Talk:420356 Praamzius

Orbit section
The language used is very confusing, in the part talking about how it relates to Neptune. I'd try to work it out but I've got somewhere to be in a few minutes and am about to leave. However the maths doesn't seem to work anyway - the orbital periods are very close to 1.7-to-1 (much closer than the 1.667-to-1 of 3:5), or 17:10. I'm not really sure what the 160 Neptune Orbits bit is about, seeing as 5 would be about 824 years, and 160 would be 26368 years, neither of which seem to relate to the other stated figures. (160/5 * 3 = 96, of course, which would be an exact resonance... but so would be 20 and 12, or just 5 and 3, so what is the significance? Never mind that the resonant point, over that length of time, could be precessing/librating somewhat).

FWIW 17:10 also comes out as 272:160... anyway still no real idea and I've really gotta go. If anyone else can figure it out properly...

NB an even closer relationship is 22:13, and there seem to be a few other TNOs that have similarly complex resonance ratios... 146.199.0.251 (talk) 10:42, 26 September 2017 (UTC)

...ok, back, let's examine. Dividing their orbital periods in terran solar days into each other gives a ratio of 1.698182(...), or 1/0.588865(...)

Multiplying those out:

2x 1.698... = 3.396...; 3x = 5.09455...; 4x = 6.7927...; 5x = 8.4909...; 6x = 10.189...; 7x = 11.887...; 8x = 13.585...; 9x = 15.284...; 10x = 16.982...; 11x = 18.6800...; 12x = 20.378...; 13x = 22.0764...; 20x = 33.964...; 23x = 39.0582...; 33x = 56.04001...; 43x = 73.0218...; 53x = 90.003656...; 159x = 270.01097... and 160x = 271.709...

So 3:5 is a moderately good estimate so long as you don't mind the actual conjunction point shifting around by 34 degrees each time, or completing approx 2 rotations for each 21 alignments (of course, not really a true resonance if they don't meet at a nearly identical place in both their orbits every X times round)... 10:17 actually a good bit closer, though it still drifts back about 6.48 degrees each time (completing about 9 backward rotations of the meeting point every 500 meetings), which could just mean an as-yet poorly documented libration either side of the closest meeting point(s). 13:22, 20:34, 23:39, 33:50 and 43:73 are better than 3:5 but worse than 10:17.

Finally 53:90 is about as precise as I can be bothered counting for... 1.316 degrees of drift each time they come together, every 90 Neptune or 53 Praamzius circuits; ie it takes 273.52 repeats of such with no other perturbation (eg libration) to complete the full precessive drift back to roughly where it was originally found...

So draw your conclusions accodingly. Having to stop again because I'm essentailly about to collacsteeeeeeeeee *wakes up with a start, deletes LOTS of e's* ... yeah, its an exercise in ... in... soething, i dunno. goodnight. 146.199.0.251 (talk) 03:17, 27 September 2017 (UTC)

...jeez. OK. New rule, don't doze and wiki.

Anyhow, let's look at that 160 orbits thing, "or 26500 years".

1 Neptunian year = 60182 terran days (and 1 Praamziusian year = 102200 terran days). So 160 of them = 9629120 TD, or approx 26363 terran solar years (plus about one month). In which time, Praamzius makes 94.218 orbits. So, uh... whaaaaat?

Alright, I might have been a bit too sleepy to be trusted with a keyboard last night, but I now suspect whoever wrote that was drunk.

Let's figure a few other things; 26500 terran years = approx 160.83 Neptunian years (94.71 Praamz). 160 Praamz years = 271.71 Neptunian = 44769.3 Terran. 160 Terran years = roughly 58440 days (depending on your exact epoch), 0.971 Neptunian years, 0.572 Praamziusian.

Yeah, at this point I'm totally stuffed for figuring it out. All I can tell is that 102200 is close enough to 90/53rds of 60182 that small perturbations, precession/libration, etc may account for the remaining difference, and it would require an orbit only slightly wider than the 3:5 resonance. Though, of course, it would also require 53 Neptunian orbits for complete such a cycle, which although not quite 26500 terran years, is still a little off 8733. A pretty long time. But then, that's a tiny fraction of the billions of years that the system has been spinning, so on a cosmic, deep time scale, it's still reasonable to expect that they might have done this dance a great many times over already and be entirely stable in it. I doubt our measurements so far, of an object that's so distant it was discovered only in the last 15 years or so (in which time it's completed only 1/19th of an orbit), have a small enough uncertainty parameter to exclude either some exotic bit of variable timing (gliding between 90/54 ie 5/3, and 90/50 ie 9/5, and currently halfway between the two, for example?), or just a highly coincidental but entirely non-resonant orbit... or even having been in a 5:3 relationship until recently but having been somehow slightly drawn out of it, and maybe on course to settle back in over the coming centuries.

