Kepler’s Third Law

Johannes Kepler, one of the greatest astronomers of the 17th century, solved one of the most important puzzles of his time with his eight year effort to understand the orbits of the planets around the Sun. Kepler formulated three laws that confirmed Copernicus’ heliocentric model which would change human understanding of the world forever. Kepler’s first law says the planets orbit the Sun in an ellipse not a circle, as was believed. Kepler’s 2nd Law explained why the planets sped up as they approached the Sun in their elliptical orbits. And Kepler’s third law relates the distance of any planet from the Sun with its period of revolution (how long it takes to orbit the Sun).

In this activity you will plot the period of each of the planets known to the ancients versus their distance in AU’s to see if you can discover a mathematical relationship just as Kepler did.

How to Make Your Graph: You will make a semi-log graph with distance in AU’s marked arithmetically on the x axis and Period in years marked logarithmically on the y axis.

1. Remember to orient your graph paper so that y axis lines begin widely spaced and become progressively narrower as you move up from the bottom of the graph. Ask if you don’t understand! Write the title: Distance in AU’s below the x axis and write the title: Period in Earth Years along the y axis.

2. Label the x axis linearly with every 4 lines equal to 1. Label the origin 0 then the 4th line 1, the 8th line 2 and so forth to the end of the x axis.

3. Label the y axis logarithmically. Label the origin 0.1. Label the first bold line up 1 (count up 9 lines from the origin). Label the second bold line up 10. Label the third bold line up 100. Label the top bold line 1000. Now fill in the numbers between the bold lines. Label 0.2, 0.3, 0.4…0.9 for the first group of lines. Label 2, 3, 4…9 for the second group of lines. Label 20, 30, 40…90 for the third group of lines. And label 200,300, 400…900 for the last group.

4. Now make a line graph of the data from the table below. Label each planet on your graph!

Period in Earth Years / Distance from Sun in AU’s
Mercury / 0.25 / 0.4
Venus / 0.6 / 0.7
Earth / 1 / 1
Mars / 1.9 / 1.5
Jupiter / 11.8 / 5.2
Saturn / 29.5 / 9.5

5. Answer the following questions.

a. Does the line you drew suggest there is any mathematical relationship between distance and periodicity? Explain why.

b. Kepler’s third law says that the cube of the average distance (D) of a planet is proportional to the square of its Period (P) from the Sun and is equal to a constant number (C) for all planets. Write the law as a simple math formula.

c. How many planets did Kepler count in his time? How many were assumed during his time?

What does the word planet mean in Greek? (Re-read page 539 if you need help with this one.)