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  • Aurora Borealis

    We are going to build a human-scale model of the astronomical system.

    1. Simulation of the Sun-Earth-Moon system

    The goal of this activity is to begin to experience the scale of the solar system: how immense the Sun is and how far away compared to the size of the Earth and the distance to the Moon. For example, we will see how the entire Earth-Moon system could fit inside the Sun with plenty of room to spare.

    A. The Calculations.

    Give students the following data: (Mature students could be assigned to retrieve these data themselves from the web or other references.)
    Body Radius Orbit radius Orbital period
    Sun 695000 km
    Earth 6378 km 149.6M km 365.256days
    Moon 1738 km 384400 km 27.322days

    Our task is to set up a scale model of the system.

    Depending on the level of the students, the teacher can be more or less involved in these calculations. Mature students could carry out the arithmetic by themselves!!

    Say you have a 100-meter by 64-meter soccer field, so make the longest distance (= diameter of Earth's orbit, approximately 300 million km) 60 meters. So 1 meter is 5 million km, and the scale of our simulation is 5 billion to 1. The Earth-Moon distance is then approximately 8 cm. Note: This scale involves a large space (60 by 60 meters) but at any smaller scale the Moon would become invisible. At this scale the simulation of a year will take about 5 minutes.

    Size of the scaled-down bodies:
    Sun (diameter 1.4 million km) becomes 28 cm in diameter.
    Earth (diameter 12756 km) becomes 2.5 mm in diameter.
    Moon (diameter 3476 km) becomes 0.7 mm in diameter.

    The length of the earth's orbit in the simulation is approx 188 m. To scale, the earth moves around the sun 188/365 = close to 50 cm per day. The moon moves about 13 degrees in a day, and close to 90 degrees in a week. (All motions are counter-clockwise, when seen from ``above'' the solar system).

    B. The simulation.

    The acting out of the simluation can be more or less elaborate depending on the number of students.

    Materials: Basketball, plumber's helper, pencil with (perferably green) eraser, small paper clip, white-out (and access to a football or soccer field, or to a space that can hold a 60 by 60-meter square).

    To set the stage we need objects of the scaled-down size of the Sun, Earth and Moon. A basketball (25 cm in diameter) can be used for the Sun, although it is about 10% too small. It should be placed at the center of the field. The plumber's helper, stuck into the ground, will hold the basketball at a nearly appropriate height. At this scale, the Earth can be represented by the eraser on a pencil, although the eraser has diameter close to 5 mm, and so is really twice as wide as it should be. Straightening out a small paper-clip gives a stiff wire 9.5 cm long and about 1 mm in diameter. This wire can represent the moon at (roughly) its distance from the earth. A drop of white-out at the end of the wire makes it more convincing. The other end of the wire should be inserted into the pencil eraser. (This should be done with care so it does not get inserted into someone's hand, but steady pressure and back-and-forth twisting will do the trick).

    52 students: Students position themselves evenly around a circle 30 meters in radius (start with four at four cardinal points and interpolate the other 48 evenly, 12 to a sector). Students will be about 3.6 meters (about 12 feet) apart.
    Simulation of a year: Students face the sun. Student 1 holds the pencil upright, with the moon pointing (say) towards the sun. Student 1 walks with the Earth-moon system to his/her right and hands it to Student 2. During the walk, the moon rotates 90 degrees to the right, so now it is pointing at right angles to the sun. Student 2 now carries the Earth-Moon system to Student 3, while turning the moon an additional 90 degrees to the right with respect to the sun. (To minimize extra movement, Student 1 can remain in Student 2's place, etc.)
    Each student's walk represents one week in the year. At the end of 52 weeks the earth is back where it started. During each 4-week lunar month the moon goes through its phases: ``New moon'' when the wire is pointed towards the sun, ``First quarter'' at the end of week 1, ``Full moon'' at the end of week 2 when the wire is pointing away from the sun, ``Third quarter'' at the end of week 3, and back to new moon at the end of the month.

