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4th Grade class: Day/Night, the Seasons, Lunar Phases, Eclipses

Joseph Mack

jmack (at) austintek (dot) com
AustinTek home page

15 Dec 2018, released under GPL-v3.


A lesson on simple celestial mechanics, given to 4th graders.

Nov 2018: I don't have a video yet. I've at least shot a few classes, but editing is a difficult task and I'm not prepared to tackle it right now.

Material/images from this webpage may be used, as long as credit is given to the author, and the url of this webpage is included as a reference.

First presentation 2-3 Dec 2015.

Table of Contents

1. Lesson on simple celestial mechanics using a Simple Orrery
2. Intro
2.1. Class Plan
2.2. Orrery

3. Early ideas about the Universe
3.1. Earth Rotates on its Axis
3.2. Stars
3.3. Copernicus
3.4. Copernicus Test

4. Day/Night
4.1. Sunrise, Sunset
4.2. Sunrise, Sunset lines
4.3. Sunrise, Sunset lines change with Seasons
4.4. Day/Night Test

5. Seasons
5.1. Earth orbits the Sun in the Ecliptic Plane
5.2. The year for a planet with axis perpendicular to the Plane of the Ecliptic
5.3. Tilt of Earth's Axis to the Plane of the Ecliptic
5.4. Seasons Test
5.5. Solstice, Equinox
5.6. The Tropics
5.7. Circles: Arctic, Antarctic
5.8. Solstice and Circles Test
5.9. Equation of Time and Sundials

6. Local time/mean time, equation of time
6.1. Local time/mean time, time zones

7. Recap Test
8. The Moon
8.1. The Month
8.2. Month Test
8.3. Lunar Phases
8.4. Phases Video
8.5. Phases Test
8.6. Solar and Lunar Calendars
8.7. Calendar Test
8.8. Late Heavy Bombardment

9. Eclipses
9.1. Mechanism of Eclipses
9.2. Moon's orbit is inclined to the plane of the Ecliptic
9.3. Eclipses of Geosynchronous Satellites
9.4. Eclipse Test
9.5. Lunar Eclipse Video
9.6. Solar Eclipse Video
9.7. Eratosthenes and the Diameter of the Moon
9.8. Predicting Eclipses

10. Vocabulary
11. Important Dates in History
12. The Video
13. miscellaneous
14. bring

1. Lesson on simple celestial mechanics using a Simple Orrery

This is given to 4th graders. It takes 2 40min classes to present the material. The classes are usually a week apart. (There are 4 sets of 4th graders at the school.)


In Mar 2018 for the 3rd grade icosahedron class, at the end of the last class, the kids were waiting to file out of class and standing next to my camera. The teacher and the assistant weren't keeping an eye on them. some brat decided to mess with my camera, including whacking the handles and turning it around 180. I yelled at him, several times, from across the room, to stop. He didn't, so I came over and yelled very loudly for him to stop. This had the unintended side effect of making all the other kids cower. He did stop. A bit later Lauri told him that messing with my equipment was not OK and said "what do you say?". He said "sorry". I glowered at him and said "OK".

Lyn afterwards didn't apologise for his behaviour, only saying "he's impulsive". This is obvious. A description of the problem isn't a path to fixing it. He will be in my 4th grade orrery class in the fall. I need to tell Lyn for the next class that this kid needs a talking to before I accept teaching him again.


Light for the Sun

In 2015 I used a 500W incandescent light (2700K, yellow/brown) for the sun. In 2016 I used an LED light for the sun (5600K, daylight). The LED light is the same colour as the room's fluorescent lights. When you turn the room's fluorescent lights out, you can leave the video camera with the same colour temperature setting, simplifying colour control for the video. However the educational point is made equally well using either light. I just happen to have an LED light available. The incandescent light is cheap and available from large hardware stores. It's also very hot and many parts of it can't be touched. The LED light is relatively expensive and only available from large camera stores. It's cool to the touch everywhere.

Tests for the kids

At the end of each section I give a test. This is to reinforce the student's knowledge and to give me an idea of how many kids are following the material. I expect to find at least one kid who absorbs the whole class with ease, and one kid who doesn't understand any of it. After giving a question, I ask kids to raise their hand when they have an answer, but not to call it out. After enough kids have raised their hands, showing that they've had enough time to think about the question, I ask one kid with their hand up. It isn't always the first kid to raise their hand. I try to let as many kids as possible get to answer a question. Unfortunately only about 1/3 of the class ever put up their hands. I assume then that the other 2/3 of the class are having trouble with the material or my teaching.

On the board is a set of vocab words from the presentation. I'll tell the students that I will explain all of the words, at that by the end of the presentation they will know what they mean.

Setup globe of the Earth on a stool/table in the middle of the darkened room. Illuminate the globe by a strong light on a stool a couple of feet away from the Earth. The light faces me (away from the class, so the class is not dazzled). A globe of the Moon is on the table. It will be moved off, when the demonstration of day and night starts.

The Moon's orbit is inclined to the plane of the ecliptic. I use a hula hoop to show the position of the Moon's orbit. Because the moon's orbit is inclined to the plane of the ecliptic, you don't get solar eclipses every new Moon and you don't get lunar eclipses every full Moon.

2. Intro

2.1. Class Plan

I'm going to be giving two classes. In the first class I'm going to be talking about why we have

  • day/night
  • the seasons

In the second class I'm going to be talking about why we have

  • phases of the Moon
  • solar and lunar eclipses

To see what's going on in this class, you're going to have to move around. Feel free to move anytime you like; you don't have to ask - just move. You don't have to stay in your seats. When you move, move slowly so you don't trip on any power cords and you don't bump anything over.

I'm going to need the room lights turned on and off a few times. Would someone in the back table there be prepared to turn the room lights on and off when I ask for it? (thanks).

To the volunteer: Can we have a practice turn-off and turn-on? Thanks. If something is happening down the front of the class, that you need to see, and I ask for the lights to be turned off, you'll need to first turn off the lights before coming down here. Can you handle that?
At the end of the class, get the class to give a round of applause for the kid who did the lights.

There's a vocab list on the board. By the end of the two classes, you'll know how to use these words.

I'm going to be asking questions during the class. If you want to answer a question, please put your hand up, rather than calling out. I won't always pick the first person, because I want as many of you to have a turn at answering a question as possible. I know you all want to say something in front of the class, but please don't put your hand up unless you have an answer. Some kids like to put their hand up, only to find that they don't have an answer. This just wastes everyone's time. So think first and then put up your hand. You're not going to be asked to give the answer, just because you were the first to put your hand up. There's no rush to be the first person with your hand up.

Some of the questions are going to have answers on the board. I'm quite happy for you to get the answer off the board.

2.2. Orrery

What you see before you on the table is called an orrery. An orrery is a mechanical device to represent the motions of the planets in the solar system.

A real orrery is mechanical; it has motors and gears and runs by itself, with the planets moving the same was they do in the sky.

Here's a wooden orrery, that just represents the Sun, Earth and Moon.


Here's a complicated mechanical orrery. It shows the planets known to the ancients, Mercury, Venus, the Earth and Moon, Mars, Jupiter and Saturn.


With my orrery, I'm only going to represent the Sun, by this light (turn on), the Earth and Moon. I'm going to move things by hand. So it's a very simple orrery.

3. Early ideas about the Universe

3.1. Earth Rotates on its Axis

take away the moon.

Here is a globe of the Earth. Over there is a light representing the sun.

turn off room lights.

As you can see, the Sun lights up half of the globe representing the earth, while the the other half of the globe is in darkness. The part of the Earth that's illuminated by the Sun, represents the earth in daylight, while the half that's not illuminated, represents the Earth at night.

Name some countries that are in day, night. Nominate a country and ask whether it's in day or night.

We all know that the Earth rotates on it's axis.

spin the Earth slowly, so that at least some of the kids see countries being illuminated by the Sun and then going into darkness.

Notice how as the Earth rotates, that some countries come into daylight, after seeing the sun rise, while other countries go into nighttime after seeing the sun set. In the middle of the day, the sun appears overhead, and this is called noon.

After the earth rotates on its axis once, the sun returns to the same position in the sky. To mark the passage of time, you could pick a convenient marker for the location of the sun, such as sunrise, sunset or noon. How long does the Earth take to rotate once on its axis?

24 hrs, 1 day; it's the definition of a day.

I just said that we all know that the Earth rotates on its axis. How do we know this?

with your hand, trace the path of the sun through the sky in the day, as viewed from the classroom, showing the elevation of the sun at sunrise, noon and sunset and then the path of the stars at night.

The sun rises over there (in what direction does the sun rise? E), comes to the highest point in the sky in the middle of the day, at a time which we call noon, and then sets over there (in what direction does the sun set? W). The same thing happens at night; the stars rise in the east, culminate above us (culminating meaning reaching the highest point in the sky), and then later in the night set in the west.

  • during the day, when we look up, as the day progresses, we see the Sun crossing the sky.
  • during the night, when we look up, as the night progresses, we see the stars crossing the sky.

Here's a time lapse photo of the passage of the sun through the sky in the day. The actual path is an arc of a circle. Because of distortion by the camera, the arc is a bit flattened.


This is one piece of evidence that the earth rotates on its axis. I will talk about this more a little bit later.

3.2. Stars

We're going to have a little diversion here. I'm going to talk about the stars, the solar system, the galaxy we live in and the universe. Then we'll return to day and night.

All the bright stars have names. Can anyone name some stars?


  • Sirius - the brightest star in the night sky. It's in the constellation of Canis major, or the big dog.
  • Canopus - the brightest star in the southern hemisphere. It's at the south pole of the ecliptic plane (which I'll talk about later). Satellites and interplanetary space probes use Canopus for setting a frame of reference.
  • Castor and Pollux - the twins in the constellation of Geminii
  • Regulus - the brightest star in the constellation of Leo
  • Antares - the brightest star in the constellation of Scorpio. It's red and has the same colour as Mars.
  • Vega, Rigel, Aldebaran, Spica.

There are star chart apps for cell phones. You hold up your cell phone to the sky and it shows the stars and planets in that part of the sky.

Most of the names of stars are Arabic. This is because the Arabs, living in the desert, had good cloudless skies to observe the night sky.

It's also because during the middle or dark ages, which lasted about 1000yrs, from about 500AD to 1500AD, in Europe, all academic and scientific work was repressed or banned by the church. Europeans lost all of the knowledge of the ancients. It was the Arabs who kept knowledge alive by translating the Greek works into Arabic. When, 1000 years later, Europe emerged from the Dark Ages, the works of the Greeks were translated back from Arabic into Latin. If it wasn't for the Arabs, who kept knowledge alive for the 1000yrs of the Dark Ages, today we wouldn't even know who the famous Greek philosophers, Plato and Aristotle were.

What's the name of the brightest star in the sky?

This was a trick question. The brightest star in the night sky is Sirius. The Sun is a star too, so the brightest star in the sky is actually The Sun. By convention we think of stars as the pinpoints of light we see in the sky at night, so most people don't think of The Sun as a star. The Sun is the pedantic or most correct answer to that quesion. Most people would quite reasonably give Sirius as the answer. Sometimes we agree to not be pedantic, so that we can get on with our lives.

The Sun has a name too. Does anyone know The Sun's name?

It's name is Sol, which is where we get the name Solar System.

Calling Sol "The Sun" is like calling someone by a generic name, like "the kid" or "the cat". But we only have one star in the center of our Solar System, so calling it the Sun works out OK enough. The Sun doesn't seem to mind and today we'll call it "The Sun" too.

Leave out.

On earth we use the term "day" to describe the period from midnight to midnight. The day on other planets occurs at differnt times to the day on earth.

Scientists planning activities for the robots running around the surface of Mars, need to know whether they're talking about their day on earth or the robot's day on Mars. They use the word "sol" for the Martian day. They talk .about "yestersol", "tosol", "nextersol" "morrowsol" "solmorrow", and for the period when you're not doing anything "soliday". ( One of the robots may be doing something later tosol, that is, later during the robot's day on Mars, even though the activity will be happening tomorrow, for the scientists on earth.

Our moon, which we call "The Moon" has a name too "Luna". This is where we get the adjective "lunar". We only have one moon, so in English we just say "the Moon".

on the board from Lyn

The existance of other moons in the solar system wasn't discovered till the invention of the telescope. In 1610 Galileo turned a telescope to Jupiter to find 4 moons orbiting Jupiter.

You can't see the moons with the naked eye, but this is the view you'll get with regular binoculars.

images/3.2/galilean_moons.jpg from SciencePhotoLibrary.

Since then, we've discovered many more moons orbiting the other planets. Most of the planets have multiple moons, and these moons all have their own names too. The earth is the only planet with one moon.

The Earth doesn't have its own name either. It's just called "earth", the material we grow crops on.

3.3. Copernicus

arc hand as you did earlier, when showing the motion of the sun and the stars across the sky, so the kids recall you talking about the earth rotating in front of the sun.

I just said that by looking at the motion of the Sun and the stars across the sky, we can tell that the Earth is rotating about its axis. But we actually can't tell that just by looking. It could be that the sun and the stars are rotating about a fixed Earth.

Picking between these two possibilities, turns out to be difficult. From our position, sitting on the surface of the earth, we'd see the same thing in both cases.

Back in the old days, people, being people, thought that they were the centre of the universe and that the sun, the planets, the stars and everything else that existed, was created for their benefit, and revolved around them. This model of the solar system, where the earth is at the centre, is called the geocentric (earth centric) model.

