Tag Archives: Saturn

The fate of the Alkyonides

Hello everybody! Today, I will tell you on the dynamics of the Alkyonides. You know the Alkyonides? No? OK… There are very small satellites of Saturn, i.e. kilometer-sized, which orbit pretty close to the rings, but outside. These very small bodies are known to us thanks to the Cassini spacecraft, and a recent study, which I present you today, has investigated their long-term evolution, in particular their stability. Are they doomed or not? How long can they survive? You will know this and more after reading this presentation of Long-term evolution and stability of Saturnian small satellites: Aegaeon, Methone, Anthe, and Pallene, by Marco Muñoz-Gutiérrez and Silvia Giuliatti Winter. This study has recently been accepted for publication in The Monthly Notices of the Royal Astronomical Society.

The Alkyonides

As usually in planetary sciences, bodies are named after the Greek mythology, which is the case of the four satellites discussed today. But I must admit that I cheat a little: I present them as Alkyonides, while Aegeon is actually a Hecatoncheires. The Alkyonides are the 7 daughters of Alcyoneus, among them are Anthe, Pallene, and Methone.

Here are some of there characteristics:

Methone Pallene Anthe Aegaeon
Semimajor axis 194,402 km 212,282 km 196,888 km 167,425 km
Eccentricity 0 0.004 0.0011 0.0002
Inclination 0.013° 0.001° 0.015° 0.001°
Diameter 2.9 km 4.4 km 2 km 0.66 km
Orbital period 24h14m 27h42m 24h52m 19h24m
Discovery 2004 2004 2007 2009

For comparison, Mimas orbits Saturn at 185,000 km, and the outer edge of the A Ring, i.e. of the main rings of Saturn, is at 137,000 km. So, we are in the close system of Saturn, but exterior to the rings.

Discovery of Anthe, aka S/2007 S4. Copyright: NASA.
Discovery of Anthe, aka S/2007 S4. Copyright: NASA.

These bodies are in mean-motion resonances with main satellites of Saturn, more specifically:

  • Methone orbits near the 15:14 MMR with Mimas,
  • Pallene is close to the 19:16 MMR with Enceladus,
  • Anthe orbits near the 11:10 MMR with Mimas,
  • Aegaeon is in the 7:6 MMR with Mimas.

As we will see, these resonances have a critical influence on the long-term stability.

Rings and arcs

Beside the main and well-known rings of Saturn, rings and arcs of dusty material orbit at other locations, but mostly in the inner system (with the exception of the Phoebe ring). In particular, the G Ring is a 9,000 km wide faint ring, which inner edge is at 166,000 km… Yep, you got it: Aegaeon is inside. Some even consider it is a G Ring object.

Methone and Anthe have dusty arcs associated with them. The difference between an arc and a ring is that an arc is longitudinally bounded, i.e. it is not extended enough to constitute a ring. The Methone arc extends over some 10°, against 20° for the Anthe arc. The material composing them is assumed to be ejecta from Methone and Anthe, respectively.

However, Pallene has a whole ring, constituted from ejecta as well.

Why sometimes a ring, and sometimes an arc? Well, it tell us something on the orbital stability of small particles in these areas. Imagine you are a particle: you are kicked from home, i.e. your satellite, but you remain close to it… for some time. Actually you drift slowly. While you drift, you are somehow shaken by the gravitational action of the other satellites, which disturb your Keplerian orbit around the planet. If you are shaken enough, then you may leave the system of Saturn. If you are not, then you can finally be anywhere on the orbit of your satellite, and since you are not the only one to have been ejected (you feel better, don’t you?), then you and your colleagues will constitute a whole ring. If you are lucky enough, you can end up on the satellite.

The longer the arc (a ring is a 360° arc), the more stable the region.

Frequency diffusion

The authors studied

  1. the stability of the dusty particles over 18 years
  2. the stability of the satellites in the system of Saturn over several hundreds of kilo-years (kyr).

