# Eclipse to Scale

Build an understanding of solar eclipses with a model that’s correctly scaled in both size and distance.

- One sheet of 8.5 x 11 (A4)
- Hole punch
- Metric ruler
- Clay (a very small amount)
- Toothpick
- Calculator (not shown)
- Large sheet of paper about 3 x 3 feet (1 x 1 m) square; can be several smaller sheets taped together (not shown)
- Length of string about 20 inches (50 cm) long
- Two sharpened pencils
- Meter stick, measuring tape, or other way to measure a long distance
- Scissors
- Tape
- A long, open space to work in, such as a playground or playing field, at least 230 feet (70 m) in length (Note: works best if you have a wall or other vertical surface at one end; not shown)
- Chalk or other way to mark the ground
- Partner (not shown)
- Optional: cardboard or posterboard about 3 x 3 feet (1 x 1 m) square (to make the model Sun more sturdy; not shown)

*Make a Model Earth*

- With the hole punch, punch out tiny circles from the edge of your 8.5 x 11 (A4) sheet of paper. Each participant will need one tiny circle to serve as their model Earth.

*Make a Model Moon*

- Determine the relative size of the moon by using your metric ruler to measure the diameter of the tiny circle. Our moon’s diameter is about one-fourth the diameter of Earth. If your hole-punched Earth (your tiny circle) is 7 millimeters in diameter, then the moon will be less than 2 millimeters in diameter. Ball up a tiny piece of clay to make a correctly-sized model moon and place it on the tip of a toothpick. (Click to enlarge photo below.)

*Make a Model Sun*

- Using a ruler, measure the diameter of your tiny model Earth (typical hole-punch sizes range from 6 to 8 millimeters). Since the Sun’s diameter is about 100 times greater than the earth’s, multiply your tiny Earth circle's diameter by 100 to find the diameter of your model Sun. Then divide that number by 2 to determine its radius.
- Make a small loop at one end of the string and tie it off with a knot.
- Place one of your pencils through the loop and hold it firmly near the center of your large piece of paper.
- Using the radius measurement worked out in Step 3, place the second pencil at that distance along the string. Wrap a few turns of string around the second pencil to maintain its distance from the first pencil.
- Carefully hold the first pencil in place at the center of the paper and—keeping the string taut—draw a circle with the second pencil. (Click to enlarge animated gif below. NOTE: This process is easier with a partner to help!)

- Use scissors to cut out the circle, and you’ll have a model Sun that’s scaled to your model Earth and moon. If you want, you can attach the paper Sun to cardboard or posterboard to make the model more sturdy.

*Make a Model Earth–Moon–Sun System*

(Note that Steps 9, 10, and 11 can be completed ahead of time.)

- If you have a wall, signpost, or other vertical surface that could mark one end of your model, tape the large cut-out Sun there at head height. (Alternatively, you can have someone hold up the “Sun” when needed.)
- Using a meter stick, measuring tape, or similar, find where the earth should be at the other end of your location. To make that calculation, note that the Sun’s distance from Earth is about 100 times greater than the Sun’s diameter. If your model Sun has a diameter of 70 centimeters, for example, the correct distance between the earth and the Sun will be 70 meters.
- Use chalk, tape, or other way to mark where the earth should be at the opposite end of your location (the earth’s location will be at “0 meters” for this model). At this point, you will be able to create a correctly-scaled model of the earth and Sun, both in relative size and distance.

Bring your hole-punched Earth, clay moon (on its toothpick), ruler, and calculator to your scale- model location, and stand at the 0-meter line. This is the position of the earth with respect to the Sun. The hole-punched Earth and paper Sun are now correctly scaled in both size and distance.

When you look toward the model Sun, what do you notice? Most people are surprised by how small the Sun looks when its size and distance are scaled correctly. But what about the moon?

The distance between the earth and moon is about 30 Earth diameters. If your hole-punched Earth is 7 millimeters in diameter, then the clay moon will be 21 centimeters away.