However to everyone's surprise, in 1543 Nicholas Copernicus ( realised that the Earth and the planets all revolved around the sun. This model of the Solar system, with the sun at the centre, was called the heliocentric (sun centric) model.

Copernicus' heliocentric model was much simpler than the geocentric model. His discovery was a major event in the history of science. It was the first step out of the Dark Ages.

The next question is how does science establish what is true. In particular how do we choose between the heliocentric model and the geocentric model of the solar system.

In the modern era, you establish truth by asking questions of Nature, (i.e. the physical world) and you do that with experiments. Nature does not lie, nor does it dissemble, nor does it make mistakes. Nature patiently gives consistent answers without favouring anyone. No matter who you are, whether you're black/white, male/female, adult/child, no matter what your creed or belief system, Nature always gives the same answer. If you drop a ball a 100 times or 1000 times, the ball always behaves the same way. Nature doesn't punish or intimidate you if you disagree with it; you'll just find out you're wrong. Nature will still continue to answer you, even if you're wrong. Because of the way Nature responds to questions, we have a lot of respect for Nature and we trust that its answers are true.

But back in Copernicus' day, the church was the arbiter of truth. The church held that the Sun and planets all orbited the Earth, i.e. the solar system was geocentric. If you said otherwise, that the Earth orbited the Sun, as Copernicus said, you were committing heresy (i.e. saying something contrary to the teachings of the church). If Copernicus revealed that the Solar system was heliocentric, he risked imprisonment, torture and death. Because of the treatment he expected from the church, Copernicus didn't dare publish his theory while he was alive and had it published posthumously.

Copernicus' fears were justified

  • In 1600, Bruno extended the Copernican system, saying that the stars were suns just like our sun (which we now know is true), and some of them likely would have planets (which we now know is true), inhabited by beings like us (which we have no information on), and that these beings would have souls. For saying this, Bruno was burned at the stake.
  • In 1615, Galileo was put under house arrest for life, for championing Copernicus' heliocentric view of the solar system.

In science, if you have two theories that explain the evidence, in this case the heliocentric model and the geocentric model, and one is simpler than the other, you accept the simpler theory and you discard the complicated one. This principle is called Occam's Razor. Copernicus' heliocentric system was simpler than the geocentric system, so in science you use Occam's Razor to pick the simpler system.

Even after accepting that the Sun was the center of the Solar system, people didn't know of anything beyond the Solar sytem. As far as they knew, the Solar System was the whole universe, with the stars fixed on a rigid transparent sphere, just outside the orbit of the outermost planet, Saturn.

Copernicus lived in the era before telescopes. With the arrival of the modern era, the view of the Solar System as being all there was, was quickly demolished. In the 1600s, the invention of the telescope revealed that the stars were at an unmeasurably large distance outside the Solar System. The universe suddenly was revealed as being a lot bigger than anyone thought and the Solar System was found to be very small.

It was only last century that people realised that our sun, was a very ordinary star in a spiral galaxy consisting of about 100 billion stars. Here's a photo of a spiral galaxy.

presumably Lyn has a photo of a spiral galaxy. There's a nice high res photo of M101 in Wikipedia.


Our galaxy looks much like this.

Does anyone know the name of the galaxy which is our home?

The Milky Way. The word "galaxy" means milk. It's where we get the words "lactose, galactose and lactation".

The ancients, when they looked up in the sky, saw a band of what look like milk painted across the sky. The ancients could easily see the Milky Way, just by looking up. Even 100 years ago, before artificial lighting polluted the night sky, you could see the stars and Milky Way from anywhere, including in cities. Where I grew up, in Sydney, after about 10pm, when everyone was home for the night, they turned off the street lights and you could see the sky clearly. But for us to see the Milky Way now, with street lighting all night, we have to go to a place with no light pollution, i.e. away from populated areas.

Here's an image of eastern USA at night from space. You can see that in populated areas it's very bright at night. (Lyn has this)


Can anyone locate Durham? (see Pamlico and Albermarle Sound. Go directly West to Raleigh and then NW to Durham/Chapel Hill. The twin cities of Greensboro and Winston-Salem are west of Durham.) Would anyone like to identify a city on this map.

Our sun is just one of billions of stars in the Milky Way. When you look at the other stars in our galaxy, you find that our Sun is a very ordinary star. It's not even located in a special part of the galaxy. Our sun is located in the very outer reaches of the Milky Way, in one of the spiral arms.

leave out

Does anyone know why I didn't show you a picture, like the spiral galaxy above, of our galaxy from the outside?

we don't have one. We haven't sent a spacecraft outside our galaxy yet to get a look at it. This journey would take millions of years. We have to infer the shape of our galaxy, by observing the propagation of radio waves through it.

Our galaxy looks like this photo of galaxy M101. Our Solar System is on one of the spiral arms. At night, when look towards the center of the galaxy, we see a dense mass of stars. This part of the sky looks like milk. This is in the direction of the constellation Sagittarius.

If we look in the opposite direction, i.e. away from the center of the galaxy, we're looking towards the edge of the galaxy, and the cloud of stars is much thinner, but still an obvious milky band. There we're looking towards the constellation of Geminii.

If we look up or down in the plane of the galaxy, we see don't see many stars at all.

Here's the Milky Way from the inside. Jewels of the night sky: time-lapse video, Chile - Nikon D810A

This is what the sky really looks like at night. We don't see this view of the sky anymore in populated areas. The night sky is washed out by street lights.

Not in class any more.

Here's a view of the earth at night. It's been assembled from multiple shots taken when there's no cloud cover. It's called the black marble, this being the night time view of the blue marble, another name for the earth, that's come about by looking at pictures of the earth from space. Black Marble

Here's a view eastern USA at night. Anywhere near lights, you're only going to see the brightest of stars. You won't see the Milky Way except in an area with no lights. The link contains two videos; The night side of earth (celebrating how cool the earth looks at night) (2mins ) and earth from the ISS at night (5 mins The last one is really nice, but not directly on the subject. The first one doesn't make the point any better than the image of eastern USA.

Just like earlier astronomers thought that the Solar system was the whole universe, the next step was thinking that the Milky Way was the whole universe.

leave out.

Astronomers didn't realise the Milky Way was just another galaxy. When astronomers first built telescopes big enough to see galaxies, they thought that the galaxies were close by and part of the Milky way. The telescopes back then weren't good enough to see that galaxies contained stars; Back then, the pictures astronomers had of galaxies just showed fuzzy blobs. Astronomers didn't realise that galaxies were billions of stars, each one a pin point.

Then early in the 20th century, astronomers built telescopes big enough to see that the galaxies contained billions of stars. They immediately recognised that the galaxies were a very long, long way away and were outside of the Milky Way. For us to see the galaxies so far away, they had to very, very big. The astronomers realised that the galaxies were as big as the Milky Way. So the Milky Way wasn't the whole universe at all; it was just another galaxy. Astronomers realised that the size of the universe was thousands of times bigger than they thought. There was nothing special about the Milky Way, except that we lived in it.

All the stars we see at night are suns within our galaxy, The Milky Way. There are stars in all the other galaxies too, but they are too far away to see as points with our eyes, or even with ordinary telescopes.

The nearest galaxy to us is Andromeda. In a dark spot, i.e. with no light pollution, you can see Andromeda with the naked eye as a faint fuzzy blob.


Here's a photo of Andromeda (presumably Lyn has this). It's the galaxy that's our nearest neighbour. With binoculars or a small telescope, you can clearly see that it's a galaxy. It's quite large, 3 across or 6 times the diameter of the Moon. In this photo, you can't see the individual stars in Andromeda; they're just a blurr. All the pinpoints you can see in the photo are stars local to the Milky way, which are much closer than Andromeda.

leave out

Andromeda is 2.5M light years away, and is 220kLight years across. This means that Andromeda is far enough away that the light we see now from Andromeda, left 2.5Myrs ago.

Remembering important dates in history, what was happening on earth 2.5M years ago?

  • Were there any humans around 2.5Mya? No. Modern humans evolved only about 1Mya. Our ancestors who were alive 2.5Mya, were still in Africa Smithsonian Family Tree and are called Australopithecines. They walked upright, but still could climb trees easily.
  • Had the Ice Ages started 2.5Mya? Yes Wikipedia Ice Ages. The Ice Ages started 2.6Mya, covering Greenland, the Artic, the Antarctic, North America, Northern Europe and Siberia, with sheets of ice, thousands of feet thick.

    Here's a map of the ice sheet Humanities7: ice age world maps (images/earth-last-ice-age.jpg). Notice the ice came down to Memphis TN.

This view didn't last long either. Very quickly astronomers realised that the Milky Way was just one of billions of galaxies.

If you have a really big telescope, like Hubble, and you look between the gaps of the stars in the Milky Way, this is what you'll see; galaxies everywhere. (show photo of many galaxies.) e.g. Hubble Ultra Deep Field containing 10,000 galaxies.


So the Milky Way is only one of billions of galaxies in the universe.

What we learn from science is that the universe was not created for us, that it does not revolve around us. Humans are nowhere near the center of anything. We're on a planet, one of many revolving around a very ordinary star, on the outer edges of a very ordinary galaxy, that is one of billions of galaxies in the universe. If you didn't already know, it was revealed that people have an over inflated sense of their importance.

3.4. Copernicus Test

  • Q: who were the people that kept knowledge alive in Europe, in the period known as the Middle Ages or the Dark Ages?

    A: the Arabs.

  • Q: the names of most stars come from which language?

    A: Arabic

  • Q: what's the brightest star in the night sky?

    A: Sirius. It's in the constellation of Canis major or the big dog.

  • Q: what's the brightest star in the sky?

    A: the sun.

  • Q: What's the name of the person, who proposed the heliocentric model of the Solar System, i.e. that the Sun was at the center of the Solar System, rather than the Earth being at the center?

    A: Copernicus.

  • Q: name two people who were punished by the church for supporting the Copernican system.

    A: Bruno, Galileo.

  • Q:What's the name of the galaxy that our Solar System is in?

    A: The Milky Way

  • Q: Name the nearest galaxy to us.

    A: Andromeda.

4. Day/Night

4.1. Sunrise, Sunset

We started talking about day and night, but first we took a diversion, where, starting with Copernicus, we found that the earth rotates in front of the Sun, while the Sun and the stars and the galaxies are stationary. (Well actually they do move a little bit, but for our purposes, they can be regarded as stationary.) The next thing, for us to establish, is in which direction the Earth rotates about its axis. (spin globe both ways; we want to find out if it rotate this way, or this way?).

Let's find the compass directions on this globe. What are the four cardinal compass directions?


Let's say I'm standing in NC, which direction is N,S,E,W?

In which direction do we see sunrise?


The sun (and the stars and the moon and everything in the sky) all rise in the east. We say that the Sun rises, but Copernicus tells us that the sun doesn't move. What's happening is that the Earth rotates in front of the sun.

show first in the sky and then on the globe

Before sunrise, you're in darkness and the Sun is below the horizon. Then at sunrise, the Sun comes up, crossing the eastern horizon. After sunrise, the Sun ascends into the sky. During the day, as the earth rotates in front of the sun, the sun rises higher in the sky, till midday, when the sun is overhead, and then as the earth rotates further, the sun goes down in the sky, till what happens?

the sun sets.

In what direction does the sun set?


The sun (and the stars and the moon and everything in the sky) all set in the west. After the sun sets, we're in night again.

Then the earth rotates some more, until we get sunrise again. How long is the interval between sunrises?


The fact that we see the Sun rising in the east, tells us which way the Earth rotates. (show the globe with NC in darkness just before sunrise, at sunrise and then as the Sun ascends into the sky.)

Does the Earth rotate with the eastern part of each continent leading or the western part of each continent leading? With the Sun rising in the east, which is it?


We know the Earth rotates eastward, because the Sun rises in the east. If the Earth rotated westward, in which direction would the Sun rise?


By looking at the globe and knowing that the direction of rotation of the Earth is eastward, we can ask about the time in LA, when it's sunrise in NC.

at sunrise in NC is it day or night in LA? (ask kids to assemble around the globe) (night)

How long after our sunrise in NC do the people in LA get their sunrise (3hrs)? How could we find that out or figure it out?

When the Sun rises in NC, you could phone a friend in LA, tell them that the Sun has just risen here, ask them, when the sun rises there, to call you back. You just have to see how long it takes for your friend to call back.

Alternately we can do it by thinking. We'd calculate the time difference. We know that it takes 24hrs for the Earth to rotate once on its axis; we know how far it is from NC to LA (it's about 1/8 the way around the Earth) and we can infer from that, that the sunrise is 1/8 of the day, or 3hrs, later in LA.

  • If it's 6am in NC, what time is it in LA? (3am, three hours earlier in their day, the people in LA are still in night).
  • Let's say the Earth rotates a bit and now it's 9am in NC, what time is it in LA? (6am, three hours earlier in their day).
  • The Earth rotates a bit more and now it's 3pm in LA, what time is it in NC? (6pm. three hours later in our day).

4.2. Sunrise, Sunset lines

leave out

Let's explore sunrise a bit more. (have the kids gather around the globe.)

The kids didn't have any idea where the sunrise line was and I had to show them. Clearly I'm not doing it right. The old text, which didn't work, is gone and I'm going to try this new section in 2018.

