This is information for members of the PS102 Astronomy Club and their families. The intent of this section is the provide access to the club meeting materials and additional resources to help your children learn more about astronomy and develop a general interest in science.
But first, a little "philosophical" background. In spite of what seems to come out of most elementary education books and tests, science is not content. Science is first and foremost a framework for understanding the natural world in which we live. Science majors, even at the college level, naturally have to learn a lot of content and in this club your children will (hopefully!) be learning a lot of astronomy content. But the real hope is not that they will come away with a lot of astronomy knowledge or that they will go into careers in astronomy, physics, or some other science. My real hope is that your children will start down the road of a scientific worldview that causes them to follow their curiosity, asking why is the world the way it is, how does that work, how do the pieces fit together. I hope they will learn to see the relationships of cause and effect in the natural world and learn to analyze effects looking for the causes. In the sciences, we refer to this as analytical thinking and contrast it (somewhat) to critical thinking.
Critical thinking has been defined in various ways1,2,3, and stresses self-analysis of belief systems. I think of this as an attempt to formalize my mother's advice: "don't believe what you hear and only half of what you read." While that advice may have been hyperbole, it points to the need to avoid credulity, something that all of our children need to learn as they grow from complete trust to a healthy skepticism.
Analytical thinking is a component of critical thinking (and by some definitions "merely" a component), but in developing a scientific worldview, this component is elevated to central role. Analytical thinking requires that one methodically break down problems into their constituent parts and examine cause and effect relationships. It involves learning to synthesize new hypotheses of behavior from the knowledge you have then subject those hypotheses to tests. [Insert comments from Mercury Magazine].4
Okay, the above was for you parents reading this. For you children in the club, Ms. Frizzle (of Magic Schoolbus fame) would put it this way: "Wahoo! Take chances, make mistakes, and get messy!" Just in case you're wondering, "wahoo" means have fun.5
2 Huitt, W. (1998). Critical thinking: An overview. Educational Psychology Interactive. Valdosta, GA: Valdosta State University.
3 CriticalThinking.org provides a definition so all-encompassing that it includes nearly all rational thought. As such, it is incorporated into scientific thinking, something with which their website agrees.
4 Mercury, vol 35, no. 1, p 11, What is it We Teach? Astronomical Society of the Pacific.
5 Okay, I made that up, but it works for me.
Even though these are in a table, the order isn't really set. Think of it as an enumerated set of ideas. This is a place holder to show what I hope to do and I'll shuffle them around a bit as I get more ideas (suggestions welcome!).
| # | Title | Topic | Comments |
|---|---|---|---|
| 1 | Constellation Myths |
Orion, the Milky Way, the Big Dipper |
Myths are often used to communicate cultural values. Cover a classical Greek myth (Orion and Scorpius) and a couple of Native American myths. |
| The Night Sky Now (March 20) | Orion, the Dogs, Gemini, Leo, Mars, Saturn |
Mars will be hard to see a month from now, and Saturn is always a winner, so we cover a lot here. | |
| 2 | The Night Sky Now (April 10) |
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| 3 | The Night Sky Now (May 8) |
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| 4 | The Night Sky Now (May 29) |
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| 5 | Its a Dizzy World! |
Days, Months, Seasons, and Years. |
It's all about geometry. We'll also cover lunar libration. This is a good one for both photo sequences and simulations. Need A/V equipment in the class. |
| 6 | Craters! |
How craters form, Mercury, Moon, Mars and Earth |
Look at pictures of craters in various planets. Talk about how they form then practice! Activity is plopping hard candies into chocolate pudding with a powdered sugar topping. This reveals both crater shape and the "rays" that can be seen around some craters such as Copernicus on the Moon. And we get to eat it at the end. |
| 7 |
Inner Solar System Planets |
Terrestrial Planets |
Similarities between Mercury, Venus, Earth, and Mars. Talk about geometry that causes Mercury and Venus to alternately appear in the morning and evening sky and why the have phases like the Moon. |
| Good opportunity for computer simulation showing Venus move around the Sun with the view of its phases as seen from Earth. | |||
| 8 |
Inconstant Star |
The Sun |
Space storms, magnetic fields and aurora. This can be a talk, but I really need some A/V props, probably NASA video "Blackout" (19 minutes). |
| Possible activity: magnetic field lines with iron filings (have to build acrylic holders to keep the mess down). | |||
| Sunspot activity tracking. If we can get Solarscopes, we can do this as a short outdoor activity for 2--4 weeks. Will require good luck with weather this time of year. Probably can't go outside and back and get the children to draw pictures in less than 30 minutes. As an alternate, we can print a series of pictures from SOHO to track sunspots. The idea is that the children can detect and measure the rotation of the Sun. If we're really lucky, they can also detect the differential rotation of the polar vs equatorial regions. | |||
| 9 |
What Makes a Star | The Interior of Stars (and our Sun). | Learn about fusion inside stars and the layered structure of the interior. Types and sizes of stars, temperature and color. Good chance to use Blackbody Physlet for illustration. |
| Decorate cookies to mimic the sun's structure. Need BIG cookies (well, maybe 6-inch diameter). | |||
| 10 |
Outer Solar Sytem Planets |
Jupiter, Saturn, Neptune, and Uranus | With apologies to Pluto, we'll only cover the gas giants. Talk about rings (they all have rings!) and gravity, the first lander on Titan and places we might find life and why scientists are so interested in trying to find life outside of earth. |
| 11 |
Space Debris |
Dwarf Planets, Minor Planets, Comets, and Dust | Pluto and friends. The make your own comet craft works here. Can I do the dry ice demo? This might be a good place for a video of the Deep Impact mission. |
| 12 |
Extra-solar Planets |
First we need to talk about the distance scale. The children need to develop a gut feel for just how far away stars are. Okay, even I don't really have a gut feel for that, but the idea is impress on them just how hard it is. Then we ask, wow can we "see" planets around other stars. |
|
| Demonstration of the Doppler effect? Any change I can get a sound recording of either a car horn or a train whistle as it passes by an observer? The Doppler Physlet is a possible resource, but it needs to be bigger. | |||
| To go along with Doppler effect, we need to understand spectral lines. I've got one spectroscope and a bunch of diffraction gratings. Can we make home-made (uncalibrated) spectroscopes? Find cost of additional calibrated ones. One for the whole class makes it unusable. | |||
| Great Galaxies! |
The Milky Way, the Local Group, the Virgo Supercluster |
What makes galzxies stick together (gravity). When galaxies collide, do stars collide? Cosmic structure, dark matter, dark energy, the Big Bang. |
Every culture has its set of myths, even modern western culture although we avoid the word "myth." In today's culture, many of these myths are passed along by a reinterpretation of modern events fitting them into our worldview. Sometimes our recounting differs from that of historians and this is where our myths become visible.
"Ancient" cultures also had their myths. Some of them were at least partially based on history---Troy was a real city and there was a real battle and the Trojan Horse might have been real, too. The stories we have from ancient Greece and Rome form the basis of most of the northern hemisphere's constellations (at least those officially designated by the International Astronomical Union). But ancient Greece and Rome were not the only cultures with myths that are immortalized in the night sky.
The Navajo (and other tribes of the American southwest) has a tale that describes how the stars came to have both the patterns we find in the sky and why so many of them have no pattern at all.1
In the beginning, when the first day dawned in the world, the first woman told the first man "The people of the world need to know the laws; they must be written for all to see."
The first man replied, "Then write them on the sand where they walk."
The first woman said, "But the will blow away with the first wind."
"Then write them on the water."
"But they will disappear in the waves as fast as I write them."
The first man, who was walking away because he had very important things to do, looked back at the first woman and saw her sitting there with her blanket covered with stars. He said, "Then take your jewels and put them in the sky; write the laws there were all can see."
So that night, and each night after, she took some of the stars from her blanket and placed them carefully in the sky, making patterns that could be seen and understood by all the people. But she was not alone there; Coyote watched here wondering what she was doing. Finally, one night, Coyote came to the woman and asked, "What are you doing?"
First woman replied, "I am writing the laws into the sky that all the people may see them."
