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)