I've positioned the globe so that NC is having sunrise. Show me the part of the globe that is having daylight, night. Show me the parts of earth that are on the edge between day and night. The edge between day and night is a line that goes the whole way around the earth. What's happening there? What's happening on the eastern part of the line? (sunrise). What's happening on the western part of the line? (sunset).

Show me the where sunrise is happening?

Show me where on Earth is having sunset. i.e. where is the sunset line?

There are two spots, near the poles, where sunrise and sunset are happening at the same time. What does it look like when you're there? Things at the poles are a little different than everywhere else on earth. At one pole you'll be having 24 hours of darkness, and the sun will just rise by crossing the horizon, only to start setting again. So the sun will rise and set at the same time. At the other pole you'll be having 24 hours of daylight, and the sun will just dip below the horizon at sunset, only to start rising again. So the sun will set and then start rising again.

The line on the surface of a planet where night and day bump into each other. is called the terminator When you look up at the Moon, you can see a line where night and day join. Depending where you are, the terminator is experiencing either sunset or sunrise. (images/moon_terminator.slideplayer.slide_4.jpg). At the terminator, the Sun is low in the sky, so objects on the terminator cast long shadows. If you're observing the Moon with a telescope, all the interesting views are on the terminator, because you can see the shadows of the mountains and the mountains are easy to see (images/moon_terminator.al_paslow.laas_org.phoca_thumb_l_moon_044054mm-x3.jpg).

(if you don't know, you can come over and look at the globe of the earth.) When it's sunrise in NC, is it day or night in LA? in Europe (day)? Is it day/night in Australia (night)?

About 12hrs after sunrise, the Earth has rotated 180 on its axis, and NC is now at sunset. What direction do we look to see the Sun setting? (W). (show Earth rotating with the Sun sinking.)

If it's sunset in NC, show me the other places on the Earth that are having sunset. (these places are on the terminator). Name them.

Point to the part of the globe that's having sunrise. Name some countries that are having sunrise.

4.3. Sunrise, Sunset lines change with Seasons

(2018) I expect the kids don't understand enough spherical geometry to get this. I'm leaving it out.

Notice that the line of sunrise and sunset through NC is different. The difference is greatest in summer and winter. One line runs NE-SW and the other NW-SE.


  • In winter sunset Boston 4:13pm, Raleigh 5:01pm, 48mins difference
  • In summer sunset Boston 8:24pm, Raleigh 8:34pm, 10mins difference
  • In summer sunrise Boston 5:07am, Raleigh 5:59am, 52 mins difference
  • In winter sunrise Boston 7:13am, Raleigh 7:25am, 12 mins difference.

4.4. Day/Night Test

  • Q: Why do we have day/night?

    A: the Earth rotates on its axis in front of the sun.

  • Q: how long does it take for the Earth to rotate once on its axis?

    A: 24hrs, 1 day (the definition of a day)

  • Q: which direction does the Earth rotate; eastwards or westwards?

    A: eastwards. (we know this because the Sun rises in the east.)

  • Q: If it's sunrise in NC, is it day or night in Europe?

    Position the globe with NC at sunrise. Europe will be in day and facing the kids. Tell them they can look on the globe if they don't know the answer.

    A: Day.

  • Q: If it's sunrise in NC, is it day or night in LA?

    A: night. It's actually early morning before sunrise.

  • Q: Let's say there's an Olympic skiing event in the middle of the day in Norway, that's being broadcast live, world-wide on TV. What time of day (approximately) will you be seeing it in NC?

    A: about sunrise in NC.

5. Seasons

5.1. Earth orbits the Sun in the Ecliptic Plane

Not only does the Earth spin on its axis, it orbits the sun. When I say the Earth orbits the sun, I mean it goes around the Sun in almost a circle, i.e. in a plane. (Walk around the Sun with the Earth, while spinning the earth.)

How long does it take for the earth to orbit the sun?

a year; the definition of the year.

The planets also orbit the sun, and in the same plane that the earth orbits the sun. This plane is called the ecliptic plane.

Why do the planets all orbit the sun in the same plane?

The solar system formed from a rotating cloud of dust. It turns out that everything in the universe rotates about something. If you start with a cloud of particles, in our case of the Solar System, where all the matter was flung out from an exploding star, it turns out that there's always some particle moving in one direction more than another. Two particles moving at different speeds, will gravitationally attract each other, and start rotating about their common center of mass while still moving forward in the original direction. (Show your hands moving, with one moving slightly faster than the other, and then the two objects orbiting their common center of mass.)

Here's a video on youtube that explains Why is the Solar System Flat. It's produced by Embry-Riddle Aeronautical University.

Not in class anymore. The video handles it.

Initially assume the cloud is anything but a disk, say a spherical cloud. Some of the objects will orbit above and below the plane. Eventually they'll gravitationally attact each other, and stick together and keep moving in the same direction. The inclination of the new orbit will be the average of the inclination of the two colliding particles. Eventually, no matter what the starting shape, the particles will all come to a very thin disk. The density of particles will be higher and they'll start colliding more, forming planets, till all of the matter is cleared out of the disk and resides in the planets.

Because the planets are in the same plane, when you look up in the sky at night, you see the planets move through the sky, along the same line, in the plane of the ecliptic.

5.2. The year for a planet with axis perpendicular to the Plane of the Ecliptic

leave out

When a planet is first formed from a disk of material rotating about the central star, the axis of rotation of the planet will be perpendicular to the plane of the disk. (demonstrate). This plane of the disk becomes the plane of the ecliptic. If nothing happens to the planet after it is formed, then its axis of rotation will stay perpendicular to the plane of the ecliptic.

The planets Mercury, Venus and Jupiter have their axes of rotation perpendicular to the plane of the ecliptic. (The Earth doesn't.)


Let's see what changes we would see throughout the year if we were on a planet like Mercury, Venus or Jupiter.

Walk around the Sun, carrying the globe of the Earth, with its axis perpendicular to the plane of the ecliptic, to show the days throughout the year, and point in the direction away from the sun, to where people at night would be looking.

In the day, when we look up, the sky looks pretty much the same all year; we just see the very bright sun.

But at night the sky changes throughout the year.

The stars we see in the night sky, make patterns that our human mind interprets as animals and mythical creatures. We call these patterns constellations.

Here's an image showing the constellations of Scorpio and Orion. (on the wall)


Can anyone name some other constellations?

Scorpio, Geminii, Sagittarius, Hercules, Orion, Andromeda, Leo, Taurus, Cassiopeia.

As our planet orbits the Earth during the year, at night when we look up in the sky we see different parts of our galaxy; so we see different stars and constellations though the year.

leave out

The constellations along the ecliptic are all animals or humans. We give these constellations a special name; the Zodiac (from the word zoo). There are twelve constellations of the Zodiac. Because these constellations are on the ecliptic, through the year, the sun passes through the signs of the Zodiac. If you were born when the sun was in a certain sign, then you can say that you were born under that sign. I was born on 1 Dec, under the sign of Sagittarius.

For a planet whose axis of rotation is perpendicular to the plane of the ecliptic, the only way you could tell that the year was progressing, would be the change of constellations at night. Every day would pretty much be the same; the temperature would be the same day after day, the length of the day and night would be equal, every day of the year. The fact that the planet orbits the Sun wouldn't be all that interesting, because all times during the year would be the same.

5.3. Tilt of Earth's Axis to the Plane of the Ecliptic

The Earth's axis of rotation is inclined to the plane of the ecliptic. This gives us the seasons, which mark the progression of the year. I'm now going to show you how the tilting of the earth's axis gives us the seasons.

All globes of the Earth, like the ones used in classrooms, have the Earth's axis of rotation tilted. (show the tilt) This means as the earth orbits the sun (walk around the sun), the axis points at an angle to the ecliptic. Does anyone know the angle of the tilt?


The planets Earth, Mars, Saturn, Uranus and Neptune have their axes of rotation tilted to the plane of the ecliptic. They all have seasons.


Planets initially form with their axes of rotation perpendicular to the plane of the ecliptic. If later we see that the axis of rotation is tilted, then we infer that something has happened to the planet since its formation.

Does anyone know why the Earth's axis of rotation is tilted?

Well we don't know for sure, but here's the generally accepted explanation. When the Earth first formed, its axis of rotation was perpendicular to the plane of the ecliptic. The earth didn't have a Moon. It's thought that very early in the history of the solar system, a Mars sized planet crashed into the Earth. The ejecta from the collision initially would have formed a ring of debris around the Earth, which eventually coalesced into the Moon. This collision was not dead centre, so it tilted the axis of rotation of the Earth. So the tilting of the axis of rotation is thought to be a result of the how we got the moon.

There's nothing special about the 23.5 tilt angle; it could be almost any angle at all. The actual angle is a consequence of the spot on earth that the Mars sized object hit the earth.

As you can see from the list of planets with tilted axes, most of them have suffered some sort of collision since they were formed.

Leave out. I assume this will overwhelm the kids. Mars' axial tilt varies from 10-25 and is caused by the eccentric orbit and non-spherical distribution of mass.

Here's a list of the axial tilt Axial tilt of the planets. Mars, Saturn, Uranus and Neptune have significant axial tilts.

(walk the Earth around the sun, spinning the earth, showing the kids that the axis points in the same direction.)

Because the Earth rotates about its axis, it behaves like a gyroscope. As a result, when the Earth orbits the sun, the axis of rotation stays pointed in the same direction in the sky. So no matter what time of year it is, the Earth's axis is always pointing in the same direction.

Show Gyroscopes in space

leave out

The fact that a gyroscope maintains its orientation in space, allows you to make what's called an intertial guidance system. In an airplane you mount a gyroscope in a gymbal mount. This allows the gyroscope to stay in its original orientation, while the airplane banks and goes up and down. An intertial guidance system can guide a plane from one side of the country to another without human intervention, by using the gyroscope to tell the orientation of the aircraft. This allows the pilot to fly and land the plane blind, i.e. in conditions when he can't see anything out the front window of the plane, like at night or in bad weather. When a computer flies a plane, as happens for much of regular passenger flights, the computer uses the inertial guidance system to keep track of where the plane is and its orientation.

Because of the gyroscopic effect, the earth's axis always points to the same spot in the sky, no matter where the sun is in its orbit. Let's say that the northern hemisphere is be tilted towards the sun, while the southern hemisphere will be tilted away from the sun. Then 6 mo later, when the Earth is on the other side of the sun, the Earth's axis will still be pointed to the same spot in the sky. Now the situation will be reversed for the hemispheres; the northern hemisphere will be tilted away from the sun and the southern hemisphere will be tilted towards the sun. A quarter the way around the year, the axis of rotation will be crossways to the sun and both hemispheres will be getting the same amount of sun.

If you extend the Earth's axis in the northerly direction, you find it points to a spot in the sky near, but not exactly on, a star. Does anyone know the name of the pole star?


The stars move through the sky too. If you look up in the sky at night, you'll see the stars all rotate around the pole of the sky. If you do a long exposure photograph of the night sky, you'll see star trails.

star trails photo on wall

During the day, the Sun and the stars that we can't see during the day, rotate around the pole of the sky too.

The fact that there is a star, Polaris, near the north pole of the sky is just a coincidence. If you extend the Earth's axis in a southerly direction, the axis doesn't point to anything interesting at all, just a blank spot in the sky.

Let's see what having the Earth's axis inclined to the plane of the ecliptic does for us. (southern hemisphere summer, northern hemisphere winter) Say "the southern hemisphere is getting the Sun overhead, while the northern hemisphere is getting the sun low in the sky".

  • Southern hemisphere summer

    Show Earth with southern hemisphere with the Sun overhead (southern hemisphere summer), the sun moves through the sky with the Sun at high elevation.

    We know that in summer, the daylight is longer than the night time. Show that in the summer, the Sun illuminates more of that hemisphere, and so more than 12hrs of the day is spent in sunlight. In summer, the days are longer than 12hrs.

    In summer the days are longer, and the sun is at a higher angle, both resulting in more heat reaching the ground. So it's hotter in summer.

    What month of the year is has the longest days in Southern hemisphere summer?

  • Northern hemisphere winter

    Show that at the same time as southern hemisphere summer, in the northern hemisphere, the Sun moves through the sky at a low elevation (northern hemisphere winter). So when it's summer in the southern hemisphere, it's winter in the northern hemisphere.


    In winter, the Sun illuminates less of that hemisphere, so less that 12 hrs is spent in sunlight. In winter, the days are shorter than 12hrs.

    In winter the days are shorter, and the sun is at a lower angle, both resulting in less heat reaching the ground. So it's cooler in winter.

    What month of the year is has the shortest days in Northern hemisphere winter?

    Northern hemisphere summer and southern hemisphere winter occur at the same time. The seasons are opposite in the two hemispheres.

    As you go closer to the poles, the sun gets lower in winter.

    Here's a time lapse photo of the sun in mid-winter from St George, ME. ME is further north than NC, so the have a shorter time of daylight in winter than we do. Notice how low the sun is in the sky.


    Here's a time lapse photo from further north, taken at mid-winter, from just outside the Artic Circle. The sun here is even lower than it was in ME.


Next orbit the Earth to the other side of the Sun (how long does this take? 6mo), pointing out that you're keeping the direction of the Earth's axis fixed, till we have the northern hemisphere with the Sun high in the sky (northern hemisphere summer). Ask which hemisphere is getting the overhead Sun now. Say "the northern hemisphere is getting the Sun overhead".

