Relationships Between the Orbital Period and Planet's Distance From the Sun

Kepler's third law of planetary motion was published approximately 10 years after his first two. This law expresses 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 14.1). When your time keeper says, "Start," count the number of revolutions the washer makes. A revolution is one turn around a circular path.



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:
   T = orbital period = time ÷ number of revolutions
   = 10 seconds ÷ 5 revolutions
   = 2 seconds/revolution

This is read as 2 seconds per revolution and means that it took 2 seconds for the washer to travel 1 revolution.

10. Repeat steps 5 to 9 four times for a total of five trial measurements.
11. 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.
12. Record the data in an Orbital Period by Orbit Distance table like Table 14.1.



13. 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.

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 an object spinning in a circular path.

This article is brought to you by: