Lecture 3 - Earth's Tile and the Seasons
All / Holidays and Seasons / Autumn
Apr 29, 2020
Hi again, everyone. Welcome to the third lecture of the semester for astronomy one O two. Topic for this lecture is the earth's axial tilt and its effect on what we see in the nighttime and daytime sky. The earth's tilt has implications for both the nightly and yearly motions that we observe, and some of these implications have been hinted at in the previous two lectures. I'll reiterate those here and explain a few more important phenomena that are caused by the tilt of the earth's axis. Let's start by briefly reviewing what we've covered so far. As you likely knew long before you took this class, the earth rotates on its axis, once every 24 hours, and it revolves around the sun once every 365 days. Rotation causes the nightly rising and setting of the stars, planets, sun and moon, and revolution causes the visible stars and planets to change over the course of the year as the sun appears to move around the celestial sphere. The Earth's rotation and its revolution don't happen in the same plane, however. The plane connecting the earth and the sun, and therefore the plane in which the earth orbits is called the ecliptic. If the earth had formed completely in isolation, its rotational axis would probably be perfectly perpendicular to the ecliptic. In reality, though, a collision or two or three early in the earth's history probably not it's on it and knocked it on its side of it. Inclining the rotational axis 23 and a half degrees. This has profound implications for what we see in the night sky, which is what we'll be discussing in this lecture. The first important thing to note is that although the earth's axial tilt is fixed at 23 and a half degrees from exactly perpendicular to the ecliptic. It's exact orientation relative to the ecliptic changes on very, very long time scales. If you imagine a line or axis perpendicular to the plane of the ecliptic like this dashed blue line here, which you could think of is where the earth's rotational axis should be, but isn't. The earth's axis spins around this imaginary axis in a motion much like a toy top spinning. We call this motion precession. The procession of the earth's axis around this imaginary line perpendicular to the ecliptic has a 26,000 year period. Because this period is so long, procession has no effect on what we observe in the night sky on the scale of a single human lifetime. However, over the scale of all of human history, it does. The human genome can be traced as far back as 300,000 years, so as many as 12 full cycles of precession have happened since man first originated on earth. This means that when our very early ancestors looked up at the sky, their view was different from what we see today. To understand how we first need to project this procession circle onto the celestial sphere, which you can see done in this figure. Precession has no effect on the location or orientation of the ecliptic shown here as a band of zodiacal constellations. However, it does affect the precise location of the north celestial pole. Which is the projection of the earth's North Pole onto the celestial sphere. Because the earth's axis precesses, the location of the north celestial pole changes relative to the stars on the celestial sphere. Completing one full circle every 26,000 years. If we project this circle onto a star map, it becomes apparent that we live in a very unusual time. If you study the yellow circles shown in this figure, you can see that the location of the earth's axis along the procession circle right now is very fortuitous in that the star Polaris is close to the circle. This means that the earth's pole is currently pointed almost right at the star Polaris, which is why we call it the north star. But this alignment is just a coincidence, and a lucky one at that. As you can see by the many empty spaces around the procession circle, there's not always been a north star. In fact, the last time there was a north star, it was the star thuban in the constellation Draco. As the ancient Egyptians were constructing the pyramids around 2600 BC, they would have been able to look up and see the entire sky rotating around this star. A natural question then is whether this is also the case in the southern hemisphere. So let's investigate this directly using a program called stellarium. This program is free, by the way, and it's very convenient, so I recommend that you download and play with it throughout this semester. It could be really helpful in planning observations. So as I open the program, you can see that my default location is set to two song. But I want to go to the southern hemisphere. So let's go to Santiago Chile. And then I'll close this. Since I'm now in the southern hemisphere, I'm going to want to look south to see the South Pole, which is here. And I'm going to turn this grid on to allow us to find oops this grid. To allow us to find this out celestial pole in the sky. So you can see it now. Where all these blue lines can merge. So as you can see, if I just flash this on and off, there aren't any stars that coincide exactly with the south celestial pole. So they're not as lucky in the southern hemisphere as we are. If I turn on the constellations and they're labels, you can actually see. That in the southern hemisphere what they tend to use to find the south celestial pole is this constellation called crux, the southern cross. And why don't I see it? 