Warning: NEVER look directly at the Sun! Not with sunglasses, not through a camera, definitely not with a telescope or a binocular, not even through a welder’s mask. NEVER LOOK AT THE SUN DIRECTLY!

Solar and lunar eclipses are the stuff of legends. The spectacle of the Moon going dark and then becoming blood-red for hours at a time, or the horror of the Sun being devoured until the world stood in darkness at midday was enough to chill the blood of any ancient or primitive soul that witnessed them. Columbus himself is supposed to have used a solar eclipse prediction to convince the Native Americans that he had great mystical powers and should be left to his business; Mark Twain incorporated this story in his book A Connecticut Yankee in King Arthur’s Court.

But why do eclipses happen? Some students may know that the eclipses have something to do with the shadows of the Earth and Moon, but if that is true, why don’t they happen every month? In this unit, we will not only investigate the phenomena of lunar and solar eclipses, we will see once again that we can take an existing model of the solar system, and add new features to it that will not only increase its richness, but also improve its usefulness and allow us to make even more testable predictions!

Activity 34. Modeling a Solar Eclipse

Solar eclipses are wonderful events, but it is quite rare to see one. The eclipse is only total along a very narrow line called the path of totality. If you are not on this narrow line at exactly the correct time and the weather is not clear – you will miss your total eclipse. Partial eclipses are easier, but they do not visit any particular continent or region very often – you may wait decades between opportunities, or have to travel thousands of miles to see one.

Since we cannot expect the Sun and Moon to cooperate and give you a wonderful solar eclipse of your own (and conveniently during school hours, too!) we must do the next best thing by modeling the solar eclipse in our classroom.

This activity will take our Earth-Moon system model to new levels of detail. In order to do this, we are going to have to make a new model on a different scale. Like so many scientific models in astronomy, this one will fib a little bit when it comes to the real scale of the solar system. As we’ve seen in Activity #3 (Making a Scale Model of the Earth-Moon System), the distance to the Moon is very large, and that would make our model rather impractical for us.

Students will do better with this activity if we confine our model to a desktop, so that they can see all the parts working together properly. We won’t put the Sun in this model either, it is sufficient that we know where the Sun is supposed to be and in which direction the sunlight is shining (this tells us which way the shadows must go!) We can accomplish this simply by putting a construction paper arrow on the desk to indicate the direction of the sunlight!

For the Educator

Facts you need to know

1. The Earth and the Moon cast shadows just as any object on Earth does when it lies in direct sunlight. These shadows stretch many thousands of miles off into space but are not visible to us unless a sunlit object passes through them.
2. Because the Earth is roughly 4x larger than the Moon, its shadow is four times wider and four times longer than the lunar shadow. This larger shadow is easier to hit, so to speak, which is one of the reasons why a lunar eclipse is much more common than a solar eclipse.
3. The Moon’s orbit is tilted by just over 5^o. This may not seem like much, but over the large distance from the Earth to the Moon, it becomes quite significant. Because of the tilt of the Moon’s orbit, the Earth and Moon dance now above, now below these shadows in space and prevent an eclipse from happening. Only when Earth, Moon, and Sun are perfectly aligned on a level plane can we have an eclipse!

Teaching and Pedagogy

This is an interesting exercise in solid geometry! Students working with their models will tend to make several mistakes, let’s look at them one at a time. Your students may want to tilt the shadow rather than keeping it perfectly horizontal. This doesn’t work in real life, the Sun is so far away that the shadow always points perfectly horizontally (in the plane of the solar system.) Remind your students what we learned using the solar clock and calendar – the angle of the shadow always points back to the Sun!

Some students may want to point the shadow in the wrong direction; the shadow must always point in the same direction as our sunlight arrow. This is really just another version of the same problem. Shadows are stubborn things, they always point directly away from the light source, and once again our experiences with the solar clock and calendar point this out to the student.

The real solution, as you see in the photo below, is to rotate the Earth-Moon model so that the Earth, orbit ring, and the Sun all line up precisely. If you think about that tilted orbit of the Moon, there are only two places where the orbit actually crosses in front of the Earth instead of being either above or below it. These points are called nodes; when the Moon is on a node – and that node lies directly between the Earth and the Sun – then an eclipse is possible.

Did you notice that for this model to work, you had to position the Moon between the Earth and the Sun? This is the new moon phase when the entire near side of the Moon is in darkness. If you wish, you can draw a new moon on the lunar orbit ring in this position with a marker and draw a full moon on the orbit ring on the opposite side of the Earth! It can be fun to have the children fill in the phases on the orbital ring to refresh them on the lunar phases again!

