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Determining the Shape of the Moon-Earth-Sun System

INTRODUCTION. At first this might seem a daunting task, but this should be a project that requires no special equipment other than a sunny day, a few clear nights, sharp eyes, four straight 3-foot stakes that can be hammered a few inches into the ground and two flat sheets of cardboard. Now it doesn't seem like it should be too difficult, does it?

Every sunny day, you see that the sun moves across the sky from some eastern point on the horizon to set in some western point on the horizon. Note that it is rare for it to rise exactly in the east and set exactly in the west (this will happen only on March 21 and September 21). The path that the sun takes across the sky is called the ecliptic. BUT you know that the sun doesn't really move across the sky, it only looks like it does as the earth slowly rotates.

How to determine where the ecliptic is in the sky. Between about 10:30 and 11 a.m. on your sunny day, go outside with your hammer and one of your stakes. Place the bottom of the stake on the surface of the ground, and then aim the stake directly at the sun. You shouldn't look at the sun, but rather tilt the stake so that it casts NO shaddow (figure to left). Then hammer the stake into the ground a little way AT THAT ANGLE. Do the same thing at between 1 and 1:30 p.m. with your second stake. "Plant" this stake very close to the first stake (figure to near right). You might now imagine that your two stakes are spokes in a great wheel. That wheel is parallel to the plane of the nearly circular orbit that the earth takes going around the sun. Now lay your piece of flat cardboard flush against the stakes (figure far right):

As just said, the cardboard determines the plane of the ecliptic because if you were to extend that cardboard all the way into the sky it would touch where the sun goes. But that is not all. After sunset, when the sun is below the horizon, it is still riding on that extended plane in the ecliptic of someone else's daytime sky. However the ecliptic line during YOUR night has another name - the zodiac. Brighter stars are grouped into what are called constellations, and those constellations spanning the line are what some call the astrological signs of the zodiac - Aquarius, Pisces, Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio and Sagittarius - in that order. (It is thought that the Christmas "star" of Bethlehem was really a combined event when jupiter, saturn and the moon were all in the constellation of Aries, which was the symbol of the Holy Land. To the ancient wisemen, jupiter represented a king, saturn represented peace, and the moon represented a god. When planets temporarily group together, they are said to be in "conjunction." To astrologers, such as were the wise men, conjunctions carry great significance.)

Anyway,

DON'T MOVE YOUR CARDBOARD!

Let's ask a new question: where does the moon travel across the sky? Once you ascertain where the moon transits the sky, you can determine if the moon's orbit around the earth is (upper right →) or is not (lower right →) in the same plane as is the earth's orbit around the sun. If you look closely at the upper figure to the right, you will see that on the night side of the earth, the moon should be aligned in the ecliptic, while in the lower figure, it would rarely be in the ecliptic. Thus all you need to do is go out on a night when the moon is visible and look to see if it is in line with your sheet of cardboard. If it is, then its orbit is coplanar (in the same plane) with earth's orbit. If it is not and found in some other part of the sky, it will be more like the lower figure. On a night with a nearly full moon, you might even be able to hammer in two "moon" stakes and add a "moon" cardboard to see what's its orbit's tilt is relative to your "solar" cardboard.

Is it like this? Or more like this:

From the two "moon" and "solar" cardboards you should be able to make an accurate visual model of your discovery. Your visual aid might look like what is shown next to the title, above. What is very important for your report is determining what the angle is between the two planes. Of course, if they are coplanar, then the angle is zero degrees.

A bit of finesse can be built into a second demonstration model IF you make you earth's orbital plane a large> piece of circular cardboard. Then make a smaller circle for the lunar orbital plane. You now want to move the lunar plane around the sun for "one year." As you do so, always keep the tilt in the same direction. (Later, for another demonstration, you can use this same setup to show how Saturn with its rings moves around the sun.)

January	→	April	→	July	→	October

Once you have made your model, you will want to have a few insightful remarks to make about it in your report to the class. For one thing, if the orbits are perfectly coplanar, what would that mean with regard to the frequency of solar and lunar eclipses? It would mean that there should be one of each every month. Do they occur that often? No. Thus the orbits are at least NOT perfectly coplanar. They might be close, but not exactly. And maybe they are not close at all. You figure it out - it's your project!

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