motariabstract

Abstract: The

Flower Constellations (FCs) constitute an infinite set of satellite constellations characterized by axial symmetric and periodic dynamics. They have been discovered on the way to generalize some existing satellite constellations.

The dynamics of a FC identify a set of implicit rotating reference frames on which the satellites follow the same closed-loop relative trajectory. In particular, when one of these rotating reference frames is Earth-Centered Earth-Fixed, then the orbits become compatible and, consequently, the projection of the relative trajectory on the planet forms a repeating ground track. These relative trajectories constitute a family of continuous, axial symmetric, closed-loop real curves.

For an assigned number of satellites, the design parameters of a FC are five independent integers. Two parameters establish the orbit period while the other three distribute the satellites into an upper bounded number of "admissible" locations. However, the resulting same satellite distribution can be obtained with different values of the five design parameters. Therefore, a given FC does not uniquely identify the five design parameters: some of the relationships establishing the equivalency of two FCs are still unknown.

Another important consequences of the FC theory is that, for a particular set of the six integer parameters, the satellite distribution highlights the existence of "Secondary Paths". These "Secondary Paths", which exhibit many beautiful and intricate dynamics and mysterious properties, are still far from being completely understood, and their prediction appears to be linked to real algebraic geometry.

The set of equations ruling the FC equivalency and the set of equations ruling the "Secondary Paths", both needed to Classify the FCs, are looking for help from the Math community.