Talk:Haumea (dwarf planet)

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“fifth-order 7:12 resonance”[edit]

> fifth-order 7:12 resonance

This non-expert reader was wondering about this resonance, and it took awhile before realising that there was a ‘title’-style tag:

> In principle, the strength of a resonance is inversely proportional to the difference between the numerator and denominator, which is called its 'order'. The lower the difference (order), the stronger the resonance will be. A 12:7 resonance is fifth order (12 - 7 = 5), which is fairly weak.

First, please could this be more obviously visible.

Second, just wow! So a 101:100 resonance is as strong as 2:1. Really?! JDAWiseman (talk) 20:40, 6 February 2015 (UTC)

Such an extreme resonance as 101:100 is simply unrealistic. The strongest resonance is generally 3:2. -- Kheider (talk) 20:46, 6 February 2015 (UTC)
I chose that example because of its manifest unrealism. Yet the current text in the pop-up says “proportional to the difference between the numerator and denominator”, which I don’t believe, because it suggests that 101:100 would be strong. I’m not an expert, so might be wrong, but I hope that the experts can see that the current text is at least one of unclear and misleading. JDAWiseman (talk) 22:07, 6 February 2015 (UTC)
And I’m surprised that 3:2 is stronger than 2:1 or 1:1. Please, is their intuitive reasoning why this is so? JDAWiseman (talk) 23:35, 6 February 2015 (UTC)
I hate semantics. It might be more accurate to write the 3:2 resonance captures more objects and is generally the most populated *if additional bodies are not acting on a 3-body system*. It is rare to find a real resonance weaker than 5:17. Something complex like 101:100 will not happen in the real world because of the n-body problem. The note can always be re-worded to mention resonances like 1:1, 2:1, and 3:2 are much stronger. -- Kheider (talk) 00:24, 7 February 2015 (UTC)
There's also the dynamic effect of these resonances. Pluto in 3:2 may have been carried along as Neptune migrated outward, but presumably a 7:12 resonance would not have been able to do that with Haumea, right? — kwami (talk) 00:56, 7 February 2015 (UTC)
Thank you. The comments here make perfect sense (at least in that they concur with my slightly-informed prejudices). Splendid.
But they clash with the wording in the article. Clearly the strength of a resonance cannot be numerator minus denominator, as that would have 101:100 ≈ 3:2, even though the former is too weak to be observed.
Hence expert re-wording of the article is needed. JDAWiseman (talk) 09:11, 7 February 2015 (UTC)
Previously doing work on resonances, I had made a calculation for the probability of a resonance. Although there are various versions of complexity, they all essentially follow the same ideas. This one I've found to be the simplest and most reliable:
Equation 1 (simplest):
where S is the strength of the resonance, N is the resonance with a larger value, and n is the resonance with a smaller value. A lower value is a weaker resonance.
1:2 = 0.33333333
2:3 = 0.14285714
101:100 = 0.00009900
5:17 = 0.00934579
exoplanetaryscience (talk) 22:19, 7 February 2015 (UTC)
Reciprocal of product plus difference makes lots of sense. But the pop-up title tag in the article fails to mention the bit about the product, saying just reciprocal difference. Please could the article match your comment.
And, FYI, your ordering is 1:1, 2:1, 3:1, 3:2 = 4:1, 5:1, 6:1, 4:3 = 5:2 = 7:1, 8:1, 5:3 = 9:1, 7:2 = 10:1, 5:4 = 11:1, 12:1, 7:3 = 9:2 = 13:1, 14:1, 8:3 = 15:1, 6:5 = 7:4 = 11:2 = 16:1, 17:1, 18:1, 7:5 = 10:3 = 13:2 = 19:1, 20:1, 9:4 = 11:3 = 21:1, 7:6 = 8:5 = 15:2 = 22:1, 23:1, 24:1, 9:5 = 13:3 = 17:2 = 25:1, 11:4 = 26:1, 14:3 = 27:1, 19:2 = 28:1, 8:7 = 29:1, 30:1, 11:5 = 13:4 = 16:3 = 21:2 = 31:1, 32:1, 9:7 = 17:3 = 33:1, 12:5 = 23:2 = 34:1, 35:1, 11:6 = 15:4 = 36:1, 9:8 = 10:7 = 13:5 = 19:3 = 25:2 = 37:1, 38:1, 20:3 = 39:1, 14:5 = 27:2 = 40:1, 11:7 = 17:4 = 41:1, 42:1, 13:6 = 22:3 = 29:2 = 43:1, 44:1, 12:7 = 23:3 = 45:1. JDAWiseman (talk) 22:50, 7 February 2015 (UTC)