"May I help?" asked Coyote.
"Yes," said the woman, "but you must be careful and place the stars as I tell you."
Coyote agreed and so began to help the woman place the stars. But after a few nights, Coyote complained. "This is slow work, it will take forever to place all these stars."
"But it is important work," said the woman, "if it take all my life, it is the most important thing I can do."
Coyote was silent and continued to help, but in his heart he was impatient with the task. One night, as the woman stopped working to rest, Coyote watched until her attention was no longer on the blanket. Then, he grabbed a corner in his mouth and ran with the blanket, flinging the stars into the sky! The woman cried out an anguish, "What have you done?" and she began to weep. Coyote just laughed and ran away.
The woman wept because the stars the Coyote had flung into the sky were disordered, without any pattern at all and so the people could not use them to understand the laws. This is why there is confusion among the people even today and all people must work to bring harmony to the world.
Another version of this myth2 is has the stars being placed by the Black God who represents order in the natural world. Coyote still plays the role of the chaotic prankster who scatters the stars. The duty of people is to try to find harmony between the order of nature and the chaos of daily life.
The Wasco (or Wascopam or Wisscopam) Indians are a tribe which lived in what is now known as the Wasco County, Oregon region. The country derives its name from the tribe. One of their stories tells of the Coyote and how he placed the stars.3 If tells of how the asterism we call the Big Dipper came to be.
One day, as Coyote trotted through the woods, he saw five wolves staring intently at the sky. The oldest wolf had a small dog with him as a companion. Coyote watched them all for a while, then walked to them and asked, "What are you looking at." But they just ignored him and did not answer. The next day, he again saw them and again asked and again they ignored him. This happened for several days and Coyote was very frustrated. Finally, one of the younger wolves asked the others, "Why don't we tell Coyote; he can't do anything about it anyway."
So they told Coyote, "We see two animals in the sky, but they are far away and we cannot tell what they are."
Coyote answered, "Well, why don't we go up and see."
The wolves laughed and said, "How can be get to the sky?"
Coyote said, "It's easy, but we must start in the day."
The next day, Coyote and the wolves gathered together and Coyote fired an arrow at the sky and it stuck! Then he shot another so it stuck into the back of the first arrow. He shot many more until they formed a bridge from the sky all the way back down to the ground. Coyote and the wolved all began to climb. It was a long climb! The climbed for three days and nights to reach the sky and cross to where the wolves had seen the animals. As they got close, the wolves could see that the animals were grizzly bears and they all stopped. After a while, seeing that he bears did not respond, the youngest two wolved moved closer facing the bears. They called back, "Come on over, they are not doing anything."
The oldest wolf with his small dog would not come; nor would Coyote who did not trust bears. Finally, after a while, all of the wolves moved closer looking at the bears, but Coyote would still not come. As Coyote looked at the wolves and the bear he thought, "What a nice pattern they form! I think I will just leave them this way." And so, he turned and ran back to the arrow bridge and began climbing down, breaking off the arrows behind him.
Later, Coyote boasted of how he had arranged the stars and told Meadow Lark. The wolves and the bears form the pattern we call the Big Dipper. The two bears are the part of the bowl that point toward the north star (Polaris). The two younger wolves are the other two stars in the bowl, and the three stars of the handle are the other wolves. The oldest wolf is the star in the middle of the handle, and if you look close, you can see the small dog close beside the old wolf.
Most of the official 88 constellations are from Greek and Roman myths, so we could talk about any of them. But Orion is still visible this time of year (March), so we'll talk about him.
The story of Orion is an old one, so old that there are different versions and they don't all agree! There are at least three versions4 of the myth which have Orion killed by Scorpius, a giant scorpion. Who sent the scorpion differs between them, but the most commonly repeated one seems to be this one.
Orion was a great hunter, perhaps the greatest hunter ever. One day Orion boasted of his skills and that he could kill any and all of the animals of the Earth. To make good on his claim, he set out to do just that and was making very good progress. This so disturbed Gaia, the Earth mother (who was naturally very protective of her parents) that she created Scorpius, a giant scorpion to fight against Orion. The battle lasted three days! Ultimately, Orion was stung by Scorpius and died. Orion was place in the sky, some say by Zeus who had pity on him. Others say it was Artemis, his lover who placed him opposite from Scorpius so Orion would never again have to face Scorpius.
Orion was honored in the constellations because of his great hunting skill, but he perished because of his pride and arrogance.
The main point is that myths capture a culture's values. Coyote was a trickster and trouble maker whose impatient lead to disorder and disharmony in the world. The value emphasized is the opposite as well as the need for people to try to work toward harmony. Orion emphasize both Orion's greatness as a skilled and brave hunter but also his downfall because he was too proud and boastful.
Take one or two of the star charts and make up your own constellation and write a short story about the constellation that expresses some important idea or value to you. You can draw a stick figure, or an elaborate illustration. Remember that the ancient Greeks and Romans didn't draw the stick figures you find on star charts today; the oldest illustrations are pictures superimposed on the sky. The Native Americans often thought of the stars in one of our constellations are all parts of a complete scene---a single star might have represented a character in their story. So use your imagination and draw whatever you would like.
If you finish all you want to do with the constellation drawings and there is still time, you can work on the word search puzzle. All of the words are names and types of objects which can be found in the constellation Orion. Page two of the word search puzzle has the answers.
1 How the Stars Fell into the Sky, Jerrie Oughton, Houghton Mifflin Company, 1992, ISBN-13: 9780395779385.
2 They Dance in the Sky, Jean Guard Monroe and Ray A. Williams, Houghton Mifflin Company, 1987, ISBN-13: 9780618809127.
3 American Indian Myths and Legends, Richard Erdoes, Ed Erdoes, Alfonso Ortiz, Knopf Publishing Group, August 1985 ISBN-13: 9780394740188.
4 See Orion and Scorpius Constellations by Paul Heckert for a synopsis.
There are two goals here. First, to help you know what you can find in the night sky during the next few weeks. Second, to help to find your way around the night sky so you know how to find those things.
When astronomers measure positions on the night sky, they use angles. There is actually a well-defined coordinate system used, but we won't be covering that here. To find things, all you need is a starting point and a way to measure angles. If you're a draftsman, an architect, a surveyor, or you play billiards, you probably have a good, intuitive sense of angles. The rest of us need some help.
You're probably used to thinking of angles as those itty-bitty marks on a protractor. While they are, they are not the distances between those marks. On your typical 6-inch diameter protractor, 1° is a bit more than 1 mm (1.33 mm) at the edge of the protractor. But if you had a 1-meter diameter protractor, 1° would be nearly 1cm (8.7 mm, about 1/3-inch). The "itty-bitty" part of the impression starts to fade.
At their heart, angles are ratios: the ratio of a size to a distance. So that 1.3 mm length at 6-inches is the same as the 8.7 mm at 1-meter. And it's the same as 2-full moon diameters (7000 km) at the distance of the moon (385,000 km).
Okay, so what, you're thinking...do I have to hold a protractor up to my eye to find things? No....
Assuming you have at least one good eye and one arm and hand, you already have everything you need to approximate positions on the sky.
Try this: the next time there is a full moon, hold up you pinky at arm's length. Which is bigger? That is, can you cover the moon with your little finger (try with only one eye open)? What about near moonrise (evening) or moonset (morning) when the moon is near the horizon and seems so big; can you cover it then?
Yes, from here in Bay Ridge, Brooklyn, north is more-or-less toward Mahattan. On the one hand, it's easy to find north by looking for that glow from the city. Or mabye not if you're having trouble figuring out which part of the glow is from Manhattan... It's pretty hard to see much in the sky, even in directions other than the north. But, with north approximately determined, where are the fun things?
At this time of the year, March, Orion is high in the southwest as soon as it gets dark. Orion is full of fairly bright stars so it is easily seen even from here in Brooklyn. The three stars of his belt are very distinctive and nearly every culture has some story related to these stars. If you've been able to find Orion in the night sky, you can probably pick him out of the star chart below.1
Star Chart: Orion, March 20 8:30 pm EDT
The above image is a printable version (linked to bigger versions). Below is the same view with guides.
