A while back I gave myself the impression (by playing with JPL Horizons) that the next instance of the famous orbital "swap" was going to take place around Jan/Feb 2006. Is that right?
I'm not familiar with the precise orbital dynamics[*], but I got the impression that the moons would become close, but not spectacularly so. (But I don't have the data in front of me now.)
Does anyone know what sort of Cassini observations are planned (indeed, what if any interesting observations can be made, other than ultra-precise trajectory determination)? Any eye candy?

[*] I had a quick Google, but couldn't find any good animation to help visualise what really happens, with a rotating frame or something - just this, which I'm not convinced by. Anyone know of anything better?)

That animation correctly depicts how the "swap" happens. They don't cross paths, they just exchange a little momentum, which tosses the lower-orbit one into a higher orbit and drops the higher-orbit one into a lower orbit.

I'm also curious if Cassini will be able to watch this happen...does anybody know when it's supposed to happen next?

--Emily

I had another go at Horizons. Attached are some rough graphs of distances between body centres. It looks like the closest approach is around 10000km (or 50-100 satellite diameters), in mid-to-late January.
I guess the ~10000km wobble, which looks like it might have a period comparable to the orbital period, is down to orbit ellipticity or something?

(This all assumes that Horizons has a good model of these satellites' orbits, which I'm not competent to evaluate...)

Click to view attachment

Click to view attachment

Current best guess is a closest approach of ~10,300 km at around 02:30:00 UTC on January 21 2006. There are no Cassini observations of this event.

Hmm. Thanks, Pat and JTN.

So, just how often do the famous close (~50km) encounters actually occur, if ever? Has a "maybe" event perhaps been hyped up to an urban space legend here?...

I get the impression that the orbits of Janus & Epithemis aren't even necessarily completely coplanar, which if true would probably reduce the likelihood of periodically swapping orbits to about zero...in fact, I can't see anything from that except chaotic behavior, like what seems to be happening with those newly discovered Uranian satellites.

Thanks!


The webternet gives me the impression that they are in horseshoe orbits with respect to each other, so may never approach each other particularly closely. (Not that I've noticed any websites claiming they approach within 50km, just that their "orbits" (semimajor axes?) are that far apart.)

FWIW, I just crunched the 2002 approach (mid-to-late Jan again) with Horizons and it looks very similar to the 2006 one. (See above proviso.) (It won't let me have ephemerides beyond about 2009-Jan...)

Great work, JTN! Five wheels:

Too bad; the periodic orbit-swap idea was a really cool concept, but the conditions required are probably just too stringent to ever occur in real life. Another victory for critical thinking, though!!!

I don't think it follows that because they don't approach within 50km, the orbits aren't modified...
(No less an authority than ) Wikipedia says: The moons thus "trade" orbits and begin moving apart again, without overtaking each other and even without actually approaching each other closely (my emphasis).
It also says: Janus' orbital radius will decrease by ~20 km, while Epimetheus' increases by ~80 km (Janus' orbit is less affected because it is 4 times more massive than Epimetheus).
No source is given for either of these snippets.

I've seen that Wikipedia article as well, and of course this idea has been common knowledge since the Voyagers...but I think that it is valid to question some of the assumptions that have been made:

1. The orbital planes of both moons would have to be completely coplanar without idiosyncratic nodal precession, or resonance-coupled so that their complementary orbital characteristics have remained perfectly synchronized over a geologically significant length of time.

2. Due to the highly asymmetric shape of each moon, they would have to encounter each other at the same physical orientation each time for each swap or the mutual gravitational forces would be slightly different, again ultimately destabilizing the system. (This effect is probably not as significant or as pronounced as those produced by point #1, but there has to be some nutation now and again...and cumulative errors should still add up over time).

Finally, as you pointed out, I haven't seen a significant amount of core research published on this topic. I suspect that there hasn't been nearly enough observation of the moons until recently (after Casinni's arrival, that is) to conduct a truly comprehensive analysis of their behavior; hopefully one is in the works right now.

Bottom line: I would be most surprised (and delighted!!!) if the orbit-swap scenario proves to be real after all, but right now I am extremely skeptical!!!

Janus and Epimetheus are in a 1:1 orbit-orbit resonance, their mean semi-major axes are effectively the same. Apart from the few weeks around the "orbit swap" epoch, at any given instant their semi-major axes are separated by only ~50 km or so. Every ~4 years they can be thought of as "swapping orbits", the inner satellite's semi-major axis increases (thus becomming the new outer satellite) and the outer satellite's semi-major axis decreases (and becomes the inner satellite). The satellites themselves never approach within about 10,000 km of each other.

