The collection of teaching resources that follows evolved, and continues to evolve, from questions sent in by ARIES teachers, SEDNet participants, or general email requests. Responses are prepared by the SEDNet staff at the Harvard-Smithsonian Center for Astrophysics and the Christa Corrigan McAuliffe/Challenger Learning Center at Framingham (MA) State College.

 

 

 

How to Make a “Moon Stick!”

A “Moon Stick” (as several of us call it) is a good model to have available when exploring the distance, size, and scale of the Earth-Moon system. The key is to remember that the distance to the Moon from the Earth is close to 29 1/2 Earth diameters. Directions for building a “Moon Stick” are:

1. Obtain a 36-inch long wooden dowel 1/4” or 3/16” in diameter. Cut the dowel to a 30-inch length. (This assumes a 2.5 cm (1”) sphere for the model Earth. See Step 4 if you work with a model Earth of different size.)

2. Obtain two spheres (cork, wood, Styrofoam, etc.). The sphere for the model Earth should have a diameter as close as possible to 2.5 cm (1”); the model Moon should be about 0.8 cm (3/8”) in diameter. (The ratio of the Earth’s diameter to that of the Moon is close to 3.5:1.)

3. Before placing the spheres on opposite ends of the dowel you might want to sharpen each end of the dowel. The sharpened points make it easier to force the spheres (cork or Styrofoam) onto the dowel. (If using wooden spheres you may need to drill small holes in the spheres before placing them on the dowels.) Use glue to hold the spheres in position (not all glues work with Styrofoam!).

4. If you use a model Earth that is not 2.5 cm (1”) in diameter, be certain the distance to the model Moon is about 30 times the diameter of the model Earth and the model Moon is a little more than 1/4 the diameter of the model Earth.

 

How to Make a Model to Demonstrate the Barycenter (Center of Mass) of the Earth-Moon System!

The Earth is roughly 80 times more massive than the Moon. The barycenter (or center of mass) for the Earth-Moon system is about 1/80 from the center of the Earth (i.e., 1/80th of the distance between the center of the Earth and the center of the Moon). That puts the barycenter of the Earth-Moon system about 900 miles beneath the Earth’s surface. To model this:

1. Start, as with the “Moon Stick,” with a dowel and spheres (Styrofoam works best for this model), and sharpen each end of the dowel. Achieving an accurate scale is difficult, since you will need to use a larger sphere for the model Earth (and it may be difficult to find dowels longer than 36 inches). A larger sphere is needed so that it can be easily cut in half and part of the inner material removed, to be replaced with a very dense substance (e.g., lead). Start with a sphere about 5 cm (2”) in diameter. (Properly scaled, you would need a five- foot dowel! You will likely have to settle for an incorrect scaled Earth-Moon distance. Be certain this incorrect scale is made apparent when using the model.) Cut the sphere in half, and remove enough of the inner material to accommodate the denser material (try lead fishing sinkers, or the lead weights used at the bottom of drapes). If you use a 5 cm (2”) diameter sphere for the model Earth you will need to use a sphere about 1.5 cm (5/8”) in diameter for the model Moon.

2. Glue the model Moon to one end of the dowel.

3. Tie a 2-foot piece of string onto the dowel and position it close to the end of the dowel where the model Earth will be fastened.

4. Determine, by trial and error, how many pieces of lead are needed inside the hollowed out model Earth to balance the system. Use masking tape to temporarily hold the two halves of the sphere together as you determine the amount of lead needed to balance the system (i.e., with the string positioned right next to the model Earth).

5. Glue or tape the model Earth together (with the lead or other dense material inside) and fasten it to the free end of the dowel. Fine tune the balance of the system by adding small amounts of tape to one end or the other.

6. Hold the model out in front of you (i.e., away from your legs and body). Slowly tap or nudge one end or the other so the Earth and Moon move around or orbit each other, with the center of the motion at the barycenter (i.e., the center of mass, identified by where the string is attached to the dowel.

 

How to find the Approximate Celestial North-South Line with an Analog Watch!

