Week 7: Chaos and Long-term Dynamics of the Solar System

Reading¶

• Chapter 9 from Murray and Dermott, sections 9.1-9.4 inclusively

• Section 5 from Duncan and Quinn ‘The Long-Term Dynamical Evolution of the Solar System’

Reading questions¶

Q1-4 are related to the first reading, Q5-7 to the second.

1. Before reading, give a definition of what you think chaos is, then update it as you go through the reading.

2. (a) How does the existence of the Jacobi constant reduce the dimensionality of phase space in the circular restricted three-body problem, and why is this reduction essential for constructing a Poincaré surface of section? (b) What’s the physical meaning of a Jacobi surface?

3. What do the islands in Fig 9.5 symbolize physically and what happens when we place the starting condition further from the center of the island that straddles $\dot{x} =0$?

4. What is the maximum Lyapunov characteristic exponent and what does it tell you?

5. What is problematic with modeling long term solar system dynamics with a perturbation expansion?

6. This review paper dates from 1993 and states that ‘a detailed understanding of Pluto’s behavior is likely to be o btained only with the next generation of simulations’. From you knowledge has this been done? (You can also quickly search this up).

7. What is the general consensus of the numerical simulations mentioned in this chapter? Does the solar system exhibit long-term stability?

Answers to these questions should be submitted to your github repository before class on Monday.