Talk:Jacobi ellipsoid

Which axis is which?
I searched up this page hoping to find some kind of guide as to which axis each of a, b and c refer to, and I've come up empty. Presumably one of them is the polar axis and therefore identical to z, but there's nothing here which tells us which. If it's some kind of fundamental mathematical truth, well, it's been about twenty years since I last took a maths class which involved any geometry of that kind, but even then I don't think I was taught it, so some kind of reference / link to those fundamentals would be appreciated.

(Why? Because a particular asteroid was described as having those three axes exhibiting a certain size relationship, caused by its rapid spin - and whilst I feel fairly confident that we can count out a, as that's given as the longest, which is unlikely if the body has been deformed by said spinning, it's not a given which of b or c it would be (if it's sufficiently deformed, the shorter equatorial axis may well be smaller than the polar one, especially if it formed as a contact binary?), and the ranges for the aspect ratios between each of those and a overlap somewhat. On top of that, I'm trying to work out which of three scenarios for the truth of an anomalous occultation event are the most likely (actually a binary / smaller than expected primary with large moon, very irregular shape, or one of two different reporting stations giving anomalous results was actually lying or gravely mistaken), and that sort of hinges on whether we take the b or c size range as the polar one...) 146.199.60.87 (talk) 23:10, 11 August 2019 (UTC)


 * Derp. It's funny how a moment of separation then return leads to a revelation. Somehow I bleeped straight over the first line of the figure caption that says "equatorial (a, b) and polar (c)". Never mind. 146.199.60.87 (talk) 23:12, 11 August 2019 (UTC)


 * All the quantities referred to in the body of the text ought to have been defined there. Now they are.  Thank you for taking the trouble to point out the deficiency. catslash (talk) 00:55, 14 August 2019 (UTC)