chaos in the solar system

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