Design of flower constellations using necklaces

This paper introduces a new approach in the design of optimal satellite constellations comprising few satellites and characterized by symmetric distribution. Typical examples are missions requiring persistent observation of sites or regions for intelligence or science. To minimize the number of satellites, the mathematical necklace theory is applied to the two-dimensional Lattice Flower Constellation framework. The necklace theory identifies in the phasing space all satellite subsets characterized by symmetric distributions. Mathematically, these subsets are parameterized by necklaces, identifying the actual satellite locations in the first orbital plane and a shifting parameter governing phasing between subsequent orbital planes. This article specifically targets the emerging importance of small satellite formations and constellations.