Did you see this? It's an artist's conception of how gravity from the tiny moon Daphnis creates ripples in Saturn's rings - created by Kevin Gill of NASA.
This image was pretty popular here, and elsewhere on the web - but people often don't come out and say from the start that it's not a photo. The actual photos are less beautiful but... hey, they're real! And the ripples look different in the photos. Let's take a look.
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This 2005 photo, taken by the Cassini probe, was the first time anyone actually saw Saturn's moon Daphnis! It's only 8 kilometers across.
This gap in Saturn's A ring was first discovered by Voyager, and it was named the Keeler Gap. It's 35 kilometers wide. I guess this gap let people guess the existence of a moon, and later the ripples in the A ring let people guess where the moon must be! I don't really know the history here.
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There's a larger gap in the A ring called the Encke cap, created by a larger moon called Pan, which you can see clearly here.
To the left you see the smaller Keeler gap. If you look very closely you can see the ripples near the Keeler gap... and if you look *very* closely you can see, or at least imagine, the moon Daphnis.
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@benjohn - I'm pretty sure that Kevin Gill's images were *not* generated from simulations. Here's the only paper I've found on modeling this sort of system:
https://arxiv.org/abs/2403.03012
The math and physics are tough but some of the pictures are great!
Observations by the Voyager and Cassini spacecrafts have revealed various striking features of the gap structure in Saturn's ring, such as the density waves, sharp edge, and vertical wall structure. In order to explain these features in a single simulation, we perform a high-resolution (N~10^6-10^7) global full N-body simulation of gap formation by an embedded satellite considering gravitational interactions and inelastic collisions among all ring particles and the satellite, while these features have been mostly investigated separately with different theoretical approaches: the streamline models, 1D diffusion models, and local N-body simulation. As a first attempt of a series of papers, we here focus on the gap formation by separating satellite migration with fixing the satellite orbit in a Keplerian circular orbit. We reveal how the striking gap features - the density waves, sharp edge, and vertical wall structure - are simultaneously formed by an interplay of the satellite-ring and ring particle-particle interactions. In particular, we propose a new mechanism to quantitatively explain the creation of the vertical wall structure at the gap edge. Inelastic collisions between ring particles damp their eccentricity excited by the satellite's perturbations to enhance the surface density at the gap edge, making its sharp edges more pronounced. We find the eccentricity damping process inevitably raises the vertical wall structures the most effectively in the second epicycle waves. Particle-particle collisions generally convert their lateral epicyclic motion into vertical motion. Because the excited epicyclic motion is the greatest near the ring edge and the epicycle motions are aligned in the first waves, the conversion is the most efficient in the gap edge of the second waves and the wall height is scaled by the satellite Hill radius, which are consistent with the observations.
John Carlos Baez
Benjohn