Talk:Orbital resonance

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Further extensions IMHO[edit]

Further extensions IMHO

  • merge with spin-orbit resonance (tidal locking)
  • brief section on ring/moonlets resonances?
  • More web-based, basic-level references.

PS. Bear with me, I'm beginning with latex Eurocommuter 22:53, 3 February 2006 (UTC)

I'm not sure if it should be merged with tidal locking since the sets of tidally locked and orbitally resonant bodies largely do not overlap (I think). Some sort of tie-in with the two articles would probably be good though, since I guess tidal forcres are responsible for the orbital resonances between e.g. Jupiter's moons. Have fun with the latex :-) Deuar 18:21, 6 February 2006 (UTC)

Is the last part of Types of resonance formatted correctly? It looks like there's a bullet point where there shouldn't be. Don 07:44, 9 February 2006 (UTC)

It is just one example, I understand; other examples could/should be given. The problem is that some theory & formulas are needed first. Without such an extension, what stands for?.Eurocommuter 11:28, 9 February 2006 (UTC)
Yeah, I've wondered about that too -- beats me, it's probably buried somewhere in an old paper. I suppose the 6 stands for Saturn. Deuar 14:35, 9 February 2006 (UTC)
Have a few papers by Malhotra but the stuff is ... a bit dry. Still, I’d like to write a bit about Neptune migration models one day, so such a background on resonances would be useful.Eurocommuter 01:23, 10 February 2006 (UTC)

Inconsistent ratios for Mimas and Tethis[edit]

In one place, the ratio of the periods of Mimas and Tethis is said to be four to two:

  • 4:2 Mimas-Tethys (Saturn’s moons)

In another place, the ratio is implied to be four to three:

So which is it? 06:42, 3 May 2006 (UTC)

Fixed. Thanks Eurocommuter 07:47, 3 May 2006 (UTC)

Isn't a 4:2 resonance the same as 2:1? Shouldn't this be simplified? Deuar 12:27, 23 November 2006 (UTC)

Oh, yeah, duh. Ignore my above comment. The 4:2 notation is important because of the exact equation which takes into account the libration of the nodes. Deuar 16:59, 28 November 2006 (UTC)

Thanks, Deuar. I was just about to post exactly the same question. PDAWSON3 (talk) 18:55, 7 March 2012 (UTC)

Planetary resonances[edit]

I've added the planetary resonances, since if there is a mention about Neptune/Pluto resonance, it should be stated, that other resonances exist and are even more precise.

The difference percents are calculated from DE406 ephemerides by means of bary-center traces between planets, and by planet orbit periods here in Wikipedia, as the ratio between the cycle length and the meet-point difference after that period, and are rounded to the precision stated (1-2 significant digits). (For example, if Earth/Venus meet-point differs by 2.5 days, it is 2.5/(8*365), which is 0.000856 of the cycle, rounded as 0.09% )

The resonances stabilize planetary orbits, since if one planets would arive to the meet-point later than the other, it is attracted to be there in time. If the period is fixed this way, the orbital distance is fixed also, see Lissajous choreography. Otherwise, the orbits would be more concentric then they are.

There was a sentence in the article, that despite of trials, no important influences are known...

The Solar bary-centric orbit cycle seems, beside the probable influence on climate, mentioned on John Daly pages, also importance on some human civilisation events. Specially the years, when the Sun passes nearby the solar-system bary-center, seem to have an importance on the civilisation evolution. The cycles of 1/(R^2) are quite complex, showing some fractal-like but irregular patterns, with peaks at years:

45, 84, 124(c), 163

223, 264, 303(c), 342

402, 443, 482(c), 520

559, 622(c), 661

800(c), 839

956, 979(c), 995, 1037

1096, 1135(c), 1158

1275, 1313(c), 1337

1453, 1492(c)

1593, 1632(c), 1671

1772, 1811(c), 1850

1951, 1990(c), 2030

(c) marks a central event in the short cycle

The longer cycles (on millenia scale), are bounded by minimums arround these years:

1000 BC (before this, there was a "silent" period of more than 1000 years)

this cycle peaked arround 235 BC

23 AD minimum

this cycle peaked arround 622 AD

1057 AD minimum

this cycle peaked arround 1632

1912 AD minimum

now the current cycle will peak arround year 2348 AD

~ By Semi Psi, 2006 June 23

Thanks for your efforts, but I'm afraid that this is simply a classic case of assinging undue significance to a bunch of random numbers. For a true resonance, the match must be pretty darn close to perfect. Otherwise it's just a conicidence whose effect on the orbits averages out over a sufficiently large number of orbits. To be in a resonance the bodies in question absolutely must often return to identical repeating configurations. See the discussion of the resonances between giant planet moons in the article for examples. Mismatches of a fraction of a percent are just not anywhere near good enough. Determining whether a resonance is present or not requires knowledge of the precession rates (see the article again), which are not tabulated in the wikipedia at present, so Wikipedia is not a good source of data for such an investigation. Besides, numerous scientists have trawled the data for such resonances over the years, and despite their hopes of discovering something significant, the consensus is that the only known planetary resonance in our solar system is the Neptune-Pluto one.
Correlations with historical events are pure speculation and sound like they should go somewhere on astrology pages. While there is a reference given, it appears to be one of the innumerable quacky sites on the web. If this Daly guy thinks he has discovered something important, why doesn't he get informed opinion by trying to publish in a scientific journal. Deuar 16:44, 25 June 2006 (UTC)
>> the consensus is that the only known planetary resonance in our solar system is the Neptune-Pluto one
This is a bad consensus. The Neptune-Pluto resonance is one of the least precise ones. Lets better say, that it is one of the least important ones and had already escaped from a censure on this topic...
>> For a true resonance, the match must be pretty darn close to perfect
The resonance of Neptune-Pluto is far from perfect. If you read on commensurability of planetary orbits, you will find, that a simple exact commensurability would be very perturbative and unstable.
Instead, the true world is much more perfect than that, since the counter-wave, that you see as unperfect, actually brings a better stabilization effect.
>> Correlations with historical events are pure speculation
Well, such correlation would be a speculation, but I did none - just listed the years. But the coincidence is much more than random... Much more probable solution to this problem, than an influence of planets onto humans, is, that someone, who knows the cycles, is scheduling these events. Well, but this would not come onto a resonance page, unless there was already a sentence saying about no significance, which I disputed...
>> they should go somewhere on astrology pages
Let astrology sleep in medieval ages, the resonance is pure physics.
How far did you scientists get from medieval ages? Is censure still among scientific methods?
Well, I am not going to promote Daly. Only needed to say, that Dr. Landscheidt is one of those few, who really try to investigate Solar activity, instead of casting mysteries, unknowns and chaos...
>>To be in a resonance the bodies in question absolutely must often return to identical repeating configurations
Which is preciselly the case with Earth/Venus (after 243 years) and Jupiter/Saturn (after 854 years).
>>Determining whether a resonance is present or not requires knowledge of the precession rates (see the article again), which are not tabulated in the wikipedia at present, so Wikipedia is not a good source of data for such an investigation
The short-scale resonance (on a scale of centuries) has got nothing to do with a precession.
And I do not say I have investigated this using Wikipedia data. I used the most precise scientific ephemerides currently available: DE405 and DE406, covering some 5 millenia. You will not determine a propper resonance rate just by dividing the orbit times, you must draw a bary-center trace to recognize 20/7 resonance of Saturn/Uranus instead of 3:1, as stated...
>>However, in spite of efforts, no significance has been identified so far...
This sentence (in the article) is one specific POV and does not belong to an encyclopedy. Nearby it, there are two obvious errors and one important ommision.
The resonance is important for synchronizing planetary orbits and preventing a chaos, that would result from perturbances, should there be no stabilization factor.
The true world is not chaotic!
I'll try to rewrite the section in a more conservative way, avoiding any POVs and undesired links, but I will have to think more about a propper formulation to meet encyclopedy standards.
Just note, that the propper planetary resonances are these:
Venus/Earth 13/8, with higher-order wave of period of 1199 years in retrograde direction, but returning to same places every 243 years (1/5 of the cycle + 2 meets).
Jupiter/Saturn 5/2, with higher-order wave of period of 854.69 years in prograde direction.
Saturn/Uranus 20/7, with higher-order wave in prograde direction.
Uranus/Neptune 51/26, with a higher-order wave in prograde direction.
Neptune/Pluto 3/2, with higher-order wave in prograde direction.
The Earth/Mars resonance of 15/8 is imperfect, due to Mars trajectory being much perturbed by asteroids and Jupiter.
The only planet not showing any apparent orbital resonance with its peers is Mercury.
Determining higher-order wave periods for outer planets is difficult from ephemerides covering 5,000 years only...
See [1] for illustrations...
~ Semi, July 5, 2006
Is there a reason that the Pluto - Neptune resonance is mentioned in the text but not the table?
Similarly, the Io/Europa/Ganymede resonances?
Robertm25 (talk) 12:07, 29 July 2015 (UTC)
Yes, those are examples of exact resonances, whereas the table lists near resonances. WolfmanSF (talk) 15:36, 29 July 2015 (UTC)

