Talk:Orbital resonance

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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 ν stands for?.Eurocommuter 11:28, 9 February 2006 (UTC)
Yeah, I've wondered about that \nu\,\! 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)

Contents

[edit] Inconsistent ratios for Mimas and Tethis

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:

4\cdot n_{\rm Th} - 3\cdot n_{\rm Mi} - \Omega_{\rm Th}- \Omega_{\rm Mi}= 0

So which is it? 66.44.0.24 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)

[edit] Planetary resonances

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)
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>> 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...
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>> 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.
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>> 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...
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>> they should go somewhere on astrology pages
Let astrology sleep in medieval ages, the resonance is pure physics.
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How far did you scientists get from medieval ages? Is censure still among scientific methods?
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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...
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>>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).
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>>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...
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>>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.
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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!
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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.
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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

[edit] Ratio notation

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)

[edit] Conventions

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. 124.191.50.199 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)

[edit] Resonance between Mimas and Pandora

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)

[edit] Explanatory note

"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)

[edit] RE: Explanatory note

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)

[edit] Mechanism

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. 124.191.50.199 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)

[edit] removal of cleanup tag

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)