For the stability of the particles, they computed the frequency diffusion index. It consists in:

  1. Simulating the motion of the particles over 18 years,
  2. Determining the main frequency of the dynamics over the first 9 years, and over the last 9 ones,
  3. Comparing these two numbers. The smaller the difference, the more stable you are.

The numerical simulations is something I have addressed in previous posts: you use a numerical integrator to simulate the motion of the particle, in considering an oblate Saturn, the oblateness being mostly due to the rings, and several satellites. Our four guys, and Janus, Epimetheus, Mimas, Enceladus, and Tethys.

How resonances destabilize an orbit

When a planetary body is trapped in a mean-motion resonance, there is an angle, which is an integer combination of angles present in its dynamics and in the dynamics of the other body, which librates. An example is the MMR Aegaeon-Mimas, which causes the angle 7λMimas-6λAegaeonMimas to librate. λ is the mean longitude, and ϖ is the longitude of the pericentre. Such a resonance is supposed to affect the dynamics of the two satellites but, given their huge mass ratio (Mimas is between 300 and 500 millions times heavier than Aegaeon), only Aegaeon is affected. The resonance is at a given location, and Aegaeon stays there.
But a given resonance has some width, and several resonant angles (we say arguments) are associated with a resonance ratio. As a consequence, several resonances may overlap, and in that case … my my my…
The small body is shaken between different locations, its eccentricity and / or inclination can be raised, until being dynamically unstable…
And in this particular region of the system of Saturn, there are many resonances, which means that the stability of the discovered body is not obvious. This is why the authors studied it.

Results

Stability of the dusty particles

The authors find that Pallene cannot clear its ring efficiently, despite its size. Actually, this zone is the most stable, wrt the dynamical environments of Anthe, Methone and Aegaeon. However, 25% of the particles constituting the G Ring should collide with Aegaeon in 18 years. This probably means that there is a mechanism, which refills the G Ring.

Stability of the satellites

From long-term numerical simulations over 400 kyr, i.e. more than one hundred millions of orbits, these 4 satellites are stable. For Pallene, the authors guarantee its stability over 64 Myr. Among the 4, this is the furthest satellite from Saturn, which makes it less affected by the resonances.

A perspective

The authors mention as a possible perspective the action of the non-gravitational forces, such as the solar radiation pressure and the plasma drag, which could affect the dynamics of such small bodies. I would like to add another one: the secular tides with Saturn, and the pull of the rings. They would induce drifts of the satellites, and of the resonances associated. The expected order of magnitude of these drifts would be an expansion of the orbits of a few km / tens of km per Myr. This seems pretty small, but not that small if we keep in mind that two resonances affecting Methone are separated by 4 km only.

This means that further results are to be expected in the upcoming years. The Cassini mission is close to its end, scheduled for 15 Sep 2017, but we are not done with exploiting its results!

To know more…

That’s it for today! Please do not forget to comment. You can also subscribe to the RSS feed, and follow me on Twitter and Facebook.

Energy dissipation in Saturn

Hi there! I will tell you today about the letter Frequency-dependent tidal dissipation in a viscoelastic Saturnian core and expansion of Mimas’ semi-major axis, by Daigo Shoji and Hauke Hussmann, both working at the DLR in Berlin, Germany. This paper has recently been published in Astronomy and Astrophysics.

Saturn’s facts

Do I need to introduce Saturn? Saturn is the sixth planet of the Solar System by its distance to the Sun, and the second by its size. It orbits the Sun at a mean distance of 1.5 billions of km, in 29.4 years. It has more than 200 satellites, which comprises small moons embedded in the rings, mid-sized icy satellites, a large one, i.e. Titan, and very far small moons which are probably trapped objects. Which means that the other bodies are expected to have formed while orbiting around Saturn, or formed from the same protoplanetary disk.
Saturn is particularly known for its large rings, which can be observed from the Earth with almost any telescope. Moreover this planet is on average less dense than the water, which is due to a large atmosphere enshrouding a core. The total radius of Saturn is about 60,000 km, which actually corresponds to a pressure of 1 bar in the atmosphere, while the radius of the core is about 13,000 km. The paper I present today is particularly focused on the core.

