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# Orbital Period

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Author: Janice VanCleave

### Time of Revolution

German astronomer Johannes Kepler (1571–1630) in his third law of planetary motion expressed the relationship between the orbital period of a planet and its average distance from the Sun. An orbital period is the time it takes a planet to make one revolution, which is once around its orbit.

In this project, you will discover how mass and distance affect a celestial body's orbital period. You will model the effect of the barycenter on the period of a planet. You will also discover how Bode's law predicts the distances of planets.

### Getting Started

Purpose: To determine the effect of distance on the orbital period of an orbiting planet.

### Materials

• 3/8-inch (0.93-cm) metal washer
• 6-foot (1.8-m) cord
• ruler
• 2 pairs of safety goggles
• timer
• helper

### Procedure

Note: This activity is to be performed outdoors.

1. Tie the washer to the end of the cord.
2. On the cord, measure 18 inches (45 cm) from the washer and tie a knot in the cord.
3. Measure 18 inches (45 cm) from the knot and tie a second knot in the cord.
4. Repeat step 3, making a third knot.
5. Put on a pair of safety goggles. In an area away from other people, hold the cord at the first knot—18 inches (45 cm)—from the washer and swing your arm so that the washer spins above your head.
6. Find the slowest speed that will keep the washer "in orbit."
7. Ask your helper to wear safety goggles and be your timekeeper (see Figure 5.1). When your timekeeper says "Start," count the number of revolutions the washer makes. A revolution is one turn around an orbit.
8. Stop counting when the timekeeper says "Stop," at the end of 10 seconds.
9. Calculate the orbital period, T, (time per revolution) of the washer by dividing the time by the number of revolutions. For example, if you counted five revolutions in 10 seconds, the orbital period would be:
10. This is read as 2 seconds per revolution and means that it took 2 seconds for the washer to travel 1 revolution.

11. Repeat steps 5 to 9 four times for a total of five trial measurements.
12. Repeat steps 5 to 10 for the two other distances: 36 inches (90 cm) at the second knot, 54 inches (135 cm) at the third knot.
13. Record the data in an Orbital Period versus Orbit Distance table like Table 5.1.
14. Make a bar graph of the average orbital periods. Place distance (the independent variable that you changed) on the horizontal axis. Place the orbital period (the dependent variable that changes in response to the independent variable) on the vertical axis. For information about constructing bar graphs, see p. 18.

### Results

The longer the cord, the greater the orbital period.

### Why?

Kepler's third law of planetary motion states that the more distant a planet's orbit from the Sun, the greater the planet's orbital period. This experiment shows that the law works for any object spinning in a circular path.

### Try New Approaches

Matter is the substance from which all objects are made. Mass is the measure of the amount of matter in an object. How does the mass of the orbiting object affect its orbital period? Repeat the experiment using two washers. As before, provide just enough energy to keep the washers in a circular orbit. In Chapter 6, "Artificial Satellites," page 57, find the orbital velocity (speed in a specific direction) of a satellite. Note that orbital velocity (revolutions/sec) is the reciprocal of the satellite's orbital period (sec/revolutions). Is the mass of the satellite part of the orbital velocity formula? Do your experimental results agree with the formula?

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