Synodic and relative Flower Constellations with applications to planetary explorations

This paper introduces the theory of the Synodic Flower Constellations and of the Relative Flower Constellations, which constitute two novel and alternative methodologies to design Flower Constellations synchronized with the motion of two celestial objects (e.g., two planets) orbiting about the same gravitational mass. These two "objects" can also be natural or artificial satellites (e.g., moons, spacecraft) orbiting about a planet and one of these two objects can also be the central body itself. In particular, a Synodic Flower Constellation is made with orbits that are compatible with a reference frame rotating with a period suitably derived from the synodic period of the two objects, while a Relative Flower Constellation is made of orbits that are, simultaneously, compatible with both the objects rotating reference frames. The latter, however, can be achieved under a very particular condition that is here approximated. The resulting dynamics of these constellations are synchronized with the dynamics of the geometrical positions of the two objects. Potential applications can be to design a Space Network Architecture for planetary communications, to design Solar Global Navigation System, to design small constellations for Surveillance and reconnaissance and well as for space and Earth science.