A new view of the formation of the satellites of Saturn

The spacecraft Cassini orbits Saturn since 2004, and has given us invaluable information on the planet, the rings, and the satellites. Some of these information pushed the French planetologist Sébastien Charnoz, assisted by French and US colleagues, to propose a new model of formation of the satellites from the rings: this model states that instead of having formed with Saturn, the rings are pretty recent, i.e. less than 1 Gyr, and are due to the disintegration of an impactor.
Once the debris rearranged as a disk, reaccretion of material would have created the satellites, which would then have migrated outward, because of the tidal interaction with the planet… This means that it is crucial to understand the tidal interaction.

Tidal dissipation in the planets

I have already discussed of tides in this blog. Basically: when you are a satellite (you dream of that, don’t you?) orbiting Saturn, you are massive enough (sorry) to alter the shape of the planet, and raise a bulge which would almost be aligned with you… Almost because while the material constituting the planet responds, you have moved, but actually the bulge is in advance because the planet rotates faster than you orbit around it (you still follow me?). As a consequence, you generate a torque which tends to slow down the spin of the planet, and this is compensated by an outward migration of the satellite (of you, since you are supposed to be the satellite). This compensation comes from the conservation of the angular momentum. You can imagine that the planet also raises a tidal bulge on the satellite, but this does not deal with our paper. So, not today.

A consequence of tides is the secular migration of the planetary satellites. Lunar Laser Ranging measurements have detected an outward migration of the Moon at a rate of 3 cm/y. It is not that easy to measure the migration of the satellites of Saturn. An initial estimation, based on the pre-Cassini assumption that the satellites were as old as the Solar System, considered that the satellite Mimas would have at the most migrated from the synchronous orbit to its present one, in 4.5 Gyr. The relevant quantity is the dissipation function Q, and this condition would have meant Q>18,000, in neglecting dissipation in Mimas. Recent measurements based on Cassini observations suggest Q ≈ 2,600, which would be another invalidation of the assumption of primordial satellites.

Several models of dissipation

To make things a little more technical: we are interested in the way the material responds to an external, gravitational sollicitation. This sollicitation is quasi-periodic, i.e. it can be expressed as a sum of periodic, sinusoidal terms. With each of these terms is associated a frequency, on which the response of the material depends. This affects the quantity k2/Q, k2 being a Love number and Q the dissipation function I have just presented. Splitting these two quantities is sometimes useless, since they appear as this ratio in the equations ruling the orbital evolution of the satellites.

Tides in a solid body

By solid body, I mean a body with some elasticity. Its shape can be altered, but not that much. An elastic response would not dissipate any energy, while a viscoelastic one would, and would be responsible for the migration of the orbits of the satellites.
It was long considered that the tidal dissipation did not depend on the excitation frequency, which is physically irrelevant and could lead to non-physical conclusions, e.g. the belief in a stable super-synchronous rotation for planetary satellites.
We now consider that the response of the material is pretty elastic for slow excitations, and viscoelastic for rapid ones. If you do not shake the material too much, then you have a chance to not alter it. If you are brutal, then forget it.
For that, a pretty simple tidal model rendering this behavior is the Maxwell model, based on one parameter which is the Maxwell time. It is defined as the ratio between the viscosity and the rigidity of the material, and it somehow represents the limit between the elastic and the viscoelastic responses.
A refining model for icy satellites is the Andrade model, which considers a higher dissipation at high frequencies.

Tides in a gaseous planet

If the planet is a ball of gas, a fortiori a fluid, then the behavior is different, actually much more complicated. You should consider Coriolis forces in the gas, turbulent behaviors, which can be highly non-linear.
A recent model has been presented by Jim Fuller, in which he considers the possibility of resonant interactions between the fluid and the satellites, which would result in a high dissipation at the exact orbital frequency of the satellite, and the resonant condition would induce that this high dissipation would survive the migration of the satellite. You can see here an explanation of this phenomenon, drawn by James T. Keane.