Star Chart: Orion, March 20 8:30 pm EDT, with guides
The first thing to note about Orion is his size. The angle from the star in the lower right (Rigel) to the one in the upper right (Betelguese) is over 20°! When you look at constellation pictures its easy to get the impression these are small patterns in the sky, but most constellations are really cover a big chunk of the sky. It's more than another 20° to reach the top of Orion's upraised club. Here in NYC, you may not be able to find the stars in his club unless you can get well away from any local street lights.
Orion has several "famous" stars among them Betelgeuse in his upper left shoulder. Betelgeuse means "armpit of the giant." Betelgeuse is a red giant star. It's diameter is larger than the diameter of the orbit of Mars around the Sun! For almost all stars, even the Hubble telescope sees them just as points of light. But Betelgeuse is one fo the very few stars which can be imaged as a small disk.
Opposite Betelgeuse is Rigel "the foot." Rigel is much smaller than Betelgeuse and it would "only" swallow Mercury and Venus.
Just to the west of Orion is Taurus. It's easy to imagine Orion battling the bull from this arrangement, but some of the oldest drawing we have show Orion facing east, not looking at Taurus at all! The stars in Taurus aren't supposed to form a complete picture of a bull, just his head and shoulders. I can't really picture most of bull, but the large V-shape does make one think of the bull's horns. The brightest star in Taurus is Aldebaran which may appear to your eyes with an orangish tint.
Just to the east and a bit south (closer to the horizon) is Canis Major, the Big Dog, one of Orion's hunting dogs. This dog is marked by the brightest star in the night sky during this time of year, Sirius. The name "Sirius" comes from a Greek word which means "scorching." Sirius is bright for two reasons: first is is very close in astronomical terms, only 9 light years away (53,000,000,000,000 miles, more or less); second, it is about twice the diameter of the Sun which makes it both hotter and intrinsically brighter. Sirius is about 10,000C while the Sun is "only" 6,000C. Just to the east an south of Sirius is the dog's front leg. The star her is called Miram and takes its name from the Arabic word for "announcer;" it announces the imminent arrival of Sirius.
One a very clear night in Brooklyn, I can see most of the stars shown in the image above to make out this constellation. Even on hazy nights, if you can see any stars at all, Sirius will likely be among them.
The constellation Monoceros, the Unicorn, is also drawn, but I've never really been able to pick out the stars of this pattern from Brooklyn. There are a scattering of stars in that area that manage to poke through the city sky glow, but most are lost.
Orion's other hunting dog is Canis Minor, the Little Dog, and it's brightest star is Procyon. You'll notice on the chart the whole stick figure consists of only a single stick! Procyon is not nearly as bright as Sirius, but it is still quite bright an easy to find from here in Brooklyn.
While Orion gets all the glory with its large number of bright stars and easily recognized pattern, another constellation appears above his head: Gemini, the Twins.
Gemini is really close to being overhead. In the charts, you can see Orion down below Gemini which should help to you get oriented.
The center of the circle for the guides represents the zenith, the point directly overhead. The two bright stars near the "top" of Gemini are Pollux (on the left and slightly lower) and Castor (to the right and slightly higher). If it's really clear, you can probably trace the outline shown in the images and see most of the stars in this chart. If it's a bit bright either due to sky glow (which is aggravated by high humidity) or if the moon is full and up, you may have trouble seeing anything more than Castor and Pollux and the star in the left "foot" of the constellation. Ah, but what's that bright blob just to the right of the stick figure? That's Mars! Mars is currently receding from us as we speed away in our orbit. Even the views in a telescope are not very good, but you can still see it with your naked eye.
Rising in the east around the same time is Leo, the lion. On March 20, the full moon will wash out most of the fainter stars in Leo and even make the brighter ones hard to see. However, two stars will be quite easy to spot. One is Regulus, at the base of the "backward question mark" that forms the head and shoulders of Leo. The other, slightly below and to to the left (east) of Regulus is not a star; it's the planet Saturn!
Star Chart: Leo, March 20 8:30 pm EDT
Below is the same image with guides.
Star Chart: Leo, March 20 8:30 pm EDT with guides
This pattern of stars been associated with a lion for a long time, since at least 2200 BC. The brightest star that we see is Regulus. Regulus comes from Latin; we get the word "regal" from the same root and this constellation has also been associated with "kingship" for a long time.
Regulus is about 6 times the diameter of our Sun. But there's another star in Leo which is even bigger. It doesn't look so bright to us because it is about 25 times further away. Eta Leonis (which doesn't even get a proper name!) is so much bigger and brighter that if we lived on a planet orbiting Regulus, Eta Leonis would be the brightest star in our night sky. If it were as close to us as Sirius (9 light years), it would 50 times brighter that the planet Venus appears to us and it would actually be visible in the daytime!
Regulus is also a double star but you need a telescope to see its companion. The companion star orbits Regulus at a distance about 100 times greater than the distance of Pluto from our Sun.
Another double star is Algieba ("lion's mane") but again you need a small telescope to see both stars. Each year, in November, the Leonid meteor shower occurs. It's called the "Leonid" shower because the meteors appear to be coming from the constellation Leo. All meteor showers get named for the constellation from which they appear to come. For the Leonids, the radiant, or central point from which all the meteors appear to be coming, is just north of Algieba.
There are also a number of galaxies which can be seen in Leo. However, we're not going to talk about those today because they are too faint to be seen without a telescope and without leaving the city for darker skies.
The last star I'll mention by name is Denebola. "Deneb" means "tail" and there are several constellations which have stars whose names have the word "deneb" in them. The most famous can't be seen until later in the year; that's Deneb, the tail of Cygnus the swan.
The idea that the world is moving seemed crazy to most everyone thousands of years ago and, lets be honest, it does fly in the face of what our senses tell us. Clearly something is moving, but how can it be us? We know what it feels like when we move. And maybe you're one of those unfortunate few who get violently motion sick so you know perfectly well that you're not moving.
But you are. You're "glued" to the Earth by gravity and it's spinning around once a day. And the Earth is revolving around the Sun once every year. And the Sun is moving along through our galaxy taking about 250,000 years to travel once around. So I ask the question: How fast are you moving when you're sitting still?
The earth is rotating on its axis, once every 24 hours we come back to the same place, facing the sun again. If we look up the size of the Earth, we can find it's diameter is about 12,750 km. But to know how far we travel (while sittting still), we need to know how far around it is. So we need the perimeter of a circle. Polygons are easy, just measure each side and add them up. How do we do it for a circle? We could just look it up, but we can also figure it out.
How long is the circumference of a circle? Unlike polygons, we can't just measure with our ruler. You could use a piece of string to wrap around a circle, mark the length then stretch it flat to get a pretty good estimate. But it's hard to do that on a piece of paper. We could also just look up the answer. But before we look it up, I'd like todo a little geometry exercise. One of the things that happens in astronomy (and much of science) is that we often have to find a way to bound our estimates. That means we try to find some pair of numbers that describe the largest and smallest the real answer might be. Sometimes we really can't figure out the exact answer. If that happens, it might still be useful to have not just an estimate, but also know if our estimate is off by a little or off by a lot.
So what we'll do is find a way to estimate using a very old technique of trying to find the limit. In the end, we'll make an estimate based on our approximations.
Tools for the Task:
First lets start with a circle with an inscribed square. That means we make the square as big as possible while still fitting inside the circle. Here is what this looks like (ignore the dashed lines, that are just guides for later):
Perimeter Step 1: Inner Square
We can use the perimeter of the square as an estimate of the perimeter of the circle. You're probably thinking its not a very good estimate and you'd be right. But it also forms a lower bound. That is, the perimeter of the circle is certainly larger than the perimeter of the square. We could have used an polygon inside the circle, but I chose a square. We'll change that in a minute, but first....
Lets draw a square around the circle so the circles is inscribed in the square. That looks like this:
Perimeter Step 2: Outer Square
Again, we can use the perimeter of this square as an estimate for the perimeter of the circle. Again, it's not a very good estimate. But this square provides an upper bound for the perimeter of the circle; that is, the perimeter of the circle is certainly smaller than the perimeter of the square.
