Chapter 7. Planetary Orbits

7.1 Introduction

The goals of this tutorial: In this module you will use Kepler's third law to identify two of the planets. Once you have identified them, you will compare and contrast the orbits of all the planets, to see how they are related.

Why you are doing it: This exercise will give you a sense of the time and size scales of the solar system. It will also give you insight into the correlations between the planes of the orbits, which is explained by the way the Solar System formed.

7.2 Background

Johannes Kepler (December 27, 1571 - November 15, 1630)

There is a systematic relationship between the periods of the planetary orbits and their distances from the Sun: Observations by his mentor Tycho Brahe led Johannes Kepler to an equation relating the period of a planet's orbit, P, and its average distance from the Sun, a, now known as Kepler's third law. Following strictly from observational data, rather than any underlying physical science, all of Kepler's laws are considered to be empirical, meaning that they lacked a scientific justification. This was provided by Isaac Newton who used physics and mathematics to derive them from "first principles."

In this module, you will make simulated observations of planet orbits and use Kepler's third law to determine which planets you are observing.

How you will determine the identities of the planets:
Imagine that you are in a spaceship far enough from the solar system so that you can see the planets make complete orbits around the Sun. We will set one unlabeled planet in motion at a time, and you will observe how many years it takes that planet to orbit the Sun. In this simulation, each orbit will take about twenty seconds, but that time interval will represent different numbers of years, shown on the counter, depending on which planet you are observing.

7.3 Planetary Orbits - Unknown Planet I

Warm-up Questions:

Click on the play icon below and observe the planet as it orbits the Sun. Click pause after one complete orbit, when the planet returns to its starting point. The counter indicates the number of (Earth) years between when you press play and pause. Kepler's third law can be written P² = a³, where P is the period of the orbit in (Earth) years and a is the distance from the Sun in astronomical units (AU).
Now for your first Unknown Planet:

Next, identify the planet using the table below. If your answer is close, but not identical to any of the planetary periods, the chances are that you stopped the planet's orbit slightly before or after one complete period.

7.4 Planetary Orbits - Unknown Planet II

Try one more planet.

Once you have determined the period of orbit in years, put this value into either of the two forms of Kepler's third law: P² = a³ or, equivalently. \(a= \sqrt[3]{ P^{2}} \)

Next, identify the planet using the table below. If your answer is close, but not identical to any of the planetary periods, the chances are that you stopped the planet's orbit slightly before or after one complete period.

7.5 Quick Check Quiz

Indepth Activity: Planetary Orbits

Now that you have experience using Kepler's third law to identify planets, we will explore the relationships between the orbits of the various planets. In the simulation below you can view the solar system from two perspectives: a face-on view and a side view, both of which can be zoomed so you can see details of the inner solar system. In both views the planets are orbiting at their correct relative speeds. The face-on view, which you see now, is from far above the Earth's North Pole.

Please explore both view of the simulation, observing the relative speeds of the planets (e.g., which moves slowest?), the shapes of the orbits (e.g., which is least circular?) and, from the side view, the planes of the orbits relative to the ecliptic. Placing the cursor over a planet or its orbit will bring up that body's name. After you are familiar with these aspects of the solar system, answer the questions that appear below to complete this tutorial. Please note that within this simulation, the Sun and planets are shown much larger than they are at these scales.