Do the reverse of above and show that the northern hemisphere summer is southern hemisphere winter.

What month has the longest days for Northern hemisphere summer and the shortest days for Southern hemisphere winter?



Show spring and fall and that they are opposite in each hemisphere. Show that in spring and fall that the amount of day and night is the same and it's the same in both the northern and southern hemispheres.

What season is it now i.e. in real life, not in the models on the table in the northern hemisphere? southern hemisphere. (The class is normally given in Dec, so it's southern hemisphere summer and northern hemisphere winter.) Let's say it's 1 Jan today; what's the season in the northern hemisphere, the southern hemisphere?

The seasons are opposite in the two hemispheres; when it's summer in one, it's winter in the other; when it's spring in one, it's the fall or autumn in the other.

So the tilt of the Earth's axis produces the seasons and makes the temperature/amount of sunlight different throughout the year. This in turn affects the weather, where the winds come from and the amount of rain we get. Adjusting our lives to the seasons is important in staying alive. We grow our crops in the summer, so we must plant our crops in the spring to be ready for summer. Animals and plants must time reproduction according to the seasons so the babies are born in spring, to be able to eat the food available in summer. Otherwise the offspring will not have grown enough to survive the following winter or the dry season. Some animals migrate to avoid winter or the dry seasons.

Name some animals that migrate to avoid winter

on wall

birds, deer, butterflies (monarch), bats, salmon, the mass migration of many animals in Africa,

whales (on wall). Whales go to the poles in summer, to feed. They then go to to the tropics in winter to give birth.

The arctic tern (poster on wall) flies every year from the arctic to the antarctic and back again, a round trip of 56,000 miles. This distance is just over double the distance it would do if it did the trip in a straight line.

5.4. Seasons Test

  • Q: How long does it take for the Earth to orbit the Sun?

    A: 1 year (the definition of a year).

  • Q: Why do we have seasons?

    A: the Earth's axis is inclined to the plane of the ecliptic. The inclination is 23.5.

  • Q: In northern hemisphere summer, what month is the sun highest in the sky?

    A: June

  • Q: In southern hemisphere summer, what month is the sun highest in the sky?

    A: December.

  • Q: When you look up at the sky in the night, you see patterns of stars, that the human mind makes into people, animals and objects. These patterns are called constellations. Name a few constellations.

    A: scorpio, geminii, sagittarius, hercules, orion, andromeda, leo, taurus, cassiopeia.

  • Name some effects of having seasons

    the hours of daylight change through the year, the elevation of the sun changes. Both of these affect the amount of heat and light we receive, making it warmer in summer and cooler in winter. Depending on where you live, the changing seasons can bring rain or dry weather, or ice and snow.

  • Q: The planets Mercury, Venus and Jupiter have their axis of rotation perpendicular to the ecliptic. Do these planets to have seasons?

    A: No.

  • Q: The Earth orbits the Sun in a plane called the ecliptic. All the other planets also orbit the Sun in this plane too. Why do the planets all orbit the Sun in the same plane?

    A: They were formed from dust and rock, which was orbiting the center of mass of the rotating matter. Through collisions, the matter formed a very thin disk. Any matter orbiting out of the plane of the disk, would eventually collide with matter in the disk. Once the disk formed, further collisions formed the planets, all in one plane.

5.5. Solstice, Equinox

If run out of time, just drop this.

Because of the tilt of the Earth's axis, as you go through the year, the height of the Sun above the horizon at noon changes. In the middle of summer, the Sun is highest. In the middle of winter the Sun is lowest.

As you watch the Sun go across the sky in summer, it's high, and in winter it's low.

(sweep hand across the sky to show the two arcs, summer and winter, of the sun.)

As you go from winter to summer and then to winter again, the Sun will get higher in the sky at noon, then stop and then get lower again. The day when the Sun is highest in the sky, the Sun is said to stand still. The word for this is "Solstice" (sun stationary). In winter, the Sun gets lower every day until the middle of winter, when the Sun stops descending and starts climbing again. Again when the Sun is at it's lowest at noon, it is said to stand still and we use the word "Solstice" again.

So we have a summer solstice and a winter solstice.


summer solstice

  • N hemisphere - about 22 Jun.
  • S hemisphere - about 22 Dec.

winter solstice

  • N hemisphere - about 22 Dec.
  • S hemisphere - about 22 Jun.

In the spring and the fall, the Earth's axis is pointing crossways to the Sun (show in model). The result of this is that for one day, the whole of the Earth from pole-to-pole is illuminated, and every spot on Earth gets 12hrs of day and 12 hours of night. Equinox means equal night. (nox comes from the same word where we get noctural, meaning being awake during the night and sleeping during the day.)

Here are the approximate dates of the equinoxes: 22 Mar, 22 Sep. These occur in the spring and the fall.

5.6. The Tropics

Half way between the two poles is a line around the middle of the earth that we call the equator. At the equinox, the Earth's axis is titled across from the sun, and the sun is directly over the equator.

There's another pair of lines called the Tropics at 23.5 from the equator.

At midsummer in the northern hemisphere (22 Jun), The sun is directly over the northern tropic, called the Tropic of Cancer. Because the Earth's axis is tilted by 23.5 the latitude of the tropic is 23.5N.

At midsummer in the southern hemisphere (22 Dec), the sun is directly over the southern tropic, call the Tropic of Capricorn. Its latitude is 23.5S.

As the year progresses, the latitude at which the sun is overhead moves between the two Tropics.

It turns out that the sun is only ever directly overhead between the two Tropics i.e. between 23.5N and 23.5S. The area between the two Tropics is called "the tropics". It's always warm there and people like to go there for holidays in winter. Hawaii, Cancun and the Carribean are in the tropics.

The Sun is always overhead somewhere in the tropics.

Outside the tropics the sun is never directly overhead at any time of year.

5.7. Circles: Arctic, Antarctic

point to the lines that are the Arctic and Antarctic circles.

There are two circles on the earth, the Artic, and Antarctic circles, 23.5 from the poles. The Arctic Circle is in the Arctic, i.e. in the northern hemisphere. The Antarctic Circle is in the Antarctic, i.e. in the southern hemisphere. At the solstices, if you're inside one of these circles, there is 24 hours of light at the summer solstice and 24 hours of dark at the winter solstice.

pick a point inside the Arctic Circle, and rotate the Earth to show that it's illumintated throughout the day.

Let's see how we get 24hrs of daylight. In northern hemisphere summer, because of the tilt of the earth's axis, all of the area inside the Arctic Circle, is illuminated. This includes the area that's on the side of the Earth away from the sun, that everywhere else on Earth is in darkness and is having night. This means that in the middle of their summer, people inside the Arctic and Antarctic Circles have 24 hrs of sunlight. So even when the clock says that it's midnight, the sun is above the horizon and we see daylight. These two parts of the Earth, inside the Arctic and Antarctic circles, are poetically called the land of the midnight sun.

Similarly, at the winter solstice, inside each of these circles, you have 24hrs of darkness.

leave out

If you're near the poles, the pole of the sky, is almost overhead.

(point to a spot on the globe in the Arctic Circle and show that the Earth's pole points to a spot almost overhead.)
The pole in the sky is the point to which the earth's axis points and about which the sun and the stars and the sky rotate through the day. If you're near the poles, because the pole of the sky is nearly overhead, the stars and the sun move through the sky in circles with a low inclination.
(show with hand, the path at low latitude and at high latitude. In summer, the Sun at its lowest point will be above the horizon.)

Here's a timelapse photo, from inside the Arctic Circle, taken in midsummer, every 15mins. It's from north of Fairbanks, AK. Because the spot is inside the Artic Circle, and it's near the summer solstice, they're having 24hrs of daylight. The camera is fixed and the sun moves through the sky.


The timelapse only covers a small part of the day. Can anyone guess what time of day it was when the sun was lowest in the sky?

It's the time when the clock says midnight.

Here's a video from inside the Antarctic Circle, taken in midsummer for the southern hemisphere, when the Antarctic is having 24hrs of daylight. It's at Scott Base, Antarctica, lat 77.51S. In this video, the camera follows the sun. Since we're having 24hrs of sunlight, the sun never sets.

(start at 0:42), from Scott Base, Antarctica, lat 77.51S

(show the path of the sun in the class room, in winter, if we're near the pole.) Here's a time lapse from Fairbanks taken 2 Dec (about a week ago). It's winter, so we expect the sun to be low in the sky and the amount of daylight to be short.


leave out

You know that the Earth's axis is tilted at 23.5. In the middle of summer, when the Sun is highest in the sky, how many degrees of the Earth's curvature, on the side of the Earth facing away from the sun, is illuminated? In other words, how big is the Arctic circle?

23.5 from the north pole to the Arctic circle.

In the southern hemisphere, which is having winter at the same time as the Northern hemisphere is having summer, the area inside the Antarctic Circle is receiving no sunlight at all.

How big (in degrees) is the Antarctic Circle? (23.5).

(put finger on spot and rotate globe from sunrise to sunset for that spot.) If you look at other parts of the northern hemisphere in summer, you'll see that more than half of the globe is illuminated. This means that in summer, daylight is longer than 12hrs. As you go towards the equator, the amount of sunlight in summer drops to 12hrs. sunrise equation The summer hemisphere is getting 12 hrs of daylight at the equator with the amount of daylight increasing as you go towards the pole, when you get 24 hrs of daylight in the Arctic circle.

The reverse is happening in the southern hemisphere, which is having winter. The amount of daylight drops from 12hr at the equator to 0hr at the Antarctic circle.

You'll notice that although the axis of the Earth is always tilted at 23.5 to the plane of the ecliptic, that the angle it makes in the direction of the Sun changes through the year. In winter the northern hemisphere pole is pointed away from the sun, in summer it's towards the Sun and in spring and fall it's straight up.

5.8. Solstice and Circles Test

  • The amount of daylight we get each day varies throughout the year. Why is this?

    The Earth's axis is tilted to the ecliptic. (by 23.5)

  • How many degrees of latitude is the Artic and Antarctic circle from the poles?


  • How many degrees of latitude are the Tropics from the equator?


  • If you're in the tropics, is the sun ever directly overhead?


  • Is you're in NC, is the sun ever directly overhead?


  • It's the northern hemisphere solstice. Where do you have to be to have 24hrs of sunlight?

    Inside the Arctic Circle.

5.9. Equation of Time and Sundials

No I'm not going to do this for 4th graders, fun though it would be.

6. Local time/mean time, equation of time

I added this into these notes in Dec 2016, but I haven't given it in class. I barely have time for the other material and the kids would be overloaded if I gave this. Perhaps I could give another class on sundials. I could move the section on the sunrise/sunset line into here. Maybe I could talk about analemmas

6.1. Local time/mean time, time zones

The original definition of noon was the time that the Sun is highest in the sky. When people were limited to walking or riding a horse for their transport, your world wasn't very big and everyone set noon for their location. The time you used is called local time.

No-one really cared about the time very much anyhow. No-one had clocks; they were expensive and needed a lot of attention. The best you could do was have a sundial in the middle of town. Usually people just looked up in the sky and said it was early or late morning, or early or late afternoon and that was it.

It turns out that places east and west of you had different times for noon and so clocks in different towns had different times. Let's see how this works. The Earth rotates in what direction (eastwards)? Raleigh is east of Durham. When does Raleigh have noon, compared to Durham? Do they have noon before, the same time or after Durham (before).

Raleigh is 0.3 east of Durham. The Earth rotates 360/day or 1 every 4mins. This means that Raleigh has noon 1.2mins or 1min 12secs before Durham. This means that the local time for Raleigh and Durham are different. If you're in Durham at noon, and you phone a friend in Raleigh and ask the time, they'll say it's 1 minute and 12 seconds past noon.

The time difference between the noons for Durham and Raleigh was not a big deal when it took you a day to ride between the two towns. But if you could travel faster over long distances, the time differences become a problem. What was the first form of transportation to arrive that was faster than a horse? (not cars. they didn't arrive till the early 1900s). The train. American's don't think of trains very much. This is because of the way the train system was set up here. The US government, priding itself in being a weak goverment, gave the rights to setup the trains to cooporations, giving the railroads much public land to build the trainlines. The corporations became fabulously rich and having no obligation to serve the public and their customers, fleeced them and became hated by all americans. This lead to the term "robber barons".

The rest of the world, having strong governments, had the government setup the railroads, to serve the citizens. The trains became communication, travel and shipping channels for the citizens, and provided good jobs. In the rest of the world, the trains are loved.

Not only could you move people and goods around quickly, you could send information quickly too. The electric telegraph was developed in the early 1800s and by 1830 was capable of delivering accurate time signals all over Britain making it possible to synchronize clocks all over the country. How fast do signals travel over the telegraph wires? (speed of light in wires, which is about 2/3 the speed of light in a vacuum).

Although many systems of electric telegraph were developed, everyone eventually adopted one system. Does anyone know what it was (The Morse system)? It was the cheapest and simplest - it used only one wire, with the Earth (ground) as a return; the information was encoded in dots and dashes called the Morse code. Ham radio operators (of which I am one) still use morse code. (play cq.mp3)(also mp4 of a ham calling CQ).

What sort of telegraph was used before the electric telegraph? (optical).

On ships and land, semaphore was used. A person would hold up a flag in each hand, each pair of flag positions representing a letter. (show positions of hands). The person receiving the message would watch with a telescope. On land, the stations would have to be on hills or towers.

Ships also use flags. Show the Blue Peter, which means "going to sea". It's the logo for the organisation Outward Bound, which runs adventure camps for young adults. I did Outward Bound when I was in college. At the time, I thought it was the best month I'd spent in my life.

At the battle of Trafalgar in 1805, in which England defeated the joint navies of Spain and France, giving England the supremacy of the seas, Admiral Nelson raised this signal (show flags) England Expects. The significance of the victory and Nelson's death during the battle led to the phrase becoming embedded in the English psyche, and it has been regularly quoted, paraphrased and referenced up to the modern day

Note that there is no flag for "duty" and the word is spelled out in letters.

In Nov 1840, the British Railways instituted Railway time. The railways set their clocks to Greenwich Mean Time (GMT). Greenwich is a place just outside of London which has a famous observatory. What do you know about Greenwich and the observatory?

You can indicate your coordinates on the surface of the Earth with your latitude and your longitude. If you look down on the Earth from the north pole, you can see that the circumference of the Earth is a circle. You can divide the circle into 360. The problem is where to set the 0 point. In a conference a while ago, everyone agreed that the Greenwich Observatory would be the reference point. Your longitude then is so many degrees east or west of Greenwich. Durham is at a longitude of -79 or 79 west if Greenwhich.

Greenwich is the place where the Longitude is 0. All maps in the world already used Greenwich as their reference point. Greenwich was an obvious place to use for your time reference.

I have been to the Greenwich Observatory and stood next to the brass plug in a block of stone with a line ruled on it, that marks the 0 longitude line. Doing this is really cool, if you're a science geek.

The key purpose behind introducing railway time was twofold: to overcome the confusion caused by having non-uniform local times in each town and station stops along the expanding railway network and to reduce the incidence of accidents and near misses, which were becoming more frequent as the number of train journeys increased.

This system of time, when everyone in a time zone, is on the same time, is called "Mean Time".

This scheme worked well for England, which doesn't extend very far east or west. However if you're a long way from Greenwich and you're using GMT as your time reference, you might find that it's dark and the middle of the night, when your clock says it's noon. Where would you have to be for it to be night time at noon in Greenwich? (put finger on Greenwich and show kids the opposite side of the globe) SE Asia, Australia, NZ, Alaska.

What people decided to do was to divide the world up into 24 time zones. The Earth rotates once on its axis every 24hrs.

show time zone map.

If you look down on the Earth from the north pole and you divide the Earth into 24 sectors, it will take 1hr for the Sun to pass overhead through that sector. With the time zone system, everyone in a time zone agrees to set their clock to the same time. When you move into the next sector, you move your clock ahead or back an hour. There are 4 time zones in the the continental US; E,C,M and W. each an hour apart. LA in the western time zone is 3 hours behind Durham in the E time zone. Because administrative (state and country) borders are not always at 15 intervals, the actual lines of timezone have been moved for convenience. (see timezone_map.jpg)

In 1883, the US and Canadian railroads adopted timezones. (Railroads create the first time zones.

The timezone system still only works if you don't move very far. If you interact with people in different timezones, then everyone adopts GMT as their time. Pilots all set their watches by GMT. Unix computers, which are designed to connect to computers anywhere in the world, all are set to GMT. (Windows computers, which are designed to only work in an office, use the local timezone.) Greenland covers 4 timezones, but sets it clocks all to the same timezone. Russia which covers 11 timezones, has all its clocks set to Moscow time and quite sensibly does not use the timezone system. I spend a lot of time on a computer interacting with people in different timezones. I set all my computers and cameras, anything with a clock, to GMT. Anything local, like my alarm clock and my microwave oven, I set to local time.

7. Recap Test

In 2017, I added more material and changed the class from one to two sessions. After having not seen me for a week, the students started the 2nd session here. I gave them these questions, to recall last week's material and to get them to remember the correct nomenclature.

  • Why do we have day and night?

    Because the Earth rotates on its axis in front of the sun.

  • How long does it take for the earth to rotate once on its axis?

    24 hrs, 1 day.

  • In what direction does the earth rotate; eastwards or westwards?


  • How do we know the earth rotates eastwards?

    The sun rises in the east.

  • When it's sunrise in NC, what time approximately is it in LA, London.

    About 3am in LA, about noon in London.

  • How long does it take for the earth to orbit the sun once

    1 year.

  • Why do we have seasons?

    The earth's axis is inclined to the plane of the ecliptic (the angle is 23.5).

  • The planets Mercury, Venus and Jupiter have their axes of rotation penpendicular to the ecliptic plane. Do they have seasons?


8. The Moon

The Earth has a natural satellite, the Moon. (Orbital plane is tilted 5 to the ecliptic, the Moon's axis is tilted 1.5 to the ecliptic; wikipedia. This information comes up when I get to eclipses.)

Don't bother. I've never found this useful for my thinking.

The Earth is unique in the solar system, in that it has a Moon of comparable size to the primary body (which in this case is the planet Earth). There are many moons throughout the solar system, but all of them are small compared to the planet. The Earth-Moon system is more like a double planet, than a planet with a moon.

Remember from the first lesson, that the Earth-Moon system was likely created at the beginning of the Solar System, when a Mars sized planet crashed into the Earth. The collision was a little off-centre, tilting the Earth's axis of rotation.

The diameter of the Earth is about what? (8000 miles). The diameter of the Moon is about what? (2000 miles). (None of the kids knew this. In the end I just gave them the numbers.) The Moon is about 1/4 the diameter of the Earth.

For the size of the models I have here, the Moon would orbit the Earth 30' away (figure out; is probably on the other side of the next room). The models here are going to show an Earth-Moon system that's more compressed than it is in reality.

8.1. The Month

The Moon orbits the Earth, in the plane of the ecliptic, i.e. in the same plane that the planets orbit the sun. Can anyone guess why this is so?

The Moon formed in the same disk and in the same plane as all the planets.

Not only that, the Moon orbits the Earth in the same direction that the Earth orbits the sun AND the Moon rotates eastwards on its axis, i.e. in the same direction as the Earth rotates on its axis. (spin the Earth, and walk the Moon around the Earth, while rotating the Moon.) Can anyone guess why that would be so?

The solar system formed from a spinning disk of matter. All the objects in the solar system, when they first formed, all would have been spinning in the same direction and would stay that way, unless there was a massive collision. Because nearly all the bodies in the Solar System rotate the same way, we can conclude that in the time since the formation of the Solar System, there haven't been too many really massive collisions.

How long does it take for the Moon to orbit once around the Earth? (a month, actually about 28 days - the original definition of a month).

If the Moon takes one month to orbit the Earth, how long does it take for the Moon to go a quarter the way around the Earth? (a week, the original definition of a week). In a few minutes, I'll show you why a week was chosen as a useful time interval.

When the Moon orbits the Earth, it always keeps the same side facing the Earth. So from the Earth, we only ever see one side or one half of the Moon. I'm going to mark the crater Tycho (point to image on white board).


Tycho is a relatively young crater, formed by the impact of an asteroid 108Mya. It's in the Moon's southern hemisphere, facing the earth. Because it's young, the ejecta, or rocks thrown out from the crater, are still light coloured, rather than the dull grey of the rest of the moon. The ejecta form rays emanating from the crater. Tycho is a bright, rayed crater, easily visible in binoculars from Earth at full moon.

I said Tycho, at 108Mya, is a relatively young crater. But young relative to what?


Important dates in history:

  • how old is the earth and moon? (About 4.6Gya, right at the beginning of the Solar System.)

    So Tycho is young relative to the age of the moon.

  • How old are the craters on the Moon? (4.1-3.8Gya)

    The Moon formed as a molten ball of rock and would have cooled to a relatively smooth sphere. So the Moon formed without any craters.

    They craters were created shortly after the formation of the planets and the Earth-Moon system, but before the planets all settled into their current orbits.

    What happened was that yet another Mars sized planet is thought to have come too close to Jupiter. When it did, it was broken up into fragments by the tidal effect of Jupiter's strong gravity field. The fragments of the broken up planet were flung out into the Solar System. Then, over a period of 300Myr, from 4.1-3.8Gya, the chunks of the broken up planet crashed into all the planets, not just the Moon, till there were no more pieces left in orbit around the sun. This period of crater formation bombarded all the planets and is called the late heavy bombardment. Today we see craters on the Moon and on Mercury. The craters that were formed on the other rocky planets, Venus, the Earth and Mars, are assumed to have since been obliterated by erosion and techtonic subduction of the crust.

The formation of the Moon we see involved two Mars sized planets. The first one crashed into the Earth, tilting the Earth's axis and giving us the Moon. The second one broke up after coming too close to Jupiter. The resulting fragments rained down on the Moon (and the other planets), giving us the craters on the Moon.

So when I say that Tycho is a young crater, it's young both relative to the age of the Moon, and relative to the age of the other craters on the Moon. It was formed by a recent impact of an asteroid and not by the much earlier Late Heavy Bombardment.

The impact that created Tycho would have made a bright flash, easily observable on earth. Back 108Mya, were there there any life forms on earth that could have seen the impact?

Let's recall some more important dates in history. Was there life on earth 108Mya?

Yes. Life started on Earth in the arduous conditions of the Late Heavy Bombardment. It seems that it was very easy to get life started on Earth, although no-one has figured out how.

What sort of life forms were on earth 108Mya? Would the dinosaurs have seen the impact? Would humans have seen it?

108Mya was the middle of the Cretaceous period, the period when all the big dinosaurs existed; the last of the three periods of dinosaurs known by geologists as the Mesozoic (or middle animal) Era; T. rex, Triceratops (the Pteranodon used to be called a dinosaur, but the flying Pterosaurs branched off earlier The Era of the dinosaurs is called the Mesozoic Era and extended from 252-66Mya. The dinosaurs went extinct 66Mya.

(As I've found out, the kids don't know that. Presumably they've been too busy being creative, learning New Math and languages that none of the adults in their world use in their daily life.)

During the Cretaceous

  • flowering plants were taking over the plant world
  • Gondwana, which consisted of South America, Africa, Antarctica, Australia, and the Indian Subcontinent, was breaking up
    images/8.1/Gondwana_420_Ma.png from wikipedia

So yes, dinosaurs would have seen the impact that created Tycho. Modern humans didn't come along till much later.

OK, we've talked about Tycho. Let's watch the Moon go around the Earth. The same face of The Moon is turned towards the earth. Tycho is faces the earth. I'm going to move the Moon in a way that the Tycho always faces the Earth.

The Moon has its own day and night too. Let's see what happens to Tycho as the Moon orbits the Earth with the same side facing the Earth.

  • Start with the full Moon and Tycho lit by the sun. Ask if Tycho can see the Sun and hence if Tycho is in daylight or night? Is it noon, midnight, sunrise, sunset for Tycho (noon)?
  • Then take the moon to 3rd quarter (one week), having rotated the moon about its axis to keep Tycho facing the Earth as you do so. What time of day it is for Tycho (sunset).
  • Take the moon to new (another week) (keeping Tycho pointing the Earth). What time of day is is for Tycho (midnight),
  • then via 1st quarter (sunrise) and full moon again (noon).

Now ask the kids how long the lunar day is (one month). All (well enough) of them get it.
The first two years I taught this class, the kids didn't get that the lunar day was a month. I assumed that it was some Piaget type of conceptual problem. Then in 2017, it occured to me I wasn't teaching it right. The thing that worked was asking the kids to explicitely track Tycho and call out the time of day for Tycho on the Moon at each quarter. It turns out that when kids don't get something, it can usually be fixed by me figuring out what I'm doing wrong with my teaching.

8.2. Month Test

  • How long does it take for the Moon to orbit the Earth?

    1 month, 28 days (the original definition of a week)

  • How long is a day on the Moon?

    One month

  • Why is the Moon's day the same length as the time it takes for the Moon to orbit the Earth?

    Because as the Moon orbits the Earth, it keeps the same side facing the Earth.

8.3. Lunar Phases

The words in the next couple of paragraphs are tortuously difficult to understand. The point is to show what's happening with the models. Words aren't great for communicating some things. Some things are better described in diagrams.

If we're out in space with the sun between us and the Earth-Moon system, we will always see a fully illuminated Moon, no matter where it is in its orbit around the Earth. We will also see a fully illuminated Earth.

Instead if we're out in space, with the earth-moon system between us and the sun, we will always see the dark side of the Moon, no matter where it is in its orbit around the Earth. We will also see a dark Earth.

If we change our viewpoint again and now we're sitting on the Earth and looking at the Moon as it orbits the Earth, we see that some of the Moon is illuminated and some of it is dark, depending on where the Moon is in its orbit around the earth.

Our view of the illuminated part of the Moon changes, because the Sun-Earth-Moon angle changes as the Moon orbits the Earth.

As a result of viewing the moon from the earth, the Moon goes through what are called phases.

point to poster on wall showing phases of the Moon. (hopefully we have a diagram of the phases).

  • When the Moon is less than half lit, it is said to be a crescent.
  • When the Moon is exactly half lit, it's at first quarter or 3rd/last quarter, depending which half is lit.
  • When the moon is more than half lit, it is said to be gibbous.
  • When the Moon is fully lit, it's said to be full.
  • When the Moon is unlit from the Earth, it is said to be new.

