# Spatial and Temporal Sampling Properties of a Large GNSS-R Satellite Constellation
## 4 Examples
### Application of Design Methodology
Starting from the baseline of a 3-Plane 30\({}^{\circ}\)-60\({}^{\circ}\)-90\({}^{\circ}\) constellation, the progression of this logic and the corresponding changes in GSC, ZSC, GTC, and ZTC are illustrated by the results provided in Table 1. After a few iterations, we find a significant improvement from the original baseline in the 3-Plane 50\({}^{\circ}\)-75\({}^{\circ}\)-80\({}^{\circ}\) constellation. In each step of the process, GSC always remains close to a complete 100%, but most progressions showed growth in the GTC of each prototype constellation. By incrementally raising the first plane inclination, we can slowly increase the GTC. However, once we reach a point where the first two inclinations are starting to get closer, we find that raising the second plane would create a more significant increase in this metric. This is evident by the GTC change between the 45\({}^{\circ}\)-60\({}^{\circ}\)-90\({}^{\circ}\) and the 45\({}^{\circ}\)-65\({}^{\circ}\)-90\({}^{\circ}\) constellations. Additionally, the increase in the inclination of the first plane from 45\({}^{\circ}\) to 50\({}^{\circ}\) allows for one more small rise in GTC without moving the first plane too close to the second plane while allowing for significant equator coverage. Finally, we can take advantage of the 10\({}^{\circ}\) reach from the set inclination to lower the third plane down from 90\({}^{\circ}\) to 80\({}^{\circ}\) while both improving ZTC at inclinations lower than 80\({}^{\circ}\) and maintaining the ZTC between 80\({}^{\circ}\) and 90\({}^{\circ}\). When comparing this 50\({}^{\circ}\)-75\({}^{\circ}\)-80\({}^{\circ}\) constellation to others with no separation in plane inclinations, such as the 30\({}^{\circ}\)-30\({}^{\circ}\)-30\({}^{\circ}\) or 90\({}^{\circ}\)-90\({}^{\circ}\)-90\({}^{\circ}\), the differences in GTC and ZTC are prominent. Since the 30\({}^{\circ}\)-30\({}^{\circ}\)-30\({}^{\circ}\) constellation's max inclination is equatorial, its mid-latitude ZTC, polar ZTC, and GTC are all much smaller than other constellations considered, making it less than ideal for a globally effective design. On the other hand, the 90\({}^{\circ}\)-90\({}^{\circ}\)-90\({}^{\circ}\) constellation has a relatively large GTC, but its equatorial ZTC is much smaller than other designs considered. Although the 50\({}^{\circ}\)-75\({}^{\circ}\)-80\({}^{\circ}\) constellation does not have the largest ZTC of these three constellations in any of the regions, its zonal and global metrics are still relatively good. Considering the goal of this design study is to maximize ZTC at all  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Constellation** & **Global** & **Global** & **ZSC** & **ZSC** & **ZTC** & **ZTC** & **ZTC** \\ **(deg-deg-deg-deg)** & **Coverage** & **Temporal** & **(eq)** & **(mid)** & **(Polar)** & **(eq)** & **(mid)** & **(Polar)** \\ \hline
30-30-30 & 62.987 & 2.254 & 99.994 & 35.505 & 0 & 3.788 & 0.983 & 0 \\
90-90-90 & 99.337 & 3.151 & 99.214 & 99.796 & 98.540  
latitudes, the 50\({}^{\circ}\)-75\({}^{\circ}\)-80\({}^{\circ}\) constellation is a good design candidate, for its zonal metrics are large at all latitudes and are further characterized by a large GTC.