Flower constellation

Flower Constellations are special satellite constellations whose satellites follow the same 3-dimensional space track with respect to the assigned rotating reference frame. More information can be found in (1)

Flower Constellations are built using compatible (or resonant) orbits. The orbit compatibility, with respect to a reference frame rotating with angular velocity w, is ruled by the relationship

where T is the orbit period, n is the orbit mean motion, and Np and Nd are two positive integers characterizing the compatibility mechanism. In the Flower Constellations theory, Np and Nd have been identified as the Number of Petals and the Number of Days. In fact, when the rotating reference frame is chosen to be the Earth-Centered Earth-Fixed (ECEF) frame, then Nd really represents the number of days. The Number of Petals, Np, that actually represent the number of orbit revolutions, finds its origin because of the petal-like shape of the relative trajectory.

Flower constellation 3 petals, 1 day, n/d = 3/5. Relative and inertial orbit views

The Constellation Wizard allows to define a Flower constellation:

Petals (Np)	Number of petals in the constellation. They refer to the petal-like shape of the relative orbit paths.
Days (Nd)	Number of days in which the constellation performs a complete cycle
Phase numerator	Phase numerator according to flower constellation theory
Phase denominator	Phase denominator according to flower constellation theory
Phase step	Phase step according to flower constellation theory
Height at perigee	Height of perigee of each satellite's orbit
Eccentricity	Eccentricity for all the satellites in the constellation.
Inclination	Inclination for all the satellites in the constellation.
Arg.Perigee	Argument of perigee for all satellites in the constellation
Epoch	common epoch time for all the constellation satellites

(1) "The Flower Constellation Set and its Possible Applications", Mortari et al., 2004