The rings of Saturn and Jupiter are circular. Orbits can be elliptical, so can rings be elliptical?
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$\begingroup$ Orbital resonance may be a reason for the circular orbits. $\endgroup$– LelouchJul 28, 2016 at 16:05
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2 Answers
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Short answer: no.
Long answer:
There are many collisions within ring systems, and collisions always work, over time, to push orbits to a circular shape (or destroy the rings). Any deviations tend to be quickly corrected.
For the same reason, rings tend to be extremely flat and extremely thin. E.g. Saturn's rings are only dozens of meters thick; given their diameter of 300 thousand kilometers, if you cut a model of the rings from ordinary size printer paper, the paper model would be too thick. (would not represent the thickness of the rings to the correct scale)
Another characteristic of rings is that they are equatorial. If they are not in plane with the equator, precession will drive them towards that configuration.
You could apply a perturbation that makes a ring non-circular, or non-flat, or non-equatorial, but then the system will quickly evolve towards circular, flat, and equatorial (or will be destroyed).
answered Jul 28, 2016 at 1:23
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$\begingroup$ If the planet has no equatorial bulge, and very low rotation speed, would the equatorial rule still apply? $\endgroup$– userLTKJul 28, 2016 at 22:28
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1$\begingroup$ No spin = no precession = no push towards equator. $\endgroup$ Jul 29, 2016 at 1:19
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Rings are made up of a large number of individual particles, each in elliptical orbits. We see rings as circular because we don't see and follow the individual particles just the overall swarm of particles. Their individual orbits average out and just appear are a circle.
The individual orbits are constantly being changed due to collisions between particles, and gravitational influences for moons. Saturn's F ring is a good example of this. As can be seen from the images the ring is not a circle.
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1$\begingroup$ Are you saying that individual particles execute noticeably non-circular orbits (note that a circle is an ellipse)? What eccentricities do you think are possible? $\endgroup$– ProfRobJul 27, 2016 at 10:23
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$\begingroup$ There will undoubtedly be a range of eccentricities, most will be near circular with number dropping off as the orbits become more elliptical. Due to the huge number of individual particles and their small size its not practical to even attempt to measure them individually, that's without even taking into effect the gravitational and light pressure effects. $\endgroup$ Jul 27, 2016 at 11:40
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3$\begingroup$ I think you should flesh this out. My understanding is that inelastic collisions circularise orbits and that in rings like Saturn's, the collisional timescale is very short. Saturn's rings look circular because the particles are on circular orbits. The same may not be true of other ring systems where some very small eccentricities have been measured, but there has to be some external "pumping" of the eccentricity. $\endgroup$– ProfRobJul 27, 2016 at 16:53
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$\begingroup$ @JamesScreech - there's some guesswork in that answer, and a few facts are wrong. Individual orbits must be very close to circular, otherwise collisions will change them quickly. For the same reason, rings must be very flat. Also, due to precession, rings must be equatorial. Any other configuration is very short-lived. $\endgroup$ Jul 28, 2016 at 1:17