'cause it's here. So they tend to use these the long arm of the southern cross, which points if you can see almost directly at the south celestial pole. Now whether we're in the northern hemisphere or the southern hemisphere, one of the most important implications of the earth's axial tilt is this phenomenon of circumpolar constellations. Maria mentioned this in the first lecture, so I won't go into too much detail here, but to reiterate just a little bit, let's speed up time and watch the sky rotate. As you can see, the constellations in the southern sky are all rotating around the south celestial pole. For stars within a certain distance of the pole, their rotations about it never bring them below the horizon. So they never set from our perspective. Of course, the sun rises and makes it so we can't see them very easily, but we can fix that in this program by simply turning off the Earth's atmosphere. So that we can see the stars in the daytime. So with the atmosphere off, you can see that these stars complete one full rotation around the south celestial pole every 24 hours. The altitude of the pole above your horizon also varies according to your latitude. Santiago, where we are now is at 33° south latitude. And so the altitude of the empty cell celestial pole is about 33° above the horizon. This means that all constellations within 33° of the pole are circumpolar. Quite a few. If we were to move closer to the equator, say to Quito Ecuador. Which is that just 1.4° south latitude, you can see that the south celestial pole would lie just barely above the horizon. And virtually no constellations would be circumpolar. Okay. So let's return to the PowerPoint here. And talk about the most important implication of the earth's axial tilt for life on earth. The seasons. Undoubtedly, you heard at some point in your education that the earth's tilt is the cause of the seasons. But there are lots and lots of misconceptions about the seasons out there. Even among highly educated and intelligent people. In fact, there's a famous series of interviews that were done with students and faculty at Harvard's graduation regarding the cause of the seasons, and many of them got it wrong. So let's break it down carefully here. In the most basic sense, the seasons are caused by the earth's being tilted towards or away from the sun. When the earth's pole is tilted towards the sun we have summer, and when its tilted away we have winter. Because the earth's axis always points in the same direction, at least on the time scale of a single orbit, these occur on opposite sides of the earth's orbit around the sun. It's important to note that this is because of the directness of the sunlight and not because of one hemisphere being closer to the sun than the other. The diameter of the earth is about one 10,000th of the distance between the earth and the sun. So going from one hemisphere to another is like taking one step closer to a fire that is 10,000 steps away. Would you feel any warmer? As long as we're on the subject of proximity to the sun, another common misconception is that the earth's elliptical orbit is the cause of the seasons on earth. This is another proximity argument and is equally false. When we say the earth's orbit is elliptical, most people picture this. You can see how this mental picture would lead you to believe that the proximity to the sun is the cause of the seasons on earth. However, there are two fatal flaws to this picture. The first flaw is that the hemispheres on earth have opposite seasons at the same time. When it's summer in the northern hemisphere, it's winter in the southern. If the earth's earth were closer to the sun during the northern hemisphere's summer, then shouldn't it also be summer in the southern hemisphere? The second flaw is that although the earth's orbit is indeed elliptical, it's just barely so. Here's a perfect circle, which we say has an ellipticity of zero. The red dashed line, on the other hand, shows an ellipse with an ellipticity of 0.0167. Equal to the ellipticity of the earth's orbit. As you can see, they're not very different at all. As a final nail in the coffin of this misconception, let me just point out that we are actually closer to the sun during the winter in the northern hemisphere than we are in the summer. Let's go back then to the real cause, which is the directness of the sunlight incident on each hemisphere. This is a consequence of whether the hemisphere in question is tilted toward or away from the earth. Note first that this naturally explains the fact that the seasons are opposite in the northern and southern hemispheres. Since one is tilted away when the other is tilted towards the sun. I think the best way to understand how tilt affects the directness of sunlight is to use the analogy of a flashlight beam. A flashlight like the sun is always emitting the same amount of light no matter how you point it. However, depending on how you hold the flashlight, you can either concentrate or diffuse this light. If you shine the flashlight straight down, you'll be concentrating all of the light in a small area, and the spot it makes on the ground will be very bright. If you shine it at a shallow angle on the other hand, you'll be spreading the light over a large area, and the spot will be relatively faint. Some light behaves the same way, except in this case the light from the sun is transformed into heat when absorbed by atoms and objects on the ground. So you could think of the beam of light from the sun as containing not just light, but heat as well. In the case of the more direct angle to the sun in the summertime, the same amount of heat is being concentrated in a smaller area, making it overall warmer. While the indirect light of the winter results in the same amount of heat. Energy being spread over a larger area. A secondary effect, the less important than the directness of sunlight, is the difference in the path the sun takes