Ratio notation[edit]

We should agree on a uniform notation for the resonances, because so far this has been a source of frequent editing, and almost permanent inconsistency.

The usual notation is where e.g. Pluto has a 2:3 resonance with Neptune. That is, 2 orbits of Pluto to 3 orbits of Neptune. (or one could also say a 3:2 Neptune-Pluto resonance, but NOT a 3:2 Pluto-Neptune resonance. Note the order!) Pluto does it twice while Neptune does it three times - hence 2:3, not 3:2.

While it is also possible to be consistent with the opposite notation where you quote the ratios of periods as in e.g. the ratio of periods of Pluto to Neptune is 3:2. However, this inverse notation is usually not used by astronomers because it requires more explaining (that the ratio is of orbital periods). I think we should avoid this.

Comments? Deuar 12:25, 23 November 2006 (UTC)


Let's go for simplicity and the conventional convention: namely that saying that B has an n:m resonance with A is a shorthand for saying that (secondary body) B completes n orbits in the same time as (primary body) A completes m orbits. As well as defining the meaning of the numbers, this prescribes the order of appearance of the two bodies: the 'secondary', or less massive, body appears first, whilst the 'primary', or more massive, body A appears second.
If anyone objects to this (relative) use of the terms 'primary' and 'secondary', we can recast this purely in terms of masses and orbits as follows: saying that B has an n:m resonance with A is a shorthand for saying that the less massive body B completes n orbits in the same time as the more massive body A completes m orbits. 16:33, 8 October 2007 (UTC)
From my perspective, there is no need to worry about which body is primary and which is secondary if you simply refer to an A:B or A-B m:n resonance, which is the same as a B:A or B-A n:m resonance. Why not just assume that the order of numbers in the ratio corresponds to the order in which the orbiting bodies are mentioned? WolfmanSF (talk) 20:28, 6 May 2008 (UTC)

Resonance between Mimas and Pandora[edit]

Does anyone know if this is an exact resonance?

WolfmanSF 18:11, 19 February 2007 (UTC)

It is - see the Spitale (2006) reference in Pandora (moon). By the way, interesting edits. :-) Deuar 18:44, 19 February 2007 (UTC)

Explanatory note[edit]

"NOTE: In this article, except where otherwise stated, a resonance is denoted as a ratio of orbits rather than by the inverse ratio of orbital periods. The 2:3 ratio above means Pluto completes 2 orbits in the time it takes Neptune to complete 3.". This note, which is supposed to clarify, does nothing of the sort. I hesitate to edit it, lest the author comes back and tells me that I've missed the point (such as it is). Paul venter 05:36, 15 June 2007 (UTC)

RE: Explanatory note[edit]

In the example of the Pluto:Neptune resonance, the ratio of orbits (orbits per unit time) is 2:3 (Pluto orbits twice in the time it takes Neptune to orbit 3 times), whereas the ratio of orbital periods (units of time per orbit) is 3:2 (Pluto's year is 1.5 times longer than Neptune's). Thus, a resonance ratio cannot be interpreted unless the convention being used is known, and the point of the note was to specify which convention would be used throughout the article. Please let me know if this is now clear.