(UC = 3, so from about 20 asec to 1.4 amin per decade... orbit is about 28 decades, so if we say that's anything upto 30 amin, ie half a degree per orbit = 1/720th variation... 5/720th = 1/144th = 5 +- 0.006944... less than a tenth of the stated ratio, fair enough; 90/720th = 0.125, however, more than 40x that variation from an exact integer relationship; 73/720 = 0.10139, nearly 5x the difference there; 56/720 = 0.0778, still comfortably enough to allow 33:56 exact... 39/720 = 0.05417... if the uncertainty was a full 1.399999 amin then that might just work, although it would be a pretty curious outlier. 34/720 = 0.04722, more than enough to allow 20:34 (vs 20:33.964), aka or 10:17, which is comparitively pretty normal. Or, in other words, don't take the stated average as absolutely correct and base too many wild arguments off it, when error bars allow for a situation that's much more normal to exist)

Anyway, aside from maybe a quick attempt to condense that sentiment on the main page, I figure I may as well withdraw at this point. Good luck to anyone who tries to clean it up for real. 146.199.0.251 (talk) 14:23, 27 September 2017 (UTC)

...

New idea: let's get Keplerian. IE, assume the two objects' own masses and their own interactions are of no consequence, and just figure out the relationship through their orbital distances (as per semi-major axes) around the sun. Any tiny effect Neptune might have on the sun would essentially not exist from the viewpoint of something as small as Praamzius as its frame of reference is essentially fixed to the sun anyway, so any way it may be perturbed by Neptune would be imperceptible. The interactions between the two planets themselves should only serve to drag their orbital relationship away from non-resonant Keplerism and into a more geometrically complex but deceptively simple-looking orbital resonance.

Anyway... when you break the equations down, the heart of the matter is that for nominally "small" bodies (which they both are vs Sol), the difference in orbital period is equal to the square root of the cube of their semi-major axis. Which I think means raise to the power of 1.5? In any case, that gives a slightly different figure for the ratio of 1.693446 (raising questions about the accuracy of the stated orbital radius and/or period figures, and if they were entered by the same person at the same time from the same set of data or not - there seems to be a definite trend amongst much of the minor planet data on wikipedia to more or less pull it out of one's ass, instead of picking a standard source, sticking with it, making sure that it gets copied over correctly, and moreover making clear any issues with said data or source), and it produces a whole different set of potential integer relationships (fwiw, 53 = 89.75something here).

To whit: 2 : 3.3869 --- 3 : 5.0803 --- 4 : 6.7738 --- 5 : 8.4672 --- 7 : 11.8541 --- 10 : 16.9345 --- 13 : 22.0148 --- 16 : 27.0951 --- 23 : 38.9493 --- 36 : 60.9641 --- 49 : 82.9789 --- 59 : 99.9133 --- 62 : 104.9937 --- 75 : 127.0085

So, 3:5 gets closer (as will have done 6:10, etc), though 10:17 is further apart and no longer be compatible with the stated uncertainty coefficient; the error on 13:22 is reduced sevenfold (to the point where 22/720 = 0.0306 is now sufficient to allow it to work even with closer to 0.5 than 1.0 arcmin of drift per decade, instead of being completely unrealistic), and 16:27 wasn't even worth mentioning before (though it does turn out to still be too far adrift to be realistic). 23:39 has actually flipped, with the calculated figure being too small instead of too large (and juuuust inside the uncertainty window), suggesting it's a strong candidate for being the actual relationship, as will have 33:56 but even moreso. Never noted down 36, 49, 59 etc before but they will all likely have flipped and are themselves strong contenders (61/720 means 0.4 amin uncertainty would do), though the fraction is of course getting ever more complex.

So on those twin bases, it could actually be 10:17 (not 3:5 unless Neptune has a stronger gravitational effect on the minor partner than first thought), 13:22, 23:39 most easily of all, 33:56 or 36:61... (predicting a little over 10,000 years ahead, which is probably as far as we can really consider in any way "safe").