You will also notice that only the point of the shadow touches the Earth! In reality, this shadow point is never more than 50 miles wide! The combined rotation of the Earth and the orbital motion of the Moon during an eclipse cause the shadow to draw a thin, gracefully curving line hundreds of miles long across the Earth’s surface. Combine this with the fact that the total eclipse lasts only a few minutes, and you will see why a total eclipse is such a rare event! To see this celestial wonder, you must be precisely on that thin line (and looking up!) at the exact time of day when the eclipse occurs. The relatively tiny size of the shadow, the motions of Earth and Moon, and the precise geometry required in space make this one of the rarest observational events!

Safety Note: Staring at the Sun is NEVER a safe activity! You can damage your vision permanently without realizing it (the eye has no pain receptors!) If you have the opportunity to observe a solar eclipse, get in touch with a local astronomy group – they can show you many safe and fun ways to observe this wonderful celestial event! See Activity #29 below for more information on this!

Student Outcomes

Conducting the Activity

Materials

1. One rubber T-ball
2. One large marble
3. 24-inch square of foam-core board
4. Sharp hobby knife
5. 4 wire coat hangers & sturdy wire cutters or 4 15-inch pieces of sturdy piano wire (a craft or hobby store should be able to help you with this.)
6. An empty soup can
7. Poster putty
8. Hot glue
9. Sheets of black (any dark color) and yellow (any bright color) poster paper
10. Can of light blue spray paint
11. Markers, tape, etc.

Building the Solar Eclipse Model

1. Spray paint your rubber T-ball blue, and set on the soup can to dry. You can actually set the ball on the soup can and spray it over a sheet of newspaper, allow it to dry and rotate it between coats to be sure that the color is even.
2. When the ball is completely dry, have the students use markers to make this into an Earth model as we did with the ping-pong balls. As before, the exact shape and placement of continents and ocean won’t matter much for our demonstration, so don’t worry about making a perfectly accurate map!
3. [Teacher] Use a string compass and draw two circles on the foam core board. The first circle should be as large as the board itself, the second should be about 2-inches smaller. Trim the outer circle with the hobby knife, (have some cardboard beneath your project to keep from scratching the table!) Trim the inner circle next, this should leave you with a 2-inch wide ring, 2-ft in diameter. The exact width of the ring isn’t important, but making it too thin will make it fragile.
4. [Teacher] The four wires must now be inserted perpendicularly along the equator of the Earth model, so they form a neat cross the same size as our foam core ring. It is usually easier to puncture the ball with the hobby knife first, and then insert the wire into the ball (you may wish to wear gardening or work gloves when you do this step to protect your hands.)
5. [Teacher] Once you have all the wires inserted and you are sure they are correctly in place so as to match the size of your foam core ring, a drop of super glue will help hold them firmly in place. Next use hot glue to firmly attach the wires to the foam core ring; it is often helpful to set the Earth model on the soup can (North Pole down!) while you do this to keep it from rolling around! When the hot glue has cooled completely, flip your model over – it is now ready to use.
6. Cut out a large arrow from yellow construction paper (use the whole length of the paper!) Draw and label a smiling sun at the base of the arrow, and label the pointed end ‘Sunlight’. Tape this arrow to your desktop.
7. Set the empty soup can on the center of your sunlight arrow and set the Earth model on top of it. Adjust the position of the Earth so the Moons orbit (foam core ring) is tipped a bit. The ring should be tipped enough so that the highest point of the ring is well above the top of the t-ball Earth. Secure the rubber ball Earth model in place on the can with some hot glue or a bit of duct tape.
8. Use some poster putty on the marble so that you can put it on the ring and make it stay put. Attach this carefully so that you don’t damage the ring! Try moving the marble moon around the ring orbit, notice that the Moon is sometimes above the Earth, and sometimes below it.

Exploring the Solar Eclipse Model

1. Now it is time to model the Moon’s shadow. Use black construction paper to make a cone shape. Its widest point should be the size of the moon marble, and it should be just long enough to reach from the orbit ring to the t-ball Earth model. This will take a little bit of practice and adjusting! When you get it just right, tape the cone together and secure it to the marble moon with some silicone glue.
2. It is finally time to make a solar eclipse! The rules are simple:
   • You can turn the soup can around, but you cannot adjust the angle of the foam ring – it must stay tilted as it is. (This is why we secured the Earth model to the soup can!)
   • The Moon’s shadow must remain horizontal, and point in the direction of the sunlight arrow.
   • When you find a place that allows the Moon’s shadow to touch the Earth – you’ve done it! Use your poster putty to secure the Moon and its shadow in place!

