Talk:Klemperer rosette

Are Klemperer Rosettes stable?

Maybe it's obvious from context, but it doesn't say anywhere in the article that Klemperer rosettes are stable. Also, why are they stable, when ordinary equal-mass rosettes are not? Is there a Copernicus out there that could provide an elementary explanation? --Chetvorno 09:53, 24 August 2007 (UTC)

• In general, they could not be stable. Consider the illustrated Rosette, and let the mass of the small planets go to 0; the configuration will reduce to an equilateral triangle. As described in the second section, those are not stable, and thus a general Rosette can not be stable. Majromax (talk) 22:29, 10 April 2008 (UTC)

I just skimmed Klemperer's original article; he states:

While the rosette configurations here studied are capable of revolving as a whole in dynamic equilibrium, they are not stable against random perturbations.

I've removed the wording that wrongly suggests stability, but we should probably have an explicit statement of non-stability in the article itself. Currently there's discussion of this in the section about Niven's misuse, but maybe that should be combined with the identical result for actual rosettes, perhaps in a new section with the title "Stability"? What do y'all think? Joule36e5 (talk) 07:52, 12 December 2008 (UTC)

Why is it called Klemperer's? Who was Klemperer? —Preceding unsigned comment added by 74.70.144.72 (talk) 02:38, 2 February 2008 (UTC)

Puppeteer Worlds

Ringworld suggests, and Fleet of Worlds and Juggler of Worlds confirm, that the Puppeteer worlds have engines and steering systems called an "outsider drive" the rosette is artificially stable. That and a number of other magical devices. It's fiction, folks. —Preceding unsigned comment added by 70.113.80.228 (talk) 07:28, 7 October 2008 (UTC)

Magical? —Preceding unsigned comment added by 96.50.86.207 (talk) 00:54, 19 October 2010 (UTC)

AKA "sufficiently advanced". 198.70.193.2 (talk) 18:46, 2 March 2011 (UTC)

TFA suggests that the "safety conscious" Puppeteers would have opted for the (very arguably) more stable hexagonal configuration over the pentagonal configuration. If you actually read the books, you'll discover that the Puppeteers encounter humanity while in the process of bring a new, sixth, planet into the system, where it will go under the name of "Nature Preserve Five" (plus "Hearth" itself). Some hundreds of years later, shortly before the "Core Explosion" is discovered, the Puppeteer's human colony rebel and take charge of the "Outsider drive" for "Nature Preserve ..." - is it 2 or 3? I forget. So when, another century or so later Louis Wu arrives early in "Ringworld", the Fleet is pentahedral. Niven & Lerner did do their retconning properly. AKarley (talk) 23:08, 13 August 2023 (UTC)

other exotic orbits

By the way, do we have an article for (e.g.) the figure-eight orbit of three bodies? —Tamfang (talk) 01:58, 23 March 2010 (UTC)

unstable at what timescale?

Well, planetary systems such as are own aren't perfectly stable; orbiting bodies can be ejected. So, the real question is, what is the timescale of the instability? Say, e.g. 5 jupiter-mass planets located at about jupiter's orbit (with no central sun). Or say 3 solar masses located 5-10 light-hours apart (or e.g. 50 au) ... ? 99.153.64.179 (talk) 20:23, 8 January 2012 (UTC)

The Solar System's planetary orbits are stable, at least for several billion years (from the LHB to the foreseeable future). The Klemperer rosette, being an unstable equilibrium, would start to "fall apart" instantly, like a (perfect) die landing on its edge. --Roentgenium111 (talk) 20:12, 24 June 2012 (UTC)

Bullshit. Its not like the masses all fly off to infinity in a nanosecond. I figure the configuration sticks together for at least one orbital period, maybe several, maybe a dozen? For Jupiter masses, orbital periods are years, so the configuration sticks together at least that long ... 99.153.64.179 (talk) 02:52, 26 September 2012 (UTC)

Both responses are unhelpful. There's a characteristic time over which errors in position are magnified by a factor of e. Not that I know how to find that value! —Tamfang (talk) 07:59, 3 October 2012 (UTC)

In fact, there are several such times, since you are talking about the Floquet spectrum of a linearisation about the ideal orbit. I meant the shortest of those, you say, but even that is not all that informative. The regular pattern begins to break up immediately, within one revolution. Then it is just a matter of taste and esthetic judgement before you feel that the pretty initial configuration has been completely spoiled, as it just gradually gets messier, more chaotic. A bit like asking at which point the egg is truly scrambled. 2A01:CB0C:CD:D800:E05A:731F:FF49:B17F (talk) 07:25, 20 July 2022 (UTC)

Playing with a gravity simulator, setting up the initial masses, positions and vectors numerically rather than graphically (which was limited to 6 figures of precision) I couldn't get the bodies to complete two orbits of the centre of mass. I believe NASA don't bother going beyond the 15th significant digit, which I guess might get you to three or even 4 orbital periods. (Self : performs the Puppeteer "doom pose" of tucking my heads under my legs and collapsing to the floor.) For my next trick, I'll work out what gravity gradient Niven considers to be a "singularity" for the Outsider's hyperdrive. Somehow, I suspect that Jinx isn't going to like the results. AKarley (talk) 23:18, 13 August 2023 (UTC)

The short-form reason

First, "short-form reason" is not English, although perhaps it should be (is this a literal calque from an Asian language?). Second, the "reason" given is just a description of instability. The longer reason given is fine, although it just comes down to gravity gets stronger the closer you are. 2A01:CB0C:CD:D800:E05A:731F:FF49:B17F (talk) 07:18, 20 July 2022 (UTC)