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News Release 05-168

Mathematics Unites the Heavens and the Atom

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Transitions in celestrial mechanics

The orbital dynamics of Oterma, a comet that is locked in a long, complex dance with the giant planet Jupiter.

In frame (a) we see a portion of Oterma's orbit from the perspective of the solar system as a whole, using a coordinate system that has the Sun at rest in the center and Jupiter moving in a near-perfect circle once every 12 years. Oterma's intricate path takes it both inside and outside Jupiter's orbit. While it is on the inside it generally stays near a "3:2 resonance," in which Oterma goes three times around the Sun for every two revolutions made by Jupiter. When it is on the outside, likewise, Oterma stays near a near a 2:3 resonance.

In frame (b) we see this same segment of Oterma's orbit from Jupiter's perspective, using a rotating coordinate system that keeps the giant planet stationary. This view makes it clear that Oterma's transition between outside and inside can occur only through a narrow bottleneck around Jupiter. Frame (c) shows a closeup of the bottleneck.

This view also highlights the parallel with atomic physics: an atom moving from one molecule to another often goes through a similar transition.

Credit: Shane D. Ross, University of Southern California

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