Barycenter: The Balancing Point

Our solar system consists of the Sun and the many millions of celestial bodies, including large planets and microscopic dust particles, which orbit around it. As a unit, the solar system has a center of mass, its balancing point. At this point, the system would balance like a spinning plate atop a circus performer's balancing stick. This point, called the barycenter, is the exact point about which all the bodies in the solar system orbit. Since the Sun is vastly larger and heavier than all the other bodies combined, the solar system's barycenter is very close to the Sun—but not at the Sun's center. Thus, while all the other solar system bodies seem to orbit the Sun, they, including the Sun, are actually orbiting a point in space just beyond the Sun's outer layer.

Binary bodies are two celestial bodies held together by mutual gravitational attraction. In this project, you will learn how mass affects the location of their barycenter. You will discover the mathematical relationship between the masses of binary bodies and their distances from their barycenter. You will prepare a model of the Earth-Moon system and determine the orbit that each body follows as it orbits the barycenter of the system. You will also discover the location of the barycenter for most planet-moon systems.

Getting Started

Purpose: To model the barycenter of binary bodies.

Materials

• one-hole paper punch
• ¹/₂-by-3-inch (1.25-by-7.5-cm) piece of thick paper, such as a file folder
• 6-foot (1.8-m) or longer cord
• 1 pound (454 g) modeling clay
• food scale
• ⁵/₁₆-by-48-inch (0.78-by-120-cm) wooden dowel
• yardstick (meterstick)

Procedure

1. Use the paper punch to make a hole in each end of the piece of paper.
2. Bend the paper to bring the holes together. Thread one end of the cord through the holes. Tie a knot to hold the holes together. You have made a paper sling for the dowel.
3. Tie the other end of the cord to a ceiling hook or other supporting object. Adjust the length of the cord so that the paper sling hangs about chest high.
4. Using the food scale, measure two 8-ounce (227-g) pieces. Shape each piece into a ball.
5. Stick one end of the dowel into one of the clay balls to a depth equal to the radius of the ball.
6. Slide the free end of the dowel through the paper sling.
7. Repeat step 5 using the remaining clay ball on the other end of the dowel.
8. Determine the balancing point by moving the dowel back and forth in the sling until it balances (see Figure 11.1).



9. Measure and compare the distance between the center of each clay ball and the center of the paper sling.
10. Gently push one of the balls so that the dowel turns. Observe the motion of the clay balls.

Results

The balancing point is in the center of the dowel, an equal distance from each of the clay balls. The balls move in a circular path around the sling.

Why?

Binary bodies are two celestial bodies held together by mutual gravitational attraction. Gravity is a force of attraction between all objects in the universe. Examples of binary bodies are two stars, a planet and its sun, or a planet and its moon. Binary bodies behave somewhat as if they were connected by a dowel. Their center of gravity is called the barycenter (the point between two binary bodies where their mass seems to be concentrated and the point about which they rotate). If the masses of the binary bodies are equal, the barycenter lies at an equal distance from each body. Binary bodies revolve (move in a circular path about a point) about their barycenter.

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