The amount by which the satellites semi-major axes changes during the "swaps" is a function of the masses of the satellites. Determining the semi-major axes (before and after the "swap") thus directly gives the masses of the satellites. For this reason the masses (and densities) of Janus and Epimethues are known to a high degree of accuracy.

This orbital configuration is referred to as horseshoe orbit. The Janus-Epimetheus system is currently the only known example of a stable horseshoe orbit in the Solar System. Its called a horseshoe orbit because the path of the satellite (Epimetheus in this case) when traced in the frame rotating with the mean motion of Janus (in their orbit plane) has a horseshoe shape (you need to trace the paths for at least 8 years or so to see the shape). Janus (being the more massive of the two) traces out a much shorter arc, looking somewhat like a short, fat sausage, in the same frame.

The Janus-Epimetheus system is the classic example of two bodies sharing the same orbit that is used in dynamics textbooks.

Oh I suppose I should mention that the "swap" happens when the satellites get close enough to each other (that ~10,000 km previously mentioned) for their mutual gravitational interaction to become strong enough to have an effect. The outer (slower) object moves closer to Saturn and speeds up while the inner (faster) object moves further away from Saturn and slows down. The satellites then get further and further away from each other until ~2 years later they start getting closer again (from the opposite direction) until they once again approach close enough for their gravitational interaction to affect them and "swap" thier semi-major axes again (~4 years after the previous event).

Yeah, it was announced the moment they were discovered to be in the same orbit (early 1980) that this must be what the situation was.

There had been a long dispute over just how many known moons Saturn really had from 1966 (when Dollfuss claimed the discovery of Janus on the basis of one photo during that period when the rings were edge-on to Earth, but encountered many skeptics), through 1977 (when a team reexamining the photo claimed to find not only Janus but an 11th moon) and 1979, when the same Pioneer 11 photo that revealed the F Ring also confirmed the existence of at least one new moon -- and a very sharp dip in Pioneer's radiation measurements indicated that, by pure chance, it had also flown within only 3000 km of that same new moon. Pioneer failed to show any trace of any dip whatsoever in radiation when it crossed the orbital distance that Dollfuss had calculated for Janus. But NOBODY expected that, while Janus and Moon #11 (aka Epimetheus) both existed, Dollfuss had simply miscalculated Janus' orbital distance, and so both moons were in virtually the same orbit! This was revealed within a few days of Saturn's next ring-edge-on period by the improved telescopes of the time -- which, only a few days later, revealed the wholly unexpected Helene sharing Dione's orbit. (A reexamination months later of the photos taken during this period revealed the existence of Telesto and Calypso in Tethys' orbit.)

It's always been assumed that Janus and Epimetheus are two pieces of a single moon that got cracked in two by a giant impact (as almost happened to Mimas), and that the two halves of that moon have been chasing each other around and around Saturn ever since in a vain effort to rejoin. However, our new density data revealing them to be rubble piles suggests instead that that moon was shattered, and that the debris later reaccumulated into two separate moons.

I suspect that the Lagrange moons of Tethys and Dione are rubble piles made out of debris blasted off Saturn's moons during their early period of intense bombardment, which got scattered all over the system, most of it finally either crashing into Saturn or one of the moons or getting catapulted totally out of the system -- but a small amount reaccumulated in the stable dynamic "shelters" of those two moon's Lagrange points. A recent analysis suggests that Enceladus has no such Lagrange points that are stable over the long term; I haven't seen any analyses yet for the Lagrange points of Mimas and Rhea. And I wouldn't at all be surprised if Hyperion turns out to be a similar accumulation of debris that wandered into a "shelter" provided by an orbit with a 4:3 resonance with Titan.

Nor have I seen anything on whether Jupiter's Galilean moons have any long-term stable Lagrange points -- I suspect that their influence on each other is big enough to prevent it. Are we going to find anything similar to Saturn when we take a closer look at the Uranus and Neptune moon systems? Who knows?

Thank you very much, Bruce; that was most interesting and informative, and I stand corrected!

I still have to question just how stable the Janus/Epimetheus configuration is in the long term, though. There seem to be too many possible peturbing factors for the system to run as-is indefinitely, unless there is some sort of corrective feedback also present. Any insight about this?