Supplemental Materials

Going Deeper

The prediction of eclipses requires complex mathematics – far beyond the scope of your class whether you teach 1^st or 12^th grade! Even so, there are a number of excellent video resources that will help your students to picture, and imagine what happens during a solar eclipse. One of the most interesting of these are a series of short videos taken from the International Space Station looking down upon the Earth as the Great American Eclipse of 2017 happened in real time.

Being an Astronomer

In spite of dire warnings to the contrary, it is possible to observe the Sun safely as long as you do not look directly at it. While this may seem like a contradiction in terms, allow me to assure you that it is not. We have examined three methods in our previous unit of observing the Sun, one using cardboard boxes that fits in nicely with our low-cost science program, the second requires a pair of binoculars; the third requires only a convenient tree, all of these are easy and fun!

Being a Scientist

Being a scientist and observing a solar eclipse is difficult because the solar eclipse is such a rare phenomenon. Still, if you get a chance in your lifetime to observe a total solar eclipse – I urge you to take advantage of it!

Following Up

Use the internet and search for the next upcoming eclipses. Even if the eclipse is too distant for you to travel to and observe, there is often live video available from scientists who have made the journey to observe and record this magnificent event.

Activity 35. Modeling a Lunar Eclipse

Activity 36. Why are Eclipses so Rare?

With our two shadow models, we have seen the mechanics of the solar and lunar eclipse. Your students should now be able to explain to someone how eclipses work, and why both light and shadow are needed to create one. But why are eclipses so rare? Most people have never seen a lunar eclipse although they are fairly common and occur in bunches of three to four events spread out over 18-24 months. These eclipse clusters occur every few years, there are many on-line almanacs that can help you find the next lunar eclipse visible from your area.

Only relatively few people have ever seen a total solar eclipse. These fleeting events last only minutes, and one has to be in a very exact position to observe them. Adventurers, astronomers, and wealthy tourists take trips to exotic locations, people even charter cruise ships to travel to a particular point in the ocean and drift motionless while those on board observe the fleeting event! The model we created seems to suggest that an eclipse should be possible every full and new moon – so why are they so infrequent?

In order to understand this last piece of the eclipse puzzle, we will create yet another model using ping-pong balls again, and our ping-pong Sun model, too. We are going to make a new ping-pong Earth model, this time with the Moon’s tilted orbit attached to it!

For the Educator

Facts you need to know

1. The Moon’s orbit is tilted 5.5 degrees with respect to the Earth’s orbital plane around the Sun.
2. A five degree orbital tilt seems very small, but this small angle carried over 380,000 kilometers often places the Moon far above, or below, the plane of the Earth’s orbit.
3. In order to have an eclipse of any kind, the Earth, Moon, and Sun must be precisely aligned in space. It is the tilt of the Moon’s orbit which interferes with this alignment.

Teaching and Pedagogy

You will remember that in Activity #30, we used a toy gyroscope to show students that a spinning object’s axis is stable in space, no matter how we move it around. The Moon in its orbit is not a solid ring like the metal ring of the gyroscope, or a solid ball of stone like the Earth, but as it spins it acts in much the same way. Spin the gyroscope up and balance it on your finger, push it over so it is tilted a bit just as the Earth’s axis and the Moon’s orbit are tilted. Students will be quick to notice that it stays upright, but it also wobbles a bit. As with our toy gyroscope, so goes both the Earth and the Moon – this ‘toy’ is an excellent scientific model!

The lunar orbit, like the Earth’s axis, stays pointed in the same orientation as the Earth-Moon system orbits the Sun. In other words, if the highest point on your model’s lunar orbit faces north, it must remain facing north as you move the model around the Sun. It may also help to have your model from Activity #34 handy to help illustrate what is happening on a larger scale!

Student Outcomes

Conducting the Activity

Materials

1. One ping-pong ball
2. A manila file folder or similar stiff card stock
3. Four 3-5 mm beads (grey is preferred, but any color will do)
4. A golf tee
5. A piece of wood or ball of modeling clay for a stand
6. Ping-pong Sun model (See Activity #20)
7. A toy gyroscope (for a teacher demonstration)
8. Markers, glue, poster putty, etc.

