Talk:Resonant trans-Neptunian object

2:3 resonance

(unsigned) Need some discussion about 2:3 orbits being a "well" for collecting object due to considerations of minimum energy differences and 2:3 being the first orbit has a large "out of phase" (non-interacting) aspect.

I’m not sure I understand 100% your comment (is it on the 2:3 as such or related to the Neptune migration?) but I believe both definitely belong here and will try to give progressively a more detailed account. It is not easy to write about subjects considered ‘dry’ and I’m afraid to get ‘too technical’ tag. In addition talking about resonances requires diagrams I hope I will have prepared in some time in the future but do not have right now. Without them, writing about islands of stability surrounded by chaotic regions or overlapping resonances for example is a bit tricky. Please elaborate on topics you would like to see here, or even better, please jump-start them directly in the article. Eurocommuter 19:41, 17 September 2006 (UTC)

I think the point being made is that it's the closest, simple, "balanced" resonance that it's possible to have (though 3:4 and 4:5 do appear to also occur). As in the two objects orbit in relation to each other such that, starting from a point of conjunction where they're essentially as close as they can get to each other, after the outer/slower object has made another full orbit on its own path and returns to that point, the inner/faster one will have managed one and a half orbits and be in exact opposition. And for each of the inner object's orbits, the outer will be in conjunction at that point, -1/3, or +1/3 (well, actually +2/3 and -2/3) of the way around in relation to it. Though I have a feeling from what else I've read so far that it's more likely they end up taking the inverse alignment, ie exact opposition, -1/6 and +1/6 (moving through 2/3 of a revolution between each, not 1/3). Which seems like a minor difference when if you count half orbits all six relative positions will of course exhibit at some point, but only actually for circular or very nearly circular orbits; for the much more significantly eccentric orbits exhibited by yer typical TNOs, it could go a long way towards evening-out the net gravitational forces throughout each macrocycle and help stabilise the resonance, for the same reason why Jupiter's 1:2:4 moons don't ever show a triple conjunction.

This would be fairly crucial for explaining why there are so many more objects around, and confirmed resonances at points such as 2:3 (when it looks like a lot of the 1:2 examples have been withdrawn - it's probably a much less stable arrangement except for the few cases where the partners are +/- 90 degrees out of phase at their closest approaches, rather than alternating between 0 and 180)... it's not that a lot of objects have fallen or been drawn into that zone, captured in the well so to speak... it's more that they haven't been kicked out of it. They may well have formed there, or close by, and it's the dynamic equivalent of a lagrange point. So long as nothing external to that dominant system acts to perturb the two actors from their current paths, they should go on dancing around in a stable fashion for a very long time to come, and that stability is the only reason why, billions of years after our system first formed, we can still observe so many objects happily cruising around with that particular gravitational relationship to both Neptune and the Sun (and, in a way, each other, as they are all each other's trojans/quasi satellites/etc). Those which were in a less stable arrangement have long since been kicked out of it and have either ended up elsewhere on a different orbit, or have collided with something else, been broken up, or ejected from the system entirely. And you can't see what isn't there any more, regardless of how long it might have sat in place until the cumulative instability grew large enough to overwhelm the regular keplerian equations.

Of course a few wanderers, including those bumped from other resonant positions, will have been captured into that orbit by chance of passing through at the right time, but I wouldn't be at all surprised to find that the majority of objects detected and confirmed in stable integer resonances have been there for quite a long time and will be there for eons to come, the lone holdouts against the fundamental forces of chaos. We notice them because they're there, and the regularity of their relationship with another already-known body jumps out at our pattern-recognition-obsessed brains. What it's always harder to do is to look for and notice what *isn't* there, and to work out why that's so. In this case, there may have been all manner of different resonant bands, and relative phases too, but over time they've been winnowed out as the net forces on them, averaged over time, would have been out of balance and caused them to lose synch.

So yeah... I suppose you could call it a well. Except we need to consider the water instead of Little Timmy who's fallen into it AGAIN. Most of the water is happy to just sit in the bottom of the well, all the forces on it are in equilibrium, on average. A bucket being dipped into it and raised will cause some of that water to escape the well system, and the molecules right at the edges where water meets either not-quite-impervious stone or the air above may find just enough energy to leach away in one direction or another. But the pulsing water table, and what little may run in from above during rain, just about counteracts all that. Plus there's a certain limit to just how low the level can fall, even in the hardest of droughts, before the bucket is no longer able to pick up a meaningful amount. There'll still be a puddle in there. And it may well be that we're looking at the well at its normal level, some time after it starting out being full almost to the brim thanks to a series of storms just after it was built, where everything has settled into balance. Or we might be looking at the puddle.

And that's the story of the 2:3 well, and to a certain extent the other similarly notable main resonances. The others which only have a small handful of members, or none at all? They aren't anywhere near as well-built (so to speak). Their stones are leakier, they haven't got the raised rim and little pitched roof over the hole and bucket crank (both of which keep the sun from evaporating it dry), they were abused by profligate users that ran them down too fast, built in an area with dry ground and no proper aquifers... etc. Or there was some geological, sociological or climatological shift that threw the demand/replenishment relationship out of balance. Which could be our 1:2 well.

A lot of what has led the objects of the solar system both to form, and to end up where they currently are, has to do with imbalanced gravitational forces ... what now *keeps* them there, and from breaking up again, is BALANCED ones.

Might be a very roundabout way of putting it, but there you are. Humans have come along after most of the dust has settled after an eons long barn dance, and we're now trying to piece together just what the dickens happened from where the diehards, stragglers, and coy sideliners are sat around fanning themselves, finishing their drinks or contemplating their introverted personalities... ;) 146.199.0.251 (talk) 18:41, 27 September 2017 (UTC)

resonance equations

I think there were a few typos in the "Toward a formal definition" section, and I have attempted to fix them according to what seemed logical − but someone who is knowledgable had better check in case I've made a dog's dinner of it. The changes were

1. $\varpi _{N}\rightarrow \Omega _{N}$ in the long equation,
2. Rearrangement of equations so that the last discussion of perihelion distances to Neptune referes only to a select class of resonances.
3. Sign change in the resulting last equation

Deuar 18:46, 19 September 2006 (UTC)

Thanks!. My apologies for leaving it without checking. Eurocommuter 19:54, 19 September 2006 (UTC)

Declassification of numerous numbered twotinos in MPEC 2009-G25

The most recent MPEC Circular declassifies a number of resonant objects. A hecatomb of the twotinos population: only two numbered objects are listed! Eurocommuter (talk) 09:34, 9 May 2009 (UTC)

Twotino Classifications:

Object	G25	C70	Quality	DES
(119979) 2002 WC19	Y	Y	3	2:1
(130391) 2000 JG81	Y	Y	2	2:1
(20161) 1996 TR66	N	Y	3	2:1
(26308) 1998 SM165	N	Y	3	2:1
(137295) 1999 RB216	N	Y	3	2:1

MPEC 2009-C70 (2009 Feb) did show all our numbered twotinos as 1:2. But MPEC 2009-E53 (2009 March) also shows them de-listed. I know the DES has just revised their classification scheme (hopefully for the better).

Should we list these numbered objects as potential twotinos? Perhaps something along the line of a tag that goes <ref name=C70>Potential twotino: listed as a twotino in [http://www.cfa.harvard.edu/mpec/K09/K09C70.html MPEC 2009-C70] (2009 Feb)</ref> Do we know why the MPC removed them? Are they waiting for a more accurate orbit to confirm their dynamical status? For example, 26308 (1998 SM165) has only an orbital quality of 3, yet the DES is still showing 26308 as 2:1. -- Kheider (talk) 18:38, 9 May 2009 (UTC)

I’ve never seen the MPC classification criteria and I ignore the reason of the de-listing. I was thinking to remove the de-listed from our article (updating the ref to the current MPC circular) but add a note, at the bottom of the sub-section, saying earlier listed with the ref to the older circular. I feel your idea of the table is very good but labour intensive as we should do it for all resonances.Eurocommuter (talk) 09:11, 10 May 2009 (UTC)

Since then I compared the entries for 1998 SM165 in the MPCORB database as of Oct 2008 and as of yesterday (MPEC format is defined here)

2008-10-05:

26308 5.8 0.15 K096I 37.39611 131.26248 183.09247 13.48154 0.3743936 0.00297152 47.9163398 2 MPO 13953 48 8 1982-2000 0.49 M-v 38h Marsden 000A (26308) 1998 SM165 20001003

2009-05-09

26308 5.8 0.15 K08BU 36.98188 131.04571 183.10754 13.48871 0.3738678 0.00297930 47.8328728 2 MPO 13953 48 8 1982-2000 0.49 M-v 38h Marsden 000A (26308) 1998 SM165

The semimajor axis is curiously smaller; please note that less observations have been taken into account that by DES and they stop in 2000! Consequently, I would suggest keep listing the twotinos that did not make it, following the DES orbit classification with a note about the MPEC Circular. BTW it will be a minor nightmare for me to update the diagrams next time as the update is done programmatically from the MPEC database and the Circular. Eurocommuter (talk) 09:11, 10 May 2009 (UTC)

The difference in semi-major axis could be a result of using say a 18-bit calculation instead of a 14-bit calculation. (I do not know if that is the case. I just listed it as an example.)

Other Resonant Objects missing from MPEC 2009-G25:

Plutino (84922) 2003 VS2 3:2 DES (dwarf planet candidate)

(84522) 2002 TC302 2:5 DES (large dwarf planet candidate)

(42301) 2001 UR163 4:9 DES

(79978) 1999 CC158 5:12 DES (shown, but de-listed)

I understand that high order resonances would be questioned more because Neptune would likely have weaker interactions with them. But why does the MPC list 2003 YQ179 in a high-order 1:5 resonance when even the 1:2 twotinos are being questioned? The DES lists all 3 clones of 03YQ179 as ScatNear. -- Kheider (talk) 21:17, 10 May 2009 (UTC)

MPEC 2009-J35 : DISTANT MINOR PLANETS is out. TC302 is back! :-) Of our 5 Twotinos only WC19 is missing. I get the impression that using different starting positions (different months) causes the simulation to de-list some objects. -- Kheider (talk) 16:26, 12 May 2009 (UTC)

If you look at this lists closely you'll see that objects with low solar elongation angles don't appear. I think

the idea is that these are observable objects. Andrew W 115.128.25.119 (talk) 11:18, 2 July 2010 (UTC)

I’ve included a rough description of the classification scheme from Gladman, Marsden (Arizona Book). One might speculate that MPC would follow this scheme. The key reason for the discrepancies might be the data set (apparently limited to 2000 for MPEC). Eurocommuter (talk) 12:44, 14 May 2009 (UTC)

Dagger Notes

The explanatory footnotes (denoted within sections by daggers and small font) appear to be argumentative and should be migrated to the Talk page, and/or their ideas should be integrated into the article text proper. Memetics (talk) 11:39, 22 July 2009 (UTC)

Done. If someone can improve the integration of the notes, please do. Wabbott9 (talk) 18:17, 18 December 2010 (UTC)

Correct resonances

I'm not knowledgeable enough to make the correction myself, but it sure looks like the last 4 resonances ought to be reversed. If not, I'd appreciate knowing why. Thanks.

66.75.198.179 (talk) 20:07, 5 August 2009 (UTC)ltaylor@csub.edu Larry Taylor

See Talk:Plutino#3:2_resonance_or_2:3_resonance. It is kind of like asking which way is up in space. -- Kheider (talk) 06:54, 21 June 2010 (UTC)

It shouldn't really matter, if you know which is the "outer" and which is the "inner" body, in relation to whatever it is they both orbit around. If you're comparing the number of orbits completed per unit time, ie how many times each one much go around the central body before they end up in conjunction at the "same" place again, then the smaller number refers to the outermost member, as it will have the slower orbit. If you're comparing how long each object's "year" (or "month", for satellites) lasts, then it's the other way round, as year length is the inverse of orbital rate... The convention usually seems to be to put the smaller number first, which doesn't feel entirely natural for some reason, but there's no reason why it can't be the other way around because unless you literally don't even know the order of orbital distances you can always figure out which one is which from that. 146.199.0.251 (talk) 17:56, 27 September 2017 (UTC)

