🔗 Klemperer rosette

🔗 Physics

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 (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).

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. While all Klemperer rosettes are vulnerable to destabilization, the hexagonal rosette has extra stability because the "planets" sit in each other's L4 and L5 Lagrangian points.