African Eclipse, The Dance of the Earth and the Moon
The day after we arrived in Livingstone, I was scheduled to give an eclipse class at the Tujatane school. The school has grades 1,3 and 5.
The children welcomed Noel, Lowell and me with a song and traditional dance. I was impressed by their sweet voices and dancing abilities. Then they put on a play for us in which students acted out the roles of adults. The children's parents laughed to see them acting as adults, but the play had a serious message: send your daughters to school so they don't have to become prostitutes, catch aids and die! Serious lessons for elementary school.
Their wonderful dancing abilities inspired me to borrow an idea from Cheri Morrow and teach my lesson on eclipses using the students as dancers. (Cheri was a team member on the 1999 Exploratorium eclipse expedition to Turkey.)
A group can dance out a scale model of the solar system showing days, months and eclipses.
To Do and Notice
In an outdoor playground area in sunlight or in an indoor space with one bright light to act as sunlight I begin by asking one brave volunteer to come forward to be the Earth.
Day and Night
This activity is easier to do in the morning and afternoon when the sun is lower in the sky, it is hard to do mid day when the sun is high in the sky. So plan accordingly.
One girl came out and I gave her the earth
Then asked her to hold it above her head and to spin around about once per second the viewers could see that the earth rotated. It was late afternoon the sun was low in the sky and illuminated the earth. They could also see that half of the earth was illuminated by sunlight, representing day and half was in shadow. I asked them what the shadow meant and one person shouted out, "night!"
I stopped the rotation of the Earth girl to bring in the next dancer, the Moon.
A scale model of the Earth and Moon
I then asked for a second volunteer, another girl came forward and I gave her the moon. Here I followed the example of Linda Shore and asked the audience to tell her where to stand to make a real scale model of the Earth and the Moon. The audience was amazed that the moon was 30 earth diameters away! Or, since each child's arm was ten earth diameters long, the moon was three full arm lengths, 3 meters, from the earth.
Next I use a string to draw a circle around the earth showing the orbital path of the moon. I use the string to scribe a circle centered on the earth and 3 meters in diameter. Pi being what it is, the circumference of the moon's orbit is about 18 meters or 18 arm lengths. It takes about thirty short child steps to walk around this 18 meter circumference circle. So the Moon child takes one step every earth rotation to make the dance of the Earth and the Moon.
The earth rotates once a second, while the moon walks around a circle once every 30 seconds. (Actually the moon takes 29 days to make one orbit of the earth, the sidereal period of the moon.)
While the moon orbits the earth it always keeps its face toward the earth. Looking at the moon, the viewers will see it makes one rotation every month to keep one face toward the earth. To help show what's happening I have the Moon student dance again, the second time keeping one face toward a distant object for one complete cycle of the earth.
I ask the earth person to stop the daily rotation and watch the moon as it circles around. The earth person sees the moon fully illuminated by the sun at one place in the orbit: the full moon; they see it completely in shade at one other time, the new moon; and partially illuminated at other times, the phases of the moon.
Adding the Sun
I ask for a third student to be the Sun.
A boy volunteers.
I bring up 4 other students. I have them stand in a line, side by side with their arms straight out and fingers touching. I ask the viewers to picture a ball of clay with this diameter. Then I ask them to picture the child carrying that ball of clay which would weigh over 500 tons! The Sun's diameter is 100 Earth diameters, a double arm span for 5 children.
I then ask him to start walking away counting his steps.
One, two three,..., ten...,twenty...,thirty...one-hundred...
He is getting farther away, I shout "keep going until you get 1200 steps away."
He stops, the audience laughs.
I point out a distant landmark two stories high, a kilometer away, and indicate that it is now the Sun.
The distance from the Earth to the Sun is 12,000 Earth diameters or 1200 meters in our scale model.
I have the earth and moon resume their dance.
As the Earth rotates in place, the moon revolves around passing between the earth and the sun once a month. Making an eclipse.
But there isn't an eclipse every month. Because the moon's orbit is tilted, The moon passes about the sun on some orbits and below the sun on others. Only twice a year does it actually eclipse the earth.
But now, each month, the earth should go 1/12 of the way around the sun. the earth is on its way around to make a year. (To actually do this to scale you should note that the circumference of the earth's orbit is about 7200 steps. So that in one month the earth moves 1/12 of this or 600 steps. Each one day spin requires 1/360 of this distance or 20 steps. These would be made in a second! This is impossible but instructive.
We have to slow down the whole model, let the daily rotation take 10 seconds. The Earth-child would have to take 20 steps during one rotation as she orbits the sun. The month will now be 300 seconds or 5 minutes. The moon will circle the earth as they both move around the sun. The year would take 3650 seconds or about an hour.
What's Going On?
The Earth orbits the sun once a year as the moon orbits the earth about once a month. Each month the moon is seen fully illuminated, as a full moon and in shadow as a new moon. If the moon's orbit were in the same plane as the earth's orbit of the sun, then there would be a solar eclipse and a lunar eclipse every month. Actually, the moon's orbit is tilted with respect to the plane of the earth's orbit. So that the moon sometimes passes ten full moon diameters above the plane that would of the earth's orbit. When this happens the shadow of the moon completely misses the earth and there is no solar eclipse.
While you are outside in the sunlight with a model of the moon look around and see if the moon is in the sky. If it is, hold your model moon at arms-length in the sunlight next to the real moon in the sky. Notice your model moon has the same phase as the real moon.
Go to Kubu Cabins
Scientific Explorations with Paul Doherty
6 June 2001