Let's see where the phases come from.

lights off. demonstrate with orrery.

Have the kids stand near me, so they can see the back of the new moon.

8.3.1. New Moon

Have the kids stand behind me.

If you're on the earth and it's a new moon, the sun and the moon are in the same part of the sky. Where do you have to be on the surface of the Earth, to see the Sun and the New Moon?

anywhere it's day

You're looking at the unlit side of the moon, which is dark. You actually can't see anything of the Moon, because the unlit Moon is darker than the very bright blue sky.

Let's say it's noon. Where are you on earth (show line of noon)? where in the sky are the sun and the new moon?

directly overhead.

If it's the new moon and now you're standing on the night side of the Earth, can you see the new Moon? (no, the Moon is below the horizon.)

Can you see the new Moon in the day? (yes, in principle, but it's hidden by the blue sky). At night? (no).

Does anyone know why you can't see the stars during the day?

They tell you it's because the sun is too bright and washes out the stars. But like a lot of things they tell you, it's wrong. You can see the stars in the day on the Moon, and the Sun is just as bright on the Moon as it is here on Earth. The problem isn't the bright Sun.

The stars aren't where the Sun is. The stars are where the blue sky is. The problem has to be with the blue sky. The reason you can't see the stars in the day is because they're dimmer than the blue sky.

Venus is bright enough that you can see it in the day, if you know where to look. Occasional comets are bright enough to see in the day.

8.3.2. First Quarter

Have the kids stand on the sunrise side of the earth and look across the earth towards the 1st quarter moon on the opposite side of the earth.

Now let's take the Moon 1/4 the way around its orbit of the Earth. How long does it take for the Moon to travel 1/4 the way around the Earth? (1 week) (first quarter). So the Moon has gone 90 in its orbit around the Earth.

(to the class) Point to the parts of the earth where you can see the first quarter moon.

the half of the earth facing the moon.

If you look at the Moon from earth, what phase of Moon do you see? (first quarter Moon). The sunward half of the Moon is illuminated, while the rear facing half of the Moon is dark.

At first and last quarter, the terminator is straight. This straight terminator makes it easy to know when a week has elapsed.

You don't get a very straight terminator in this setup. If the orrery was scaled properly, the Moon would be 30' away, and you'd see a straighter line.

Let's find where in the sky the first quarter Moon will be, at noon, then sunset and then midnight.

(show with orrery). Point to a place with noon, sunset and midnight and ask the students to say whether it's noon, sunset, midnight or sunrise at that spot.
  • noon: the moon is in what direction - east/overhead/west (east)? The moon is on the eastern horizon and as the earth rotates you will see the moon doing what - moonrise/moonset (moonrise)? Why is it moonrise? (show earth rotating eastwards, with the moon getting higher in the sky.) Everything rises in the east.

    Because it's daytime, the sky will be what colour - blue/black (blue)? and you'll see the first quarter moon rising, silhouetted against a blue sky.

  • sunset: moon is where - horizon/overhead (directly overhead)? If you look at the moon shortly before sunset, the sky will be what colour - black/blue (blue, because it's still day time) and you'll see the first quarter moon against a blue sky. If you look at the moon shortly after sunset, the sky will be what colour black/blue (black, because now it's night time), and the stars will be out, and you'll see the first quarter moon directly overhead against a black sky.
  • midnight: the moon is in what direction - east/overhead/west (west)? It is - rising/setting (setting)? Everything in the west is setting. (on the model, show the moon setting.) Because it's midnight, the sky will be what colour - blue/black? (black), and you'll see the first quarter moon setting against a black sky.

If it's sunrise, where are you? (have them point to model.) If it's first quarter moon and you're at sunrise, can you see the Moon? (no, the moon is below the horizon).

8.3.3. Full Moon

Put moon at full. Have the kids stand out in the classroom, looking towards the line of Sun-Earth-Moon. Tell them to pretend that they're actually standing on the night side of the Earth facing the Moon.

How long did it take for the moon to get from 1st Quarter to Full (1 week)?

Now you have the Moon opposite the Sun and you're standing on the night side of the Earth, you'll see a fully illuminated Moon. What phase of Moon is this (full Moon)? Let's says it's midnight, where are you on the Earth? Where is the Moon in the sky - horizon/overhead? (overhead).

If you're standing on the day side of the Earth, Can you see the full Moon?

no, the full Moon is below the horizon.

What time of day can you see the full moon?

You can see the full Moon if you're in darkness, i.e. anytime from sunset to sunrise. (Moonrise of a full moon at sunset is quite dramatic, as will will see in the lunar eclipse video a bit later.)

Where in the sky is the full moon at sunset/midnight/sunrise?

  • sunset: it's moonrise (in the east). If you're lucky you can see the sun setting as the full moon is rising. (show on model).
  • midnight: the full moon is directly overhead.
  • sunrise: it's moonset (in the west). If you're lucky you can see sunrise and moonset at the same time.

Can you see the full moon in the day? (no). You can only see it at night.

8.3.4. 3rd Quarter

Now let's look at the 3rd or last quarter Moon. Let's say we're in NC at sunset (have the kids orient the earth), can we see the 3rd quarter Moon? (no)

When can we see the 3rd quarter Moon?

Any time from midnight through sunrise to noon.

Where is the 3rd quarter moon at midnight/sunrise/noon?

  • midnight: moonrise in the east
  • sunrise: directly overhead
  • noon: moonset in the west.

Can we see the 3rd quarter moon at sunset? (no).

It turns out you can't see all the phases of the Moon from just anywhere. You have to be at the right place and right time.

8.3.5. Crescent Moons

Something that I think is particularly beautiful is the crescent Moon. You get a crescent Moon a couple of days after the new Moon and a couple of days before the new Moon. Let's look at the Moon a couple of days after it's new. (move the Moon about 30). You'll all have to stand on one side. This is called the waxing crescent Moon (waxing == getting bigger) or the new crescent Moon.

I'm now going to move the Moon to the end of the lunar month when we again get a crescent Moon, called the waning or old crescent Moon. Can you see the waning crescent Moon at sunset (no, the Earth is in the way). What time of day do you see the waning crescent Moon (sunrise)? If you're up early, you can see the old crescent Moon in the early morning.

Nn winter, when you get up in the dark, go out and look for the waning crescent Moon.

You will notice that most of the time, the terminator, i.e. the boundary between light and dark, is curved. However at 1st and 3rd (or last) quarter, the terminator is straight. It's easy to tell when this happens. As well it's easy to tell a full Moon just by looking at it. The new Moon, the quarters and the full Moon are all a quarter of a month, or a week apart. Because it's easy to mark the passage of a week, it became a useful length of time.

Some exercises

(Position NC at sunset with the Moon just a day or two after new). Let's say it's sunset. Where are you on the Earth? (show line.) If you look up to the Moon, what do you see? (This phase is called a crescent Moon or a new Moon). (have everyone stand behind the Earth.) Is the Moon near the horizon or overhead?

If you're at sunrise, where are you? Can you see the new (crescent) Moon? (no). Can you see the old (crescent) Moon? (yes).

8.4. Phases Video

Here's a video of the phases of the moon through the lunar month video of phases of the moon.

At the terminator (the sunrise or sunset line), it's sunrise or sunset. The mountains cast long shadows making it easier to see them. If you're observing the moon, you usually look at features along the terminator, because the shadows give you a better idea of the features you're looking at.

If we knew the orientation of the telescope to the horizon, we could tell whether the moon was rising, going parallel to the horizon (overhead) or setting. If we assume the horizontal is the horizon, the moon is rising except at 1:00 when the moon is overhead, and the last two, then the moon is descending. (the old moon sets against a blue sky, so the scope must be tilted to the horizon.)

  • 0:14: new crescent moon. You observe the new crescent moon at or just after sunset - note the sky is still partially blue. In the sky the crescent new moon is not far behind the sun, so both are setting, the sun first, then the moon.
  • 0:27: first quarter. Note at the terminator, how much better the mountains are defined because of the shadows.
  • 0:45: Tycho comes into view. Tycho is having sunrise. It's not clearly defined yet.
  • 1:00: near full moon.
  • 1:10: near full moon again.
  • 1:30: a better shot of Tycho. The exposure is lower and the moon's features aren't washed out.
  • 1:56: 3rd quarter. note the accentuation of the mountains on the terminator. Those mountains are having sunset.
  • 2:01: old crescent moon

8.5. Phases Test

  • The pattern of illumination of the Moon as seen from the Earth changes through the month. Why is this?

    It's because as the Moon orbits the Earth, we get a different view of the illuminated part of the Moon.

  • When can we see the full moon at (night/day)?


  • Why can't we see a new moon?

    we only see the dark side of the Moon and it's dimmer than the blue sky.

  • How long does it take for the Moon to go from 1st quarter to full?

    1 week.

  • Point to globe of the Earth, but don't put the Moon in till you give the answer

    I'm at sunset and I see the Moon directly overhead. What phase is the Moon?

    First quarter.

  • (same again, don't put Moon in till the answer) I'm at midnight and I look up and see the Moon overhead. What phase is the Moon?


  • I look on the calendar and find that the Moon is 3rd quarter. What times (or part) of the day can I see it?

    Any time between midnight, through sunrise to noon.

8.6. Solar and Lunar Calendars

Leave this out for 2018. I need to cut the presentation down.

The first calendars were lunar. It was easy to see the changing phases of the Moon. It was obvious that the position of the Moon affected the tides, and this affected your fishing, or collecting clams and oysters by the shore. As well at night, the Moon provides some light. This light allows some movement at night, an otherwise dangerous time to move, as you could be eaten by a nocturnal predator. So if you're out hunting and gathering, and you know the moon is going to be in the sky after dark, you might be able to stay out a little later, if you know you can get back home in moonlight. There are prehistoric cave paintings with sets of 28 tick marks, indicating that someone's job was to track the Moon.

With a lunar calendar, you counted time in moons. If something happened a long time ago, you might say "it was many moons ago".

The advantage of the lunar calendar was that it was simple. The month only lasted 28 days, and it was easy to see the passing of the month with the phases of the moon.

However the seasons were determined by the sun. Hunting depended on the seasonal migrations of deer and buffalo. You had to store up food for winter when animals were scarce and you risked dying of cold if you went out hunting. Our ancestors survived for 100,000s of years in the tough conditions of the ice age Europe, living much like the Innuit of northern Canada do now. Your survival was more determined by the sun than the moon.

It turns out that once you stop hunting and gathering and society becomes agricultural, it's more useful to have a solar based calendar. The solar based calendar keeps in synch with the seasons. All agricultural activities depend on the seasons; planting crops in the spring, the arrival of the new babies from the farm animals in spring, and harvest in the fall.

With a solar calendar, you counted time in years. If something happened a long time ago, you might say "it was many years ago".

However if you want to have a solar calendar with 12 months filling out the year, you have to lengthen the month from 28 to 30 or 31 days. These longer months no longer stay in sync with the 28 day period of the lunar month. So you can't have a calendar which stays in sync with the Moon and in sync with the Sun at the same time. You have to pick one.

A solar calendar is more complicated. It requires some understanding of astronomy and someone to keep track of 365 days in a year.

Modern European man is on a solar calendar, because we've stopped hunting and gathering, and we became an agriculture based society.

Cultures which predate modern astronomy, such as the Chinese and the Judao-Christian cultures, have calendars which are still partially lunar based.

  • what Chinese festival is set according to the Moon? (Chinese New Year).
  • What Christian festival is based on the Moon? (Easter). Easter follows the Judean lunar based festival of Passover.

For agricultural societies, the beginning of the year was in spring, when after being trapped by the cold of winter, suddenly in spring you became very busy. You planted your crops and the baby farm animals were all born. So just about all societies and cultures have their new year celebrations in spring; well all cultures except one, and that's ours. We have new year in the middle of winter; that's because the Romans shifted the new year for political and religious reasons. Do you remember from the icosahedron class that October isn't the 8th month? That's because the politicians moved the new year from March to Jan. The politicians don't care about the concerns of the farmers.

8.7. Calendar Test

  • Are we using a solar or a lunar calendar?


  • Why do we use a solar calendar?

    it stays in sync with the seasons

  • why do hunter/gather societies use a lunar calendar?

    it's simple to keep time.

  • In what season do most agriculture based societies have their new year?


8.8. Late Heavy Bombardment

I added this in 2017, but didn't deliver it (I haven't finished writing it either).

Here's a movie of the Moon crossing the face of the Earth, taken by a satellite which is monitoring global warming, the Deep Space Climate Observatory, from a distance of 1,000,000 miles above Earth, or about 4 times the distance of the Moon from the Earth., dscovrepicMoontransitfull.gif, EPIC_View_of_Moon_Transiting_the_Earth-DMdhQsHbWTs.mkv,

Since the same side of the Moon always faces the Earth, this movie shows side of the Moon that faces away from the Earth, called the far side of the Moon. Note the uniform appearance of the far side of the Earth, compared to the familiar near side of the Moon that we see from Earth. (show photo of full Moon as seen from Earth). (Have Lyn stop the animation in the middle and point to the far side of the Moon as seen in the movie and to the image of the full Moon on the white board.) Compare the uniform appearance of the far side of the Moon with the side that faces the Earth that is covered in dark smooth basalt lava flows called Mare (Maria pl. which means seas, this is where we get the word "marine"). People originally thought that the maria were oceans like we have on Earth. But when the telescope was invented and turned on the Moon, it was obvious that the maria were solid rock.

