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Article Published in International Journal of Advanced Computer Science and Applications(IJACSA), Volume 4 Issue 2, 2013.
Abstract: For many space missions using satellite constellations, symmetry of satellites distribution plays usually a key role. Symmetry may be considered in space and/or in time distribution. Examples of required symmetry in space distribution are in Earth observation missions (either, for local or global) as well as in navigation systems. It is intuitive that to optimally observe the Earth a satellite constellation should be synchronized with the Earth rotation rate. If a satellite constellation must be designed to constitute a communication network between Earth and Jupiter, then the orbital period of the constellation satellites should be synchronized with both Earth and Jupiter periods of revolution around the Sun. Another example is to design satellite constellations to optimally observe specific Earth sites or regions. Again, this satellites constellation should be synchronized with Earth’s rotational period and (since the time gap between two subsequent observations of the site should be constant) also implies time symmetry in satellites distribution. Obtaining this result will allow to design operational constellations for observing targets (sites, borders, regions) with persistence or assigned revisit times, while minimizing the number of satellites required. Constellations of satellites for continuous global or zonal Earth coverage have been well studied over the last twenty years, are well known and have been well documented , , , , , . A symmetrical, inclined constellation, such as a Walker constellation ,  provides excellent global coverage for remote sensing missions; however, applications where target revisit time or persistent observation are important lead to required variations of traditional designs , . Also, few results are available that affect other figures of merit, such as continuous regional coverage and the systematic use of eccentric orbit constellations to optimize“hang time” over regions of interest. Optimization of such constellations is a complex problem and the general-purpose constellation design methodology used today is largely limited to Walker-like constellations. As opposed to Walker Constellations , , which were looking for symmetries in inertial reference frame, Flower Constellations  were devised to obtain symmetric distributions of satellites on rotating reference frames (e.g., Earth, Jupiter, satellite orbit). Since the theory of Flower Constellations has evolved with time the next section is dedicated to the summary of the theory up to the current status. The FCs solution space has been recently expanded with the Lattice theory , , encompassing all possible symmetric solutions.
Daniele Mortari, Jeremy J.Davis, Ashraf Owi and Hany Dwidar, “Reliable Global Navigation System using Flower Constellation” International Journal of Advanced Computer Science and Applications(IJACSA), 4(2), 2013. http://dx.doi.org/