This paper

This paper aims at checking whether a dissipation of the planet, which would be essentially viscoelastic, could be consistent with the recent measurements of tides. For that, the authors modeled Saturn as an end-member, in neglecting every dissipation in the atmosphere. They considered different plausible numbers for the viscosity and rigidity in the core Saturn, in assuming it has no internal fluid layer, and numerically integrated the migration of Mimas, the variation of its orbital frequency in the expression of tides being taken into account.

And the result is that the viscosity should be of the order of 1013-1014 Pa.s. Smaller and higher numbers would be inconsistent with the measured dissipation.
Moreover, some of these viscosities are found to be consistent with the assumption of a primordial Mimas, i.e. with an inward migration from the synchronous orbit in 4.5 Gyr.

Perspectives

This letter probably presents a preliminary study, the whole study requiring to consider additional effects, like the pull of the rings, the influence of the atmosphere, and the mean-motion resonances between the satellites (see this post), which themselves alter the rate of migration. And this is why this letter does not invalidate Charnoz’s model of formation, nor Fuller’s tides, but just says that other explanations are possible.

Useful links

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The dynamics of Saturn’s F Ring

Hi there! Today: a new post on the rings of Saturn. I will more specifically discuss the F Ring, in presenting you the study A simple model for the location of Saturn’s F ring, by Luis Benet and Àngel Jorba, which has recently been accepted for publication in Icarus.

The F Ring

The F Ring of Saturn is a narrow ring of particles. It orbits close to the Roche limit, which is the limit below which the satellites are not supposed to accrete because the differential gravitational action of Saturn on different parts of it prevents it. This is also the theoretical limit of the existence of the rings.

The F Ring seen by Cassini (Credit: NASA)
The F Ring seen by Cassini (Credit: NASA)

Its mean distance from the center of Saturn is 140,180 km, and its extent is some hundreds of kilometers. It is composed of a core ring, which width is some 50 km, and some particles which seem to be ejected in spiral strands.

Orbiting nearby are the two satellites Prometheus (inside) and Pandora (outside), which proximity involves strong gravitational perturbations, even if they are small.

The images of the F Ring, and in particular of its structures, are sometimes seen as an example of observed chaos in the Solar System. This motivates many planetary scientists to investigate its dynamics.

Mean-motion resonances in the rings

Imagine a planar configuration, in which we have a big planet (Saturn), a small particle orbiting around (the rings are composed of particles), and a third body which is very large with respect to the particle, but very small with respect to the planet (a satellite). The orbit of the particle is essentially an ellipse (Keplerian motion), but is also perturbed by the gravitational action of the satellite. This usually results in oscillating, periodic variations of its orbital elements, in particular the semimajor axis… except in some specific configurations: the mean motion resonances.

When the orbital periods of the particle and of the satellite are commensurate, i.e. when you can write the ratio of their orbital frequencies as a fraction of integers, then you have part of the gravitational action of the satellite on the particle which accumulates during the orbital history of the two bodies, instead of cancelling out. In such a case, you have a resonant interaction, which usually produces the most interesting effects in planetary systems.

There are resonances among planetary satellites as well, but here I will stick to the rings-satellites interactions, for which a specific formalism has been developed, itself inspired from the galactic dynamics. Actually, 4 angles should be considered, which are

  • the mean longitude of the particle λp, which locates the particle on its orbit,
  • the mean longitude of the satellite λs
  • the longitude of the pericentre of the particle ϖp, which locates the point of the orbit which is the closest to Saturn,

and

  • the longitude of the pericentre of the satellite ϖs.

The situation is a little more complicated when the orbits are not planar, please allow me to dismiss that question for this post.

