# The Symmetry of GPS Orbit Ascending Nodes
## 3 Results
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{1}{c}{\(\mid\!\!\mid\!a\!\mid\)} & \multicolumn{2}{c}{**Active SVs**} & \multicolumn{2}{c}{**Inactive SVs**} & \multicolumn{2}{c}{**SVs**} & \multicolumn{2}{c}{**SVs**} \\ \cline{1-1} \cline{5-10} \multicolumn{1}{c}{[\({}^{\circ}\)/Year]} & \multicolumn{1}{c}{**Active SVs**} & \multicolumn{2}{c}{**Inactive SVs**} & \multicolumn{2}{c}{**Inactive SVs**} & \multicolumn{2}{c}{**SVs**} \\ \hline \(<\)0.1 & 5 & 16.1\% & 5 & 15.6\% & 10 & 15.9\% \\
0.1–0.2 & 7 & 22.6\% & 10 & 31.3\% & 17 & 27.0\% \\
0.2–0.3 & 10 & 32.3\% & 9 & 28.1\% & 19 & 30.2\% \\
0.3–0.4 & 3 & 9.7\% & 3 & 9.4\% & 6 & 9.5\% \\
0.4–0.5 & 4 & 12.9\% & 4 & 12.5\% & 8 & 12.7\% \\ \(>\)0.5 & 2 & 6.5\% & 1 & 3.1\% & 3 & 4.8\% \\ \hline
**Total:** & 31 & & 32 & & 63 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Absolute values of the GPS satellite separation trends. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{1}{c}{\(\mid\!\!\mid\!a\!\mid\)} & \multicolumn{2}{c}{**Active SVs**} & \multicolumn{2}{c}{**Inactive SVs**} & \multicolumn{2}{c}{**SVs**} \\ \cline{1-1} \cline{5-10} \multicolumn{1}{c}{[\({}^{\circ}\)/Year]} & \multicolumn{1}{c}{**Active SVs**} & \multicolumn{2}{c}{**Inactive SVs**} & \multicolumn{2}{c}{**SVs**} \\ \hline \(<\)0.1 & 5 & 16.1\% & 5 & 15.6\% & 10 & 15.9\% \\
0.1–0.2 & 7 & 22.6\% & 10 & 31.3\% & 17 & 27.0\% \\
0.2–0.3 & 10 & 32.3\% & 9 & 28.1\% & 19 & 30.2\% \\
0.3–0.4 & 3 & 9.7\% & 3 & 9.4\% & 6 & 9.5\% \\
0.4–0.5 & 4 & 12.9\% & 4 & 12.5\% & 8 & 12.7\% \\ \(>\)0.5 & 2 & 6.5\% & 1 & 3.1\% & 3 & 4.8\% \\ \hline
**Total:** & 31 & & 32 & & 63 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mission duration (MD) and absolute value of the separation trend. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{1}{c}{\(\mid\!\!a\!\mid\)} & \multicolumn{2}{c}{**Active SVs**} & \multicolumn{2}{c}{**Inactive SVs**} & \multicolumn{2}{c}{**1\(\mid\!\!a\!\mid\) [\({}^{\circ}\)/Year]**} & \multicolumn{2}{c}{**MD [Years]**} \\ \hline \multirow{2}{*}{\(<\)5–10–15} & 5 & 16.1\% & 6 & 18.8\% & 11 & 17.5\% & 0.14 & 0.10 \\
5–10 & 9 & 29.0\% & 6 & 18.8\% & 15 & 23.8\% & 0.24 & 0.11 \\
10–15 & 8 & 25.8\% & 6 & 18.8\% & 14 & 22.2\% & 0.22 & 0.09 \\
15–20 & 5 & 16.1\% & 13 & 40.6\% & 18 & 28.6\% & 0.27 & 0.17 \\ \(>\)20 & 4 & 12.9\% & 1 & 3.1\% & 5 & 7.9\% & 0.54 & 0.41 \\ \hline
**Total:** & 31 & & 32 & & 63 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Absolute value of the separation trend and mission duration (MD) of GPS satellites in OPs. Excluding the block I satellites from the analyzed population, slightly larger numbers of satellites located on OPs B, E, and F than in the cases of the A, C, and D orbital planes are noticeable. Similarly to the previous analysis in Table 4, a significant impact of the PRN46 satellite with OP D on the mean value of \(\left|a\right|\) was noted. The highest absolute value of the separation of the AN from the OP is obtained in OP D and equals 0.37\({}^{\circ}\)/year. At the same time, the corresponding value of the standard deviation indicates the presence of smaller values of the remaining satellites from OP D. The other OPs' \(\left|a\right|\) values range from 0.19\({}^{\circ}\) (OP F) to 0.26\({}^{\circ}\)/year (OP B). The values of their standard deviations indicate a similar separation rate of the remaining OP satellites. The average satellite mission durations range from 10.59 to 12.86 years. The longest mean MD was recorded for OP A and OP D.  
The study showed a stepwise but systematic increase in the standard deviation of d\(\Omega\) separations in the case of all six OPs (Figure 8). OP D stands out with a 5-fold increase in the last 24 years from a value not exceeding 2\({}^{\circ}\) in 1996 to 10\({}^{\circ}\) in 2020. The impact of the anomalous position of SVN46's orbit is apparent. The A, B, E, and F OPs' d\(\Omega\) standard deviations ranged from 2\({}^{\circ}\) to 3\({}^{\circ}\).