## 6 Space-Segment Optimization Aspects
### Constellation Topology  
The major constellation topologies are the following four topologies:  
* **Street of Coverage Constellations:** Multiple satellites placed in circular or near circular orbital planes with the same altitude and inclination and phase separation creates a Street of Coverage constellation. The number of orbital planes (streets) then determine a zonal or global coverage and can be optimized accordingly. The planes are distributed in a non-symmetric way [87; 93].
* **Walker Constellations:** A Walker constellation contains satellites in circular orbital planes with the same altitude and inclination distributed symmetrically along the equatorial reference. The inclination depends on coverage over the area of interest on the globe. A Walker constellation includes the star pattern, where orbital planes are evenly distributed over 180 degrees of the Right Ascension of the Ascending Node (RAAN) range, and the delta pattern, where planes are distributed over 360 degrees RAAN range. The rosette pattern is similar to delta based on [PERSON]'s earlier work. The other constellations based on Walker Delta include sigma pattern and omega pattern. An example constellation is the Galileo satellite constellation, which is deployed in a Walker 24/3/1 in MEO, where 24 satellites are distributed in 3 orbital planes inclined at 56\({}^{\circ}\)[94]. Another one is the Iridium constellation, which is a 66/6/2 Walker Star constellation with a near polar inclination of 86.4\({}^{\circ}\). The 66 satellites are distributed in 6 orbital planes [95].
* **Draim Constellations:** A Draim constellations use elliptical orbital planes with a similar period and inclination to achieve 1-fold or multi-fold continuous global coverage with fewer satellites than required for constellations with circular orbit or near circular orbits.
* **Flower Constellations:** A Flower constellation is a symmetrical constellation proposed by [PERSON] et al. [96] in a rotating frame of reference giving flower-like geometry. They have similar values for semi-major axis, eccentricity, inclination, and argument of perigee and differ in mean anomaly and RAAN. The Flower constellations were modified in a 2D lattice flower by [PERSON] et al. [97] and 3D lattice flower by [PERSON] et. al [98] models and 2D necklace flower [99] and 3D necklace flower  
Figure 4: Satellite Coverage.  
constellation [100]. Walker and flower constellation configurations provide global coverage [101].  
Table 6 presents the mathematical modeling of the two most encountered constellation topologies, namely Walker and Flower constellations. In Table 6, \(i\) is the inclination of orbit, \(N_{T}\) is the total number of satellites, \(Np\) is the number of orbital-planes of the constellation, \(F\) is the relative phasing parameter between adjacent orbital planes, and \(h\) is the Satellite (Sat) altitude. \(\Delta\Omega_{jk}\) is the RAAN and \(\Delta M_{jk}\) is the mean anomaly with respect to the reference Sat, with \(j\) as the orbital plane number and \(k\) as the Sat number within the orbital plane. For Flower constellations, \(N_{p}\) is the number of orbital revolutions of Sat, and \(N_{d}\) is the number of rotations of the rotating reference frame; for the Earth-centered, Earth-fixed frame (ECEF), \(N_{d}\) is equal to the number of days. These design parameters are related as \(N_{p}\frac{\Delta\tau}{n}=N_{d}\frac{2\pi}{\omega_{E}}\). Here, \(n\) is the orbital mean motion of the Sat, and \(\omega_{E}\) is the angular velocity of the rotating frame. \(F_{d}\), \(F_{n}\), and \(F_{h}\) are independent integers for phasing. \(\Delta\Omega_{k}\) is the RAAN, and \(\Delta M_{k}\) is the mean anomaly, with \(k\) as the Sat number with respect to first Sat [101,102].  
Figure 5 visualizes examples of constellations at various altitudes and with various number of orbital planes and inclinations.