You have a mean-motion resonance when you can write <pλp-(p+q)λs+q1ϖp+q2ϖs>=0, <> meaning on average. p, q, q1 and q2 are integer coefficients verifying q1+q2=q. The sum of the integer coefficients present in the resonant argument is null. This rule is sometimes called d’Alembert rule, and is justified by the fact that you do not change the physics of a system if you change the reference frame in which you describe it. The only way to preserve the resonant argument from a rotation of an angle α and axis z is that the sum of the coefficients is null.

It can be shown that the strongest resonances happen with |q|=1, meaning either |q1|=1 and q2=0, or
|q2|=1 and q1=0.

In the first case, pλp-(p+1)λsp is the argument of a Lindblad resonance, which pumps the eccentricity of the particle, while pλp-(p+1)λss is a corotation resonance, which is doped by the eccentricity of the satellite. Here I supposed a positive q, which means that the orbit of the satellite is exterior to the one of the particle. This is the case for the configurations F Ring – Pandora and F Ring – Titan. However, when the satellite is interior to the particle, like in the configuration F Ring Prometheus, then the argument of the Lindblad resonance should read pλs-(p+1)λpp, and the one of the corotation resonance is pλs-(p+1)λps.

As I said, these resonances have cumulative effects on the orbits. This means that we could expect that something happens, this something being possibly anything: a Lindblad resonance should pump the eccentricity of a particle and favor its ejection, but this also means that particle which would orbit nearby without being affected by the resonance would be more stable… chaotic effects might happen, which would be favored by the accumulation of resonances, the consideration of higher-order ones, the presence of several perturbers… This is basically what is observed in the F Ring.

The method: numerical integrations

The authors address this problem in running intensive numerical simulations of the behavior of the particles under the gravitational action of Saturn and some satellites. Let me specify that, usually, the rings are seen as clouds of interacting particles. They interact in colliding. In that specific study, the collisions are neglected. This allows the authors to simulate the trajectory of any individual particle, considered as independent of the other ones.

They considered that the particles are perturbed by the oblateness of Saturn expanded until the order 2 (actually this has been measured with a good accuracy until the order 6), Prometheus, Pandora, and Titan. Why these bodies? Because they wanted to consider the most significant ones on the dynamics of the F Ring. When you model so many particles (2.5 millions) over such a long time span (10,000 years), you are limited by the computation time. A way to reduce it is to remove negligible effects. Prometheus and Pandora are the two closest ones and Titan the largest one. The authors have detected that Titan slightly shifts the location of the resonances. However, they admit that they did not test the influence of Mimas, which is the closest of the mid-sized satellites, and which is known for having a strong influence on the main rings.

A critical point when you run numerical integrations, especially over long durations, is the accuracy, because you do not want to propagate errors. The authors use a symplectic scheme, based on a Hamiltonian formulation, i.e. on the conservation of the total energy, which can be expanded up to the order 28. The conservation of the total energy makes sense as long as the dissipation is neglected, which is the case here. The internal accuracy of the integrator was set to 10-21, which translated into a relative error on the angular momentum of Titan below 2.10-14 throughout the whole integration.