Upper and lower bounds appear all over the place in daily life. When you drive down the road and you pass another car, you automatically know an upper bound for the speed of the other car---it's your speed. The other car must be travelling slower than you or you couldn't pass it. When another car passes you, you automatically know a lower bound for the speed of the other car---again, it's your speed. The other car must be travelling faster than you or it couldn't pass you. You can probably think of other examples.
Back to our circle. We can do better by turning our squares into octagons. First lets do this for the inner square. To convert it into an octagon, we will keep the four corners we had and add four more vertices (this is the plural form of vertex which is just the point where the two sides meet). Those dashed guide lines show us where we want to put the new vertices; right at the half-way points between the old vertices like this:
Perimeter Step 3: Inner Octagon
If we measure the perimeter of this octagon, then we have a better estimate of the perimeter of our circle. It's still too small, but not as bad as the first try. So our new estimate forms a better lower bound that the first estimate. Its a better lower bound because we know it is closer to the correct answer without going over.
Let's do the same thing now for our outer square, converting it into an octagon. That looks like this:
Perimeter Step 4: Outer Octagon
At this point, you know the drill---measure this perimeter and we get a better upper bound on the perimeter of the circle. It's better because is closer to the real perimeter without going under.
Okay, we could repeat this again, using a decahexagon which is the fancy name for a 16-sided regular polygon. But that not only gets tedious, but it's hard to measure accurately with just a ruler. So instead, we'll take our upper bound and our lower bound and average them and call that our best estimate.
If you print out the file Perimeter.pdf (attached below) you can do the exercise yourself. The starting image looks like this:
Perimeter Exercise Handout (Preview)
You'll have to convert the squares to octagons then measure. If you use a metric ruler, you can probably measure each side to the nearest 1/2 mm. The circle has a diameter of 120 mm. I measured the inner octagon as 368 mm (8 x 46 mm) and the outer octagon as 396 mm (8 x 49.5 mm). The average of these two gives 382 mm.
Okay, so that's nice for our circle. What if I have a different circle? If the circle is twice the diameter, what happens to the octagons? They end up twice as big, too. So if we look at the ratio of the perimeter to the diameter, we have a way of converting the diameter of any circle into a perimeter. For our estimate, this ratio is 382/120. That's a pretty awkward number, but its a bit more than 3 (use a calculator and you get 3.18).1 An even better "simple" estimate is 22/7 which is about 3.14 which is what we would get if we worked very hard and split our octagons into decahexagons.
I know that in your math classes, you've talked about using an estimate of about 3 for the ratio of a circle's perimeter to it's diameter. Now you can explain where that "magic number" came from and you can tell people you know how to get an even better estimate.
NB: Parents, if you are feeling ambitious, you can download the ZIP archive below which contains high-quality PDFs of all of the above images as well as a drawing of the decahexagon arrangement that you can use to do your own estimating. The PS102 mathematics text has a section on geometric constructions, but I'm not sure if they will actually do this in class. I've taken a somewhat different approach than the classical methods which emphasize constructions using only a straight-edge and a compass because we're interested in making a measurement which is much less abstract.
1 This is an error of only just over 1% which is quite good. If you are willing to be very careful and actually construct the decahexagon, you can get an error of much less than 1%. I tried and was able to get an error of about 0.4%. But that's an exercise for the adults, not the children....
Now that we know how to estimate the circumference of a circle from its radius we can go back to what we really want to know, if we travel around the earth in 24 hours, how far do we go and how fast? Okay, get out your calculators (or you pencils and paper)....
The Earth is about 12,750 km in diameter. We'll round that up to 13,000 km and multiply by 3 to get the circumference as 39,000 km. It takes you 24 hours to travel that distance. So we divide by 24 hours to get just over 1,600 kph (1,000 mph)! That's faster than the speed of sound! It's a good thing the Earth also drags the atmosphere along with it, too.
Actually, that's the speed at the equator. We're pretty far north compared to the equator so it turns out we' "only" travelling about 1,200 kph (760 mph). That works out to be about 1 km every 3 seconds. Quick question: how fast would you be travelling if you were standing at the North Pole? At the South Pole?
Now let's repeat our estimate for our annual trip around the Sun. The distance to the sun is 150 million kilometers. So the trip around the Sun is almost 900 million kilometers. Let's estimate the year as 360 days just because we can do the math easier:
900,000,000 km / 360 days = 2,500,000 km/day.
Okay, there's 24 hours in a day, so since we're estimating, 2,400,000 km/day is pretty close and it divides by 24 easily, so we'll just "round" down a little to get 100,000 kph. Yep, you read that correctly, 100,000 kilometer every hour. That works out to almost 28 kps (kilometers per second).
You might have thought we were done. Heh, heh. The Sun is not sitting still, it's orbiting the galactic center. It takes a very long time to go around. People have not been around on Earth long enough to have witnessed a single full orbit, but we can still measure the distance to the galactic center and how fast we're moving. The distance to the center of our galaxy is about 28,000 light-years. That makes the diameter of our orbit about 56,000 light-years. Since it takes 250,000,000 years to cover "onlhy" 56,000 light-years, that sounds pretty slow compared to all the other speeds. Get your calculator and you find that works out to 0.000672 light-years per year. But...
A light-year is the distance traveled by light1 in one year. And light travels fast. 300,000 kps (that's kilometers per second) fast. It takes light a bit over one second to get to the moon. In that same second it goes around the earth 7-1/2 times.2 And there are a lot of seconds in a year: (60 sec/min) x (60 min/hour) x (24 hour/day) x (365 days/year) gives 31,536,000 seconds/year. The official definition of a light-year is a little different and it works out to be 9,460,730,472,580,800 meters.3 Call it 9.5 trillion kilometers.
Okay, at the risk of being boring, we do the math again, and just get out your calculator:
(9,500,000,000,000 km/ly) x (3 x 56,000 ly) / (250,000,000 year) = 6,384,000,000 km/year
Convert it to kps and we get just over 200 kps!
Okay, so we're spinning around the Earth at a "mere" 1200 kph taking a whole 3-seconds to travel one kilometer. Then the Earth is whipping around the Sun at nearly 28 kilometers every second. And if that wasn't enough, the whole Solar System is whizzing around the galactic center at over 200 kilometers every second. Whew, that's fast. But wait! Our galaxy isn't sitting still. We're currently on a collision course with M31, the Andromeda galaxy speeding toward one another at about 130 kps4. And our entire local group of galaxies is heading in the general direction of galaxies in the constellation Virgo at a speed of about 5,000 kps!.5
1 Technically, its the distance traveled by light in a vacuum. That may sound picky, but light slows down when it has to travel through matter, even the air. It can slow down a lot in certain types of naturally occuring crystals and glasses. In fact, your eyes depend on this effect in order to focus! Light coming in at an angle to a medium where its speed changes results in the light bending. The same thing happens to water waves when, for example, the cross from a deep to a shallow area (or vice-versa). Also, while we talk about "light," the speed really applies to any form of electromagnetic radiation, including things like radio and X-rays.
2 The numbers I used here are not consisten with our earlier estimate of the size of the earth but used the slightly more accurate number of 40,000 km for the radius.
3 http://en.wikipedia.org/wiki/Light_year. The IAU uses 365.25 days/year for their calculation and a more exact speed of light number.
4 See http://www.cita.utoronto.ca/~dubinski/tails/node11.html.
Well, this is being written as a retrospective since I just came back from the session. The handout for Orion is attached; there are three pages, the first is a star chart printed with Starry NIght Pro 6 showing the constellation outline and with the stars all labelled. There are also several nebula indicated by outlines. Nebula are "clouds" (the Latin word literally means "cloud") of dust and gas. Some of these glow due to nearby stars which heat them. Other glow from reflected light, and some do not glow at all.
The second page is taken from the book Uranometria, originally published by Johan Bayer in 1603 as a set of copperplate engravings. His illustration of Orion was both artistic and state-of-the-art as far as star charts go.