I've never heard of any study suggesting that the Janus-Epimetheus pair isn't stable over the very long run -- after all, if they weren't, they wouldn't still be here!

By contrast, the trio of Prometheus, Pandora and the F Ring may NOT be stable over periods of more than a few tens of millions of years -- it's quite possible that one or both of those moons were created comparatively recently from F Ring material, and will be destroyed fairly soon, with more new moons later being created out of F Ring material to replace them.

Can someone tell me what was going on here?...

http://saturn.jpl.nasa.gov/multimedia/imag...eiImageID=59067

That's one of what the spacecraft team calls "mutual events". Since right now Cassini is still in the plane of the rings (though that may not be the case after T9?), it's got a nice edge-on view of the entire satellite system. Most of the satellites are practically in the same plane as the rings. Every now and then they "appear" to be passing by or even eclipsing each other.
Given the vast distance these shots were taken from combined with Cassini's narrow FOV gives the impression the moons are on top of each other, when in reality they're all normally following their mostly circular orbits.

Thank you ugordan.

It occurred to me that I should probably mention that the Janus-Epimetheus 'orbital swap' is a VERY slow event, taking several weeks to play out. We quote exact times e.g. 2006 JAN 21 around 2 am but these are either times of closest approach or sometimes the event midtimes.

I don't know the exact time offhand but I'd guess that it takes on the order of a month of so for the semi-major axes to change from their low to high (and high to low) values. This is because the relative motion of Epimetheus w.r.t Janus ( or Janus w.r.t Epimetheus if you prefer ) is low, they are after all in (almost) the same orbit with (almost) the same orbital speeds.

According Tilmann Denk, currently in Boulder (CO) attending a Cassini-Imaging-Team meeting, the minimum distance between the moons take place tomorrow Jan. 21 at 02:00 to 04:00 UTC. The distance is around 15'000km. But as mentioned the whole process takes a long time - approximate three months and it's already "in process" for weeks.

I'm trying to write a description of this for a Web story but I'm not confident that I have the details exactly right. Can anybody critique this and tell me if there's any errors?

Here is how the dance works. Epimetheus and Janus are small, irregularly-shaped moons with diameters of about 120 and 180 kilometers (about 75 and 110 miles), respectively. Their orbits around Saturn are separated by only 50 kilometers (30 miles). Since Cassini arrived at Saturn, Epimetheus has been the inner of the two satellites. Because it is closer to Saturn, Epimetheus travels at a faster angular rate than Janus, so inner Epimetheus has slowly, inexorably been catching up to outer Janus. As the two have approached each other in their orbits, Epimetheus tugs on Janus from behind as Janus tugs on Epimetheus equally. The mutual tugging causes them to exchange angular momentum. Epimetheus gains momentum and rises in orbit as Janus loses an equivalent amount of momentum and falls. But this switch of orbital altitudes makes Janus -- still ahead of Epimetheus in its orbit -- the faster of the two. As a result, Janus creeps ahead. It will continue to creep slowly ahead of Epimetheus until it catches up from behind in four more years.

Thanks! --Emily

You might want to add that since Janus is more massive than Epimetheus its orbital altitude decreases by less than Epimetheus' orbital altitude increases (conservation of angular momentum etc). So Janus doesn't 'occupy' Epimetheus' old orbital position and vica versa. Janus moves in but not as far in as Epimetheus' pre-event orbital radius while Epimetheus moves out past Janus' pre-event orbital radius. Four years later the event happens the other way around with Janus catching up to Epimetheus.

Thanks, Pat, I'd forgotten about that detail. I just posted the story here.

--Emily

Thanks to Emily's discussion I think I'm beginning to understand this process. If I could add a thought here, perhaps considering this in terms of velocity and energy exchanges as the two moons are influencing (almost swinging around?) each other might be useful.

That's a nifty little write-up, Emily. Thanks!

Hello - my first post on UMSF !

Just wondered if people here might find it interesting to have a look at Tony Dunn's "Gravity Simulator" software - it includes a simulation of the Janus/Epimetheus orbital behaviour (as well as a lot of other interesting stuff).
And it's free info and download from www.orbitsimulator.com

cheers
Brian

Here's a nice long-term plot of the semimajor axes (which is sort of like the average orbital distance from Saturn for the uninitiated) of Janus and Epimetheus for about 25 years.

Click to view attachment

Thanks for the plot!

Do you know who it made or is there a "linkable" work on the web?