San José State University

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Thayer Watkins
Silicon Valley
& Tornado Alley
USA

The Formation of a Planet Near the Resonance Band

The following diagram depicts matter in a solar ring with tangential velocities indicated by the arrows. The tangential velocity is Keplerian; i.e., the velocity is inversely proportional to the square root of the radius. The red circles represent a resonance band for a planet beyond the diagram.

The next diagram depicts material from the resonance band being nudged out into an orbit with a greater radius. The material in the red resonance band had a greater tangential velocity than the material in the blue outer band, but when the red material is pulled out into the blue band its velocity decreases. Because angular momentum is conserved the velocity is inversely proportional to the orbit radius. Its speed thus slower than the material in the band it enters.

Thus the material shown in blue crashes into the material from the resonance band. As the material agglomerates it acquires speed approximately equal to speed of the material in the blue band. However now the material is swept into the protoplanet.

The process continues until all of the material in the red resonance band has been nudged into the blue band and all the material in the blue band swept into one mass.

A similar process would occur if material in the resonance band were nudged into the inner green orbit. In that case the material from the resonace band would be traveling faster than the material in the green band and hence would sweep it up. The end result is the same; the resonance band cleared and a planet formed near the resonance band.

(To be continued.)


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