The Earth turns on its spin axis one time per day, or 360º, about every 24 hours. At that rate the Earth is turning close to 15º every hour. On a 24-hour analog watch, the hour markers on the watch face are 15º apart, and the sweep of the hour hand models the rate at which the Earth spins. (On the common 12-hour analog watches, the hour markers are 30º apart and the hour hand moves at two times the rate of the Earth’s spin.) In this respect, an analog watch can be seen as a flattened model of the Earth, and in the daytime can be used to find a key directional marker (i.e., the Celestial or North-South line).

1.Outside on a sunny day point, hold your analog watch in your hand with the face of the watch level to the ground. Turn the watch so the hour hand points directly to the Sun. NOTE: Never look directly at the Sun!! You can easily align the hour hand to the Sun as follows: Obtain a small twig, toothpick, match stick, or the like. Hold the twig upright directly over the center of the watch face (i.e., the center post for the watch hands). Move your watch until the shadow cast by the twig falls directly away from the hour hand. That is, the hour hand and the shadow form a continuous straight line. Since the shadow is falling directly away from the Sun, the hour hand points directly at the Sun.

2. Without moving the watch, and keeping its face level to the ground, locate the Noon hour marker on the watch face. (Remember, that will be the 1:00 pm marker during Daylight Saving Time.)

3. You can now find the approximate North-South line using the hour hand and Noon marker. Continue to hold the watch level with the hour hand pointing directly to the Sun. Identify the angle formed by the hour hand and an imaginary line between the watch post center and the Noon marker. For example, if it was 10:00 am on a summer day, the angle would be that formed between the hour hand and an imaginary line between the center post and the 1:00 pm hour marker on the watch face. Imagine a line bisecting that angle. That is, using the 10:00 am time example, the midpoint on the watch face between the 10:00 am and 1:00 pm markers is halfway between 11:00 am and 12:00 Noon markers. Imagine a line extending from the watch post center crossing that bisection point. That line defines the approximate North-South line for your location.

4. The line you identify will only be approximate. The differences can be as much as ± 5º, and on some rare occasions even more. The reasons are beyond the scope of these notes. Part of it has to do with where you are located east or west from the standard meridian in your time zone. Another factor has to do with the irregular apparent motion of the Sun (it is really the Earth that is the culprit!). The net effect is that that time as given by a watch and the time from the Sun’s angle (such as with a sundial) differ on most days, sometimes as much as 16 minutes. There are four days when an accurate watch and “Sun time” are together. These occur at about 16 April, 14 June, 2 September, and 25 December. On or near those days the north-south line you locate using an analog watch will match most closely the actual Celestial North-South line.

 

A Fine Time to Observe the Moon!

One of the better ways to come to understand the changing appearance of the Moon (i.e., the Moon’s progression through its phases) is to observe the Moon when the Sun is also visible. This is best done during the first and last quarter moon phases. First Quarter Moons are visible in the afternoons, Last Quarter Moons in the mornings. Check calendars to determine the moon phases.

1. Obtain a white sphere to model the Moon in space. A tennis ball is a good size, but any small sphere (baseball, softball, golf ball, etc.) will be appropriate.

2. Go outside and locate both the Moon and the Sun in the sky. Stand in the open where you can see both the Sun and the Moon, and your own shadow being cast on the ground. Make note of the direction of your own shadow. The Earth’s shadow extending into space is cast in the same direction.

3. Hold up the sphere at arm’s length in the sunlight so that the sphere is aligned just to one side or the other of the Moon. Compare the shape and the location of the terminator on the Moon’s surface (i.e., the line separating the illuminated portion visible to you and the darkened portion of the Moon facing the Earth) to the terminator visible on the sphere in your hand. How do the two terminators compare? If a portion of the sphere is darkened by a shadow (slightly, since there is scattered light all around), what is the source of the shadow? Check to see if the Earth’s shadow (its direction is defined by the direction of your own shadow) can be striking the Moon during this phase. 

4. For closure, think of the sphere in your hand as a model for the Moon. The amount of the illuminated portion of the sphere that you are able to observe (ask yourself: How much of the sphere is illuminated by the sunlight?) matches the amount of the illuminated portion of the Moon that you observe. And the portion of the Moon facing the Earth but invisible to you matches the darkened region of the sphere you observe.

 

 

 

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