Luna-see: Your own Earth/Moon(s) model

Yes, that’s “Moons” plural because in this little project we make two just as a matter of convenience.

The idea here is simple. I believe that concrete demonstrations stick with us and allow us to internalize abstractions – so I found the time invested in developing a simple Earth/Moon model deepened my understanding of why we see what we see, and I hope it will do the same for you. So here it is. The major abstract ideas that are made concrete here include:

• The relative sizes not only in diameter, but volume, of the Earth and Moon.
• The phases of the Moon and why it changes from night to night and changes position in our sky as well.
• The true-to-scale distance between the Earth and Moon and why this simply isn’t shown in most books.
• The reason why eclipses of the Moon do not occur at each full Moon, but are relatively rare.

Step 1

First you need to gather a few simple materials and tools. Here’s what I used, but for the wood you could easily substitute cardboard – or some other material – and use clay for the Earth ball as well as the two moons. I just like wood and found what I wanted in a local craft store that’s part of a national chain and so I assume, commonly available. Clay for the Moon balls works best because shaping them to size is a learning experience and because they cling to the wires that are used as stands – no glue needed, and you can adjust their position quickly.

Tools and materials for model - click image for larger view.

Materials needed:

1 large disc approximately 6 inches in diameter
2 small discs about 3/4-inch in diameter
1 small disc about 1/2-inch in diameter
1 1-inch ball
1 piece of string 30 inches long
2 thin, stiff wires such as used in floral arrangements – one should
be 1-inch long, the other 3-inches long
clay

Tools needed:

protractor
pen or pencil
black felt-tipped pen (fine or very fine tip works best for writing)
ruler
small flashlight

Step 2 – Prepare a “month disc”

Using a pencil or fine ballpoint pen and protractor, carefully mark off 15 points along the perimeter of the disc, each 12 degrees apart, starting at “0”. These marks will cover half the disc.

Putting marks every 12 degrees starting at 0 and going a full 180 degrees.

Use the ruler to draw 15 lines on your disc, each going from a mark at the perimeter, through the center and clear to the other edge – this will divide the disc into 30 equal spaces, separated by 12 degrees each. Twelve degrees is the approximate amount the Moon covers in our sky each 24 hours, and the 30 divisions mark out a lunar month from New Moon through First Quarter, Full, Last Quarter and back to New.

Choose one line as your zero point, and about halfway between the perimeter and the center, place an arrowhead pointing towards the center (see highlighted area on picture above) – on this line
write “SUN” – the arrowhead indicates the direction of sunlight which for our purposes will remain constant through the month.

Considering the line just labeled as your zero point, the other lines can be numbered going counterclockwise 1-29 – the days of a lunar month – the period between two “new” Moons.

The space either side of this “0” line can be labeled “NEW.” On the other side of this line, near the perimeter, you can label the space either side of it “FULL” – Notice “NEW” moon is between the Earth and Sun; the “FULL” Moon is always opposite the Sun. You can label space 7 “FIRST QUARTER,” and on the opposite side to it, “LAST QUARTER.”

Step 3 – Adding the Earth

In the center of the disc put a small mound of clay about half-an-inch high and about an inch in diameter – take care to center this – and using the ball that is the Earth, make a depression in the top of this mound to hold the “Earth” in position at the center. (You could make the Earth ball of clay, in which case the raised mound isn’t necessary – it’s just there to keep the Earth ball from rolling away.)

If you’re satisfied everything is marked correctly, you may want to go over your labels with the black, felt tip pen to make them more prominent.

Step 4 – Adding the Moons

Make two Moons.

Take a small pinch of clay and roll it into a ball 1/4-inch in diameter. Repeat so you have two small clay balls. These represent scale models of the Moon. (The Earth is about 8,000 miles in diameter, the Moon about 2,160.) Did have trouble estimating how little clay you would need to come out at exactly one-quarter-inch in diameter? Many people do. It’s a good lesson in the difference between the diameter of a sphere and the volume.)

Put another small mound of clay about half-an-inch high on the 1/2-inch disc.

Place the short wire in the center of this mound so it is sticking straight up.

Place one of your Moons on this wire.

Step 5 – And now the shadow

Make an Earth-shadow disc

Take a 3/4-inch disc and using a marker, crayon, or whatever – color it black on both sides. This disc represents the Earth’s shadow at the distance of the Moon from the Earth.

