning Satellites, or GPS, which emit constant radio signals. A hand-held detector allows you to figure out exactly where on the globe you are -- so in a sense we have created our own network of 'stars' for use as precise navigational aids.
For timekeeping: For centuries, all our timekeeping has been predicated on the fact that the sky provides a great natural clock for us: we see the sun go around us once a day (since we spin) and go across the field of background stars once a year (since we orbit around it and see it in front of different stars at different times). There are now other ways of keeping time, using atomic clocks for instance; but astronomical timekeeping services are still important.
To have frontiers to explore: Human society, and the human psyche, has a certain fragility, and there are reasons for thinking that it may be important for our continued stability to have some sense of purpose, some unexplored frontier to investigate. Eventually we will have visited every corner of the Earth, including the deep oceans, and space will then remain, in the words of Star Trek, the 'Final Frontier.'
To appreciate our own insignificance: The history of the human race is unfortunately filled with examples of arrogance and arbitrary behaviour, often predicated on the presumption that we have a right to despoil the planet as we see fit by virtue of our pre-eminence on Earth. A consideration of our insignificance on the scale of the cosmos itself might be salutary from time to time.
To appreciate our planet's fragility: The Earth has a fragile ecosystem, and most of us are well aware of the dangers of producing uncontrolled amounts of toxic waste. But it is also true that there are dangers from the reaches of space, two of which are or have lately been on dramatic display.
The first is the danger of global warming, the steady climb in the Earth's atmospheric temperature because of our production of exhaust gases and our depletion of forested areas. The planet Venus provides a clear warning: the greenhouse effect there has made that planet utterly uninhabitable, with a surface hot enough to melt lead.
The second threat comes from the fact that we are, in a sense, in a cosmic shooting gallery, in a solar system filled with small chunks of rock and ice (asteroids and comets) flying about in all directions. Occasionally, these chunks can hit the Earth, and indeed such an impact is thought to have led to the extinction of the dinosaurs 65 million years ago. This danger was reinforced some years ago when Comet Shoemaker-Levy (found by a team which included David Levy, a Queen's alumnus) ran into Jupiter, with spectacular consequences.
To search for nearly inexhaustible supplies of power and resources: The Earth has limited resources, and if the human population is to continue to grow (which we might not all think is a good idea!) it will need new sources. There is no reason, for instance, why we might not go out to one of the millions of asteroids to find fresh supplies of easily-extracted metal ore for manufacturing purposes. Similarly, it may be possible to collect from space the energy produced by the sun and stars in a more efficient manner than at present from the ground. We may even, through a study of astronomy, learn to mimic on Earth what only the stars can do so far: contain a controlled nuclear fusion reactor yielding a long-term, reliable source of energy.
To search for habitable external worlds: A growing population also needs more room, and it may be necessary at some stage to provide other habitable locations for the human race. Even if you think that unconstrained growth is unwise, there may be good sociological reasons (allied to the point I made above) for providing the prospect of colonization and expansion to other worlds. Indeed, if some global catastrophe should befall the Earth, this might prove the salvation of the human species.
To search for intelligent extraterrestrial species: The question of our uniqueness in the cosmos is a very deep one, but, as I noted in the first lecture, we now live at the very special time at which it may be possible to make a first contact with ETs - if they exist! If we were to make contact, the consequences would surely be profound: such a discovery would have a huge impact on our society and psychology. We might hope to learn a great deal from such species and, perhaps, to learn how really insignificant are the differences between ourselves, differences to which people pay far too much attention.
On the chance that some really important technical discovery may be made: There is an unfortunate tendency for modern governments and funding agencies to want to see evidence of immediate payoff in return for supporting research. (Does your research show us how to build better toasters? Will we be able to compete better with the Japanese in the marketplace?) But history has shown that unfettered fundamental research can lead in unexpected but very productive and important directions. A century ago, for instance, basic research on the nature of the electron was being carried out at Cambridge University, in England, with no thought of immediate marketability. Yet that provided the fundamental understanding which has led us to television, modern electronics, computers, and so on. In astronomy, we study the physics of matter in extreme conditions: in intensely strong gravitational fields, the vacuum of space, weightless conditions, or the unimaginably high densities in neutron stars or near black holes. Who can
predict what important understanding might result, and where it might lead?
Just for the love of knowledge! `In the beginning was curiosity,' as the science writer Isaac Asimov put it. We should never feel that we must justify our sense of wonder and curiosity about the world and cosmos in which we live. This is the best reason of all for doing astronomy!
