Due:
A mnemonic for the sizes of the orbits of the planets in our Solar System known as the Titius-Bode Law. It is given by
where N = 0, 1, 2, 4, 8, 16, 32, 64, 128, and so on (see lecture 3). It would be interesting to see if this rule (or a similar rule) applies to other planetary systems? Let's check.
1. Are any of the recently discovered planetary systems going to lead to reasonable tests of the generality of the Titius-Bode Law? (You need to look at planetary systems with more than 1 observed planet to perform this exercise.) Use the website www.princeton.edu/~willman/planetary_systems (or see this plot) for your reference. (You can actually use any source of information which is at your disposal.) When you compare the data to the Titius-Bode Law, note that we do not appear to see Terrestrial-type planets (so that you may feel free to assume that the planets in the extra-solar planetary systems correspond to the Titius-Bode law starting with an N greater than 0, e.g., for N = 8, 16, 32, ...).
2. The Galilean moons of Jupiter can also be used to test the generality of the Titius-Bode Law. Why? Use the table below for the orbital properties of the Galilean moons (see lecture 3) to test this possibility.
How well does the Titius-Bode Law predict the relative spacing of the Galilean moons of Jupiter? What if you assume that the Galilean moons of Jupiter are more similar to the Jovian planets than they are to the Terrestrial planets?
3. What does Part 2 tell you about the validity of the Titius-Bode Law (e.g., or is it a Law in the strict sense of the word, does it contain physical information or is it just a curiosity valid only for our Solar System?)? Do you feel that the Titius-Bode Law is a numerical oddity or that it contains physical information about the dynamics of our Solar System? Explain why you feel as you do.