Eclipse in a Cup
Why doesn’t a solar or lunar eclipse happen every month? It’s because the moon’s orbit around the earth is tilted in relation to the earth’s orbit around the Sun. In this Science Snack, you’ll make a model that helps explain this phenomenon. (Note: This model is not to scale.)
- Tennis ball or similarly-sized sphere, such as an orange
- Three clear plastic 9-ounce disposable tumblers/cups made from #1 plastic (Note: Some brands work better than others; wide-mouthed cups work best)
- Two different colors of polymer clay—blue or green to represent the earth, for instance, and gray or white to represent the moon (be sure it’s a type of clay that will stick to the plastic cup!)
- Two different colors of permanent marker (we used red and blue)
- Large, flat table
- Flashlight or other point-source of light (your cell phone’s light will work fine)
- Optional: partner
Make models of the earth and moon
- Make a model Earth by rolling out a small ball of green or blue clay. The ball should be between ½ to ¾ inches (about 1.5 to 2 cm) in diameter (click to enlarge photo below).
- To represent the moon, roll out a small ball of white clay. It should be about one-quarter the diameter of your model Earth (see photo above).
Make an Earth cup (EC)
- Make a stand to hold your model Earth so that it sits at the same level as the center of the Sun (the tennis ball). To do this, use your scissors to evenly cut an inverted cup to the right height. Your Earth and Sun should be at the same height, parallel to the tabletop. When you’re done, set the cup cut-side down and push your clay-ball Earth onto the top, so that it sticks, but is not deformed. This is your Earth cup (EC). (Click each photo below to enlarge.)
Make an Ecliptic-Plane cup (EP)
- Invert a cup and place it between the earth (clay ball) and the Sun (tennis ball). With one color of marker (we used blue), draw a circle around this cup that is parallel to the tabletop and even with the center of the earth and Sun. An easy way to do this is to hold your pen still and spin the cup (see first photo below: click to enlarge). When you’re done, insert a pushpin anywhere on the circle (see second photo below: click to enlarge). This is your Ecliptic-Plane cup (EP). The pushpin will be used to tilt the cup you’ll make in the next step, and act as a handle for your explorations.
Make a Tilted-Lunar-Orbit cup (TLO)
- Invert your third plastic cup. Then, using the second colored marker (we used red), draw a circumference low down, close to the cup’s brim. It should be parallel to the tabletop, about ⅜ inch (1 cm) above the brim. To make an even circle, hold your pen and spin the cup, as you did in Step 4.
- Stick the white-clay moon anywhere on the circle (click to enlarge photo below). (Try not to smash the model moon; just make it stick.) This is your Tilted-Lunar-Orbit cup, or TLO.
Assemble your model
- Stack your cups in the following order: Earth cup (EC), Ecliptic-Plane cup (EP), Tilted-Lunar-Orbit cup (TLO). Let the inverted brim of the TLO rest on the pushpin. This should allow the TLO cup to tilt. When all the cups are stacked, you should see that the red circle on the TLO cup crosses the blue circle on the EP cup. (Click to enlarge photos below.)
- Place your tennis-ball Sun in the middle of the table, next to your model, and you’re ready to go.
Investigation I: Modeling the moon orbiting the earth
Hold the pushpin with your fingers, allowing the Tilted-Lunar-Orbit (TLO) cup to turn freely at an angle. With your other hand, spin the TLO cup counterclockwise (see photo below; click to enlarge). Watch as your moon travels along its tilted path.
Note that your earth does not spin in this model. The motion of the moon here defines one month of its orbit. If it could, the earth would have rotated about 30 times during this period.
Investigation II: Modeling the earth-moon system as it orbits the Sun
Hold the pushpin so that it always points in the same direction—at the same corner of a room, for example, or other distant fixed point. Hold onto the pushpin and use it to drag the stack of cups counterclockwise around the tennis-ball Sun. This motion represents the orbit of the earth-moon system around the Sun.
Pull the stack once around the Sun while simultaneously turning the TLO cup counterclockwise 12 times. (Click to enlarge photo below.) Try to space your 12 rotations evenly as you revolve around the Sun. This represents the tilted orbit of the moon as the earth and moon go around the Sun.
Note that your earth does not spin in this model. The time period defined is a 12-month year. If it could, the earth would have rotated about 365 times during this period.
Investigation III: Finding three-in-a-row alignments
As you drag your stack of cups around the Sun, locate and count the number of places where the earth, moon, and Sun line up on the same plane. The moon can be in the middle of the alignment, or the earth can be in the middle of the alignment.
There are a few things to look out for as you move your cups about: The moon may be too low or too high for a straight alignment (see first and second photos below: click to enlarge); or the moon may be on the right plane, but still not line up with the earth and Sun (see third photo below: click to enlarge). When the earth, moon and Sun come into alignment, an eclipse occurs! (Click to enlarge final photo below.)
