## 2 Constellation Dynamics (Walker)
\begin{array}{c}\Omega_{ij}=\frac{2\Pi}{P}(i-1)\\ M_{ij}=\frac{2\Pi}{S}(j-1)+\frac{2\Pi}{N}F(i-1)\end{array}  \tag{2}\]  
where \(S=N/P\) represents the number of satellites per plane, \(\Omega\) is the RAAN and the \(M\) represents the mean anomaly respectively. The reference to the user position is also of importance when the coverage of the satellite is considered for the disaster relief management. According to Ref. [4], there must be at least four satellites in sight at any time for determining a position of a potential user. The equation for the same is given by Ref. [5] as:  
\[\sigma=\alpha.\sigma_{REF} \tag{3}\]  
where \(\sigma\) is the user position error, \(\alpha\) is the factor depending the relative position of the satellites, and \(\sigma_{REF}\) is the pseudo range error factor. In fact, the reference mentions that the role of \(\alpha\) is so large that the larger its value, the lower the quality or coverage of the given constellation with respect to the location of the end-user. Equation (3) and Refs. [4; 5] are quoted to understand the concept and importance of end user position error. This also determines and implies that the case of a global augmentation constellation with a single objective function is considered as having a global average of four visible satellites at each time of the pass over a ground station or an end-user location. Due consideration of this concept was given while formulating the design constraints and the configuration of this paper by first selecting the areas of interests and aligning the ground stations across them. Then, the constellation design was prepared to suit the orientation of the ground stations with a 45-degree inclination of each orbit to cover the areas as mentioned in the following sections. The optimization of these trajectories to find the best travel path is necessary to obtain the shortest path for satellites to travel and deliver the data in the quickest way possible. However, the end-user position error analysis is not included in this paper as the focus remained on the optimization and factors mentioned in the abstract. In the near future, a detailed study on the visibility and end-user positioning and error analyses is planned with a similar configuration. There is also a need for establishing the ground stations in sync with satellites deployed to receive the data and track the satellites in operation. For the same, the repeating ground track (RGT) was selected as continuous revisits are essential for LEO-based constellations. The Ref. [6] show a detailed overview of the dynamics involved in ground tracking and following it, the required equations were determined as below:  
\[\aleph=[\tau,e,i,\omega,\Omega,M]^{T} \tag{4}\]  
where \(\tau\) is the ratio of number of revolutions (\(N_{p}\)) and the number of nodal periods (\(N_{D}\)). A very interesting fact noticed here with regard to the walker constellations is that under certain ground conditions, the Common Ground Tracking (CGT) utilizing the circular Repeat Ground Track (RGT) orbits is expressed as follows:  
\[i:N/N/(N-N_{p}) \tag{5}\]  
where \(N_{D}\) is 1 and follows the same notation as the walker constellation as represented in Equation (2), respectively. That means the CGT constellation with RGT orbits is a common scenario used extensively by the constellation operators globally. Moreover, the access profile condition was also determined using Ref. [6], which provides the actual relation between the relative position vectors from the ground to the satellite as follows:  
\[\gamma=r_{s}-r_{g} \tag{6}\]  
where \(r_{s}\) is the satellite position vector from Earth's center and \(r_{g}\) is the target point position vector from the Earth's center. The elevation angle for the same is given as follows:  
\[\varepsilon=\sin^{-1}\!\left(\frac{r_{g}\gamma}{\left\|r_{g}\right\|\left\| \gamma\right\|}\right)=\sin^{-1}\!\left(\widehat{r}_{g}.\widehat{\gamma}\right) \tag{7}\]  
On the other side, Ref.