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)