Models and laws: Planets 2006 part 5. The model you found in Exercise 20 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 21 23 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 20 suggests that we have found a physical law? In the future, we may learn enough about a planetary system around another star 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 the next system we find does not follow this pattern?