Chaos in the Clockwork

The work of Newton and Laplace suggested to many that the solar system was like a giant clockwork, which was illustrated by beautiful mechanical models called orreries. The controversial Molchanov hypothesis avers that every oscillatory system evolves to a resonance governed by a family of integers, like the 3/2 resonance between the orbits of Pluto and Neptune, or the 2/1 resonance between Jupiter’s giant natural satellites Ganymede and Europa, and Europa and Io. (Europa orbits Jupiter once when Io orbits twice.) Yet my research this sabbatical suggests that the irrational golden ratio describes some variable stars. Indeed, overlapping resonances may account for evidence of chaos in the solar system.

Saturn and two of its natural satellites, giant Titan and tiny Hyperion (left), and the Pluto-Charon binary system and one of its small satellites Nix. Hyperion and Nix appear to tumble chaotically in their orbits. The systems are not drawn to the same scale.

Saturn and two of its natural satellites, giant Titan and tiny Hyperion (left), and the Pluto-Charon binary system and one of its small satellites Nix. Hyperion and Nix appear to tumble chaotically in their orbits. The systems are drawn to different scales.

In the Saturn system, the 3/4 orbital resonance between tiny, irregularly-shaped Hyperion and planet-sized Titan causes Hyperion to tumble chaotically in its orbit. If you lived on Hyperion, the sun would appear to rise and set at irregular times. Last week, researchers announced that something similar occurs in the Pluto-Charon binary system. Using archival Hubble space telescope data ahead of the New Horizon’s July flyby, Mark Showalter and Doug Hamilton argued that the tiny moons are in orbital resonance but light curves of Nix and Hydra are not sinusoidal, suggesting chaotic tumbling. Nix’s small size implies an irregular shape. (We should know for sure next month.) Just as the dynamic gravity of Saturn and Titan chaotically tumble irregular Hyperion, the dynamic gravity of Pluto and Charon chaotically tumble irregular Nix. If you lived on Nix, the sun might one day rise in the east and set in the north.

About John F. Lindner

John F. Lindner was born in Sleepy Hollow New York and educated at the University of Vermont and Caltech. He is a professor of physics and astronomy at The College of Wooster. He has enjoyed multiple yearlong sabbaticals at Georgia Tech, University of Portland, and University of Hawai'i. His research interests include nonlinear dynamics, celestial mechanics, and variable stars.
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