chaos in the solar system
DESCRIPTION
This is a talk I've give to various astronomical societies about chaos theory and how it affects the UniverseTRANSCRIPT
Chaos in the Solar SystemEdward Gomez
Las Cumbres Observatory - Cardiff University
Chaos in the Solar SystemJohannes Kepler
Solar System runs like clockwork
Chaos in the Solar SystemJohannes Kepler
Solar System runs like clockwork
Chaos in the Solar System
Sir Isaac Newton
Theory of gravity instantly has implications against a clockwork solar system
Chaos in the Solar System
Sir William Herschel
Discovers Uranus - 1781
Arguably starts the descent into ‘Chaos’
Chaos in the Solar System
Edward Lorentz
Meteorologist
Realised that there was a sensitivity to initial conditions in weather simulations
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)
Periodic motion
Periodic motion
Chaos in the Solar System
Benoit Mandelbrot
1979 working at IBM invented term ‘fractal’
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
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
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
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
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
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
Mandelbrot setZoom: 0
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Solar System Chaos
Asteroid orbit
Asteroid rotation
Great Red spot
Pluto is chaotic
Fractal nature of 2df
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
2-body Resonance
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
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
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
Asteroid rotation
Great Red spot
Chaotic motion in Pluto’s orbit
3:2 Resonance with Neptune
Digital Orrery prediction
Stable over Myr’s
3-body Resonance
© 1993 Nature Publishing Group
Chaos in the Universe