Building the Rare Eclipse Model

1. Use markers to decorate a model Earth – your students should be getting good at this by now! You will see why we need a new Earth after we add the lunar orbit to our model!
2. Use silicone glue to attach the South Pole of your model to the golf tee and set it in a ball of clay to stand and dry. Remember that silicone glue needs 24 hours to cure properly. Hot glue can be used to speed up the process if you wish.
3. On the file folder, use a compass to draw and cut out a 5-inch circle. Then cut out a 4.0 cm wide circle from the center of this to create your lunar orbit. If you have done things properly, you should have a lunar orbit ring that will fit nicely over your ping-pong ball. You may use markers to color this black or dark grey if you wish, but do not use crayons, the waxy finish will interfere with attaching our little moon beads to our model later!
4. Place your lunar orbit on the ping-pong Earth model. Be sure the orbit it tilted enough so that the ends of the orbit are well above and below the level of the Earth itself. When you are satisfied that you have everything in the correct position, go ahead and secure your orbital ring with a couple of drops of white glue or super glue. With this large and tilted orbit attached, you can see why we needed to put our Earth model on a stand such as a golf tee! Remind your students that the real lunar orbit is 60x the size of the Earth, we have cheated a bit with a lunar orbit just 5x as wide as the Earth to keep the size of our model manageable.
5. Use some poster putty to attach your four moon beads. One each should go at the highest and lowest position on the orbit, and at the nodes where the orbit crosses the Earth’s equator. Younger children might find four moons a bit confusing, in that case simply keep one bead on the orbital ring and move it about as you need to. You must be careful to treat the lunar orbit ring carefully lest you bend it up and damage the model! In any case, with your moon bead now attached, your model is ready to use.

Exploring the Rare Eclipse Model

1. Have your students begin with the moon bead at one of the node positions. Adjust your model so that the Earth is directly between the Moon and the Sun – this is the correct position for a lunar eclipse with the Moon on the node and the node pointed directly at the Sun.
2. Now advance the Earth 90-degrees anti-clockwise (keep the orbit ring oriented in the same direction!), and advance the Moon bead the same 90-degrees anti-clockwise around its orbit ring. Remind your students that this represents three months of time (¼ of a year!) The Moon is now between the Earth and Sun again, but it is either too high above or too far below the Earth for its shadow to create an eclipse!
3. Continue to advance the Earth and Moon 90-degrees at a time and observer the results. You will quickly see that there are only two times per year, six months apart, when an eclipse is possible. These are called eclipse seasons. For an eclipse to occur, the Moon must be precisely on a node on exactly the correct day when the node is pointed at the Sun. No wonder the eclipses are so rare!

Supplemental Materials

Being an Astronomer:

Did you know that you can see eclipses happening on other planets? The Galilean moons of Jupiter are large enough that it is possible to observe, and even photograph these moons and their shadows as they pass in front of their planet Jupiter.

Observing such events requires a relatively large telescope; either a refractor of 100 mm aperture or greater, or a reflector of at least 8-inch aperture, preferably 12-inches or even larger. Once again, your local astronomy club may come to your aid. Most clubs have at least one member with a large reflector telescope of the type required to see the shadow of a moon cross the face of Jupiter.

Observing such an event takes planning! These events can be predicted months in advance, just as eclipses on Earth can, but they do not always happen in the early evening when it would be convenient for students and parents to participate. Meet with your club at the beginning of the school year and see if you can plan an effective observation schedule!

Being a Scientist:

If you have a chance to observe an eclipse on Jupiter, you may be able to set up a live video feed for all of your students to look at. If the eclipse happens at an inconvenient time, you may find that your astronomy club may be able to provide you with a video of the event for your class to look at in the comfort of your classroom.

Scientists observe events making careful note of first contact, time of totality, and last contact. You can observe these events either live, or from a video. It can be interesting to compare eclipse events from the different Galilean moons (Io, Europa, Calisto, and Ganymede.) Because of their different distances from Jupiter, each of the Galilean moons travels at a different speed in orbit. This can greatly affect the time of totality as the moon’s shadow crosses the face of Jupiter.

Following Up

Predicting eclipses is a very difficult endeavor! Looking at modern calculations of past eclipses that were visible over the Mediterranean and Middle East from 100 BC to 1000 AD, we find that some solar eclipses were just 18 months apart, other times the next solar eclipse might be 400 months apart – that’s more than 33 years separating two solar eclipses.

To predict a solar eclipse, you must know the shape of the Moon’s orbit precisely, and determine how the Earth and Moon speed up and slow down in their orbits. The Greeks reached this level of sophistication in the first century BC, and the Chinese astronomers reached that level of knowledge about 300 AD. There are rumors that Maya or Inca astronomers may have reached that level of knowledge, but much of their mathematical literature was destroyed by their Spanish conquerors in the early 1500’s, so it is unlikely that we will ever know how far these new world astronomers had progressed.