# The Symmetry of GPS Orbit Ascending Nodes
## 3 Results
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**SVN** & **PRN** & **OP** & **SVA** & \begin{tabular}{c} **\(a\)** \\ [\({}^{\circ}\)/**Year**] \\ \end{tabular} & \
\begin{tabular}{c} **MD** \\ **[Year]** \\ \end{tabular} & **n** &
\begin{tabular}{c} **d\(\Omega\)** [\({}^{\circ}\)] \\ \end{tabular} \\ \hline
15 & 15 & D & NO & 0.18 & 10.64 & 2029 & - \\
17 & 17 & D & NO & 0.29 & 8.91 & 1427 & - \\
24 & 24 & D & NO & 0.06 & 15.6 & 3720 & - \\
34 & 04, 18 & D & NO & \(-\)0.25 & 23.53 & 5845 & - \\
45 & 21 & D & **YES** & \(-\)0.45 & 17.44 & 6059 & \(-\)4.3 \\
46 & 11 & D & **YES** & \(-\)1.34 & 20.69 & 6648 & \(-\)27.65 \\
61 & 2 & D & **YES** & \(-\)0.3 & 15.84 & 5668 & \(-\)4.34 \\
63 & 1 & D & **YES** & 0.2 & 9.15 & 3320 & 0.4 \\
67 & 6 & D & **YES** & 0.2 & 6.32 & 2299 & \(-\)0.07 \\
75 & 18 & D & **YES** & 0.4 & 0.51 & 187 & 1.12 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Descriptive parameters of the OP D satellites. Figure 5: Separation of satellite ANs from the hex-LS-estimated position of the OP D AN with satellite dot(\(\Omega\)) values. The comparison of the separation rate of all analyzed satellites is shown in Figure 7. The plot has two vertical scales. The scale on the left shows the rate of separation (SR) of the AN from the OP and refers to the left bars of the presented GPS satellites. Red and green bars represent inactive and active satellites, respectively. The blue bars on the right indicate the duration of the space mission (MD) described by the vertical scale on the right side of the plot. An additional element of the figure is information about the generations of individual GPS satellites expressed by circles in different colors placed above the SR and MD bars for different blocks. A detailed interpretation of the chart is divided into three aspects presented in Tables 3-5. The first analysis shows the division of active and inactive satellites according to the absolute value of the satellite AN separation trend from the OP. Figure 6: The trend of separation of satellite ANs from OP D.  
Figure 7: Separation rate (SR) and space mission duration (MD) of GPS satellites. The number of active and inactive satellites in the applied ranges is similar. About 65% of the analyzed satellites achieved \(\mid\!\!\mid\!a\!\mid\) values less than 0.3\({}^{\circ}\)/year with approximately 50% within the range of 0.1\({}^{\circ}\)-0.3\({}^{\circ}\)/year. The highest values exceeding 0.5\({}^{\circ}\)/year represent ca. 5% of the total population of satellites. The relationship between the duration of the satellite mission and the trend of separation is presented in Table 4.  
The statistical sample was divided according to the duration of the satellite space mission. The difference in the percentages of the active and inactive GPS satellites is noticeable. Increases of 9.8% and 7.0% in the number of active satellites compared to the inactive in the 5-10 years and 10-15 years MD groups, respectively, occurred. A significant decrease in the number of active satellites amounting to 24.5% occurred in the range of 15-20 years. In the current GPS constellation, four out of all five satellites operate with a mission duration longer than 20 years. The corresponding mean absolute value of the OP AN separation trend equals 0.54\({}^{\circ}\)/year. However, in that case, a significant value of the standard deviation should be noted, caused by the anomalous and several times greater separation trend of the SVN46 satellite. The results show a general upward trend of \(\mid\!\!\mid\) while the duration of the satellite space mission increases. However, this relationship is not close to linear, as the correlation coefficient of both parameters is 0.36. The third analysis of the separation trend based on the data in Figure 7 is shown in Table 5.