Of course, in a given example, if the reader knows which orbit is interior and which is exterior, the convention being used is obvious, but this will not always be the case. Your contribution fails to point out that 2 conventions are possible, and could be easily missed by someone merely skimming over the article. If there are no strenuous objections, I would like to reinstate something similar to the previous note. Is a more detailed note required? WolfmanSF 02:34, 16 June 2007 (UTC)

How about "NOTE: In this article, the resonance ratio should be interpreted as the ratio of number of orbits completed in the same period and not the ratio of orbital periods (which would be the inverse ratio). The 2:3 ratio above means Pluto completes 2 orbits in the time it takes Neptune to complete 3." and if there is some place in the article which uses a different convention then it should be altered to fit in with the above. cheers Paul venter 07:56, 16 June 2007 (UTC)
OK, I will use your suggestion with a slight modification to avoid repetitive use of "period." The only place in the article a different convention is used is in the figure showing the Laplace resonance, which unfortunately I am unable to edit. Thanks for your input. WolfmanSF 16:00, 16 June 2007 (UTC)


This page needs a clear explanation of the best available theories as to how orbital resonance occurs. For an example, see the section Tidal_locking#Mechanism. Without that, this page represents astronomy at its scholastic stage, a mere record of remarkable facts, and unfortunately lends credence to numerological or astrological interpretations. The physical science of astronomy must explain observed facts in terms of more general and fundamental physical laws. 16:46, 8 October 2007 (UTC)

Well It's not so much a matter of there being competing theories, but a matter of delving into mathematical complexity and making the relevant part of the page rather technical. Worth doing of course. The article also lacks an explanation of the difference in conditions which make a resonance destabilize or stabilize an orbit. Deuar 08:34, 9 October 2007 (UTC)
I agree. I came to this article having just found out about Laplace resonance, and wanted to understand how something like that comes about. After reading a loong article, and realizing that there are many such resonances in the solar system, I still have no idea how any of them come about! And I'm a physicist, and have done my share of resonance related readings and calculations! --Gargletheape (talk) 20:07, 12 August 2009 (UTC)

removal of cleanup tag[edit]

I've removed the cleanup tag after well over a year. No description of the deficiencies of the article that prompted placement of the tag was ever given, so it served little purpose. WolfmanSF (talk) 20:21, 6 May 2008 (UTC)

I placed clarification tags at two points where the terms or symbols weren't defined or linked. kwami (talk) 21:37, 10 February 2009 (UTC)

local fluctuation of gravity?[edit]

"The near resonances may be maintained by a 15% local fluctuation in the Pluto-Charon gravitational field. Thus, these near resonances may not be coincidental." That seems odd, what is it trying to express? Midgley (talk) 00:56, 24 August 2008 (UTC)

Yeah, it does seem odd. I believe the refs are in the moons of Pluto article. I don't remember them being very clear, but maybe you'll get more out of them than me. kwami (talk) 21:36, 10 February 2009 (UTC)


Should we add 12:7 Neptune-Haumea? kwami (talk) 21:34, 10 February 2009 (UTC)

Gravitational "Influence"[edit]

The introduction of this article currently says "Orbital resonances greatly enhance the mutual gravitational influence of the bodies." What is "mutual gravitational influence?" When I hear "gravitational influence," I think of the force of gravitational attraction between the two bodies. This force, however, depends only on the masses and the (square of) the distance between the bodies, according to Newton's law of universal gravitation, which states that F = G * m1 * m2 / r^2. I think we should consider removing or rephrasing this sentence to prevent the confusion that arises from seeming to contradict basic laws of physics. MathEconMajor (talk) 13:17, 27 August 2009 (UTC)

"Mutual gravitational influence" is not intended as a synonym for the strength of the the force of gravitational attraction. It is meant to include the consequences of that gravitational attraction, such as changes in orbits over time. Orbital resonance really can dramatically change orbits over time in ways that would not be possible without that relationship. WolfmanSF (talk) 18:07, 5 July 2010 (UTC)
I tweaked the intro for clarification. WolfmanSF (talk) 23:01, 10 August 2010 (UTC)


I made a little change here. See Talk:Lindblad resonance. DVdm (talk) 07:53, 30 May 2010 (UTC)

little numbers, big numbers[edit]

This sentence in Metonic cycle

The periods of the Moon's orbit around the Earth and the Earth's orbit around the Sun are believed to be independent, and have no known physical resonance.