Find another three-in-a-row alignment, but this time, use your flashlight to mimic the light emitted by the Sun. You can do this by shining a flashlight, or the light from a cell phone, as if it were shining from the middle of your tennis-ball Sun. (Click to enlarge photo below.)
Point the light at your cups and see if a shadow is broadcast either by the earth onto the moon, or by the moon onto the earth (click to enlarge photo below). (Be careful that you don’t confuse the shadow of the pin with either the earth or moon.)
As you might have discovered, locating where these three celestial bodies align is no easy task.
As this model shows, there are four locations, or regions, in space where the earth, moon, and Sun line up as they move. These sets of alignments happen on the opposite side of the earth-moon system’s journey around the Sun.
Alignments can occur several times during a single lunar orbit, or month: first, when the moon is located between the earth and Sun, and then two weeks later, when the earth is between the moon and Sun (click to enlarge first photo below). (Note that the order of these events can be switched.) Another set of alignments can happen six months later, after the earth-moon system has danced halfway around the Sun (click to enlarge second photo below).
The geometric lineup of three celestial bodies is called syzygy. Syzygy only happens when the moon (on the red circle of your Tilted-Lunar-Orbit cup) crosses the blue circle of your Ecliptic-Plane cup. That blue circle represents the ecliptic, the flat disk traced out by the earth as it moves around the Sun. In fact, all the planets in our solar system orbit the Sun roughly on this same astronomically large, flat, imaginary plane. (Click to enlarge image below.)
Source: Courtesy NASA, Credit: ESA
The point at which the moon’s tilted orbit crosses the ecliptic plane (that is, where the red and blue circles cross on the cups) is called a lunar node. The moon has to be at a lunar node at the right time for syzygy (an eclipse) to happen. (Click to enlarge photo below.)
If you used your flashlight to mimic the light coming from the Sun, you probably found that shadows were cast only when the moon was at or near the lunar nodes.
So what does this have to do with our actual earth-moon-Sun system? The moon’s orbit is tilted! It’s angled at 5.14 degrees from the ecliptic plane (click on image below to enlarge). Because the moon is far away (about 240,000 miles, or 385,000 kilometers from Earth), this tilt makes a big difference on where celestial shadows are cast.
The moon’s tilt causes the moon’s shadow to miss the earth most of the time, and the earth’s shadow to miss the moon most of the time. (Click to enlarge two images below.) It’s only during syzygy that these shadows can land on another celestial body. When this happens, the result is an eclipse.
There are two types of eclipses: solar eclipses and lunar eclipses.
Solar eclipses occur when the moon’s shadow falls upon the earth. During a solar eclipse, you can watch the moon block out the light of the Sun. Since the moon is relatively small compared to the earth, the shadow it casts is also relatively small. Those lucky enough to see a solar eclipse have to be watching at the right time on the daylight side of the earth under clear skies in the narrow path of the moon’s shadow. (Click to enlarge image below.)
Lunar eclipses occur when the earth’s shadow falls upon the moon. During a lunar eclipse, you can watch as the moon is darkened by the shadow of the earth. The shadow cast by the earth onto the moon is huge! You can see a lunar eclipse if you’re on the night side of Earth with clear skies at the right time of the event. (Click to enlarge image below.)
The motions that allow for the geometry of an eclipse to occur can last over a long period of time. This time frame, called the eclipse season, can last several weeks (about 35 days). Usually, during an eclipse season, two eclipses are possible and, surprisingly, every once in a while a window opens in which three eclipses are possible (a combination of solar and lunar eclipses).
Count the eclipses
Many publications and websites show eclipses incorrectly, depicting the earth, moon, and Sun orbiting on the same plane. What would happen if this were really the case? You can see by using the cup models you’ve made in this Snack.
First, remove the pin from your Ecliptic Plane (EP) cup. Then, move the small clay moon from the Tilted Lunar Orbit (TLO) cup (with the red circle) and gently stick it onto the blue circle of the EP cup. (Click to enlarge photo below.) Twirl your moon around the earth while revolving it around the Sun to model the earth’s movement for about 12 months, or one year. Watch carefully, and notice how often syzygy (an eclipse) occurs. You’ll see that there would be at least two eclipses per month—that’s 24 or more a year! Clearly, this model does not reflect what really happens.
You may want to do this demonstration before beginning this Snack, since it can correct initial misunderstandings and help give learners a way to see why this oversimplified model does not work.
Check out the Exploratorium's collection of videos about eclipses, including one that shows the phenomenon explored in this Science Snack.
The material contained in this document is based upon work supported by a National Aeronautics and Space Administration (NASA) grant or cooperative agreement. Any opinions, findings, conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of NASA.