Participants should work in pairs to complete this part of the model, with one person (“the measurer”) helping with measurements, and the other (“the eclipser”) using their clay moon to eclipse the Sun. Using a ruler, have the measurer help the eclipser by holding the moon model at the correct distance from the eclipser’s face. The eclipser should close one eye and imagine that their open eye is an observer on Earth. Then, without changing the moon’s distance from their face, the eclipser should line up their open eye with the moon and Sun. (Click to enlarge photo below.)

For the person in the role of the eclipser: What do you notice? You should see that the moon completely blocks the Sun, appearing to be the same size as the Sun from your Earth point of view. This is a scaled model of a *total solar eclipse*.

Try making slight adjustments to the position of the clay moon. What happens when the moon is slightly higher or lower in the sky? What happens when the moon is slightly farther away from the earth? What happens when the moon is off to the side?

Partners should change roles and repeat the creation of this model.

Most astronomical scale models do not scale both sizes and distances simultaneously. The distances are so large that it’s usually impossible to do.

The Sun is much, much larger than the moon, and also much farther away, both of which are apparent here. In this scaled model, from our point of view on the hole-punched Earth, the tiny clay moon will perfectly cover the far-away Sun, resulting in a total solar eclipse (click to enlarge photo below), but only when the moon is exactly in the correct position.

###### Total Solar Eclipse Photo Credit: NASA

When the moon is in between the earth and the Sun, the moon is in its new-moon phase. Solar eclipses can only happen when the moon is in this position.

The moon’s orbit is actually tilted 5 degrees with respect to the *ecliptic*, the apparent path of the Sun across the sky (called “ecliptic” because this is where eclipses can happen when crossed by the moon). The moon’s tilted orbit is why we don’t have solar eclipses during every new moon: The new moon is usually too high or too low to block out the Sun.

As it orbits, the moon crosses Earth’s ecliptic twice a month. These are the two orbit locations where eclipses can occur. One is called the *ascending node*; the other is the *descending node*. The moon must be at one of these nodes, and in its new-moon phase, in order for a solar eclipse to occur.

For those who want to explore more mathematics, here are some ways to think about setting up this scale model on your own.

First, some information about the earth and the Sun:

**Earth’s Diameter: 12,756 km****Sun’s Diameter: 1,392,000 km****Earth–Sun Distance: 149,600,000 km**

There are two ways to find out how big the Sun would be if the earth were the size of a hole-punched circle: 1) Set up a proportion to determine the scaled diameter of the Sun, or 2) Find the scaling factor and use it to determine the scaled diameter of the Sun.

Here are the numbers needed to make a correctly-scaled moon out of clay:

**Moon’s Diameter: 3,475 km****Earth–Moon Distance: 384,000 km**

For more, see the Earth and Moon Science Snack to investigate the sizes and distances between the earth and the moon.

Most eclipse models do not show these celestial objects to scale. This scale model shows the correct positions as well as the sizes and distances of the earth, moon, and Sun. This model also helps to show why eclipses don’t happen every month during a new moon: If the new moon is just a bit too high or a bit too low, there is no solar eclipse.

It’s important for learners to understand that the position of the hole-punched Earth is where they are standing (at the 0-meter mark, some distance away from the Sun model). Designated “measurers” can help make sure designated “eclipsers” maintain the correct Earth-moon distance, closing one eye and using the other eye to line up the clay moon with the paper Sun.

This Snack works best if learners are familiar with the relative motions of the earth, moon, and Sun (for example, that the earth orbits the Sun, and the moon orbits the earth).

You can introduce the basic concepts of solar eclipses with the Solar Eclipses Science Snack, which requires no special materials and is a good entry point for younger learners.

To emphasize mathematical thinking and computational skills, older students can use proportional reasoning to determine the scaled sizes of their Sun and moon models, and find the correct scaled distances between the earth, moon, and Sun. See the Going Further section, above, for more information to help get started on these calculations. Older students can also make their Sun and moon models based on their own calculations, and find the correct scaled distances between the earth, moon, and Sun.

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.