Both sides of the Moon are covered in craters. There just happen to be a lot more craters on the far side of the Moon than there are on the near side of the Moon. These craters are from asteroids slamming into the Moon. The cratering mostly happened in the early days of the solar system, in a period called the Late Heavy Bombardment. (4.1-3.8Gya), when yet another Mars size object broke up, presumably after having come too close to Jupiter, the biggest planet in the solar system. The breakup scattered debris throughout the solar system, which came raining down on all the planets and the Earth and the Moon.

The reason the far side of the Moon is so uniform in the video, is that it's densely covered in craters, more densely covered in craters than the near side of the Moon. Any maria that had formed on the far side of the Moon, would have been obliterated by the Late Heavy Bombardment.

So why is the far side of the Moon densely packed with craters, while the near side of the Moon is relatively sparsely covered in craters? It turns out that the near side of the Moon is protected from asteroid bombardment by the Earth. Most of the asteroids heading to the near side of the Moon will hit the Earth first, after being attracted by the earth's greater gravity. If the asteroid is heading from outer space towards the far side of the Moon, there will be no Earth to protect it.

When the Moon formed it would likely be rotating much faster than it is now. But some time after its formation, it became tidally locked to the Earth, with the same side of the Moon always facing the Earth. The same thing is true of the other Moons in the solar system; they all rotate with the same face to the primary body.

Let's see if we can determine the order in which these 3 events happened: synchronous rotation, late heavy bombardment and the formation of the Maria.

We know this about the Moon:

  • There are lots of craters on the far side of the Moon, while there are fewer on the near side of the Moon. The craters were all produced in a short period of time in the early days of the solar system in a period called the Late Heavy Bombardment.
  • The Moon used to rotate much faster than it does now. Now it keeps the same side towards the Earth, (the Moon rotates synchronously around the Earth).

From this we can order the bombardment event and the slowing down of the Moon's rotation to become synchronous with the Earth.
  • bombardment then synchronous rotation
  • synchronous rotation then bombardment

A: synchronous rotation, then bombardment. (If the reverse, then the Moon would be evenly cratered.)

So synchronous rotation was the first to happen.

Next we have to determine when the Maria flows occured.

We know this about the Moon

  • While the surface of the near side of the Moon has few craters (compared to the far side), the Maria have almost no craters at all.

From this we can order the bombardment and the maria flows.
  • bombardment then maria flows
  • maria flows then bombardment
bombardment then maria flows. If it was the reverse, then the maria would have the same density of craters as the rest of the near side of the Moon.

From this we have two pairs: synchronous rotation then bombardment; bombardment then maria flows.

If you're a scientist, you try to check your answer. If you've just made a new medicine or a rocket ship, you want to be confident that it's going to work. The ordering of the two pairs implies that synchronous rotation occured before the maria flows. How are we going to test this?

We know this about the Moon;

  • the Maria are all on the side of the Moon facing the Earth.

From this we can order the slowing of the Moon's rotation to become synchronous with the Earth and the maria flows

  • synchronous rotation then maria flows
  • maria flows then synchronous rotation

Let's test synchronous rotation then Maria flows. If it was the reverse, then the Maria would be on both sides of the Moon. However the next thing that happened was the bombardment. This would obliterate the Maria on the far side of the Moon. So we can't be sure of this one.

Let's test Maria flows first then synchronous rotation next. If it was the reverse, then we would possibly see Maria flows on one side or other of the Moon, but we don't know enough to know which side it would be on.

The evidence is consistent with synchronous rotation first and maria flows 2nd, but we can't exclude the reverse. Science is like this. You don't always get the complete answer. You have to find another way to get the missing information.

The most likely ordering of events then is synchronous rotation, then bombardment then maria flows.

9. Eclipses

9.1. Mechanism of Eclipses

An eclipse occurs when a celestial body (i.e. planet or moon) casts a shadow on or blocks the view of another celestial body.

A lunar eclipse occurs when the Earth casts a shadow on the Moon (hold Moon up behind the Earth, show shadow). This occurs when the Moon is at what phase? (full).

The Earth is 4 times the diameter of the Moon, so the earth's shadow is large compared to the Moon. It takes a couple of hours for the Moon to move through the Earth's shadow.

Where do you have to be to see a lunar eclipse?

anywhere it's night time, i.e. half the world sees a lunar eclipse.

Two weeks later, the Moon moves around in front of the sun. When the Sun is blocked by the Moon, we have a solar eclipse. The phase of the Moon is what? (new).

The Moon is small compare to the Earth, so the shadow of the Moon on the Earth is small and only a small part of the earth sees a solar eclipse. The shadow of the Moon is only a couple of miles wide at the most. While you can see a Lunar eclipse from anywhere on the night side of the Earth, the only way to see a total solar eclipse is to travel to the exact location. If you stand on Earth on either side of the area that's totally eclipsed, you will see a partial solar eclipse, where part of the Sun is blocked by the Moon. A partial solar eclipse can be seen for several 100 miles on either side of the area that's totally eclipsed.

Where do you have to be to see a solar eclipse?

On the day side of the earth.

right under the shadow. you can't see it from just anywhere on the daylight side.

The names Solar and Lunar eclipse are a little confusing. You'd hope that the name for the eclipse would indicate the object that's in shadow, or maybe the object that disappears from view, or maybe the object that blocks the light. Whatever it is, you'd hope that the same convention would be used for naming all eclipses. Instead the name used came from what humans, standing on the earth, saw, back in the days before they understood the mechanism for an eclipse. So (show with model) a solar eclipse occurs when you can't see the sun; a lunar eclipse occurs when you can't see the moon. Human language is like this; it isn't precise. The listener has to pay attention and disambiguate the speaker's words on the fly.

9.2. Moon's orbit is inclined to the plane of the Ecliptic

I've told you that the moon orbits the earth in the plane of the ecliptic (the plane that the earth and the planets orbit the sun). With the sun, Moon and Earth all moving in the same plane, how often would we have eclipses? (twice a month). We'd have a lunar eclipse every full Moon and a solar eclipse every new Moon.

It turns out that eclipses only occur twice a year. Let's see why.

In fact, the Moon doesn't orbit the earth in exactly the plane of the ecliptic. The Moon orbits the Earth in a plane that's tilted 5 to the ecliptic plane.

show exaggerated tilt with hoop.

Can anyone guess why the Moon doesn't orbit the Earth in exactly the ecliptic plane, the plane where all the other planets do their orbiting?

It's left over from the collision that formed the Earth-Moon system. The collision wasn't dead-centre. Not only was the Earth's axis of rotation was tilted, but the collisional debris was sprayed out in a plane tilted to the ecliptic. This collisional debris later coallesced to form the Moon, which now orbits the Earth in a plane tilted 5 to the plane of the ecliptic.

Now with the moon's orbit tilted to the ecliptic plane, let's see how often we get eclipses.

As the Earth orbits the sun, the plane of the Moon's orbit stays (essentially) fixed, just as the direction of the axis of the Earth's rotation stays fixed. It's the same gyroscopic effect.

Do the Lunar Ballet. First walk around the room, showing the moon orbiting the earth though a year, but not showing the eclipses. Spin the earth (day/night), and have the moon orbiting out of the plane of the ecliptic. You don't have enough hands to hold the hula hoop (unless we get Lyn Streck to do it). Show the plane of the Moon's orbit pointing to Polaris, but say that in real life it's pointing somewhere else, but we're just pointing to Polaris to show how it works.

let the line normal to the plane of the Moon's orbit tilt backwards a little bit. Have the Earth's axis tilt somewhere else. use a few kids to walk the Earth Moon system around the room. Have the kid with the Earth spin it slowly.

Show that eclipses do not occur for most months. Show that eclipses can only occur twice a year.

We've seen that eclipses only occur as the Moon crosses the ecliptic plane. This is where the word ecliptic comes from. The ancients noticed that eclipses only occured when the Moon was in a certain position in the sky. They joined up all the places where eclipses occured, and found this was the line that the planets travelled on too.

We've shown that eclipses are only possible when the moon crosses the ecliptic plane AND if that place is on the line between the earth and the sun.

We get approximately two solar eclipses and two lunar eclipses a year. If you can travel anywhere, anytime, you can see two solar eclipses and two lunar eclipses a year.

9.3. Eclipses of Geosynchronous Satellites

not in the 2 week class.

The earth has a natural satellite, the moon, that orbits nearly in the plane of the ecliptic. If the moon orbited exactly in the plane of the ecliptic, we would get lunar eclipses every orbit of the moon i.e. every month. However the orbit of the moon is sufficiently tilted that we only get eclipses at two points of the earth's orbit, i.e. twice a year.

The actual time of year depends on the actual plane of the moon's orbit. The plane of the moon's orbit itself rotates, with a cycle of 18.6 years (Saros cycle),; so the time of year for the eclipses returns every 18.6 years.

As well as the natural satellite, the moon, the earth has many artificial satellites, in fact thousands of them. One set of them is in orbit around the earth in the plane of the equator at a distance of 36,000km miles. These are called geostationary satellites, because their orbit takes the same time as the earth's rotation. A geostationary satellite then is above the same point on the earth's surface all the time. These satellites are good for monitoring the weather, vegetation and for communications, such as providing TV services to people on the ground. They orbit in the plane of the equator, so they're directly above the equator. What is the angle between the plane of the equator and the plane of the ecliptic? (23.5). Remember the earth's axis is titled to the ecliptic.

How often are they eclipsed? Twice a year. They are also eclipsed at the equinoxes. (They aren't orbiting in the plane of the ecliptic.) How long are they eclipsed? There's two answers to this eclipse seasons

  • The shadow of the earth is relatively large and the satellites move into the shadow in two "eclipse seasons" from 26 Feb - 13 Apr and 30 Aug - 15 Oct.
  • At maximum eclipse, the satellite is eclipsed for 72 minutes.

A geosynchronous satellite gets its power from solar cells. When it's eclipsed, it's in the dark and must get its power from batteries. A geosynchronous satellite must have enough battery capacity to run for 72 min without any solar power. Batteries are very heavy and so it's often simpler to not provide full services during the eclipse.

9.4. Eclipse Test

  • Where can see a lunar eclipse?

    from anywhere on the night side of the Earth.

  • Can you see a lunar eclipse from the day side of the Earth (no)?


  • Can you see a solar eclipse from the night side of the Earth?


  • Can you see a solar eclipse from the day side of the Earth?

    Sometimes. It depends where you are. The shadow of the Moon on the Earth's surface is small, only a couple of miles wide. You have to be exactly in the right spot.

    In the '80's I travelled from MD to GA to see an annular solar eclipse. We had great weather and we saw it perfectly. In 2017 I went to MO to see a total solar eclipse: I've been waiting for this eclipse for 20yrs. I chose that spot as historically it had the lowest chance of cloud east of the Rockies at that time of year. It rained. You learn to be philosophical when observing nature. You don't always see what you hoped to see.

  • If you stay in one place, how often are you going to see a total solar eclipse?

    Never. You have to travel.

    The partial eclipse has a wider path, so if you don't travel, you can expect to see a partial solar eclipse a couple of times in your life.

  • how often are there lunar eclipses?

    There are two lunar eclipses a year.

  • That's how often lunar eclipses occur. The next question is how many of those eclipses are you going to see?

    You have to be on the side of the earth that's in night, and you have to be prepared to be awake at the time of the eclipse, which could be the early morning, so you don't get any sleep. As well you have to be prepared for it to be cloudy.

    So, if you're prepared to travel, so you can be on the night side of the Earth, and you're prepared to stay up all night and the skies are clear, how often will you see a lunar eclipse?

    you'll see a lunar eclipse twice a year.

    I've seen maybe half a dozen eclipses. So if you live in places where there's clouds, you might only see a lunar eclipse every 10yrs.

  • Since the time I taught this class a year ago, there have been the expected two lunar eclipses. However we didn't see them in NC. Can anyone guess why we didn't see them?

    The two lunar eclipses were during the day.

    The next lunar eclipse visible here in NC, will be in the middle of the night of 20-21 Jan 2019. (EST 20 Jan 22:33 - 21 Jan 01:50. Partial 03h16m, Total 01h01m.) That's a sunday night through early monday morning. If the sky is clear, I'll be watching it. If you're interested in seeing it, ask your parents to wake you up for the total part of the eclipse.

    dates are on the board.

9.5. Lunar Eclipse Video

The size of the earth's shadow is large enough that a lunar eclipse takes about 4hrs.

(images from The shadow of the earth is 4 times the size of the moon, so the moon can take longer or shorter paths across the earth's shadow;

When the moon is eclipsed, it's in a shadow that's not completely dark. The moon sees sunset through the earth's atmosphere, the whole way around the earth's circumference. So an eclipsed moon is red rather than black. The reddened eclipsed moon is much darker than the moon lit by the sun, but still bright enough that it's easily visible in the sky. So the moon doesn't go completely dark for most lunar eclipses.

It's only when the moon goes across the diameter of the earth's shadow, that it gets black enough that it's hard to find in the sky. I've seen about half a dozen lunar eclipses and only one of them was so black that I couldn't see the eclipsed moon anymore. In a chordal eclipse, one side of the moon will be almost black, while the opposite side will be bright red.

We're about to see a video of a lunar eclipse, where the moon goes across a chord of the earth's shadow. Most of the moon will stay red the whole time. Only one side will look near black.

