The Seasons: Welcome Fall! Each year, the third week of September heralds the arrival of fall, and indeed my discussion of this interesting topic was presented on the very day of the start of that season in the Northern hemisphere. (In the Southern hemisphere, of course, people are moving into spring.) Why is this? What causes the seasons? It is a common misconception that we have summer because we are closest to the sun in June or July and feel the heat of the sun more intensely. It is certainly true that the Earth's orbit around the sun is not quite a perfect circle, but in fact we are closest to the Sun in early January, so this cannot be the cause of the seasons. In any event, if this were the cause, then the Southern and Northern hemispheres would experience summer at the same time, which they don't. (As one who lived in Australia for a few years, I can testify that the summer months there are December, January, and February.) The actual reason for the changing seasons is something else entirely. In the summer we see the sun high in the sky, and its rays strike us more directly and lead to efficient heating of the ground and water. In the winter, the sun is low in the Southern sky, and the sunlight, arriving at a grazing angle, is less effective, being spread over a larger area. A simple analogy is provided by a flashlight which can be held so that it shines directly at your feet or out in front of you, as the following figure demonstrates: Before considering this analogy in the context of the changing seasons, you should realise that the effects of the oblique arrival of sunlight are felt not only in the slow yearly changes, but every single day. When the sun is high overhead, near the middle of the day, the rays are more concentrated than when the sun is low in the sky, as happens as we approach sunset. Late in the day, therefore, the ground and the atmosphere of the Earth are less directly heated, so everything cools off as the sun descends. The morning hours are typically cool because the sun has not yet reached a high enough elevation to blaze down on us with full intensity. A common misunderstanding: Many people think that the obvious daily temperature variations occur because the sun is farther away from us at dawn and sunset than it is at noon. There is indeed some tiny element of truth to this, as you can see from the attached figure: the rotation of the Earth carries us back and forth a little, and at sunset we find ourselves, as individuals, about 6400 km farther from the sun than we are at mid-day. The figure is not drawn to scale, of course: the distance to the sun is actually more than ten thousand times the Earth's diameter, and the sun itself is a hundred times bigger in diameter than the Earth! In percentage terms, then, our back-and-forth motion is utterly negligible and can have nothing to do with the cooling. No, the daily cycle of heat and coolness is simply the direct consequence of the sun's rays arriving at changing angles, and sometimes being spread out over a wider area, in a manner which is entirely analogous to that of the flashlight shining onto the floor. Of course, changing weather patterns can modify this behaviour! It is certainly possible, for instance, to experience a day which is quite cool at noon but hot in the evening as a 'warm front' approaches. In general, however, the hottest part of the day is near noon, for the reasons I have explained. In investigating the causes of the seasons, however, there is a bit more to it than just this. It is actually hottest in July for two reasons, although both of these are a consequence of the greater altitude of the sun. First, the sun's rays are more concentrated on the surface of the Earth, which leads to greater localised heating effects. This is shown again in the following figure, which makes the obvious point that the heating is more intensely felt near the equator than near the poles. (Unlike the case of the flashlight, we are not tipping the source of the light so that it meets a flat floor at a different angle. Instead, we have sunlight impinging on a surface which is itself curved. At any given instant, the part of the Earth directly 'below' the sun is heated more strongly than the parts of the Earth which are curved away from that direction.) Secondly, because the sun climbs higher in the sky in the summer months, it is above the horizon for a longer total time in a given day (there are more hours of sunlight) so the heat builds up to a greater degree. There are correspondingly fewer hours of darkness in which the ground can cool off by radiating away the accumulated heat into the night sky. (Look at Figure S1.17 on page 102 of your text.) There are other factors which must be considered. For instance, in the summer there are typically fewer overcast days than in the winter (for complex meteorological reasons), and that actually makes the summer days a little hotter, since sunlight can reach the ground rather than being reflected out into space by clouds. Conversely, the extra cloud cover in the winter means that even less sunlight reaches us, and the climate is cooler than it might otherwise be. One last point: this notion of the directness with which the sun's rays impinge on us leads to a related consideration for those of us vain enough to want to get a good tan while spring skiing. To do so, you prop yourself up (perhaps by leaning against a pair of skis plunged into the snow) so that you are facing as directly as possible into the sunlight.

The Sun's Motion Differs from That of the Stars.