Astronomy as a Science.Astronomy is indeed a science, and moreover it is often said that it is the oldest of all sciences. In a sense this is true, since people must have been aware of the sun, moon, and stars from time immemorial, and speculated about them; but I suppose one could say with equal justice that Physics is the oldest science on the grounds that people have been informally carrying out experiments for an equally long time - experiments in which, for instance, we determine through trial and error that it is harder to throw a huge boulder than a small stone at a woolly mammoth, but that the heavier stone, once thrown, has a greater impact. So I am not particularly persuaded by or interested in claims about which is the oldest science. In any event, a more important question is the issue of how science itself works. What makes a particular subject scientific? There are, of course, philosophers of science who can provide very profound discussions of such matters; for my purposes, it will suffice to say that any science should ideally: present theories which are testable by experiment encourage and allow rational tests of theories rather than emotional adherence to them regardless of the evidence resist the urge to trust in some supreme scientific authority. (Even Einstein can get it wrong!) The critical consideration is what the experiments and tests show. seek "cause and effect" explanations: what makes things happen the way they do? be as quantitative and mathematical as possible have the power to predict consequences This particular course, Physics 015, fails to live up to this ideal in the very important respect that I choose not to treat the subject mathematically, for the reasons described in the first lecture, although the discipline itself is actually intensely mathematical. But astronomy as a science is itself unlike many other sciences in at least three important respects: 1 We cannot do experiments, except in certain limited respects such as the study of lunar rocks and meteors. We simply cannot tinker with the specimens we are observing - the stars and galaxies. 2 The very nature of the universe itself is a central part of the subject, but there is only one universe. We can only hypothesise about what "might have been" if the laws of nature were different in some other imaginable universe; we cannot test these ideas. 3 We have to extrapolate the laws of physics to scales where they may no longer apply. The third point is an important one, and needs some elaboration. Like many people, you may have taken this remark to mean that astronomers have a particular problem in that they have to deal with extremely large numbers, but that is not an issue at all, as we will now explain.
The Unimportance of Large Numbers.The size of the numbers astronomers must handle is not the problem. Handling big numbers is technically very easy - there are simple mathematical tools for doing so, such as the `powers-of-ten' notation explained in Appendix C, pages A-4 to A-6 of your text, and astronomers are no worse off in that respect than you are in, say, working out your bank balance. The fact that the numbers are sometimes much bigger does not make the task any harder. My point is quite different, and an analogy may help you to understand the distinction. Imagine a social science which successfully explains the behavioural patterns which are observed in a nation of one million people. Would the same patterns be seen if the nation were very much more populous - say, a hundred billion people? Or would some new patterns arise? It could be, for instance, that restricting people to a small area of land, closely surrounded by other people in every direction as far as the eye can see, would lead the average person to a claustrophobically-induced paranoia and irrational behaviour of an utterly unpredictable sort. As a social scientist, you might be unaware of this because you had never seen such overpopulation before; but your simple laws of rational behaviour simply could not be scaled up to the new large numbers, in this simplistic example. This is the problem we face in astronomy. We can hang a couple of massive lead weights on thin wires near each other in a laboratory, and see that they don't hang quite straight down. They attract each other by gravity and are slightly drawn together, as is shown in the attached figure. If we hang the weights rather far apart, the effects are small; if they are placed closely side-by-side, the effects are larger (but still rather small and difficult to measure precisely). It is through experiments of this sort that physicists determine the `strength of gravity' and find out that that the force gets weaker, in a predictable way, the farther apart the lead weights are placed. We then realise, as Newton did, that the Earth's gravitational influence determines the motion of the moon (which is nearly 400,000 km away), and moreover that the sun has a similar influence on the planets surrounding it - a larger influence because of its great mass, but a much reduced influence because of the enormous separations of the sun and planets. By the way, the genius of Newton was that he recognized this very early on. The experiment which I have described, using the lead balls to measure the strength of gravity, came considerably later, in quantification of Newton's insight. We now boldly assume that the gravitational influence of the sun reaches right out into the depths of space, that it pulls on other stars (and they pull on the sun) to an extent which our `Law of Gravity' allow us to quantify. But how do we know that the law of gravity works on such big scales? Isn't it possible that some new law of physics should be used? Maybe gravity has some sort of limit beyond which it cannot reach, regardless of how massive the object is that you are considering. As it happens, we aren't working completely on blind faith: there are `consistency checks' which we can carry out to provide some support for our assumption that the law of gravity can safely be extrapolated to the very large distances we encounter in astronomy. For instance, we can watch two stars in a binary system orbit around each other in a mutual gravitational grip, and deduce how massive they must be to behave in this fashion. Encouragingly, we discover that they are about the same mass as the sun itself, which reassures us that gravity is the same 'out there' as here and that it works just as predicted on scales much larger than we can test locally. But there is no absolute proof, and we should always be aware of the underlying assumption. We do not merely extrapolate over great distances. We also have to assume, among other things: that the laws of physics are the same elsewhere in the universe as they are here; that the laws of physics are the same now as they were in the distant past, and as they will be in the remote future; and that the laws of physics are the same, or at least predictable, in extreme conditions (such as in the very dense matter we find in neutron stars, or at the high temperatures we find inside stars or in the early stages of the universe). Please remember, then, the distinction I have made between big numbers (which are not a problem) and big scales (i.e. applying laws to scales on which they have not ever been tested). With respect to the former, there is absolutely no need to feel intimidated, as many people are, by the thought of `trillions of miles' or `billions of stars.' There are, for instance, many more molecules of air in the classroom than there are stars and galaxies observable through the great telescopes of the world. Nor do we think of our friends as so many quadrillions of atoms: we see them as individuals, with unique characteristics. Likewise, astronomers consider the billions of stars in the Milky Way galaxy as making up a single identifiable stellar system. It is, of course, trillions of miles across, but we can introduce new units of distance (like light years) to make the numbers more accessible! This is entirely analogous to the fact that you express the distance to Toronto in kilometers rather than millimeters. Pick the scale to suit the application!