— made me wonder what are the biggest numbers in known resonances. I imagine that a 235:19 resonance would be too weak to notice. —Tamfang (talk) 22:20, 10 August 2010 (UTC)

Maybe you should ask instead, what are the limits of stabilization. I suspect there is no general answer to this question; probably each dynamical pairing will have different susceptibilities to falling into resonance. WolfmanSF (talk) 23:07, 10 August 2010 (UTC)
I have the impression that you misread my word known as possible, or some such. Likely I'm misunderstanding something. —Tamfang (talk) 05:55, 11 August 2010 (UTC)
There are unconfirmed examples as high as 7:12 and 5:17 for resonant trans-Neptunian objects. The ability to "notice" these resonances is currently constrained by the amount and quality of orbital data that has accumulated to date. It's just a matter of time until we know whether they exist. With enough data, a 235:19 resonance should be detectable if it exists (not likely). WolfmanSF (talk) 08:24, 11 August 2010 (UTC)
Thank you, that's the kind of answer I hoped for. —Tamfang (talk) 22:00, 12 August 2010 (UTC)


Pluto and the plutinos are in stable orbits, despite crossing the orbit of the much larger Neptune. This is because a 2:3 resonance keeps them always at a large distance from it.

The wording could be improved: resonance would not keep them apart if the orbits were circular and coplanar! —Tamfang (talk) 01:24, 2 December 2010 (UTC)

The resonance would still keep them apart if they were coplanar; see If the orbits were circular, they wouldn't intersect, so no resonance would be needed to keep them apart. WolfmanSF (talk) 08:49, 2 December 2010 (UTC)
If they were circular, they wouldn't stay circular. I just think the language ought to be expanded a little bit, along the lines of: the resonance means that, at the time of Pluto's perihelion, Neptune is consistently far from that part of its own orbit.Tamfang (talk) 10:17, 2 December 2010 (UTC)
See discussion about (119951) 2002 KX14 on the stability of near-circular orbits. However, your proposed change is fine. WolfmanSF (talk) 17:48, 2 December 2010 (UTC)
What discussion? That article does mention that KX14's orbit is not resonant. —Tamfang (talk) 23:06, 2 December 2010 (UTC)

Gaps in Saturn's Rings[edit]

Would it be appropriate to include in this article some discussion on how the Encke and Cassini divisions (and probably a few others whose names I dunno) are maintained ("swept") due to orbital resonance? All other examples discuss resonances between two relatively large bodies ("peers" was the word used and it is to me an excellent choice), but this is a resonance between a relatively large body and an arbitrary number of miniscule ones. This would therefore appear to be intrinsically "interesting" because it is conceptually different to all the other examples. -- (talk) 11:37, 15 January 2011 (UTC)

The Cassini Division is already discussed. I've added mention of the Encke and Keeler gaps. It may well be appropriate to add more examples from Saturn's rings, especially if they represent a type of resonance not discussed elsewhere in the article, but we don't necessarily need to discuss every gap and ringlet. The main objective is to mention at least a few examples of each type of resonance. WolfmanSF (talk) 19:39, 15 January 2011 (UTC)

Reference to Definition of a Planet[edit]

I'm a bit confused on the reference here, and perhaps it could use a little clarification. This article makes reference that the 1:1 resonance is used in the definition of a planet, but the article Definition of planet does not directly mention orbital resonance. It only refers to the body’s ability to clear the area around its orbit. Does this mean that by inference a planet exists in a 1:1 resonance with another object, or does it simply mean that a planet can clear its surroundings? If it is the latter, then does the reference in this article to the definition of a planet need to exist? If it is the former, does the definition of a planet then contain the necessity of being in a 1:1 resonance? FrankCarroll (talk) 23:06, 27 April 2011 (UTC)

