Planets, models, and laws The model you found in Exercise 68 is a relationship noted in the 17th century by Kepler as his Third Law of Planetary Motion. It was subsequently explained as a consequence of Newton’s Law of Gravitation. The models for Exercises 69, 70, and 71 relate to what is sometimes called the Titius-Bode “law,” a pattern noticed in the 18th century but lacking any scientific explanation.

Compare how well the re-expressed data are described by their respective linear models. What aspect of the model of Exercise 68 suggests that we have found a physical law? In the future, we may learn enough about planetary systems around other stars to tell whether the Titius-Bode pattern applies there.

If you discovered that another planetary system followed the same pattern, how would it change your opinion about whether this is a real natural “law”? What would you think if some of the extrasolar planetary systems being discovered do not follow this pattern?