The third page has all of the named stars in Orion listed which a few brief facts about them and the origin of their names. Because of time, the children spent only a short time coloring the picture which they took home. We'll talk more about Orion next time and spend a little time on question and ansnwers.
Coordinates are still a bit new to 4th graders at this point---I know 4th graders have started using maps and map coordinates but only a little. Even though they are a bit new in school, you probably hear about them all the time, especially if your parents have a GPS.
On Earth, we use a set of coordinates called longitude and lattitude. Every place on Earth can be designated with two numbers, one for lattitude and one for longitude. If we look at a globe, you will find it has lines drawn on it forming a grid of coordinates. Because the Earth is a sphere, the coordinate system uses angles instead of fixed-distance separations between grid points. For lattitude, 1° is about 70 miles no matter where on Earth you are. But for measuring longitude, 1° is about 70 miles at the equator, but at the north and south poles, all longitudes converge!
The stars are not really little dots on a sphere; they are all at different distances. Earth is also not really a sphere (although it is very close); it has mountains and valleys, caves, oceans, an atmosphere, and buildings.
The celestial sphere is also marked off using angle, much like the Earth. For north-south angles, instead of lattitude, astronomers call the measurement declination. For practical purposes, you can imagine the lines of lattitude extending up into the sky and just being called something different. One small difference is that instead of referring to north and south lattitude, astronomers label north declination as positive and south declination as negative. A star that passes directly overhead here in NYC at lattitude 42° North has a declination of +42°. A star that passes overhead at lattitude 42° South has a declination of -42°.
Longitude is different. For Earth, the lines of longitude are fixed on the surface of the Earth. It's hard to imagine anything different: you don't want your longitude to change just because the Earth is spinning! But for coordinates in the sky, we don't want the way we measure tied to the Earth because then the coordinates would change as the Earth spins. We need a grid attached to the sky. The measurements are called right ascension and it is very similar to longitude with two differences. First, it is fixed on the sky; the "zero point" for right ascension is a line drawn from Earth through the Sun on the vernal (spring) equinox. It doesn't really matter where you start for your zero point, just like there is nothing really special about Greenwich, England, the zero point for longitude. But the convention (that is, the agreed upon standard way of doing this) is to measure from that line. Second, right ascension is measured in hours instead of degrees and the numbers from from 0 hours to 24 hours; there are no negative right ascensions.
Most stars do not have names. Only a few hundred have names and even fewer are what would be considered "well-known." Most stars are referenced just by the coordinates. So while we won't be using coordinates (much) in the club, it's important to at least know what they are and how they work.
The stars we see in in the night sky form 2-D patterns which we label as different constellations. The stars themselves are, of course, all at different distances just like the people in a family photograph. However, unlike people, the stars all appear as little dots on the sky and it is hard to tell which ones are further away. Astronomers have devised various ways to measure their distances which we won't discuss here. We're going to take the distances which have been determined and turn them into a way to make a 3-D model of a constellation. Since we've been learning about Orion, we'll model that constellation.
There are two angles we have to use; the two coordinates we learned about before: right ascension and declination. Right ascension will turn out to be easy, so we'll come back to that in a minute. Declination is the only one we have to worry about.
Orion is very close to being centered on the celestial equator: his legs hang below the celestial equator, his arms above, and his belt is more-or-less on the celestial equator.
Distances and Angles
In the image above, imaging the blue-green dot as Earth and the yellow dot as the star. The red line goes straight to the star and represents the distance to the star. The white line is the celestial equator extended into space. In fact, think of it as something you could walk on, walking out from Earth until you are standing directly underneath the star. How far is this distance? It's shorter than the distance to the star, but how much?
There is a way to calculate this, but we can do a good enough job just by measuring with a ruler. But why do we care?
Well, if we are making a model of the stars, we can't just hang them out in space. They have to be supported on something. So we'll be mounting (via hot-glue) beads on bamboo skewers. We need to know the length to cut the skewer (that's how high up the star is above our celestial equator) and how far away from earth to put it (that's the distance we "walked" to get directly underneath the star).
Actually, for the length of the skewers, we'll add a bit. Some of the stars in Orion are below the celestial equator and its rather inconvenient to have skewers coming out of the bottom of the model. So we'll offset the bottom of the model to keep all the stars above.
There are only seven stars in our model. We'll model the two shoulders, the two legs/knees, and the belt but skip the other stars. Otherwise it gets too crowed. To do this, you'll need the following items:
The attached PDF has two templates, one for cutting the bamboo skewers to the correct length and another for how to position them onto the base. First attach the template to the base. You can tape, glue, or just pin it in place. The template has to be placed diagonal onto the base or it won't fit. You can also trim the template to eliminate any wrap over the edges.
Next, for each star, cut a skewer to the correct length, glue a bead to the top, stick the skewer into the corresponding spot on the base template/styrofoam. I cut my skewers so as to leave the pointed edge attached which made it easier to poke a hole through the paper, but it really doesn't matter which end you cut. Do try to put the skewers in so they stand straight up from the base.
When you're done, you'll probably be thinking this doesn't look much like Orion. Well, it won't unless you put your eye in the correct vantage point so you are looking at the "stars" from the position of Earth. If you've followed the template on this page, then that place is about 8-12 inches from the edge of the base in the direction where all the lines drawn on the base converge. You want to try to place your eye at the height of the belt stars. It works best for me if I only use one eye. Then I have to move the base around a little to find the right spot where the three belt stars line up. Once I have that, I can see the shape of Orion.
The real "fun" is when you move your head away from that spot. This is like flying around in space and viewing the stars of Orion from different places where it really doesn't look anything like our familiar constellation. The point of the exercise is that the constellations we are used to seeing are really just accidental alignments that our imaginations turn into pictures.
I've also added a model template for the Big Dipper which we did not use in class but which I later used at the Northeast Astronomy Forum (NEAF) 2008. It works the same way and the supplies are the same since there are only seven stars used. This model is, however, somewhat more user friendly since many of the stars are at a similar distance making the placement of your head a little less critical.
These models are not to scale! In order to make for comfortable viewing, I cheated on both of them, but especially on Orion.
With Orion, the distance ratio between the farthest and the nearest stars as about 6:1. So if I try to put them all on a single 6-inch by 12-inch foam board, my eye needs to be about 2-inches from the front of the board to be in the same location (to scale) as the Sun's position. At that distance, I can't focus on the closest bead at all and the view is very uncomfortable. So I kept the same relative distances (sort of) and added a large offset (1000 light years!) effectively making Earth much further away. But that creates another problem. If I use the same angular separation, the stars begin to cluster together very tightly. So I increased the angles by a constant scale factor of 3 to spread them all out again. This makes it possible to put your eye about 8-12 inches from the front of the board and get a nearly correct visual view of Orion while still getting a sense of the 3-D structure.
I did the same thing for the Big Dipper, but the distance offset was 300 light years and I actually shrank the angles by 2/3 to fit them on the board.
The constellations of the zodiac have a "reputation" as being special; they appear in daily in every newspaper (albeit, "mispelled" compared to their official names) in the horoscope section. We will not be talking about horoscopes, but we are going to learn a little about these constellations and what make them "special."
We've already learned a little about celestial coordinates (right ascension and declination) and now we have to learn a little more. This time, it's about the Earth's orbit. The Earth orbits the Sun in an ellipse as do all of the planets. The Earth's orbit is, however, very nearly a circle and if drawn to scale on this page, would be indistinguishable from a circle with the Sun at the center. As the earth revolves around the Sun, it always stays in the same plane; it doesn't wiggle up and down. This plane is called the ecliptic.
In many drawings of the solar system, all the planets are shown in the same plane. Its a bit hard to draw the 3-D nature of the solar system on a 2-D sheet of paper, but it is important to realize that he planets do not all orbit the Sun in the same plane as the Earth does. Each has it's own plane. These are all very close to one another, and all are focused on the Sun. This is why, for example, that although a drawing of Pluto's orbit shows it crossing the orbit of Neptune, they don't crash into one another. Even if they were in the same place on the 2-D sheet of paper, the orbits are tilted such that Pluto passes safely above or below Neptune.