Position the shadow by placing a small mound of clay about half-an-inch tall on the line marked “FULL” about 3/4 of the way between the “Earth” and the perimeter of the month disc.

Stand your Earth shadow on its edge in this clay.

Time to demonstrate lunar phases

For these demonstrations we use just the month disc, Earth, and the Moon on the one-inch wire – oh, and you’ll need a flashlight, and while the room doesn’t need to be pitch black, it’s good to lower the lights.

There are two keys here:

1. Always point your flashlight -which represents the Sun – in the same direction – the direction indicated by the arrowhead you put on the New Moon line.
2. Always position yourself as if you were standing on the side of the Earth looking up at the Moon in your sky. Another way to think of this is if the Moon is placed at Day 3, you should place yourself so you are looking along the line that connects Day 18 and Day 3 and runs through the Earth.

Move your Moon around the perimeter of the disc. To see its phase on any given night, shine the flashlight on it to simulate sunlight – and sight along the line from the Earth to the Moon for that particular night.

Position yourself so you are looking in the direction of the arrowhead, and you will see a "new" Moon - completely dark and lost in the glare of the Sun!

The person holding this flashlight is positioned to see a 2-day-old crescent Moon - the photographer was at a somewhat different angle and so saw a larger crescent. Remember - keep flashlight pointed in the same direction and position yourself along the line that is nearest to where you have placed the Moon.

Now here we are at full Moon - oops, but we forgot the earth's shadow!

Put the Earth's shadow in place and it should be clear that - ooops, the shadow is blocking the Moon! But if it does that we would have an eclipse every full Moon - every month! Clearly we don't, so ...

You should notice one problem. When you get to full Moon, the shadow of the Earth blocks the Moon from view. This would mean there would be an eclipse every month at full Moon – but we know there isn’t. What’s wrong with our model?

Step 6 – Going full scale and setting things right!

Our model is convenient for showing the phases of the Moon – and actually keeping track of them each month by advancing the Moon on the monthly disc each day. But it has two problems. First, it doesn’t show the distance between the Earth and Moon to scale – and second, it doesn’t show that the Moon’s orbit is tilted about five degrees to the orbit of the Earth!

So here’s how we’ll correct that situation.

Take the second 3/4-inch disc and place a clay mound on it about half-an-inch high.

Place the long wire (3 inches) vertically in this piece of clay.

Place your second clay Moon on top of this wire.

Now use the string to place your new model of the Moon 30 inches from the Earth. You have now created a scale model of the Earth/Moon system. But why is the Moon so much higher than the Earth in this model? Actually, the Moon could be that much lower than the Earth as well – we are showing it in one direction only because we’re building our model on a table. The Moon, at any given moment, could be just as far below the tabletop as it is above it – or anywhere in between these two extremes!.

To show the distance to scale, place the Moon about 30 inches from the Earth.

Placing the Moon 3 inches above the table seems high – does a five-degree tilt in the Moon’s orbit really amount to that much at the distance of the Moon from the Earth?

If the table edge represents the plane of the Earth's orbit, then the string will represent the plane of the Moon's orbit, tilted five degrees to the orbit of the Earth.

Five degrees doesn’t sound like much – but this is how much the Moon’s orbit tilts with respect to the Earth. You can get a rough idea of what this means on the scale of the Earth/Moon system by using your protractor and the string. Line your protractor up with the edge of a table. Then have your string come out at five degrees from the center of the protractor. Thirty inches later you’ll find that five degrees is now represented by about three inches – the height of our second model of the Moon.

That’s why our second wire was three inches long.

And now it should be clear why we don’t have an eclipse each month. Place your Earth’s shadow out near your Moon, and you can see that most of the time the Moon is going to miss the shadow – it will either be above it or below it.

At full the Moon may be well above the Earth's shadow, well below it, or on relatively rare occasions, pass right through it - and at those time we see an eclipse of the Moon.

You can also see that the Moon might pass through the shadow briefly, or it may take nearly three hours to get through it. But it won’t take 24 hours. Three is about the maximum. And so when an eclipse occurs at full Moon, the Moon for those few hours may, or may not, be in your night sky. That’s why eclipses are visible from only part of the Earth, and they may occur at any time of the day or night.