The part of the moon that's illuminated by the sun is white. The part of the moon which is eclipsed is red. The white part is very much brighter than the red part. Because of the difference in light intensity, you won't see the red of the moon until the moon is almost totally in shadow.

The moon is moving through the sky in the same way that the sun moves over a long period of time. To keep track of the moon over the 4 hours of an eclipse, the camera has to be on a tracking mount, usually a telescope.

2015 Super Moon Lunar Eclipse in HD through a telescope This is an edited version of, by scannerguy1968. It's a time lapse. The actual eclipse took about 4hrs.

We're going to see the eclipse twice. The first time I'm going to stop the video and point out a few things. The second time, I'm going to let it run.
  • 0:11: the full moon is rising through the trees. The trees appear tilted because the camera is tilted.
  • 0:36: a plane flies across the bottom of the moon. Because the sun and the moon are so large, you often have planes photobombing the sun or the moon. People have movies of the ISS crossing the face of the sun.
  • 1:21: he brightens the exposure in an attempt to show the reddened eclipsed part of the moon. This has the side effect of washing out the features on the illuminated part of the moon.
  • 1:41: the moon is fully eclipsed and he turns up the exposure to see the reddened moon.
  • 1:43/1:58: after turning up the exposure, two stars become visible (top left quadrant). The two stars appear to move away from the moon. In fact the stars are stationary in the sky; the moon, not the stars, is the one that's moving through the sky.
  • 2:37: he turns down the exposure, allowing the features on the illuminated part of the moon to be seen. Tycho is visible in the bottom right of the moon.

9.6. Solar Eclipse Video

A solar eclipse is a little different to a lunar eclipse

  • It turns out that the sun is 400 times the distance of the moon, and, by a staggering coincidence, it's 400 times the size of the moon. Thus the moon is the same apparent size as the sun. Because the moon's orbit is not quite circular, sometimes the moon is a little bit further away and hence smaller than the sun, so at the peak of the eclipse, you see a ring of the sun around the moon. This is called an annular eclipse. If the moon is just a little closer and hence bigger than the sun, then, at the peak of a solar eclipse, the disk of the sun is completely covered by the moon. This is called a total eclipse. At totality, you can see solar prominences and flares on the edge of the sun, the sky becomes as dark as 30mins after sunset and the bright stars and planets become visible.
  • As the last part of the sun is covered and then again after the eclipse, when the first part of the sun is uncovered, you will see a pinpoint of light on the edge of the disk of the sun. This is called the diamond ring effect.
  • A totality of a solar eclipse takes about 2 minutes. Unlike a lunar eclipse, you don't have time to do anymore than say "Ah!" or "wow". Since seeing a solar eclipse is so much rarer and involves a lot more work to get there, than does a lunar eclipse, just about all you want to do when you see a solar eclipse is go "wow" and "ah". If you want to look for particular stars or the planets, you have to know where they are in the sky or you won't have time to find them.
  • The surface of the sun has dark spots on it called sunspots. These are storms on the surface of the sun, where the sun is colder. As well the sun throws up matter above the surface called prominences. These are hotter than the surface of the sun. You can see the prominences on the edge of the sun at totality.
  • A total solar eclipse is only visible from a narrow track on the surface of the earth, maybe only 10-20 miles wide. Unless you travel, you're unlikely to see one in your lifetime. I've seen two solar eclipses in my life. Both of them required me to travel a couple of days each way.

The video Total Solar Eclipse, 21 Aug 2017 Oregon Star Party. by Bill Basham.
  • The sun is orange because of the type of solar filter used to prevent damage to the telescope and camera.
  • 1:30: the moon starts to fully cover the sun's disk. The photographer slows down the replay. The small lines of the sun at the bottom right of the frame will appear to the eye, which is adjusting to the lower light, to be bright pinpoints of light, called the diamond ring effect. The photographer is still using the solar filter, so the exposure is low and we don't see the diamond ring effect.
  • 1:35: totality. The photographer has removed the solar filter and we see the light of the sun as being white. The photographer superimposes many pictures taken at increasing exposure, to show the dim photosphere and corona around the sun. This is called high dynamic range photography. Your eye cannot see most of the corona and you do not see with your eye, what the camera is showing. All you see with your eye, is a very small ring of light around the edge of the moon. Note the prominences at the edge of the moon; this is matter being thrown off the surface of the sun.
  • 1:51 the diamond ring effect. The photographer shows in a loop, different attempts to show the diamond ring over the next minute. It's hard to show with a camera, as the adjacent pixels overload, so you don't see the very bright small white area characteristic of the diamond ring effect.
  • 2:56 the orange solar filter is put back on the telescope and the timelapse movie is speeded up.

Here is the solar eclipse of 2017 as seen from a satellite. Notice the shadow of the sun as is goes across the USA. What are all the lights flashing that we see (lightning)?

9.7. Eratosthenes and the Diameter of the Moon

not in lecture.

The Chaldeans, who lived, back in 600-500BC, in what is now known as Persia, were great astronomers. They figured out all there was to know about the motion of the moon, and they knew how to predict eclipses perfectly. Thanks at least partially to the Dark Ages, it took another 2,000 years before there were any further great advances in astronomy. The Chaldeans also knew that eclipses were due to the sun, earth and moon lining up. Thus the circular terminator on the moon during a lunar eclipse was the shadow of the earth. From this they infered that the earth was round, just like the sun and the moon. From the curvature of the shadow of the earth on the moon's surface, they could tell the relative size of the earth and the moon. However they didn't know the size of the earth.

The size of the earth was figured out by a guy called Eratosthenes in 240BC. He was the head of the library at Alexandria and he read that at the town of Syene, in southern Egypt, on midsummer's day, that a stick cast no shadow and that on looking down a deep well, you could see a reflection of the sun.


  • Syene is on the tropic of Cancer. At the summer solstice, the sun is exactly overhead.
  • Syene is now called Aswan and is the location of the Aswan High Dam on the Nile River.
  • Syene has a quarry where the granite like rock syenite is quarried. ( In some forms, it's pink. The quarries of ancient Egypt located here were celebrated for their stone, and especially for the granitic rock called Syenite. Syenite is also found in Eno River State Park. The quarries furnished the colossal statues, obelisks, and monolithal shrines that are found throughout Egypt, including the pyramids. One of the famous Syene obelisks is now found in England where it's called Cleopatra's needle by the British, Cleopatra's needle,_London. Cleopatra's needle was originally erected about 1450BC, long before the time of Cleopatra. But the English gave it the name Cleopatra's Needle, as it was a name that the populace would recognise. The heiroglyhics on it commemorate the military victories of Ramesses II.
  • Syene is one of the hottest, driest and sunniest places in the world. It hasn't rained since 2001.

The video on Eratosthenes How Eratosthenes calculated the Earth's circumference from

Here's a clip from Carl Sagan's Cosmos TV show, about the well at Syene. Eratosthenes from

Once we knew the diameter of the earth, we knew the diameter of the moon. The distance to the moon was determined by Hipparchus about the same time, using Lunar Parallax.

9.8. Predicting Eclipses

Dec 2017: haven't finished this section. I'm not going to ever do this.

We've known how to predict eclipses since the days of the Chaldeans (Saros cycle) in 600-500 BC. These were people who lived in what became Persia.

Acropolis, dragon's head, dragon's tail. nodes

Humans have a large interest in figuring out how things work. It helps you get food, makes you comfortable, and stops you from doing things that will kill you.

After society became agricultural, and produced more food than was needed to feed the people who did the farming, you could have people who didn't need to work in the fields all day. You wound up with a king and his court, an army, people who could plan earth works, irrigation and build buildings (engineers), troubadors, and tax collectors and accountants, to make sure the people fed the king and all the other people who weren't farmers anymore. Because of the necessity to record taxes, writing developed.

A class of people developed to explain all the things that no-one understood. These are the priests, mathematicians, astronomers and philosophers. For some of these people, is was convenient to attribute the unknown to the action of gods. Since the King told the peasants that he was descended from the gods, it was most important that the King be able to maintain this fiction. For this he had to be forewarned of communications from the gods.

All these people, I'll call the leisure class.

An eclipse, where the moon disappeared out of the sky, clearly was a communication from the gods. If you were the King's astronomer, you could expect to loose your head if you didn't predict an eclipse. The King had to tell the populace that he, the mighty one, by his great strength, would in the coming weeks, be doing battle with the forces of evil, who would attempt to swallow the moon. When, after great struggle, the moon reappeared, the King would be declared victorious and the populace could be appropriately grateful.

It wasn't too long after the arrival of the leisure class, that they learned to predict eclipses. They did so without our modern understanding of celestial mechanics i.e. how the planets move. We don't know how they did it, but here's how they could have done it.

Let's go back to our model. The plane of the moon's orbit is inclined to the plane of the ecliptic, not by much, only 5 but it's enough that you only get eclipses at the two points, where the moon's orbit crosses the plane of the ecliptic. These points are called nodes. There is one point, where the moon is going from the southern hemisphere of the sky, to the northern hemisphere. This point is called the ascending node. The other point is 180 away and is where the moon is moving from the northern hemisphere of the sky to the southern. This other point is called the descending node.

So let's say you're a priest and it's your job to follow the moon. You know that all the planets follow the ecliptic. You also notice that during the month, the moon swings above the ecliptic and then below the ecliptic, for half the month each. The phase of the moon, as it crosses the ecliptic, varies throughout the year. Priests have been recording eclipses for ages and you've all noticed that eclipses of the moon only occur when the moon is full and it crosses the ecliptic. Clearly the ecliptic is important, even if you don't know why.

Here's a photo, xistock-157180942.jpg.pagespeed.ic.atZTcttunj.jpg, of the Acropolis from Visiting Greece: Climbing to the top of the Acropolis by Judy Freeman. The rectangular building with all the columns is called the Parthenon. We're looking north. Approximately what time of day is it? (hint, what's the elevation of the sun?) (sunset).

10. Vocabulary

These words are printed on sheets of paper, taped to the white board. I tell the students that I will talk about these things during the presentation. Perhaps I should test the day's words at the end of each class.

  • plane, perpendicular
  • ecliptic, eclipse, node
  • orrery
  • constellation
  • orbit
  • terminator
  • Copernicus: heliocentric, geocentric
  • gravity
  • galaxy: Milky Way, Andromeda
  • axis, gyroscope
  • inertial guidance system
  • hemisphere: northern southern
  • season
  • migration
  • circles: Arctic, Antarctic
  • latitude, longitude
  • Mare, Maria
  • moon: gibbous, crescent
  • lunar phases
  • calendar: solar, lunar
  • Equator

New for 2018

  • Stars: Sirius, Canopus, Castor and Pollux, Regulus, Vega, Rigel, Antares, Aldebaran, Spica, Arcturus.
  • Occam's Razor
  • Gondwana (South America, Africa, Antarctica, Australia, and the Indian Subcontinent)
  • Sol, solar system

    for Mars yestersol, tosol, nextersol, morrowsol, solmorrow and soliday

  • solstice, 22 Jun, 22 Dec
  • equinox, 22 Mar, 22 Sep
  • lunar eclipse in NC, night of 20-21 Jan 2019.
  • Planets with tilted axes: Earth, Mars, Saturn, Uranus, Neptune.
  • Planets with perpendicular axes: Mercury, Venus, Jupiter.
  • Equator
  • Tropics: Cancer, Capricorn
  • Circles: Arctic, Antarctic

11. Important Dates in History

  • Creation of the Earth/Moon system: 4.6Gya
  • Late Heavy Bombardment: 4.1-3.8Gya
  • Age of the Dinosaurs, Mesozoic: 252-66Mya
  • Tycho: 108Mya
  • Start of Ice Ages: 2.6Mya
  • First Humans: 1Mya

12. The Video

13. miscellaneous

I can do 4 classes with a single 64GB SD card in the video camera.

The batteries in the lav mikes last all day. On the Sennheisers, the battery meters show about half left. A voltmeter shows the batteries almost full. The other lav mike, the transmitter's batteries are almost dead. The receiver I run off 120V.

In 2017 I added extra videos for the eclipses. These the teacher ran off her Mac laptop. This was a nightmare; the Mac is a walled garden and hides a lot of stuff from the user. The teacher thought she'd downloaded the files from my website, but she'd only stored a link on her desktop. You need a computer that clearly lets you know whether you have a link or a file, not one that goes to some length to hide the difference from you. As far as she was concerned, if it was on her desktop, it was on her computer. In the class, the teacher wound up running the videos off my website, a halting procedure at best. Safari wouldn't download the files, apparently because they were not .mov files. A computer savvy teacher was consulted, who said that you needed a plug-in to play files other than .mov. (No. You just need to get out of the Apple controlled world, use non Apple software, like vlc, and Chrome or Firefox.) Presumably the teacher was required to use a laptop that had been handed to her by some beaurocrat, and which she was expected to figure out herself, when its main function was to receive e-mails from beaurocrats about meetings. Next time I'll bring the videos on my own laptop. (i.e. don't have anyone do something you can do.)

Moon at perigee/apogee supermoon_explanation_graphic_december_03_2017-1.png

14. bring

  • LED light for sun
  • Earth, moon globes
  • 3D printed moon (and Earth)
  • win7 computer for projector (brought my own projector, but Lyn's works fine). extension cord, power strip (3 way plug was enough).
  • Lyn has posters.
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