You may rightly object that I have not so far given you a real answer at all! I have told you that fall and winter arrive because the sun is seen lower in the sky during those months. But exactly why does the sun appear to change in elevation during the year? Before addressing that fundamental question, let's first remind ourselves that, unless you are in the very special location of the North or the South Pole, everything in the sky changes in elevation every single day! [The words elevation, height, and altitude can be used interchangeably in this context. They simply refer to how high above the horizon an object appears to be at a given moment.] Because of the rotation of the Earth, we see the sun rise in the East, climb into and cross the sky in a long lazy arc, and drop down to set again in the west. This behaviour is repeated by the moon, the visible planets, and all the stars at night. If you watch attentively, though, you will discover that the sun differs from the stars in one critical respect, and that is the key to our understanding of the seasons. If you pick any star, and watch it night after night, month after month, year after year, you will find that it follows the same path across the sky every time. This is not so for the sun: its path through the sky changes from one day to the next, from one month to the next, and from one season to the next. In your text, the figures on pages 33 and 99-101 show how stars behave, depending on where they are found in the sky; the figures on pages 102 and 103 show that, on a given day, the sun behaves like one such star, but as the year progresses it changes location, moving north or south of the equator. In our summer, it behaves like a northern star, and passes nearly overhead; in the winter, it mimics the behaviour of a more southern star. [The moon likewise drifts about, being sometimes farther north and sometimes farther south.] Why should the sun be thus distinguished? One obvious distinguishing feature of the sun is its fantastic brightness, of course, which is a result of the fact that we are so close to it, but mere proximity is not the reason for its wandering ways. The critical point is that we are on the move around it, and thus looking at it from changing positions in space. Let's explore that thought a little, but in a perhaps unfamiliar way.

The Orientation of the Earth: An Introduction to 'Limiting Cases'

