Klemperer rosette

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A Klemperer rosette is a gravitational system of a number of heavier and lighter bodies, set out in a regular repeating pattern around a common barycenter, around which they all orbit. The simplest rosette would be series of four alternating heavier and lighter bodies, 90 degrees from one another, in a rhombic configuration [Heavy, Light, Heavy, Light], where the two heavier masses weigh the same, and likewise the two lighter masses weigh the same. The number of "mass types" can be increased, so long as the arrangement pattern is cylic: e.g. [ 1,2,3 ... 1,2,3 ], [ 1,2,3,4,5 ... 1,2,3,4,5 ], [ 1,2,3,3,2,1 ... 1,2,3,3,2,1 ] etc.

"Such symmetry is also possessed by a peculiar family of geometrical configurations which may be described as 'rosettes'. In these an even number of 'planets' of two (or more) kinds, one (or some) heavier than the other, but all of each set of equal mass, are placed at the corners of two (or more) interdigitating regular polygons so that the lighter and heavier ones alternate (or follow each other in a cyclic manner)" - Klemperer

A simple hexagonal rosette with two kinds of bodies. Klemperer also makes mention of octagonal and rhombic rosettes.

They were first described by W. B. Klemperer in 1962.^[1]

[edit] Misuse and misspelling

The term "Klemperer rosette" (often mis-spelled "Kemplerer rosette") is often used to mean a stable configuration of three or more equal masses, set at the points of an equilateral polygon and given an equal angular velocity about their center of mass.

Klemperer does indeed mention this configuration at the start of his article, but only as an already known set of stable systems before introducing the actual rosettes.

A pentagonal rosette as described in Larry Niven's novel Ringworld.

In Larry Niven's novel Ringworld, the Puppeteers' "Fleet of Worlds" is arranged in such a configuration (5 planets spaced at the points of a pentagon) which Niven calls a "Kemplerer rosette"; this mis-spelling (and misuse) is probably the main source of confusion. Simulations of this system raise questions about its stability,^[2] but unless they incorporate the motion of the Fleet away from the Core Explosion, discussions as to whether Niven's worlds need the input of further navigational tweaks is rather moot. This modelling is not powerfully relevant to a discussion of Klemperer rosettes as gravitational systems.