Getting Used to Large Numbers.In developing this theme in class, I presented some everyday examples where large numbers are encountered and easily handled. There are some very interesting observations which come out of these considerations: Death rates: The present population of the Earth is about six billion people (6,000,000,000). Using powers-of-ten notation, we can write this compactly as 6 times 10-to-the-ninth power, which is a 6 followed by 9 zeros. (In these notes, I will use the notation 6 x 10**9 to express such numbers.) Now stop to think that essentially all of these people will have died by the time another century passes. This is not quite true, of course: there are a few infants who were born just a few days ago who will live to be more than one hundred years old. But by and large the statement is a reasonable one. Exactly when will these people die? Some are dying right now, in hospitals here and there, or in accidents; others will live another ten years; yet others will survive another twenty; and so on. But for the sake of simplicity let us assume that there is some uniform average rate at which people are dying, and that at the end of the 100-year period the last few will just be expiring. This means that of the 6 billion people on Earth right now, all will be gone after exactly a century of uniform death rates. Now, how many seconds are there in 100 years? Each year contains 365-1/4 days, each day contains 24 hours, each hour contains 60 minutes, and each minute contains 60 seconds; thus one century has (100) x (365.25) x (24) x (60) x (60) = about 3.1 billion seconds. In other words, if the 6 x 10**9 people now alive die at a uniform rate during the next 3.1 x 10**9 seconds, the average death rate will be about 2 per second. (The actual death rate will be even larger since I have not taken into account the fact that there will be more births in the coming century, and some of those people will die prematurely, adding to the total.) This is a sobering thought! Try snapping your fingers that quickly, and imagine keeping it up day and night, non-stop. That is approximately the present rate of human deaths on Earth. Of course, the rate of births is greater still, since the total human population is growing. As a parent, I find this astounding! The slow pre-natal development of one's own child, the building up of expectations, the thinking about baby names and the preparation of the house, and the long focussed labour all seem so elaborately drawn out - yet this is being repeated, a few times a second, all around the globe. A big number indeed! Inspiration: In the lecture, I invited you to take a deep breath, and then to consider that it is a statistical certainty that the lungful of air you inhaled contained some of the very atoms which had been breathed in by Julius Caesar, William Shakespeare, Florence Nightingale, Jimi Hendrix, and countless others. The reason is that every lungful breathed by those people contained many molecules which passed in and then right back out. For instance, there was inert argon gas and a lot of nitrogen which did this. (Of course, many of the oxygen molecules didn't get back out of the lungs of those people, since they were absorbed into the bloodstream for metabolic purposes. For simplicity, I'll consider only the metabolically unimportant gases in this discussion.) The unused atoms, once breathed back out, got mixed up in the atmosphere of the Earth by winds, air currents, and so on, until eventually - and actually suprisingly quickly! - they were fairly uniformly distributed. Although only a tiny fraction of the total content of the Earth's atmosphere ever passed into and out of the lungs of William Shakespeare, this still means that every lungful of air subsequently breathed in by anyone else, consisting of many trillions of atoms, contains some small number which were once in that special location. If you find this hard to believe, consider the analogous situation of pricking your finger and letting a single drop of blood fall into a swimming pool. Eventually the water in the pool becomes thoroughly mixed up, and the molecules in your blood are distributed more or less uniformly throughout. A teaspoonful of pool water will now certainly contain some of your molecules of blood, simply because there were so many molecules in the original drop! In the next few paragraphs, I am going to take the time to justify this remark, but let's start by considering a simple counter-example. When I was a young boy, it was not uncommon at birthday parties for the mother of the birthday boy or girl to bake a cake into which a dime had been put, usually wrapped in a bit of wax paper. One lucky kid would get the piece of cake with the dime in it - I never did! - and, of course, you could buy a whole chocolate bar or a comic book with a dime in those days. (In retrospect, it is easy to see that this was a rather dangerous party trick. A child could easily choke on a dime, although I never heard of that happening.) But it is interesting to ask just how many dimes you would need to mix into the batter to be sure that every kid stood an excellent statistical chance of getting at least one dime in his piece of cake. The 'blood in the pool' argument is just like this, except that it is analogous to mixing trillions of tiny dimes into a rather large cake, and then cutting off and eating a small piece of it. So let us now take the time to justify the remark I made earlier, partly because it will give you a sense of just how straightforward it can be to handle large numbers. (Please note, however, that I am definitely not asking you to commit the following argument to memory, or the numerical details; nor will I expect you to be able to reproduce it. If you like, you can safely `bleep over' the next few paragraphs.) The argument is most easily followed if it is broken down into a series of simple steps: First, consider the poolful of water: 1 what is the total mass (weight) of water in the pool? 2 what is the mass of a molecule of water? 