Abstract

Scientists develop and use models to better understand and teach about natural phenomena. This lesson will lead you through a series of short exercises to develop a model for eclipses using common household materials. Participants will be led to explore the different types of eclipses, how often they occur, and the reason behind the recurring patterns that we see. Educators will enjoy using this model as an engaging, low-cost, anytime teaching tool.

1. Introduction

In preparation for the solar eclipse on April 8^th, 2024, I spent many evenings browsing the Internet for hands-on activities related to eclipses. I wanted to find the perfect activity to accompany a presentation I was giving for teenage volunteers at my local space center. My goal was to support the volunteers in answering public inquiries about solar eclipses. So, I began by putting myself in the shoes of someone hearing about an upcoming solar eclipse for the first time. It is likely that anyone in that situation would have a lot of questions such as how often eclipses occur and whether they should travel to get the best view or wait for the next one.

NASA’s “When Do Lunar Eclipses Happen?” activity provides a good foundation for answering these types of questions. There are other activities and models out there, but this one met all of my requirements. It is engaging, educational, low-cost, and able to be completed in 15-30 minutes. Using NASA’s activity as my base, I added a few extensions of my own and designed a lesson around a series of short exercises that develop the model over time.

2. The Double-Paper-Plate Eclipse Model

2.1 Materials

• Two 8 ½-inch paper plates (thicker paper is recommended)

• Ruler

• Scissors

• Pen or marker

• Pushpin

• Gallon-sized storage bag (optional)

• Round object to trace a circle about five inches in diameter (optional)

2.2 How many solar and lunar eclipses occur each year?

Whenever I teach about eclipses and I ask this question, I am often fascinated by the varied answers I receive. Usually, the range of answers is somewhere between a few weeks to several years. The range will depend on the participants’ understanding that you must be in the right geographical location to view an eclipse, especially a solar eclipse. Before diving into how often solar and lunar eclipses occur, it is important that participants understand the different types of eclipses. Broadly speaking, there are two types of eclipses, solar and lunar. NASA has some nice diagrams for showing the alignment of the Sun, Earth, and Moon during a solar eclipse and during a lunar eclipse.

Let’s start building a model! Take one of your paper plates and cut off the rim (Figure 2). You can discard this. Take the other paper plate and cut a circle about five inches in diameter out of the center. Label the circle you cut out “Sun”. We will use this later. Tip: Use your pushpin to help get the cut started.

Next, take the paper plate with the circle cut out of it and place it face down. Then, take the paper plate with no rim, also face down, and place it on top. Congratulations! You have created your first Double-Paper-Plate Eclipse Model. Now using your Sun, trace a circle on the top of your model to represent the orbit of the Moon. Poke a hole in the middle with your pushpin and label this “Earth”. Finally, add the numbers one to four inside of the Moon’s orbit in a counterclockwise fashion beginning at 12 o’clock then moving to the 9 o’clock, 6 o’clock, and 3 o’clock positions (Figure 3).

Whenever I teach using a model, I like to emphasize that all models have accuracies and inaccuracies. In this model, the size of the Earth compared to the diameter of the Moon’s orbit is close to the correct scale. Comparatively, the size of the Sun is not to scale. The distance between the Earth and Sun is also not to scale, and it would be difficult to use this model if it were. I have found that making mention of these accuracies and inaccuracies can help to avoid creating misconceptions when teaching.

This first exercise is focused on how often eclipses occur. It builds upon the knowledge that participants should already have of the positions of the Sun, Earth, and Moon during solar and lunar eclipses. If that knowledge has not already been established, you may want to begin with the diagrams linked earlier in this section. Place your model to the right of the Sun and ask at what positions (1-4) an eclipse will occur (Figure 4). Once participants have a basic understanding of eclipses, they will most likely answer that two positions are involved, position two and position four. In this example, position two corresponds to a solar eclipse during a new Moon, and position four corresponds to a lunar eclipse during a full Moon.

At this stage in the development of the model, eclipses occur every full Moon and every new Moon regardless of the position of the Earth in its orbit around the Sun. Ask participants to try a few different orbital positions for the Earth (at least the four seasons) to demonstrate that the pattern holds. You can accomplish this by letting the Sun be your center and moving your model in a circle around it.

Think about a time when you have seen a full or new Moon without an eclipse. Lead participants to recognize that eclipses do not occur every full or new Moon so something must be inaccurate about our model. Now take your model and carefully cut around the Moon’s orbit. Leave about a ½-inch (the width of the base of a pushpin) attached at position 2 and position 4. Once complete, carefully bend the Moon’s orbit so that it is now inclined. The Moon’s orbital inclination is only about 5 degrees, but you can exaggerate this as far as the model will allow (Figure 5).

