Satellite constellations design is an important and often intriguing subject for space mission planners. The single overriding concern is cost: cost to launch, cost to construct the satellites, cost to maintain them in orbit, etc. The goal then is to find a constellation design that achieves the mission objectives but also minimizes the number of satellites or places them into an orbit that is more cost effective to launch into and maintain, for instance.

Currently, there are a number of constellation concepts that allow one to generate a particular kind of constellation design. Walker constellations, probably the most notable, are created from sets of circular orbits with a given number of satellites in each orbit plane. This type of constellation is used in the current GPS system and in the Galileo constellation proposed by the European Union and the European Space Agency. More closely linked to the Flower Constellation Set are Multistationary Inclined Orbit Constellations such as JOCOS, LOOPUS, and COBRA. These particular constellations use highly eccentric orbits with repeating ground tracks to maximize coverage of the Earth's surface and improve accessibility for high latitude regions versus geostationary satellites for telecommunications applications. A more detailed background on these constellation types can be found in our recent conference paper. The theory of Flower Constellations is a natural consequence of the theory of compatible orbits (also called resonant or repeating ground track). The Flower Constellations have been developed at Texas A&M University by Prof. Mortari and two of his former PhD students, Matthew P. Wilkins amd Christian Bruccoleri. The orginal conception was derived while trying to generalize the 4-satellite constellation called "Sistema Quadrifoglio" (four-leave system) dating back to 1967 by Prof. Luigi Broglio on the San Marco Project.

The Flower Constellation Set

The Flower Constellation Set is an infinite set of possible constellation designs based upon a particular formulation. This set of constellations was originally conceived
of as a constellation of satellites that all have the same repeating ground track. However, what we discovered is that these constellations can be arbitrarily oriented. For the special case when the axis of symmetry of the constellation is coincident with the spin axis of the Earth, then the \FC\ will have the property that all the satellite ground tracks will be identical. Generally, all the orbits in a given Flower Constellation:
-Have identical orbit shape: anomalistic period, argument of perigee, height of perigee, and inclination.

-Have equally displaced node lines along the equatorial plane for each satellite in a complete Flower Constellation.

-Restricted or incomplete Flower Constellations have orbits with RAANs that are integer multiples ofeach other.

Because the resulting orbit path in the relative frame resembles the outlines of a flower petal, this set of constellations is called the Flower Constellation Set.

A phasing rule that couples the right ascension of the ascending node (RAAN) angle to the mean anomaly (MA) angle is the cornerstone of our formulation. The phasing rule that we have developed is extremely general in that you can select any number of satellites and any desired phasing arrangement based upon a set of integer parameters. Overall, there are 8 parameters that control the overall design of a given Flower Constellation: Np, the number of petals; Nd, the number of days for a given satellite to repeat its groundtrack; Ns, the number of satellites; Fn, the phasing fraction numerator; Fd, the phasing fraction denominator; and three orbit parameters, the argument of perigee, the orbit inclination, and the height of perigee. Np and Nd, along with the orbit parameters, control the shape of the constellation while Fn and Fd together control the phasing. While the choice of values for these parameters are generally independent and solely up to the designer, they have some interplay that affects the overall look of the constellation. This interplay is discussed in the JLJ conference paper. Additionally, we have a new paper to be published at the Winter 2004 AAS Astrodynamics Symposium that covers the forward design process of constellation design using Flower Constellations. A paper cover the inverse design process will be the subject of a future paper.

A Versatile Constellation Design Tool

What we have discovered by playing with the selection of these parameter values is that we can generate some heretofore-unseen constellation designs. Interestingly, while all of these constellations are based upon a repeating ground track design and, therefore, have an axis of symmetry with respect to the North pole of the Earth, the axis of symmetry can be rigidly rotated to some other arbitrary orientation. While this destroys the repeating ground track phenomena, this serves to demonstrate that the Flower Constellation Set is a truly universal constellation design tool. We are currently looking into applications in the areas of Earth observation, deep space observation, global navigation system augmentation, distributed space systems, and formation flying to name a few. Additionally, we have discovered ways of creating repeating patterns of satellites that resemble a choreographed space dance. Our search for potential applications and new designs is under way while we also attempt to understand the implications of everything we have done to date.