This paper introduces a methodology to design a set of satellite constellations, called the Flower Constellations, which is generally characterized by repeatable ground tracks and a suitable phasing mechanism. A Flower Constellation, which can be complete or restricted, is identified by a number of parameters. Three are integer parameters: the number of petals (N p), the number of sidereal days to repeat the ground track (N d), and the number of satellites (N s). The others include the phasing parameters and three orbit parameters equal for all satellites: the argument of perigee (), the orbit inclination (i), and the perigee altitude (h p). Flower Constellations present beautiful and interesting dynamical features that allow us to explore a wide range of potential applications that include: telecommunications, Earth and deep space observation, global positioning systems, distributed space systems, and new kind of formation flying schemes. A Flower Constellation can be reoriented arbitrarily; however, the repeating ground track property is lost. To demonstrate their potential, some specific Flower Constellations are briefly described and discussed.
