page_title: Klemperer rosette
section_title: Misuse and misspelling
hierarchical_section_title: Klemperer rosette / Misuse and misspelling
context_page_description: 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, and is a special case of a central configuration.
  Klemperer described the system as follows:
  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 kinds, one heavier than the other, but all of each set of equal mass, are placed at the corners of two interdigitating regular polygons so that the lighter and heavier ones alternate.
  The simplest rosette would be a series of four alternating heavier and lighter bodies, 90 degrees from one another, in a rhombic configuration [Heavy, Light, Heavy, Light], where the two larger bodies have the same mass, and likewise the two smaller bodies have the same mass. The number of "mass types" can be increased, so long as the arrangement pattern is cyclic: 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.
context_section_description: 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. It is notable that these fictional planets were maintained in position by large engines in addition to gravitational force. Another is the similarity between Klemperer's name and that of Johannes Kepler, who described certain laws of planetary motion in the 17th century.
caption: A pentagonal rosette as described in Larry Niven's novel Ringworld.