The ‘nb 3’ is clearly wrong, so, I’ve removed it and slightly changed the sentence which contained it. JDAWiseman (talk) 16:31, 14 February 2015 (UTC)
User:AnomieBOT has added back the wrong reference. I lack the confidence to argue with a machine, so am leaving it wrong. JDAWiseman (talk) 19:33, 14 February 2015 (UTC)
A more complicated version of the previous equation also takes into account difference between true resonance compared to the length of the resonance:
Equation 2 (more complicated):
Firstly, the period of a body in orbit around the Sun in years is determined by the square root of the semimajor axis in AU cubed. AKA p=√(a^3). Although typically in AU and years, it can theoretically be applied to any orbit; if the inputted a value is in terms other than AU, then the result of the equation would be in multiples of the time it takes a body with the semimajor axis reciprocal(A) to make an orbit around the Sun. I did a bad job of explaining that.
Next, assuming the period of both bodies are known in the suggested resonance, divide the longer period by the shorter period, and find the least common multiple over one to at least a decimal place or two. The given value is the likely resonance between the bodies. However the further it is from a full number, the less likely it is.
To calculate the vicinity to the resonance, multiply the orbit of the primary body by the resonance ratio in the format Primary:resonating (such as a 7:12 to Neptune being 164.791*(12/7)=~282.5) Then find the difference of the resonating body (Haumea) to the true resonance; 284.12-282.50=1.62. Divide 284.12 by 1.62; 175.38. how many orbits it takes Haumea to become a full orbit behind a 7:12 resonance. Multiply 175.38 by 284.12 and you get ~49830 years for Haumea to become a full orbit behind a 7:12 resonance. Find the reciprocal of 49830; 0.00002007, and multiply it by 284.12-0.005702. This means every orbit, Haumea becomes one 0.005702 orbits behind where it should be in resonance to Neptune. Yes there are simpler ways to do this (like finding the reciprocal of 175.38), but no I didn't do them because I wanted to demonstrate what the different values meant and their relation to each other.
Finally take the rate of change per orbit (0.005702) and subtract it from one (0.99430) and you multiply that by 1/((N*n)+(N-n)). This gives Haumea, which would otherwise have the value 0.011236, now has the value 0.011172.
OK. We need a source on this subject that can be quoted, to correct the current error. Please recommend one. JDAWiseman (talk) 23:53, 14 February 2015 (UTC)
The exact reason I had hesitated was because of the fact that this is all original research of mine. Although based on clear, simple ideas, it still ventures far enough into the territory original research to require a reliable reference or similar material. exoplanetaryscience (talk) 17:15, 15 February 2015 (UTC)
Ah. That makes it more interesting. Please can you, exoplanetaryscience, take charge. The article is currently wrong. Please make it right. As the article as about Haumea, rather than about resonances, this could be very concise. Indeed, my attempted edit, reverted by a bot, deleted the note and softened the description of the resonance to ‘weak’ (does ‘fifth-order’ add anything useful?). — Preceding unsigned comment added by JDAWiseman (talkcontribs) 11:14, 16 February 2015 (UTC)
That is now accurate. Thank you. I’m not a Wikipedia expert, so don’t know, but I expect that linking to a user’s talk page is officially discouraged. JDAWiseman (talk) 07:15, 17 February 2015 (UTC)