Measuring the stability

It might be tough to determine from a numerical integration whether a particle has a stable orbit or not. If you simulate its ejection, then you know, but if you do not see its ejection, you have to decide from the simulated trajectory whether the particle will be ejected one day or not, and possibly when.
For this, two kinds of indicator exists in the literature. The first kind addresses the chaos, or most specifically the hyperbolicity of the trajectory, while the second one addresses the variability of the fundamental frequencies of the system. From a rigorous mathematical point of view, these two notions are different. Anyway, the ensuing indicators are convenient ways to characterize non-periodic trajectories, and their use are commonly accepted as indicators of stability.
A hyperbolic point is an unstable equilibrium. For instance a rigid pendulum has a stable equilibrium down (when you perturb it, it will return down), but an unstable one up (it stays up until you perturb it). The up position is hyperbolic, while the down one is elliptic. The hyperbolicity of a trajectory implies a significant dependency on the initial conditions of the system: a slightly different initial position or different initial velocity will give you a very different trajectory. In systems having some complexity, this strongly suggests a chaotic behavior. The hyperbolicity can be measured with Lyapunov exponents. Different definitions of these exponents exist in the literature, but the idea is to measure the evolution of the norm of the vector which is tangent to the trajectory. Is this norm has an exponential growth, then you strongly depend on the initial conditions, i.e. you are hyperbolic, i.e. you are likely chaotic. Some indicators of stability are thus based on the evolution of the tangent vector.
The other way to estimate the stability is to focus on the fundamental frequencies of the trajectory. Each of the two angles which characterize the trajectory of the particle, i.e. its mean longitude λp and the longitude of its pericentre ϖp can be associated with a frequency of the problem. It is actually a little more complicated than just a time derivative of the relevant angle, because in that case you would have a contribution of the dynamics of the satellite. A more proper determination is made with a frequency analysis of the orbital elements, kind of Fourier. You are very stable when these frequencies do not drift with time. Here, the authors used first the relative variations of the orbital frequency as indicator of the stability. The most stable particles are the ones which present the smallest relative variations. In order to speed up the calculations, they also used the variations of the semimajor axis as an indicator, and considered that a particle was stable when the variations were smaller than 1.5 km.

Results

A study of stability necessarily focuses on the core of the rings, because the spiral strands are supposed to be doomed. And the authors get very confined zones of stability. A comparison between these zones of stability shows that several mean-motion resonances with Prometheus, Pandora and Titan are associated with them. This could be seen as consistent with the global aspect of the F Ring, but neither with the measured width of the core ring, nor with its exact location.

This problem emphasizes the difficulty to get accurate results with such a complex system. The study manages, with a simplified system of an oblate Saturn and 3 satellites, to render the qualitative dynamics of the F Ring, but this is not accurate enough to predict the future of the observed structures.

Some links

  • The study, also made freely available by the authors on arXiv. Thanks to them for sharing!
  • The web page of Luis Benet (UNAM, Mexico).
  • The web page of Àngel Jorba (University of Barcelona, Spain).

Thanks for having read all this. I wish you a Merry Christmas, and please feel free to share and comment!

A new ringlet around Saturn

Hi there! Today I will tell you about the detection of a ringlet in the rings of Saturn, by Matthew Hedman and Brian Carter, at the University of Idaho (USA). This ringlet presents an interesting dynamics, this is why it caught my attention. Such a discovery is made possible thanks to the Cassini-Huygens space mission, which orbits Saturn since 2004.

The mission Cassini-Huygens

Cassini-Huygens is a joint mission of the NASA, the ESA, and the Italian Space Agency ISA. It consists of a spacecraft, Cassini, which orbits Saturn since 2004, and a probe, Huygens, which landed and died on Titan in January 2005.
This mission Cassini-Huygens is one of the most ambitious ever made, this is why it required an American-European collaboration. It has given us, and is still giving, invaluable information on the system of Saturn. For instance, it permitted the expected discovery of a global subsurface ocean for Titan, and a more surprising one for Enceladus,. Mimas may also have one, from the measurements of its rotation, and that would be even more surprising. Before Cassini-Huygens, we thought that the system of Saturn was a kind of old, frozen and boring world, while it is actually pretty recent, and even the mid-sized icy satellites may present complex interiors. As a consequence, this pushed some of our colleagues to propose new scenarios of formation of the satellites of Saturn, either as droplets composed of ring material which would have migrated outward, or as remnants of larger progenitors, which were impacted.
These are just examples, and I cannot give an exhaustive list of discoveries due to Cassini-Huygens. We have now images of the surface of Titan, we have in situ measurements of its winds, we know the satellites and the planet Saturn much better… Let us focus on the rings.

