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Daphnis the Wavemaker

Daphnis is a tiny moon of Saturn, one of seven discovered by the Cassini probe as it explores the space around the ringed planet. In this incredible picture taken by the probe, you see Daphnis causing a ripple in the rings.

Cassini took the image on January 16, 2017, while 17,000 miles (28,000 kilometers) away from the moon. Measuring 5 miles (8 kilometers) along its longest axis, irregular Daphnis resides in the 26-mile (42-kilometer) wide Keeler Gap in Saturn's outer A ring. The Keeler Gap seems narrower than it really is in this image because of foreshortening due to the spacecraft's viewing angle. You can just see grooves along the long axis of Daphnis in the image, as well as a few impact craters.

Despite its small size, Daphnis' gravity is causing the ripples in the rings. Cassini's 20-year mission will end on September 15, 2017, when it crashes in the surface of Saturn. -via Metafilter

(Image credit: Cassini Imaging Team, SSI, JPL, ESA, NASA)

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Daphnis is tidally locked to Saturn, so the "wavelength" you propose would be the size of the orbit.

The moon pulls stuff in the ring toward it, but the material in the ring is orbiting slightly slower or faster, so eventually one moves past the other. The wave structure comes from the material being pulled back to the plane of the ring by the gravity of the ring, and its wavelength would depend upon the strength of that force.
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I don't expected ripples to be present... However i suppose that the longitudinal shape of the moon in combination with an rotation of the moon may cause the ripples. I even expect that the "wavelength" of the ripples divided by the speed of thr rings equals the time required for a single rotation of the moon.
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