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Binomial Expansions and Series

Explore if Saturn's rings are solid using simple physics concepts by comparing tidal forces with gravitational forces. Learn how the Roche limit determines the structure of Saturn's rings. Discover the insightful connection between binomial series and tidal disruption limits.

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Binomial Expansions and Series

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  1. Binomial Expansions and Series Are the rings of Saturn solid?

  2. Simple Physics Compare the gravitational force that the sun (red ball) exerts on the near and farblue spheres. The difference is called the TIDAL force. Next, compare the tidal force with the force of attraction that each blue sphere exerts on the other. If the tidal pull of the sun is greater than this “mutual” gravitational force the spheres will be pulled apart or tidally disrupted. R

  3. We can show, by using binomial series that the tidal disruption limit isIf you try and put the two masses closer to the big mass they will get ripped apart! (rM and rm are the densities of the big and small masses)

  4. So what about Saturn? Saturn’s rings are almost completely inside the Roche limit and hence cannot be solid! They are typically compact car sized chunks of ice.

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