Inner Planet Orbits, cropped
The above image shows the orbits of the inner planets on April 8, 2008. If you look closely, you can see the tilted nature of the orbits. Earth's orbit is marked in red to make it easy to find. The other planet's orbits are in blue. Parts of Venus' orbit appear to lie outside the orbit of Earth from this angle. And Mercury's orbit appears to come all the way out to Earth's. This is partially an effect of perspective, but it is also due to the relative tilt of the different orbits. If they all lay in the same plane, you would not see them appearing to cross.
But the other thing you will notice is that they really aren't tilted very much to one another. While the ecliptic is defined as the plane of Earth's orbit, all planets orbit the sun in planes very close to the ecliptic.
The above YouTube video shows a flyby through the solar system which might help visualize the 3-D structure of the orbits. At about 2 minutes into the video, we stop and take a look as we cross the ecliptic the second time so that we can see the orbit of the Earth (again in red) edge on. The view is somewhat messy with orbits from all planets shown in blue. After crossing the ecliptic, the speed picks up to "warp 8" then jumps to about warp 25(!) to exit the solar system.
The only real point in all of the above is to see that the planets all orbit in their own planes and that those planes are actually quite close to one another.
Imagine we could put a dimmer switch on the Sun so we could turn down the brightness until the stars were visible in the daytime. Don't turn it off, just make it dim. If we could do this, then the Sun would appear as a (very) bright star in one of the constellations. But which one would be continuously changing as we revolve around the sun. Think of it like sitting on the merry-go-round looking through the middle and out the other side. The distant scenary is not moving, but it is changing as we move in a circle.
The constellations that the Sun appears to be moving through are the constellations of the zodiac. Wow, that was a lot of build-up to such a simple idea.
But what makes them special? Nothing really, but our ancestors, not really knowing what those moving lights in the sky were, attributed the motion to ancient gods moving through the heavens. Just like the Sun moves through the constellations of the zodiac, so do the planets simply because the plane of their orbits is so close to the ecliptic. So, they concluded, it might be important which constellation the Sun was in when you were born and where those "gods" were wondering around. Fortune tellers loved this and its popularity has never completely gone away. There is, of course, no science behind it.
Traditionally, there are twelve of these. For astronomers, the "first" one is Pisces. It is first because astronomers measure right ascension (the coordinate which is like longitude) starting from the position the Sun occupies on the spring equinox. But since we travel around the whole sky in a big circle, it doesn't really matter where you start. We'll go over them very quickly from east to west.
This session is mostly going to be a "lab" activity. But first a little background.
Everyone "knows" that the moon is covered with craters. But in fact, until the invention of the telescope, this was not at all obvious. While the craters on the moon are large, the moon itself is so far away that it is hard to tell that the brightness differences across the face of the moon are due to terrain changes. But ever since Galileo turned that first telescope onto the moon and discovered that it has craters, craters have been turning up everywhere.
How hard it is to find craters on a planet all depends on the weather. No, not whether or not it is cloudy or raining, but how much weather it has in the first place. The normal weathering processes which cause erosion here on Earth slowly erase craters from the terrain. On the Moon, with no atmosphere and no weather, craters are more-or-less forever. Mercury also has craters. So do most of the moons of other planets. Venus is shrouded in clouds (made of sulfuric acid!) but radar images of the surface reveal craters. Earth has a few crater remnants, mostly in arid regions, but even sandstorms will erase them. Mars has craters. We can't even see the surface of the gas-giant planets (Jupiter, Saturn, Uranus, Neptune), but they probably don't have any craters left from any impact they had in the past. Jupiter was smacked hard by the fragments of comet Shoemaker-Levy in 1994 but whether or not it made any craters is anyone's guess.
Barringer Crater, Arizona, United States
The first meteor crater I learned about was Barringer Crater in Arizona. Before people realized that a meteor impact was probably a major cause for the extinction of the dinosaurs, this was probably the most famous meteor crater on Earth and the first crater to be clearly identified as a meteor impact. Barringer Crater is about 1,200 meters in diameter, the rim rises about 45 meters above the surrounding plain, and the crater center is about 170 meters deep. The force of the impact vaporized the meteor and all that remains are several tons of iron chunks scattered across an area 8--10 miles in diameter centered around the crater.
Barringer Crater is not very old, only about 50,000 years or so. While this is fairly recent in geologic terms, it is probably too long ago for there to have been people in North America. Most scholars believe there were no humans in North America before about 20,000 years ago although one archeological dig1 has found human artifacts in South Carolina which were dated to about 50,000 years ago. It's fascinating to imagine what a person might have seen (assuming they were far enough away to survive!) but there probably wasn't anyone around to witness the event.
Lohar Crater, Deccan Plateau, India
The Lonar Crater was initially assumed to be like any other crater in the area, which is to say, it was a volcanic crater. The Deccan Flats are a region with a long history of volcanic activity and large-scale volcanic activity there may have also played a role in the dinosaurs demise. Howver, the Lonar Crater is meteor impact between 35,000 and 50,000 years ago. It is somewhat larger than Barringer crater at 1,800 meters in diameter but is also shallower, possibly due to the harder rock (basalt) where the impact occurred.
Tenoumer Crater, Sahara Desert, Mauritania
This impact crater is 1,900 meters across and is one of three craters which occur in almost a straight line in the region. Sometimes, a meteor will break up as it enters the atmosphere and result in several craters all lined up. Although that can happen, it turns out that that is not the case here. All three of the craters date to different periods. The Tenoumer Crater is "only" about 10,000 to 30,000 years old again raising the possibility that there were actually humans around to see it.
Kebira Crater, Western Desert, Egypt
This is a very old crater and is, in fact, nearly impossible to identify as a crater. It dates to probably 100 million years ago and shows a double ring structure. The crater is about 31 kilometers across and mostly buried in desert sand which has eroded much of the structure. While the area has an abundance of "desert glass," a form of melted sand that occurs when a meteor impact causes such high temperatures that then rock and sand melts and then is flung across the region, it wasn't until after 2006 that anyone thought to use satellite images to try to find the crater remnant itself.
Pingualuit Crater, Quebec, Canada
This crater was noticed by a US Air Force crew when flying over the region in 1943 but wasn't explored until the 1950s. The crater is about 3,440 meters across and 267 meters deep. This is also an "old" crater by human standards, having been formed by an impact about 1.4 million years ago. The discovery and exploration of this crater eventually led to identifying more than 20 other impact structures in eastern Canada.
The lower part of the Chesapeake Bay, about 85 kilometers across, was also formed by a meteor impact about 15 million years ago. Some have wondered if the Hudson Bay may have been formed by an ancient impact, but an analysis of the rock structures do not show the normal signs of a meteor impact. The best source for finding confirmed meteor impact sites is the University of New Brunswick's Earth Impact Database.
The University of New Brunswick's Earth Impact Database, http://www.unb.ca/passc/ImpactDatabase/, has maps and lists of verified impact sites around the Earth.
The Lunar and Planetary Institute, http://www.lpi.usra.edu/, has research material on impact crater formation, including the figure used on page two of the class handout.
http://www.barringercrater.com/ has a complete history of Daniel Moreau Barringer's misguided efforts at mining to retrieve the meteorite that caused the crater.
1 The Topper archeological site in South Carolina has been reported to have artifacts of human origin that date to 50,000 years ago, but the evidence not conclusive due to natural weathering which has eroded the artifacts.
To form realistic craters you need realistic materials. However, we can't reasonably fire slugs of iron or rock at speeds up to 60 kilometers per second at slabs of rock (not and expect to survive anyway). But that doesn't mean we can't come up with an analog which will demonstrate many of the characteristics of a real impact. One idea I came across is the use of fine sand and a projectile like a marble. I haven't tried this and it may work. Another idea was to use flour instead of the sand. Again, I haven't tried that one, but it sounds like it might work. Here's what I have tried.
