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# Demonstrating Orbits

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Source:
Author: Marc Rosner

All the planets of our solar system, including Earth, orbit the Sun in elliptical paths. An ellipse is a curve generated by a point moving in such a way that the sum of the point's distances from two fixed points on the curve is a constant. You can imagine an ellipse as an oval-a circle that is squashed a bit, as if someone sat on it. In fact, Earth's orbit is nearly circular. In this activity, you will generate orbits and analyze their shapes.

Nicolaus Copernicus (1473–1543) was the first astronomer to propose a Sun-centered or heliocentric model of our solar system. Earlier, people believed that Earth was the center of our solar system. Johannes Kepler (1571–1630), a mathematician, was the first to conclude that planetary orbits are elliptical.

### Materials

• 2 sheets of white paper
• pencil
• piece of corrugated cardboard (or a bulletin board)
• 2 sturdy push pins (Dissection pins work well.)
• metric ruler
• 30-cm string with ends joined in loop

### Procedure

1. Fold a sheet of paper in half, then unfold it and fold it in half again, this time the other way. Open the paper and mark the point where the two folds cross with the letter C (center).
2. Place the paper lengthwise on a piece of cardboard or a bulletin board, and tape it down.
3. Place a pin along the long fold 1 cm from the left of the marked center. Label this pin "Sun." Its position will remain fixed throughout the experiment.
4. Select five points along the long fold at different distances to the right of the center mark and number them 1,2,3, 4, and 5. Place the second pin in position 1.
5. Place the loop of string over both pins. Put the pencil through the loop and pull the string until it's taut. Move the pencil to a 12 o'clock position. Trace an ellipse by moving the pencil all the way around the "clock," keeping the string taut.

1. Measure (in centimeters) and record the following: (a) the distance between the Sun and the second pin, (b) the lengths of the orbit along the long and short folds of the paper (orbits 1 and 2), and (3) the shape of the orbit.
2. Repeat steps 5 and 6, placing the second pin in each of the other four positions you marked in step 4.
3. Record your data in a table like the one shown.

Eccentricity is the deviation of an orbital shape (ellipse) from a perfect circle.

You can use this formula to calculate the eccentricity of your ellipses.

When the minor axis equals the major axis (as in the case of a circle), the fraction in the formula equals 1, so the eccentricity equals O. Earth's eccentricity is small: e = 0.00167. When e = 1, the geometric figure is a parabola, a curve generated by a point moving in such a way that the point's distance from a fixed line is equal to its distance from a fixed point not on the line.

The Moon's orbit of Earth is fairly eccentric (e = 0.55), giving rise to noticeable effects, such as the easily observed changes in apparent size of the Moon and noticeable differences in tides. Comets have highly eccentric orbits. Pluto has such a high eccentricity that astronomers recently debated whether it should even be considered a planet.

1. How did the orbital shape change as the distance between the two pins increased? Predict the shape you'd obtain if you placed the two pins very close together.

### References

Janice VanCleave's the Solar System: MindBoggling Experiments You Can Turn into Science Fair Projects by Janice VanCleave (New York: John Wiley & Sons, 2000).

Raman's Orbital Simulator: http://physci.kennesaw.edu/javamirror/explrsci/dswmedia/orbit.htm

Views of the Solar System: http://hubblesite.org/hubble_discoveries/hstexhibit/planets/