This is a talk I've give to various astronomical societies about chaos theory and how it affects the Universe

1. Chaos in the Solar System
Edward Gomez
Las Cumbres Observatory - Cardiff University

2. Chaos in the Solar System
Johannes Kepler
Solar System runs like clockwork

3. Chaos in the Solar System
Johannes Kepler
Solar System runs like clockwork

4. Chaos in the Solar System
Sir Isaac Newton
Theory of gravity instantly
has implications against a
clockwork solar system

5. Chaos in the Solar System
Sir William Herschel
Discovers Uranus - 1781
Arguably starts the descent
into ‘Chaos’

6. Chaos in the Solar System
Edward Lorentz
Meteorologist
Realised that there was a
sensitivity to initial conditions
in weather simulations

7. To save paper he recorded his calculations to 3 dec. places
0.567234 0.567
Butterfly effect
Periodic motion
Developed ‘Strange Attractor’ model based on 3 variables
(+ time)

8. Periodic motion

9. Periodic motion

12. Chaos in the Solar System
Benoit Mandelbrot
1979 working at IBM
invented term ‘fractal’

13. Found self similar structure on all scales while looking at cotton
prices
Divided up graph, always had structure
Order matched Cantor set
Found in many areas of nature
Infinite area in finite space

14. Found self similar structure on all scales while looking at cotton
prices
Divided up graph, always had structure
Order matched Cantor set
Found in many areas of nature
Infinite area in finite space

15. Found self similar structure on all scales while looking at cotton
prices
Divided up graph, always had structure
Order matched Cantor set
Found in many areas of nature
Infinite area in finite space

16. Found self similar structure on all scales while looking at cotton
prices
Divided up graph, always had structure
Order matched Cantor set
Found in many areas of nature
Infinite area in finite space

17. Found self similar structure on all scales while looking at cotton
prices
Divided up graph, always had structure
Order matched Cantor set
Found in many areas of nature
Infinite area in finite space

18. Found self similar structure on all scales while looking at cotton
prices
Divided up graph, always had structure
Order matched Cantor set
Found in many areas of nature
Infinite area in finite space

19. Mandelbrot set
Zoom: 0

20. Zoom: 10

21. Zoom: 100

22. Zoom: 1000

23. Zoom: 10,000

24. Zoom: 100,000

25. Zoom: 1,000,000

26. Zoom: 10,000,000,000

28. Solar System Chaos
Asteroid orbit
Asteroid rotation
Great Red spot
Pluto is chaotic
Fractal nature of 2df

29. 2-body Resonance
Kirkwood gaps in distribution of
semi-axis
only where period is a rational
fraction of Jupiter’s period
Implies resonance
Resonance = Stable orbits (Trojan
asteroids 1:1, 3:2)
Unstable 3:1, 2:1

31. Asteroid rotation
Rotation of most Solar System bodies is stable because of tides
Hyperion tumbles chaotically
First seen to tumble by Voyager
4:3 Resonance Titan
Irregular shape

32. Asteroid rotation
Rotation of most Solar System bodies is stable because of tides
Hyperion tumbles chaotically
First seen to tumble by Voyager
4:3 Resonance Titan
Irregular shape

33. Asteroid rotation
Rotation of most Solar System bodies is stable because of tides
Hyperion tumbles chaotically
First seen to tumble by Voyager
4:3 Resonance Titan
Irregular shape

34. Great Red spot

35. 3-body Resonance
Chaotic motion in Pluto’s
orbit
3:2 Resonance with
Neptune
Digital Orrery prediction
Stable over Myr’s

36. Chaos in the Universe