3 how many molecules of water must there be in the pool in order that they can make up the total mass of water present? Next, think along parallel lines for the drop of blood: 1 what is the mass of the droplet of blood? 2 what is the mass of a typical molecule in the blood droplet? 3 how many molecules are there in the blood droplet? Finally, we visualise mixing the blood thoroughly into the water in the pool, and extracting a teaspoonful: 1 what are the relative numbers of blood molecules and water molecules? 2 how many molecules of water will you pick up in a teaspoon? 3 how many blood molecules will there be in this teaspoonful? Let us visualise an Olympic-sized pool, 50 meters long, 20 meters wide, and 2 meters deep. Multiplying these together, we discover that such a pool contains (50) x (20) x (2) = 2000 cubic meters of water. Since one cubic meter of water has a mass of one thousand kilograms (one metric tonne), the pool contains two million kilograms of water. A water molecule consists of one oxygen atom and two hydrogens, and thus has a total mass of about 30 x 10 ** (-27) kilograms. (You can find the necessary numbers in any basic physics or chemistry text. Remember that oxygen is 16 times as massive as hydrogen.) Now, how many of these tiny entities must the pool contain to make up a total mass of two million kilograms? The answer is that there must be about 60 x 10**30 of them -- sixty million trillion trillion molecules. (By the way, this number is very much greater than the number of stars in all the known galaxies.) Similar considerations for the drop of blood follow straightforwardly, so I can be brief. The tiny drop might measure 1 millimeter across, so that its total volume is about a billionth of a cubic meter. It is about as dense as water, as I think you know, so the droplet must have a mass of about one milligram (a thousandth of a gram). If it were made of water (which blood largely is) it would contain about thirty million trillion water molecules; but hemoglobin and the other molecular constituents of blood contain many atoms, so they are quite heavy and less numerous in total. Let us pessimistically assume, therefore, that the molecules in the blood are, on average, a million times (10**6 times) as heavy as water molecules, and correspondingly fewer in total number. This means that your drop of blood contains at least thirty trillion molecules. (The actual number will be much greater since the blood molecules are not really so heavy on average as we have assumed.) You can see where this is leading! After we mix the blood into the water, the pool will contain about 60 x 10**(30) molecules of water, with at least thirty trillion (30 x 10**12) molecules of blood distributed throughout. In other words, there is likely to be one molecule of blood in every randomly-chosen sample of two million trillion (2 x 10**18) water molecules. How much is a teaspoon? Those of you who cook may know that a standard teaspoon holds about 5 cubic centimeters of fluid. This volume of water will have a mass of 5 grams, and contain 1.7 x 10 ** 23 molecules. Mixed in with that will be about 10 ** 5 (one hundred thousand) blood molecules!! That was a longer mathematical digression than I had intended, but I hope that it demonstrates the flexibility with which one can handle big numbers. With luck, it also makes the point I wanted about the Earth's atmosphere, which follows a completely parallel exposition. So, the next time you need to compose an English essay, I encourage you to give a moment's thought to the appropriateness of the word "inspiration" before simply breathing in some of the very air enjoyed by Shakespeare himself! Ages: Speculate for a moment: do you think that you have yet lived for a total of a billion seconds? Many of you will (correctly) think that you have not, but the average student is well over half-way there, and I certainly have, because a billion seconds is just over thirty years. Since your heart beats at roughly one beat per second (this depends on the individual), this means that that particular organ is good for at least a couple of billion beats for most people. Ants: In sections to follow, I will be spending a bit of time discussing ants, for reasons to be explained. You may be interested to know that there are estimated to be about one quadrillion ants on the Earth - that is, ten-to-the-fifteenth power - and that they make up about 10-15% of the mass of all living animals on the planet. (I believe that the termite population, known as `white ants' to the South Africans, is included in this total.) Among other things, this large population implies that there are about a million ants for every human being on Earth. But other issues of size and scale are more interesting, as we will soon see. 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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(Wednesday, 21 April, 2021.)