As I (mis)understand, a body "clears its orbit" if it is not in or near 1:1 resonance with any other large body. Does that help? —Tamfang (talk) 23:16, 28 April 2011 (UTC)
What the article says (or tries to say) is that "clearing the neighborhood" is used in the definition of a planet, and that 1:1 resonance interactions are involved in clearing the neighborhood (there are only a few orbital locations where a 1:1 resonance is stabilizing). But there's a lot more to clearing the neighborhood than just 1:1 resonance interactions. I agree, the presentation should be clarified. WolfmanSF (talk) 01:21, 29 April 2011 (UTC)
Here is the original sentence: "The special case of 1:1 resonance (between bodies with similar orbital radii) causes large Solar System bodies to eject most other bodies sharing their orbits; this is part of the more extensive process of clearing the neighborhood, an effect that is used in the current definition of a planet." How about if we changed it to: "The special case of 1:1 resonance (between bodies with similar orbital radii) causes large Solar System bodies to eject most other bodies sharing their orbits; this is part of the more extensive process of clearing the neighborhood, an effect that is also used in the current definition of a planet." —Preceding unsigned comment added by FrankCarroll (talkcontribs) 16:06, 29 April 2011 (UTC)
Sorry, can't see how that helps (note that the original sentence has already been modified). WolfmanSF (talk) 01:21, 30 April 2011 (UTC)
Much better than my suggestion, thanks! FrankCarroll (talk) 23:32, 5 May 2011 (UTC)

Secondary resonance[edit]

Can anyone tell me what a 'secondary resonance' is supposed to be? I have seen this mentioned in several places, including this article, but never with an explanation as to what it is. --JorisvS (talk) 10:57, 5 April 2012 (UTC)

There's some discussion of it here re. asteroids. — kwami (talk) 12:30, 5 April 2012 (UTC)
From Malhotra & Dermott (1990): "A secondary resonance arises when the libration frequency of a primary resonance is commensurate with the circulation frequency of a nearby primary resonance." Circulation is a continuous change, as opposed to libration, which is an oscillation (see Encyclopedia of the Solar System, p. 561). WolfmanSF (talk) 21:03, 5 April 2012 (UTC)

Exoplanet resonances[edit]

It might be worth mentioning KOI-351. This is a hierarchic seven planet system, where candidates "b" and "c" are very close to a 4:5 resonance and candidates "d", "e" and "f" appear to be in a 2:3:4 Laplace resonance. See and

Ajebson (talk) 14:51, 4 November 2013 (UTC) Tony

Yes, interesting case. WolfmanSF (talk) 09:29, 1 April 2017 (UTC)

Tethys:Mimas 2:4?[edit]

How this is different from 1:2? Double sharp (talk) 13:53, 2 June 2014 (UTC)

See first section above. WolfmanSF (talk) 16:37, 2 June 2014 (UTC)
Ah, I see. Then I think there should be a note right next to it for added clarity. Double sharp (talk) 01:21, 3 June 2014 (UTC)
 Done Double sharp (talk) 01:23, 3 June 2014 (UTC)

Planet Nine and Sednoids[edit]

what is the ratio of resonance between the hypothetical planets such as Planet Nine & Sednoids, Detached objects & Sednitos etc? J mareeswaran (talk) 12:10, 28 January 2016 (UTC)

No one has made any specific predictions. WolfmanSF (talk) 17:39, 28 January 2016 (UTC)

Check Earth-Venus near-resonance mismatch[edit]

The article states the angular difference after 13 Venus orbits is about 1.5 degrees from Earth, but I'm getting 0.92438 degrees Numbers I'm using...