    13 students: Students position themselves evenly around a 30-meter-radius circle (put one at ``noon'' and two 24 feet on either side of ``6 o'clock'', then interpolate 6 more evenly on each side). Students will be about 14.4 meters (48 feet) apart. The simulation of a year runs just as with 52 students, except now each student's walk represents one lunar month (four weeks): during each walk the moon should be rotated one complete turn (to the right) and end up pointing towards the sun if that is how it started.

    Music. If you can rig up a portable sound system (a good boom-box could do the trick) an appropriate musical accompaniment can enhance the seriousness and the ritual/magic possibilities of the simulation. An obvious choice: something slow-paced from Gustav Holst's ``The Planets.'' --I'll try to be more specific.

    Here's where to find the exact astronomical data.

    Here is another cool site on the solar system that you may want to check out.

    2. Other things to think about.

    A. Suppose you wanted to model the Sun-Jupiter-Ganymede system. Here are the data:
    Body Radius Orbit radius Orbital period
    Sun 695000 km
    Jupiter 71492 km 778.3 M km 4332.71days
    Ganymede 2631 km 1.07 M km 7.155days

    To help compare this system with the Earth-Moon, here are two pictures from NASA:

    Suppose you were using the same 30-meter radius, but now that it represented the distance Sun-Jupiter. What would the new scale be? How big would the three objects be when scaled down to that size? Where would the Earth's orbit be on the field, and how big would the Earth be? Can you think of a way to simulate all or part of a Jupiter ``year'' including the motion of Ganymede?

    B. The plane of the Moon's orbit is actually slightly different from that of the Earth's orbit around the Sun. Find the exact amount of this difference. Can you think of how to change our simulation to reflect this difference? Suppose the planes were exactly the same. Would we notice anything different?

    C. The orbital period of the Moon is given in the table as 27.322 days, but the lunar month is very close to 28 days. Can you explain this discrepancy?

    D. The night sky varies from season to season because we see the stars that are on the side away from the sun. The Zodiac is made up of 12 constellations that lie near the plane of the Earth's orbit. so that the Sun seems to ``pass'' from one constellation to another as we circle the Sun. The Zodiac constellations on the opposite side are the ones we then can see at night. Can you think of a way to enrich the simulation by including some of this information?

    E. Think of how to design a much larger-scale simulation of the Earth-Moon system, so that the phases of the moon could be seen. Use it to answer questions like: ``Why is it that when people in the Northern Hemisphere see the moon near the horizon in the evening, it is always in its first quarter (D-shaped)?'' If you can enrich this model to incorporate the tilt of the Earth's axis of rotation (with respect to the plane of the Earth's orbit) then you can analyze questions like: ``Why is the Moon higher in the sky in winter than in summer?''

    F. The Sun is a star like many others in our galaxy. Its nearest neighbor star is Alpha Centauri (a bright star in the sky in the Southern Hemisphere), about four light years away. Given that light travels at 300,000 km/sec, estimate the distance to Alpha Centauri in kilometers. At the scale of our simulation (5 billion to one) how far away would we have to put the object corresponding to Alpha Centauri? (The nearest conspicuous star visible in the Northern Hemisphere is Sirius, 8.6 light years away.)

    G. The French physicist, philosopher and mathematician Blaise Pascal (1623-1662) said of the universe: ``The eternal silence of those infinite expanses frightens me.'' The Italian poet Giacomo Leopardi (1798-1837) wrote a poem ``L'Infinito'' (short but perhaps his most famous) where he meditates on this theme and concludes ``Thus in this immenseness drowns my thinking; and shipwreck in this sea is sweet for me.'' Does either of these attitudes towards the size and emptiness of the universe strike a chord in your own sensibility? Another project would be to find out more about Pascal and Leopardi and to try to understand where their thoughts on the universe fit into the rest of their thinking and into the set of ideas about man and nature that were current during their lifetimes and where they lived.