# Cosmic Coincidence

Build a deeper understanding of how we see solar eclipses by focusing on the size-and-distance ratios of the Sun and moon from our perspective on Earth.

- One sheet of 8.5 x 11 (A4) white or other color paper (not shown)
- Metric ruler
- Scissors
- Tape
- Toothpick or similar (skewer or pencil, for instance)
- Calculator (not shown)
- Mathematical compass or objects that can be traced to make circles
- Chalk or tape to mark the ground
- Meter stick or measuring tape
- Partner (not shown)
- Optional: hole punch (not shown)

- Measure the length of your arm (in centimeters) from the top of your shoulder to the base of your thumb. (Click on photo below to enlarge.) Make note of this measurement, which gives you the distance between the location of your model Earth (consider this at your eye) and your model moon, held at the end of your straight arm.
- The moon’s diameter is about 100 times smaller than the distance between the earth and the moon. Based on your result from Step 1, determine the diameter of your moon model, which will be 100 times smaller than the length of your arm. (If your arm is 60 centimeters long, for instance, you would make a moon model 0.6 centimeters, or 6 millimeters in diameter.)
- Using scissors, cut out your moon model from the sheet of paper, and carefully tape it to the tip of a toothpick, making sure its circular shape isn’t obscured by the tape. (Note: If you have a hole punch, punch out a few bits of circular paper. Some hole punches make circles that will be the correct size to be used as a moon model.)
- Next, use a compass to trace a circle with a diameter at least 10 times larger than the moon model you made in Step 3. Use scissors to cut out this larger circle, and note its diameter. This larger circle will be your Sun model.
- Tape your Sun model to a wall where there’s enough space for you to back away from it. (Click on photo below to enlarge.)

Face the paper Sun taped to the wall and stand a few feet away. Then, close one eye. In this model, where you stand represents the position of Earth. Your open eye represents the position of an observer on Earth.

With your arm straight and your elbow locked, hold your paper moon in front of your open eye. (Click on photo below to enlarge.) Line up your eye with the moon and Sun. What do you notice? Is the Sun “eclipsed” by the moon? If not, carefully back away until your moon just barely covers the entire disk of the Sun. (Remember to keep your arm out straight!) When you find the distance where the moon perfectly eclipses the Sun, you will have modeled a total solar eclipse! Mark your position on the ground or floor with chalk or tape.

Measure the distance from where you marked the ground (where your moon could block out the Sun) to the wall where the Sun is taped. How does this distance compare to the diameter of the Sun? This Earth-Sun distance has a special relationship to the Sun’s diameter!

Now that you’ve found the perfect location to create a total solar eclipse, try making slight adjustments to the position of your paper moon. What happens when the moon is slightly higher or lower in the sky? What happens if the moon is slightly farther away from Earth? Without moving your own position, see what happens when a partner moves the moon a bit closer to the Sun, increasing the distance between the Earth and the moon.

The focus of this Science Snack is the amazing coincidence of the diameter/distance ratios of the Sun and moon with respect to the earth.

The Sun’s diameter is about 1,000,000 miles, and its distance from Earth is about 100,000,000 miles. What is the ratio of the Sun’s diameter to its distance from Earth?

The moon’s diameter is a bit less than 2,300 miles, and its distance from Earth is a bit more than 230,000 miles. What is the ratio of the moon’s diameter to its distance from Earth?

The moon and Sun share a coincidental relationship: From our perspective on Earth, each has a size/distance ratio of 1 to 100. Both the moon and Sun are about 100 times farther from Earth than the sizes of their respective diameters. This means that the moon will block out, or “eclipse,” anything behind it that has the same 1-to-100 size/distance ratio. This is the “cosmic coincidence” that makes solar eclipses possible.

Though the Sun is much, much larger than the moon, and much farther away, from our point of view on Earth the moon can perfectly cover the far-away Sun, resulting in a total solar eclipse (click to enlarge photo below).

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

*Note: This activity does not create a correctly scaled model of the Sun and moon; the real Sun’s diameter is 400 times that of the moon. Instead, this model highlights the ratios of the diameters and distances of the Sun and moon, revealing the “cosmic coincidence.”*

*Our Moon’s Tilted Orbit*

The moon’s orbit is actually tilted 5 degrees with respect to the *ecliptic*, the apparent path of the Sun across the sky. (It’s called “the ecliptic” because this is where eclipses can happen when crossed by the moon.) The tilt of the moon’s 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 earth, the moon crosses the 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.

*Scaling the Earth, Moon, and Sun*

The Sun is about 100 Earth diameters across, and 100 Sun diameters away from Earth. The moon’s diameter is about one-quarter that of the earth’s diameter, and the moon is about 30 Earth diameters away from Earth. There are many handy ways to scale the earth-moon-Sun system. For more, see the Earth and Moon Science Snack to investigate the sizes and distances between the earth and the moon.

*Handy Measuring Tool*

From our perspective here on Earth, both the moon and Sun sweep out about half-a-degree of arc in the sky. That means it takes about half of your little finger, held out at arm’s length, to just barely cover either one. While it’s not safe to test this with the Sun (*never look directly at the Sun!*), you can test it for yourself with a full moon. Check out our Handy Measuring Tool Science Snack to learn to use nonstandard measurements and simple ratios to estimate sizes or distances.

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.

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

As they set up their models, learners can also explore other relationships related to the cosmic coincidence. In the To Do and Notice section above, for instance, learners are directed to make a paper Sun model that’s at least 10 times larger than their moon model. So if the moon is 0.6 centimeters in diameter, for instance, then the Sun could be 6 centimeters or larger in diameter. Working in pairs or small groups, learners can make different-sized paper Suns and explore how the distances regarding where they need to stand to “eclipse” their Suns with their moons change. A larger Sun would require a greater Earth-Sun distance, but the ratios of any Sun diameter to its Earth-Sun distance will remain constant: 1 to 100.