Right I really am going to stop now unless something extra weird leaps out. 146.199.0.251 (talk) 15:21, 27 September 2017 (UTC)

--

Postscript: OK, I've given it my best shot. I also now know a lot more about space than I did 24 hours ago. Hopefully that'll do, but if it still seems insufficient, fix it further please :) 146.199.0.251 (talk) 20:17, 27 September 2017 (UTC)

ah, never mind
The data in the sidebar (and some of the main text) is out of date anyway - one of the existing links to the MPC goes to a page with much better quality info ... orbital period, uncertainty parameter, number of observations and the period they cover all that... rather different. Will update those and then see how the new situation looks. 146.199.0.251 (talk) 22:40, 27 September 2017 (UTC)

......i'm getting annoyed now. If you look at the MPC and the JPL pages, both of them appear to use almost exactly the same data (although the start/end dates are the same, JPL claims an observation period 2 days longer than MPC, and with one additional observation - 205 vs 204 - inserted from who-knows-where), but the figures they've pulled out of them are entirely different and indeed the basis for my reworking, as it looked like the MPC data was more up-to-date. How the hell do you take the same planetary observation data and end up with significantly different results like that? As in a good six months adrift after 280 years, or about 0.35%... seems pretty bad. Thing is, who's got it right and who's cocked up?

Partly because I've gone and done all the graft already, and partly because the twin aspects of a) it's their primary job and one hopes they wouldn't get it wrong, seeing as they use the same algorithms to predict the tracks of potentially hazardous NEOs, b) their site is rather more slick, up to date (looks and works like it was made in the 2010s not 1990s), functional and provides a better range of data including all the known observations, I'm going to side with the MPC here. The JPL maybe should stick to dealing with jet propulsion (and producing the occasional xkcd). 146.199.0.251 (talk) 01:34, 28 September 2017 (UTC)

.........

now, here's interesting. if I use the semi major axis as the basis for comparison again, instead of the orbital period in days (which is given to fewer sig figs), with the "new" mpc data... 42.8883361AU divided by 30.110387AU, cubed, and square rooted, gives... 1.6999427. That looks rather convenient doesn't it?

It's still not close enough for 3:5 to be the case (as the relationship comes out to 3:5.0998 with no more than +- 0.0212 uncertainty after that timespan), but 10:17 works pretty well; the cumulative uncertainty after 17 Pramz orbits is between 0.0162 and 0.0722 orbits (approx 5.83 to 25.99 degrees), which given that 10 Neptune orbits comes out as 16.9994 for Praamzius is far more than ample leeway for that to come good without even considering the effects of libration. And whilst it would be one of the more extreme resonant relationships still (6:11 or 7:12 are otherwise more the max), it's only slightly further up the scale, rather than eg. 53:90. In fact, it's decidedly too "good" for U=2 to make any kind of threat to it; with U=1 (1.0 to 4.4 arcsec/decade), the range of likely variance is 0.0037 to 0.0162 orbits (1.33 to 5.83 degrees... after 4775 years), still not excluding the possibility, and in fact even with U=0 ("no more than 1.0 arcsec/decade", so <0.0037 orbits or <1.33 degrees) there's no clear reason to not suggest it.

With a small amount of libration on top, it would be the most likely option out of everything, would it not?

Odd, I didn't do anything to engineer it this way, even though it took a lot of time arriving at this point. It was all just natural progression through digging out the more up to date (?) information and looking at the maths a different way. In this case, considering the problem of orbital period as a pure derivative of the semi major axis. Quite how different figures have been arrived at for it, I'm not entirely sure, but then depending where you look on Wikipedia, even Neptune itself orbits at either 30.11 or 30.06 AU, and that would also be enough to significantly affect the relationship between them. Seems we're continually fumbling in the dark somewhat even whilst some very brainy folks up on the side of mountains are using ever more sophisticated methods to improve the primary source data that's then stomped into an unrecognisable mess by the time it gets out the other end of repeated cycles of interpretation, lazy rounding-off and forever-delayed updates. 146.199.0.251 (talk) 02:14, 28 September 2017 (UTC)

The Minor Planet Center and JPL SBDB will give you somewhat different numbers if they are using a different epoch (date) as orbits change as a result of ongoing perturbations. Both solutions are just a generic 2-body solution that is sensitive to little things like the current position of Jupiter, etc. To really know if this object is in resonance with Neptune you would need to perform an integration of numerous clones of this object for 10 million years or so. -- Kheider (talk) 07:29, 13 February 2018 (UTC)