## 7 Optimization Results (LEO)  
This ipopt optimizer was integrated with the small satellite constellation shown in the Section 3 with similar configuration and the optimization was carried out for a thorough coverage analyses as detailed pictorially below:  
For this analysis, the master region of interest was set to a Korean peninsula operating other region of interests and their respective ground stations from this base. The set-up was same with 48 small satellites operating in eight different planes, respectively.  
Inclination:  
As mentioned earlier, the inclination of each plane is crucial to arrive at the nearest ground station optimally in a lesser time period. After running the simulation for optimizing the constellation, the following iterations for inclination and semi-major axis were obtained as shown in Figures 16 and 17 below:  
In the figures above, the variations started with initial iterations adjusting to the best inclination possible for the constellation for a better coverage, which stabilized well in the later iterations, significantly reaching the most optimal solution as shown in the concluding iterations. The inclination still held itself for later iterations with few dips to the lower inclinations but stabilized back to the optimal mode, giving best solution possible for each plane. The semi-major axis along with inclination plays a vital role in establishing an optimal solution to the propagation of an entire constellation of small satellites. The semi-major axes of the orbital planes take their points to stabilize the first 50 iterations and  
Figure 16: Inclination optimization process for the first 50 and concluding iterations.  
Figure 17: Semi-major axis optimization process for the first 50 and concluding iterations.  
yield enough feasibility analyses for determining the best solution of optimal travel for a total coverage in the given constellation scenario.  
This leads to analyzing the final solution with the best optimal iterations for coverage fraction, cost, and objective functions as depicted in Figure 18 below:  
The pictorial representation of a process in obtaining an optimal solution for the constellations given in Figure 19 reinstates the fact that this portion of research contributes significantly to the design and orientation of the constellations using small satellites for a long-term operation in LEO region. The ipopt optimizer passed through this evaluation thoroughly as intended.  
After all the iterations the optimizer performed, the best solutions with the proposed objective function, coverage fraction, and cost function were obtained as shown in Table 2 below:  
Figure 19: Best solution process and step-wise on-board sequencing.  
Figure 18: Cost, coverage, and objective optimization process for the first 50 and later iterations.  
After the best feasible solution numerically was obtained as given above, the orbital trajectories with the master region of interest (Korea) were attained. This was pictorially shown with a fully optimized coverage with the given constellation along best the travel paths taken by satellites in Figure 20 below.  
An extensive analysis was carried out to make a better understanding with feasibility and associated parameters to it. The impact that the optimal parameters and trajectories have will add tremendously to the overall operation of the constellation in a harsh and tightly managed environment for the proposed configuration. Over a period of time, the operators of the constellations may actually reap the benefits from this optimization in terms of faster data, cost reduction and so on.  
These considerations and obtained results will turn out to be game-changer to implement the cost-effective LEO constellations of small satellites if utilized strategically. The timely distribution of the data to the end-user with reduced cost and enhanced performance for a long duration of time along with effectively reduced revisit intervals adds significantly a lot to the disaster management applications.