Resonant angle

Are there any other possible resonant angles than 180°? --JorisvS (talk) 23:23, 20 September 2012 (UTC)

Very distant resonances

This pdf (p.6) gives some candidates for distant resonant SDOs, going up to the 1:18 (2002 GB₃₂?) and 4:79 ((148209) 2000 CR105?) resonances. (Though our article on the latter states that it is not gravitationally influenced by Neptune.) Double sharp (talk) 04:29, 9 June 2014 (UTC)

Updated graphic for TNO distribution

I've created a new diagram with the distribution of all known TNOs, including the known confirmed resonances. I noticed that the article itself is based on information as old as 2008, with some of the resonances now known to be erronous (including the notable 1:5). I will try to rewrite the article, but that could take some time. If somebody else comes with a better version, that would be fine, too.Renerpho (talk) 20:13, 9 August 2015 (UTC)

How complex a fraction might be realistic for a resonant relationship?

Just looking at the "real vs coincidental" section (which seems to anthopomorphise things somewhat - there's not really anything so much as a coincidence in space, as that suggests some kind of agency in the other cases; if things are walking and quacking like ducks, then they probably are ducks, even if arrived at from totally different ancestors by a bizarre quirk of convergent evolution)... the example given for the "coincidence" that isn't *quite* 3:7, with a graph of calculated orbital libration (thus, NOT progression! just a different libration! someone messed up there, I think?) seems to show a pretty clear centreline around 2.305 to 2.310 (wheres 3:7 is 2.333). Noodling around with a calculator I find 13:30 to give a result of 2.3077, which is a more or less perfect match for the figures. But is this too extreme a figure? There seem to be others which are e.g. 6:11 or such, just a little shy of some more fundamental, simple fraction or halfway between them (1:2 or 3:5 in that case - 3:6 and 3:5 if you prefer, and 12:30/14:40 above, ie 6:10 (3:5 again) or 7:10).

I don't see why nature would abhor it particularly, it would just be less likely - ie in space terms, less common - that we might find such a thing occurring naturally, and it would be more sensitive to being fatally perturbed by novel external forces, compared to the far more common and routinely observed simple versions. But surely there might be one or two orbital pairs showing such a high numbered relationship? If you spread it out over cosmic time, even if they're far-TNO they'll have a steady, long-running "beat" in terms of their phase waveforms drifting apart, being in total opposition, then coming back together for a near-perfect repeated conjunction every 13 times one of them finishes an orbit, and every 30 times the other does. Of course as mentioned, the forces keeping them in that relationship are fairly fragile, but if enough of the dice of chance come up sixes on the next roll, they'll get to go round again, and again, until after eons something might finally knock one of them just hard enough to disrupt that.

(I've arrived here from trying to work out how to fix some very awkward wording on the Praamizus (cubewano) article, which has been with it since the page was first created for the then not-yet-named MP, saying something about it being almost a 5:3 relationship but needing 160 too many (too few?) Neptune orbits (??)... failed at figuring that out so have tried to come back to first principles in understanding what goes on with orbital resonance to interpret the known data for it and Neptune for myself and see if there's a relationship there. Depending on how the maths works out, it could realistically rate a not-too-extreme 10:17 relationship thanks to a moderate uncertainty parameter and figures for the orbital period and the semi-major axis that don't quite gel with each other... however, when we split the difference between the latter two, the strongest candidate by miles is 13:22 (a little off 2.95:5), which is a bit "high" for the ratio between one of those fundamental stats, and a bit "low" for the other, by about the same proportion. And if we trust one or other of them alone, the best candidates are either 53:90, or 59:100, which makes it look relatively tame.

So, resonances where the smaller figure is in the low teens, and/or the larger around 20 to 30... allowable? Both of these cases have an odd number for the inner cycle and an even one for the outer, and I don't know if that works as well as the reverse, but it seems to me that combining the two instead of two odd numbers (two even ones would of course decompose to one or the other anyway, as you could immediately divide them by 2) allows a more stable relationship to develop as each particular relative position around the macrocycle has an exact opposite that occurs a half-macrocycle before/after, helping to balance out the forces, particularly if the position of aphelion and perihelion are suitably tuned)146.199.0.251 (talk) 19:07, 27 September 2017 (UTC)