You'll need the following:
Pick you favorite flavor of instant pudding. Most of the small boxes are designed to make about 2 cups of pudding and require 2 cups of cold milk to make. However, that results in a pudding which is a little thick for our needs. I use 2-1/2 cups of skim milk (skim milk supposedly makes for thinner pudding in the first place). Chill the pudding for an hour or two so it is set. This will not be runny pudding, but it will certainly not hold its shape very well. I put the entire 2-1/2 cups of pudding into a rectangular plastic container so the pudding itself is 1- to 1.5-inches deep. Congratulations! You've just made your analog Earth for our impact tests.
To best demonstrate what happens with the ejecta, sprinkle powdered sugar over the top of the pudding. You want to wait until the last minute before the experiment to do this part because the pudding is moist and the powdered sugar will immediately start to soak up that moisture and stop being powdery. Note: the powdered sugar will make the experiment significantly more messy! When our "meteor" imacts you are going to get a spray of powdered sugar. You'll also get a spray of pudding, but the powdered sugar will travel quite a bit further.
Now, while the powdered sugar is still powdery, sit the pudding container on the plastic garbage bag. Fling your M&Ms at the pudding. This isn't a carnival contest, so there is no need to stand far away, but do try to hit the container!
The first batch of pudding we made was the stuff you cook. Nothing wrong with it for eating, but.... We made it according to the recipe and it was a bit thick. It also tends to form a crust on top as it cools. When Matthew and Jonathan made their first throws, the M&Ms bounced off! That's when I went out and got the instant pudding and made it a little thin.
Sometimes, perhaps even quite often, the M&Ms will manage to hit the pudding edge-wise. When this happens, instead of making a nice round entry hole with a splat, the M&M may actually sort-of cut its way into the pudding. Just ignore those as unrealistic. Our boys are both allegic to nuts, so at home we used M&M-clones from Vermont Nut-Free Chocolates. These are a bit more round than regular M&Ms and didn't have this "problem." But you probably don't want to order these more expensive candies just for the experiment.
The children have to kneel down near the pudding container to throw. That bowl looks easy to hit when standing up, but you'd be surprised at home many misses you get.
First, its fun to just fling the M&Ms at the pudding, so its easy to let things get out of hand and not pay attention to what's happening. When we did this at home, there were several things we noticed. First, the powdered sugar goes in all directions, but more goes away from the direction of the incoming M&M. Second, the pudding itself creates a small crater rim around the impact site. Third, while the hole formed is approximately circular, it's not symmetrical like a bowl; if the M&M went in at an angle, the hole goes down at an angle. Fourth, the pudding is watery enough that if we wait a few minutes, the pudding fills in around the M&M and the bottom starts to look more bowl-like (think "simple crater").
I'll add one more thing, too. When I flung an M&M at the pudding, both of my sons standing off to the side commented that the felt splatters from the pudding. This was a good opportunity to comment on both how far the splat can go (remember Barringer Crater, ejecta spread over a 10 mile circle) and how the splat is not confined to the "downrange" direction from the impact.
Usually in science, eating your experiment is a bad idea. In this case, enjoy!
It's everywhere and can't be escaped. Articles have been written on it's dangers. Special glasses and creams are designed to protect you from it. But some leaks right through the walls of you house. Some passes right through you! What is it?
Electromagnetic radiation comes in many forms; most of you know if at light. But light is just one tiny part of the electromagnetic spectrum, the full range of radiation that exists. Your eyes are designed as very efficient detectors of light, but they can't see infrared radiation; but you can feel it with your hands---infrared radiation is detected as heat. The microwaves that heat your food are another form. And every house has another detector (or more) that detect radio and television waves, both types of electromagnetic radiation. Summer is coming and the commercials will be full of warnings about wearing sunglasses and using sun block lotion to protect against ultraviolet radiation, another kind that you can't see. When you go to the dentist, they might X-ray your teeth; that's another kind.
Electromagnetic radiation is all very much the same in some ways even though the kind of detector you need is very different and what you can do with it (or what it does to you) can also be very different. But all of them are "cousins" of the ordinary visible light you can see with your eyes.
Electromagnetic radiation is a kind of wave, much like waves on water. For a long time, scientists thought that just like water waves, light needed something to travel in. They called that something ether. No one had ever seen it, but they figured it had to exist because all waves travel through something. There was a lot of work done trying to find the ether. No one ever found it and after a while, some experiments were able to show that it didn't exist. That's one thing that makes electromagnetic waves different from other waves---they can travel in empty space. They are affected by matter (you hand can stop visible light!) but they don't require some special think like water for ocean waves or air for sound waves.
There are two ways of measuring waves: frequency and wavelength. The two are related like multiplication and division. In fact, if you multiply the frequency and wavelength of a wave, you get back its speed. For electromagnetic waves, that speed is the speed of light.
You know what a meter is and a centimeter. The microwaves in your microwave oven have a wavelength of about 12 centimeters. Personally, I find that confusing. I would have thought that a microwave would have a wavelength measured in micrometers. There are one million micrometers in one meter. I can't find any clear origin of the why they got called "micro" waves since they are only about 1,000 times smaller than AM radio waves, not 1,000,000 time smaller. I think the word micro simply got stuck on because they are much smaller, kind of like today it's popular to put the prefix "nano" in front of high-tech things to indicate "really, really small" not because it's really one billion times smaller (think of the problems if your iPod nano really were "nano" sized!).
AM radio waves have wavelengths from about 560 meters (corresponding to 535 on your AM dial) down to about 230 meters (corresponding to AM 1300). FM wavelengths are shorter, but still measured in meters. And TV are even shorter. Microwaves range from about 1 millimeter to about 30 centimeters. Below that range, the waves are called infrared, Infrared waves go down to about on micrometer, that is, one millionth of a meter. A little below that is were the deepest red light become visible to our eyes. With waves a little shorter than what our eyes can see you find ultraviolet. Shorter still are X-rays, and shorter yet are gamma rays. Waves shorter than that don't have names or just get called "high energy gamma rays."
Almost everything we know about astronomy comes from what we can "see" through electromagnetic radiation. The Hubble Space Telescope can "see" both infrared and visible There have been specialized space telescopes which can "see" radio waves, ultraviolet, or X-rays. Some of these telescopes can tell the difference between different wavelenghts of ultraviolet radiation just like our eyes can tell the difference between different colors of light. Those telescopes convert the different "colors" of ultraviolet radiation into colors our eyes can see. One of the bettern known such space telescopes is GALEX, the Galaxy Evolution Explorer which has produced a lot of pretty pictures.
Today we are making ultraviolet detector bracelets using special beads which are sensitive to ultraviolet light. In addition to turning bright colors when exposed to the Sun, you can use the beads to test your sunglasses. Put your finished bracelet behind your sunglasses and see if the beads turn colors. If they do, how much longer does it take?
So what is the nearest star to Earth? If you answered Alpha Centauri, you're wrong. And if you're smugly thinking that Proxima Centauri is closer, your right (it is closer) but it's still not the closest star to Earth. That honor goes to...the Sun. Our star is a rather ordinary star in many ways. It is special to us because it is so close. Nearly all life on Earth depends on the Sun. But what makes the Sun shine?
People have probably wondered about this as long as there have been
people to wonder. By the middle of the 1800s, the size of the Sun was
known well enough to estimate how long the Sun could burn. The first
idea was what if the Sun was made of nothing but pure carbon
(the chemical found in coal and gasoline which makes them burn) and
oxygen? In this case, the Sun would burn for only about 1,500 years.1 Another idea was that the Sun was giving up it's energy from gravitational collapse.
When an object is compressed (squeezed) together, it gets hot. Gravity
can do the squeezing. In 1847, a man named Hermon von Helmholtz
calculated that if this were what caused the Sun to shine, it would
last for about 20 million years. That was the best idea anyone had for
about the next 50 years.
Fusion just means joining things together to form a new thing. The glue that is used to attach parts of a plastic airplane model melt the plastic parts a little so they are fused together like one part. For the Sun, fusion is what makes it shine, but the parts that get fused are atomic nuclei (nuke-lee-eye, the plural form of nucleus), specifically, the nuclei of hydrogen.