Sidereal orbits: Earth, 365.25636d; Venus, 224.701d

8 Earth: 2922.05088d

13 Venus: 2921.113d

Difference: Earth behind 0.93788d

Approximate angular difference: 360deg * 0.93788d / 365.25636d = 0.924383083deg

Could someone check this, please? — Preceding unsigned comment added by Nielsed (talkcontribs) 17:30, 22 March 2017 (UTC)

No, the article states the mismatch is calculated after 8 Earth years. WolfmanSF (talk) 02:02, 23 March 2017 (UTC)
I wrote "8 Earth" orbits. I've adjusted the spacing to clarify. Nielsed (talk) 02:16, 22 April 2017 (UTC)
The article states the angular difference after 8 Earth orbits is about 1.5 degrees, and so it is: 8 Earth orbits x 365.25636 d/Earth orbit = 2,922.0509 d; that value/224.701 d/Venus orbit = 13.0041 Venus orbits; 0.0041 Venus orbit*360 degrees/orbit = 1.50 degrees. WolfmanSF (talk) 05:34, 22 April 2017 (UTC)

Challenging the existence of orbital resonance[edit]

The mutual gravitational attraction between two planets passing each other in adjacent orbits can be decomposed into three vectors in space. They are analogous to the orthogonal forces produced by spacecraft thrusters at a ‘maneuvering node’ ( [1] ‘prograde/retrograde’ appear in succession in opposite directions during the passing and thus cancel each other out; [2] ‘normal/anti-normal’ can change the orbital inclination but would have negligible effect for coplanar orbits; and [3] 'radial-in/radial-out' reaches a maximum at conjunction of the planets and will have no effect on the shape of each orbit but will rotate both orbits in their own planes, moving the apoapses and periapses in opposite directions around their respective ellipses. The ratio of orbital periods has nothing to do with those three effects, which puts the whole subject of ‘orbital resonance’ in doubt. Surely there must be plenty of authoritative references that establish this reality.Paul Niquette (talk) 08:15, 27 May 2017 (UTC)

Given that the existence of the phenomenon is well recognized in the field, expecting the article to logically prove the phenomenon's existence to the satisfaction of doubters who have not bothered to read up on the subject is not reasonable. The math is not simple. The many examples of extremely precise orbital period commensurabilities should convince you that it is real. (Please start new discussions at the bottom of the page.) WolfmanSF (talk) 17:28, 27 May 2017 (UTC)

Kepler-80 4-planet resonance[edit]

Regarding the 4-body Kepler-80 resonance, skepticism has been expressed regarding the reality of the 62:41:27:20 orbit ratio resonance mentioned. This is simply the combination of the 27.21-day 9:6:4:3 orbit ratio resonance that occurs in the backwards-rotating frame of the conjunctions, and the 190.5 day "super-period" in which the planets' configuration repeats in inertial (nonrotating frame) space. 7 x 27.21 = 190.5; 7 x 9:6:4:3 = 63:42:28:21, but then we have to subtract one from each orbit total because the conjunctions circulate backwards relative to orbital motion. I agree that the 62:41:27:20 commensurability is remarkable, but it's not ridiculous. Strange things can happen in tightly packed planetary systems. WolfmanSF (talk) 19:05, 5 June 2017 (UTC)

Still, this numbers are not in one of the three references that were given, and should not appear here without explanation. A 9:6:4:3 resonance is much more believable than :41:, which is a large prime. Maybe this discussion belongs into the Kepler-80 article, not here, where it leads people to think that 62:41 resonances are reasonable things to expect. (In fact, a discussion with somebody not trained as a scientist is how I stumbled upon this bit of info.) In this way, Kepler-80 is an outlier and not a typical example. Marquenterre (talk) 20:37, 6 June 2017 (UTC)
I've added a bit more explanation. Please look at the 2016 reference cited, which contains all the necessary information to verify what I've said. You can easily check the 62:41:27:20 ratio of the commensurabilities of the periods with the 190.5 day super-period, and obtain the intervals between the conjunctions. Everything else is obtainable from those values via simple algebra. No, you will not find the numbers expressed as such in the reference; astronomers normally discuss resonances in terms of equations that describe the evolution of the system in time (a type of description much less accessible to nonspecialist readers of Wikipedia). We are not just trying to provide typical examples here; exceptional examples are somewhat more interesting. WolfmanSF (talk) 21:35, 6 June 2017 (UTC)