Next, repeat the previous exercise with an inclined orbit for the Moon. Now, eclipses can only occur at positions two and four when the Sun, Earth, and Moon are aligned. By orbiting your model around the Sun, you can demonstrate that a solar eclipse will take place twice a year (generally), and that each solar eclipse will occur about sixth months apart. This pattern is also true for lunar eclipses. Tip: For now, be sure to keep the Moon’s orbit in the same orientation as you move it around the Sun.

As an extension activity, you could show videos of solar eclipses and ask participants why the Moon always moves across the Sun from right to left when viewed from the northern hemisphere. You could also ask participants why the slope of the path of the Moon across the Sun differs between solar eclipses. Both of these are related to our perspective and the inclination of the Moon’s orbit. With a little extra thought, and remembering that the Moon orbits Earth counterclockwise, you can explain both phenomena using your model.

2.3 What is a hybrid eclipse?

One of the other inaccuracies about the Double-Paper-Plate Eclipse Model is that the Moon’s orbit is elliptical, not a perfect circle. At this scale, the Moon’s distance from the Earth fluctuates about one inch causing it to appear slightly larger or smaller in Earth’s sky. This means that solar eclipses can be further divided into four types: a partial solar eclipse when the Moon partially covers the Sun, a total solar eclipse when the Moon completely covers the Sun, an annular solar eclipse when the Moon is centered on the Sun but appears too small to cover it completely, and a hybrid eclipse when a solar eclipse is both total and annular in the same event.

Using a pushpin or ruler, measure inwards from the connecting point at position two about ½-inch and label this “Total”. Similarly, measure outwards from the connecting point at position two about ½-inch and label this “Annular”. As I mentioned previously, a hybrid eclipse is when a solar eclipse switches between total and annular partway through the event. This can only occur when the Moon’s distance from the Earth is near halfway between the total and annular extremes. For this reason, label the connection point at position two “Hybrid” (Figure 6). As you move through this activity, you may want to provide other models or visual aids to help teach about the different types of eclipses depending on your audience.

2.4 What type of eclipse will occur next?

When you look at eclipse data using tools like timeanddate.com it is easy to tell that lunar and solar eclipses alternate as do partial and total/annular eclipses. Although the pattern is not perfect, we can use our model to explain what we see. Place your model to the right of the Sun so that eclipses occur at positions two and four. Because the Moon completes one orbit in about one month, lunar and solar eclipse occur about two weeks apart in an alternating pattern. However, we cannot dismiss that within the span of two weeks the Earth has moved some in its orbit around the Sun (about 14 degrees). This means that the Earth, Sun, and Moon are no longer in alignment in the same way that they were two weeks previously. As a result, we see a pattern of alternating partial and total/annular eclipses as well. To demonstrate this concept, try orbiting your model 14 degrees while keeping the Moon’s orbit in the same orientation.

2.5 Why do eclipses occur at different times of year?

So far, we have established that eclipses are seasonal (they do not occur every full and new Moon) and that they occur six months apart, but we have not yet modeled why an eclipse can take place in April one year and in January several years later. We can see this in the data available on websites like timeanddate.com. This change in eclipse dates is due to the slow movement of the Moon’s non-circular (elliptical) orbit. In other words, the rotation of the paper plate on top of your model will change as time passes. In celestial mechanics, we call this nodal precession. For a nice animation of this, check out NASA’s Scientific Visualization Studio.

The Moon’s orbit precesses westward/clockwise by 360 degrees (one full rotation) in approximately 18.6 years. This translates to a little under 20 degrees each year. We will be able to visualize this by labeling every 90 degrees on our model. On the rim of the paper plate at the bottom of the model, label the 12 o’clock position “Spring”, the 9 o’clock position “Summer”, the 6 o’clock position “Autumn”, and the 3 o’clock position “Winter”. Then add a single mark at the midpoint between each season (Figure 7).

Place your model to the right of the Sun and rotate the top paper plate if necessary to demonstrate a solar eclipse at position two in summer. Then, complete one orbit around the Sun and rotate the top paper plate about 20 degrees clockwise (halfway to the midpoint mark). Place the model in the position where a solar eclipse will once again occur at position two. This should be at a different orbital position around the Sun than it was previously. Repeat this process several times and the solar eclipse will occur in a entirely different season. Given enough time, eclipses will occur during every month of the year due to the nodal precession of the Moon’s orbit.

3. Conclusion

Models are useful tools for teaching, and developing the Double-Paper-Plate Eclipse Model can be a lot of fun. You may want to consider packaging and distributing the materials in a gallon-sized bag for each participant. That way, they can easily take their model home and share it with others. I am happy to report that my presentation was a huge success, and I am grateful to have learned some things about eclipses along the way.