Author 1: Daniele Mortari
Author 2: Jeremy J.Davis
Author 3: Ashraf Owi
Author 4: Hany Dwidar
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 [1], [2], [7],
[8], [11], [13]. A symmetrical, inclined constellation, such as a
Walker constellation [1], [2] 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 [7], [8]. 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 [1], [2], which were
looking for symmetries in inertial reference frame, Flower
Constellations [11] 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 [13], [14],
encompassing all possible symmetric solutions.
