Klemperer rosette

A Klemperer rosette is a gravitational system of heavier and lighter bodies orbiting in a regular repeating pattern around a common barycenter. It was first described by W. B. Klemperer in 1962.

Klemperer described the system as follows:

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. Klemperer also mentioned octagonal and rhombic rosettes. While all Klemperer rosettes are vulnerable to destabilization (read below), the hexagonal rosette (as in the adjacent diagram) should have extra stability due to the 'planets' sitting in each other's L4 and L5 Lagrangian points.

The term "Klemperer rosette" (often misspelled "Kemplerer rosette") is often used to mean a 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 equilibrium systems before introducing the actual rosettes.

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 (possibly intentional) misspelling (and misuse) is one possible source of this confusion. Another is the similarity between Klemperer's name and that of Johannes Kepler, who described certain laws of planetary motion in the 17th century. It is notable that these fictional planets were maintained in position by large engines in addition to gravitational force.

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