across the sky on these days. To visualize this, let's start by labeling four special points in Earth's orbit. The point when the earth's axis is tilted most directly at the sun is called the summer solstice. And when it's pointed directly away, it's called the winter solstice. These happen around June 21st and December 21st every year. Midway between the solstices are the equinoxes. The vernal meaning spring and autumnal, meaning autumn or fall, equinoxes, around March 21st and September 21st, respectively. These are the times when the earth's axis is pointing sideways. Neither towards nor away from the sun. Of course, we're being pretty northern hemisphere centric in this view. Recall that the seasons are opposite in the earth's hemispheres. So when the northern hemisphere is pointed directly at the sun, the southern is pointed directly away. Therefore, the northern hemisphere summer solstice occurs at the same time as the southern hemisphere's winter solstice. And so on and so forth. The solstices are special in that they are the yearly extremes in the length of the day versus night. The summer solstice is also often referred to as the longest day of the year, and the winter solstice is the shortest day of the year. The equinoxes, on the other hand, have equal amounts of night and day. 12 hours each. These differences in the length of a day are a consequence of how the sun's path across the sky varies on these days. So with these new vocabulary words, let's visualize the sun's path across the sky on these days. Let's make a Verizon from east to west, looking south. And we'll draw the meridian, which is an imaginary line that connects north and south, passing through the zenith. As the sun rises in the east, we see that it's morning or a.m.. Which stands for anti meridian or before the meridian. As the sun sets in the west, we say that it's evening or p.m., which stands for post, meridian, or after the meridian. So where's the sun at noon? Well, it should be on the meridian since it's halfway between east and west or halfway between rising and setting. You might expect that it would be right at zenith. But from Tucson, the sun actually never passes directly overhead at noon. In fact, the only places on earth where this happens are in the tropics between the tropic of cancer and the tropic of Capricorn, which are 23 and a half degrees on either side of the equator. It's no coincidence that that number is exactly equal to the earth's axial tilt, but I digress. Let's take for granted for now that the sun passes high in the southern sky, but not directly overhead at noon in Tucson. If I put it here today, where will it be tomorrow? Well, we're currently in late January, just over a month after the winter solstice or the shortest day of the year, and moving towards the vernal equinox. The days are therefore getting longer at this time of year, so it should make sense that the sun will be just a little bit higher in the sky at noon tomorrow. In fact, this trend will continue all the way until the summer solstice or longest day of the year. On that day the sun will be higher in the sky at noon than it is at any other time during the year. It will then get lower every day until the other extreme the winter solstice, and this cycle will repeat every year. The sun is at its lowest point at noon on the day of the winter solstice, and it at its highest on the summer solstice. He gets a little higher in the sky every day from the winter solstice, through the vernal equinox and on to the summer solstice. And then it gets a little lower in the sky every day through the autumnal equinox and back to its lowest point on the winter solstice. This is a bit of an oversimplification because in fact the exact time of noon varies a little over the course of the year as well. So that if you took a picture of the sun every day at noon, it would trace out a figure 8 shape called an analemma, such as the one shown in this picture. Here the large vertical motion is due to the changing height of the sonnet noon throughout the year, and the much smaller horizontal motion is a result of a slight change in the exact time of noon throughout the year. But here, again, I digress. Back to the path of the sun across the sky on these days. If the sun is to reach its highest point at noon, on the summer solstice, it must trace a long, high path across the sky, and rise earlier and set later than at other times of the year. Although it never reaches the exact zenith outside of the tropics, this long high path means that the sun shines rather directly on the surface of the earth all through the summer. Making summer days warm. While the winter solstice, the sun does not need to rise very high above the horizon. So it can rise later and set earlier. Its low trajectory means that sunlight is shining more indirectly on the ground and less warming occurs. Making winter days cool. There's again a lovely symmetry here with the southern hemisphere, as the sun is tracing its shortest path across the sky in the northern hemisphere, it's tracing its longest across the sky in the southern hemisphere, and vice versa. In between these two extremes of the summer and winter solstice, there are the equinoxes, where the sun traces an intermediate path across the sky. On these days in both hemispheres, it rises directly in the east, sets directly in the west, and the day and night are each precisely 12 hours long. This should give you plenty to think about until next time one will throw the moon into the mix. In the meantime, I'll leave you with the following real picture of the path of the sun across the sky on the day of the summer and winter solstices, as seen from somewhere in Scandinavia.