Rings of Saturn facts

The rings of Saturn are known since Galileo Galilei, and the evolution of Earth telescopes made possible the discoveries of structures in them. The most famous of them is the Cassini Division, which is a 4,000 km wide gap between the two densest of Saturn’s rings, i.e. the A and the B rings. To have a quick overview:

  • 186,000 km: Orbit of Mimas, the closest of the major satellites of Saturn
  • 141,800 km: Orbit of Pandora
  • 140,200 km: The F ring (pretty faint)
  • 139,500 km: Orbit of Prometheus
  • 139,350 km: The new ringlet
  • 122,000 to 137,000 km: The A ring (dense)
  • 133,600 km: the Encke gap, i.e. a lack of material in the A ring
  • 117,500 to 122,000 km: The Cassini Division (still some material, but pretty few)
  • 92,000 to 117,500 km: The B ring (the densest one)
  • 74,600 to 92,000 km: The C Ring (faint)
  • 67,000 to 74,500 km: The D Ring (faint)
  • 58,200 km: Radius of Saturn, where its atmospheric pressure reaches 1 bar

It is known whether a ring is faint or dense from its optical density, which is then associated with an estimated surface density of the ring, seen as a flat structure. Here, I have mixed the main structures of the rings with fainter ones, which are more relevant in this study. I have particularly emphasized the new ringlet, which discovery is presented in this study.

Beside this, you can notice the presence of some small satellites embedded in the rings. I mention Prometheus and Pandora since they are close to the new ringlet, but there are actually more, e.g. Janus, Epimetheus, Atlas, Pan,…

Discovering this new ringlet

A ringlet is a kind of narrow ring of dusty material, i.e. small particles, their radius being something between the centimeter and the meter. Discovering a new ring is challenging because it is very faint. Here, it was discovered on images of the Narrow Angle Camera (NAC) of the Imaging Science Subsystem of the Cassini spacecraft. To make its presence obvious, it is necessary to use images which are not saturated, to remove the background luminosity, and to equalize the response of the different pixels constituting the image (flat-fielding). For this study, the authors used mostly images taken between 2012 and 2014, but some in 2006 as well.

An interesting dynamics

The authors find that this ring is an ellipse with a small eccentricity (0.0012), which precesses. This means that this ellipse is not fixed, but moves around Saturn, while the particles constituting the ringlet move much faster, on the ellipse. Their orbital period is pretty the same as Prometheus’, i.e. some 15 hours, but surprisingly the precession period of the ellipse is longer, i.e. 133 days, against 130 for Prometheus, and is very close to the one of the F Ring.
This is pretty unexpected for the following reason: in an ideal (keplerian) problem, i.e. a point-mass planet around which orbits a particle, the orbit does not precess. The precession is due to departures from this problem, mostly the polar flattening of Saturn, but also the gravitational perturbation of the other satellites. It can be easily shown that, if you get closer to Saturn, you precess faster. Here, the ringlet precesses slower than Prometheus while its orbit is inside. The authors have an elegant explanation, in showing convincingly that the collisions between the particles can synchronize the precession of this ringlet with the one of the F ring, providing that this ringlet is faint enough. I admit that I had not heard of this mechanism before, but the authors convince me. I would have a priori suspected the gravitational interaction of Pandora, but its precession is even slower than the measured one. There is at least one another example of synchronization of the precessions in the system of Saturn: Titan is so massive that it forces the precession of the orbit of Rhea.
The authors also mention the possibility that the particles of this new ringlet are affected by a co-orbital mean-motion resonance with Prometheus. I choose to focus on the synchronization of the precession with the F Ring, since I consider this is the most exciting result of the study. This would be the first accurate measurement of this collision-assisted synchronization, and we can expect in the future many other examples of this mechanism.

Some links

  • The webpage of Matt Hedman
  • The study, accepted for publication in Icarus, and made freely available on arXiV by the authors, many thanks for sharing!
  • The space mission Cassini-Huygens

That’s all folks! Please, don’t hesitate to leave a comment!