Hydrogen is the simplest atom. It has one proton, a positively charged particle in its center, which we call the nucleus. It has one electron, a negatively charged particle, orbiting around the proton. The center of the Sun is very hot and the pressure is also very large. This high pressure and temperature squeezes the protons and electrons very close together. Sometimes they get close enough that they can fuse together to form a helium nucleus. A helium nucleus is made of two protons and two neutrons. Where did the neutrons come from? Well, it turns out that sometimes, when you're squeezing electrons and protons close together, they can combine to form a neutron. It's a little more complicated than that, but that's the basic idea. The recipe in the middle of the Sun is something like this: take four protons and four electrons, squeeze them together really hard, and sometimes you end up with a helium nucleus (composed two protons and two neutrons all stuck together) and two left-over electrons.
If you add up the mass of the original four protons and four electrons and compare them with the final mass of the helium nucleus and two electrons, there's are tiny bit of mass missing. Where did it go? Albert Einstein had the answer: E=mc2. The missing mass ("m" in his equation) was converted into energy ("E" in his equation). The process is called nuclear fusion. All stars "burn" by this process, converting hydrogen to helium, and the helium into other elements all the way up to iron while producing energy that makes them get very hot and shine.
It is only in the very center of the Sun that the temperature and pressure are high enough to cause nuclear fusion. A little further out, the Sun is still very hot, but not quite hot enough for fusion. Each of the regions on the inside of the Sun that all behave a little differently.
First there is the core, the central part where nuclear fusion is really taking place. This region is the source for all the energy that has to works its way out of the core to the outer edge where it escapes into space to provide us with light and warmth.
Second is the radiative zone. This is where the energy radiates or spreads outward by having the atoms of hot gases (mostly hydrogen) bump against each other and emit electromagnetic radiation that is captured by the next atom over.
Third is the convective zone. This is where there the hot gases churn and move around much like the water in a boiling point. Instead of the heat moving outward by electromagnetic radiation, it is moving outward because the hot gases themselves are moving.
Fourth is the photosphere. The prefix photo just means "light." This is the layer of the sun that produces the light we see. This layer can be thought of as the Sun's "surface;" but the Sun doesn't really have a surface like Earth since it is not really solid. Sunspots, which are places where the Sun is actually a little cooler, appear on the photosphere. This part of the Sun is about 5,800ºC. The sunspots can be much "cooler" at a mere 3,700ºC!
Fifth is the chromosphere. The prefix chromo just means "color." This region can only be seen here on earth during an total solar eclipse. During a total eclipse of the sun, around the edge of the moon you can see the sun's colorful red edge sticking out. There is a good picture of the Sun's chromosphere (http://apod.nasa.gov/apod/ap040611.html) taken during the last time Venus appeared to cross in front of the Sun.
The sixth and last region is the corona. The word corona means "crown" and you can think of this as the part that sits on "top" of the other layers like a crown sits on top of a king or queen. The corona can also only be seen during a total eclipse of the sun as rays or streamers that seem to pour out from the Sun just above the chromosphere. There is a good picture of the Sun's corona (http://apod.nasa.gov/apod/ap010408.html) on the Astonomy Picture of the Day website.
1 How Did We Find Out About Sunshine, Isaac Asimov, Walker & Company, 1987, Paperback ISBN 0802766986.
When you think of exploring someplace, you probably think of going there and looking around. However, with the exception of our own Solar System, astronomical exploration is done remotely, by looking with specialized instruments. Most of these are right here on our planet. While none of you in this class can remember a time when we didn't have the Hubble Space Telescope or the Space Shuttle, it was really not so long ago that none of these existed. For most of the past 400 years, since the invention of the telescope, earth-bound telescope were the only way to explore space. But since then, spacecraft have advanced quickly.
The first spacecraft didn't go far, venturing barely outside Earth's atmosphere. The first of these was the Soviet sputnik (which just means satellite) launched in 1957. It was in some ways more a "proof of concept" than anything else and, at that time, due to the competition between the USA and the USSR, it was a chance fot the USSR to claim the lead on the "space race." Sputnik 1 was followed by Sputnik 2 which carried a dog named Laika. The dog travelled into space and returned home safely. While it may seem obvious today, before Sputnik 2 it was not known if living creatures could survive in space.
The USA followed with the Explorer 1, 2, and 3 satellites. Explorer 2 failed to reach orbit. Explorer 3 carried a Geiger counter, a special instrument for detecting radiation. This experiment was designed by James van Allen and it discovered the existence of zones high above the Earth's atmosphere where the Earth's magnetic field trapped radiation from the Sun. Today, those regions are still called the van Allen radiation belts.
In the 1960s, most of the attention about spacecraft was focused on manned spacecraft like the USA's Mercury, Gemini, and Apollo missions. The Mercury spacecraft carried only one person, the Gemini two, and the Apollo three. At that time, the focus was a space race to the Moon. However, manned spacecraft were not the only ones.
Starting in 1962, NASA launched a series of spacecraft called Mariner to explore Venus and Mars. The first one failed during launch and was destroyed. However, of the 10 attempts to launch over the next 11 years, 8 were successful and provided the close looks at those planets. During the same time period, the USSR launced a series of spacecraft to explore Venus called Venera. Venera 1 was actually the first successful interplanetary probe. Later, in December 1970, Venera 7 became the first spacecraft to land on another planet (Venus) and transmit data back from the surface.
The Pioneer series of spacecraft were first launched in 1958. However, the most "famous" were Pioneer 10 and 11, launched in 1972 and 1973, respectively. Pioneer 10 was the first spacecraft to travel to Jupiter, and Pioneer 11 the first to travel to Saturn. The power source for both have failed and while they are still travelling away from the Sun, it is no longer possible to communicate with them.
The two oldest spacecraft still transmitting are Voyager 1 and 2, both launched in the late 70s. They are far past the orbit of Pluto now. Voyage 1 is about 106 time s farther from the Sun than the Earth while Voyager 2 is "merely" 85 times farther. Both are still working and sending back useful information about the far reaches of our Solar System. Both visted Jupiter and Saturn, the first spacecraft to do so. Voyager 2 was also able to visit Uranus and Neptune. You can learn more about them at http://voyager.jpl.nasa.gov/.
For the past 4 years, the two robotic landers Spirit and Opportunity have been cruising around the surface of Mars. The images they have sent back have made it hard to remember that less than 100 years ago, people still believed Mars might harbor large creatures and canals full of water!
The two most recent additions to NASAs interplanetary explorers are MESSENGER, which has recently begun to send back images and other information from Mecury, and New Horizons, which is on its way to Pluto.
Everyone knows about the Hubble Space Telescope which was carried into orbit by the Space Shuttle in 1990. But it was not the first space telescope.
In 1970, NASA launched Uhuru, also called the Small Astronomy Satellite 1 (SAS-1) which was the first to study the sky using X-rays. It was followed by SAS-2 and SAS-3 which also studied X-rays.
NASA launched three X-ray telescopes, one each in 1977, 1978, and 1979. Like infrared electromagnetic radiation, X-rays are also blocked by Earth's atmosphere.
The Infrared Astronomy Satellite (IRAS) was launced in 1983 and was the first spacecraft to study most of the sky using infrared electromagnetic radiation. Most of this type of electromagnetic radiation is blocked by the Earth's atmosphere. IRAS only lasted about 10 months.
The Solar and Heliospheric Observatory (SOHO) studies only the Sun. It can take pictures of the Sun using specific wavelengths of light emitted only by helium, calcium, or iron. It also has a special instrument called a coronograph which blocks out the body of the Sun and allows only the Sun's corona to show around the edges. These images are very useful for studying the solar wind which is made of the gases blown off by the Sun. You can see the latest images from SOHO at http://sohowww.nascom.nasa.gov/.
When someone says robot you probably don't think of spacecraft. But that's exactly what they are. Because of the great distances involved, may of these spacecraft have computers on board which not only gather information and transmit it back to Earth, but also make decisions on what to take pictures of an what to send back. Many of the "decisions" these robots make are simple to us, like keept the antenna pointed at Earth, but they have to be made without anyone there to fix things.