I remember being told, when a schoolboy, that the Earth `tips back and forth' as it goes around the sun, so that we see the sun from different aspects. This conjurs up the image of the spinning Earth wobbling about in unstable fashion, which is not correct. In fact, the contrary is true: it is the very stability of the Earth's spin which causes the sun to change in its apparent position as the year progresses. The Earth rotates on an axis which is somewhat tipped relative to the Earth's orbital plane around the sun, but that axis maintains a nearly constant orientation in space as we go around the sun. (Look at the figure on page 36.) This directional stability explains why a person at the North Pole sees the Pole Star overhead every night of the year, as we noted earlier. As a fruitful way of understanding this, let me introduce a way of thinking about physical or astronomical phenomena which we will use again and again -- the notion of 'limiting cases.' In a (non-physics) self-analysis, for example, it might prove fruitful to speculate about how different you might have turned out in temperament and behaviour if you had been born exceedingly rich or dirt poor. Similarly, in the physics context, you can imagine considering a law which (say) describes the force one electron feels when it moves past another. To deepen your understanding, or perhaps merely to test whether or not the law seems reasonable, you could ask yourself what the law predicts in the two 'limiting cases': if the electrons get very close to one another; or if, conversely, they are really very far apart. "[Let's take a moment to consider a really silly example. Imagine that you are a free-thinker whose innovative 'Theory of Everything' has produced an equation which says that the force between two electons should obey a law of the following unconventional form: "Force = 2 x (separation in metres) x (age of your astro professor in years) x (your I.Q.)" Is this worth taking seriously? (Obviously not, but let's focus on the 'separation' term instead of the nonsense in the equation!) A non-physicist might think that you would need to test the law by putting two electrons exactly one metre apart, and measuring the force they feel; then repeating the experiment with the electrons two metres apart, and so on, to see if the results are consistent with predictions of the equation. But a physicist can see instantly that the 'law' can't possibly be correct, because it implies that two electrons an infinite distance apart will exert an infinitely large force on each other -- something which is contrary to the established behaviour of all known forces.] In like fashion, we can try to understand the importance of the tip of the Earth's rotation axis in two "limiting cases," as follows: If the Earth were spinning absolutely upright, so that its rotation axis were perpendicular to the plane in which we orbit the sun (as in the attached sketch), a person on the Equator would always see the sun rise in the east, pass directly overhead, and set in the west, regardless of where we were in our orbit around the Sun (i.e regardless of the time of year). For a person at the North or the South pole, the Sun would always appear to be low on the horizon, and to move steadily and uniformly along the horizon as the day passes. For people elsewhere on Earth, the sun would follow the same path through the daytime sky every single day, in monotonous regularity. There would be no seasons at all, except for the small temperature effect of sometimes being closer to the sun and sometimes farther away in our slightly non-circular orbit. If the Earth were tipped right over on its side, at 90 degrees, what would we experience? [You might find this is a little harder to visualise! You could try for yourselves what I did in the lectures: hold out an apple at arm's length, with the stem pointed towards you. Now pretend that your eyes are the sun, radiating light at the Earth/apple. Let the stem represent the North Pole of the Earth. Move the apple in a great circle around you, keeping the stem always pointed the same direction in space but with the apple spinning slowly to represent the passage of days. Now visualise yourself as a bug or some microscopic creature on the surface of the Earth/apple, and imagine how that small creature would see the sun behave, depending on its location on the apple's surface.] Now the situation is very different! At one stage of the year -- in June, in the diagram -- a person at the North Pole would see the sun nearly motionless overhead, an effect which would last for weeks. The North polar regions would get very hot indeed, with no respite from the direct light of the sun. Meanwhile, people at the Equator would see the sun hovering motionless on the Northern horizon, so the equatorial regions would be very cold, in a state of near-perpetual twilight. The entire Southern hemisphere - Rio de Janiero, Australia, Cape Town, Antarctica - would see no sun whatever for weeks or months and would have a very long and unimaginably bitter winter. But this situation would not last. As the Earth continued its orbit around the sun, people at the equator would see the sun, formerly low on the northern horizon, start a long, slow migration towards the south. As it did so, it would participate in the rotation of the whole sky more and more obviously. At first, it would rise just to the east of the most northerly point, cross the sky in a tiny arc, and set just to the west. As the months passed, this behaviour would increase in amplitude until, three months later, the sun would be rising directly in the East, passing through the middle of the midday sky and setting straight down into the West. It would continue its migration southwards, like some determined bird, until it reached its most extreme point and hovered on the southern horizon. There would now be a period of intense winter all across the Northern hemisphere, and blazing heat at the South Pole. But again this would not last forever: the sun would soon begin a slow northward track. 2 so that its rotation axis were perpendicular to the plane in which we orbit the sun (as in the attached sketch), a person on the Equator would always see the sun rise in the east, pass directly overhead, and set in the west, regardless of where we were in our orbit around the Sun (i.e regardless of the time of year). For a person at the North or the South pole, the Sun would always appear to be low on the horizon, and to move steadily and uniformly along the horizon as the day passes. For people elsewhere on Earth, the sun would follow the same path through the daytime sky every single day, in monotonous regularity. There would be no seasons at all, except for the small temperature effect of sometimes being closer to the sun and sometimes farther away in our slightly non-circular orbit. In short, if the Earth were tipped exactly on its side, there would be no place on the planet which would escape very dramatic seasonal changes, from extreme heat to bitter cold! (Remarkably, there is a planet just like this. Uranus is tipped almost exactly on its side as it orbits the sun. See Chapter 12 of your text to learn more about this strange planet.) On the other hand, if the Earth were exactly upright, there would be no seasons at all. But in fact the spin axis of the Earth is tipped at an intermediate angle of about 23-1/2 degrees, and we have moderate seasonal changes. Just to repeat: It is critical to understand not only that the Earth's axis of rotation points in a particular direction in space but that it maintains that direction over the course of a year, in contrast to the misleading impression of wobbly behaviour I was given as a child in primary school. (Indeed, it maintains that orientation not just for a year but for many centuries, although it does slowly change direction as thousands of years pass, in a phenomenon known as precession. We will explain this effect later.) During our winter, we are on the side of the Earth's orbit which has us tipped away from the sun: for us, it is low in the sky and provides little heat. The Australians, tipped toward the sun, enjoy summer then. Six months later, in our summer, we are tipped towards the sun, and feel the benefit of its more concentrated rays (and the fact that it is above the horizon for more hours per day). One immediate consequence of this tip is that, during our summer, the sun never sets in the Arctic regions, which is why it called "the land of the midnight sun". The figure on page 86 shows what the path of the sun looks like as seen on a summer day from a location in the high Arctic. (Note that this series of photographs was not take right at the North Pole itself. From the pole, the sun would appear to move in a path of constant altitude, parallel to the horizon.) You must remember, however, that ynlike the second limiting case discussed above, the sun never gets very high in the sky as seen from the Arctic. Although it is above the horizon all day, it is always rather low in altitude and the climate is never more than moderately warm. Conversely, during our winter months, people at the North Pole are tipped away from the sun and do not see it at all for months on end. In some ways, the most important lesson to be learned from this discussion is the general notion that the Earth's axis of rotation does not wobble about freely in space. This understanding can be profitably generalised to a host of physical situations, and to another profound 'conservation law.' Indeed, that is the topic of the next section of the notes. 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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Mystery destination!

(Friday, 28 January, 2022.)