Barycenter: The Balancing Point (page 2)

Try New Approaches

Different masses affect the distance of each body from the barycenter. Mold the clay into one large ball and one tiny ball. Weigh the balls on the food scale and prepare a Celestial Body Mass vs. Distance table like Table 11.1. Call the mass of the smaller ball m₁. Let the mass of the larger body equal m₂. Call their distances from the center of each clay ball to the barycenter d₁ and d₂, respectively. Use the dowel and sling to find the barycenter as in the original experiment (see Figure 11.2). Measure d₁ and d₂.

For example, when m₁=1 ounce (28 g) and m₂=15 ounces (426 g), and d₁ = 45 inches (112.5 em), then d₂ = 3 inches (7.5 em). Notice that mass and density have an inverse relationship, which means that when one term increases, the other decreases.

In our example, m₁ × d₁ = m₂× d₂, or m₁/m₂ = d₂/ d₁ = 3/45, which reduces to 1/15. Thus, m₁ lies 15 times farther from the barycenter than does m₂, and m₂ is 15 times more massive than m₁.

Design Your Own Experiment

The Earth and Moon are binary bodies with a barycenter that lies about 1,000 miles (1,600 km) beneath Earth's surface on the side facing the Moon. Design a model to show the paths of Earth and the Moon as they orbit their barycenter. One way is to use a 2-by-12-inch (5-by-30-cm) strip of poster board. In the center of one end of the strip make a dot and draw a circle with a 4-mm radius around the dot. Label this circle "Earth." Lay a ruler across the length of the poster board and make two dots at these distances from the center of the circle: 3 mm and 240 mm. Label the first dot "Barycenter." Draw a second circle as small as you can around the second dot. Label this circle "Moon." Stick a pushpin through the barycenter dot into a pencil eraser on the underside of the dot (see Figure 11.3). Holding the pencil in one hand, rotate the strip around the pushpin in a counterclockwise direction. Use the equation in the previous experiment and these distances to calculate the ratio of the Earth/Moon masses. Compare this ratio with a ratio of Earth's and the Moon's mass found in a reference book. Display the model and a legend of the scale.

Get the Facts

The average barycenter of our solar system lies just outside the surface of the Sun. It changes depending on the location of the planets. Jupiter, the most massive planet, has the greatest effect. Find out more about the barycenter of binary bodies in the solar system. Where does the barycenter lie for most planet-satellite (moon) systems? Which planet has such a massive moon that the barycenter lies in the space between them? For information, see Thomas R. Watters, Planets: A Smithsonian Guide (New York: Macmillan, 1995).

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