# Impact of Groundtrack Pattern of a Single Pair Mission on the Gravity Recovery Quality
## 3 Results
### Mission Scenarios and the Regional Gravity Recovery  
#### 3.2.1 West Africa as an Example  
Two scenarios of Table 2 with almost same altitude and similar gap evolution (both has 6-day sub-cycle time-span) are investigated for their regional gravity recovery. Figure 18 depicts the groundtrack of the two scenarios on the selected area in West Africa for different RAAN angles after 6 days. Figure 17: Covariance matrices of 6-day solutions of the scenario (a) Pendulum formation for \(\Omega=116^{\circ}\). **Top left**: \(L_{max}\) = 32, **top right**: \(L_{max}\) = 64, **bottom left**: \(L_{max}\) = CNR, and **bottom right**: \(L_{max}\) = MCNR. Figure 18: _Cont._The error RMS of the gravity recovery in terms of geoid height for global and regional (West-Africa) 6-day solution of different cases are shown in Tables 3-10. The results from the tables imply that the best global performance (the smallest error) usually happens at \(\Omega=132^{\circ}\). That might be expected, since among the three different \(\Omega\) values, the mission track passes over the biggest signals when \(\Omega=132^{\circ}\) (i.e., over East-Africa). In terms of regional investigation, the results are usually optimal when \(\Omega=116^{\circ}\). That is, in fact, the area where sub-cycle happens. However, for both global and regional cases, the above statements are not always valid. When the maximum spherical degree and order of the solution goes above the Colombo-Nyquist rule (CNR), exceptions can be observed. One possible explanation for those exceptions is the large spatial aliasing and the leakage from the surroundings which may deteriorates the impact of sub-cycle. Clearly, more detailed studies should be conducted in this direction. The impact of the mission formation on the error can also be seen in the results. The outcomes show that the Pendulum formation usually outperforms the inline (GRACE-like) formation. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Inline (GRACE-Like)**} & \multicolumn{3}{c}{**Pendulum**} \\ \cline{2-7}  & \(\Omega=0^{\circ}\) & \(\Omega=116^{\circ}\) & \(\Omega=132^{\circ}\) & \(\Omega=0^{\circ}\) & \(\Omega=116^{\circ}\) & \(\Omega=132^{\circ}\) \\ \hline Global & \(3.3169\times 10^{-4}\) & \(3.1218\times 10^{-4}\) & \(3.0947\times 10^{-4}\) & \(3.3759\times 10^{-4}\) & \(3.0026\times 10^{-4}\) & \(2.8424\times 10^{-4}\) \\ Regional: & \(1.4774\times 10^{-5}\) & \(8.3863\times 10^{-6}\) & \(1.2509\times 10^{-5}\) & \(1.4533\times 10^{-5}\) & \(7.0561\times 10^{-6}\) & \(1.2401\times 10^{-5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Error RMS in terms of geoid height for global and regional (West-Africa) 6-day recovery up to \(L_{max}=32\) of the scenario (b) inline and Pendulum formation. The smallest values in global and regional cases for each inline and Pendulum formation are written in blue. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Inline (GRACE-Like)**} & \multicolumn{3}{c}{**Pendulum**} \\ \cline{2-7}  & \(\Omega=0^{\circ}\) & \(\Omega=116^{\circ}\) & \(\Omega=132^{\circ}\) & \(\Omega=0^{\circ}\) & \(\Omega=116^{\circ}\) & \(\Omega=132^{\circ}\) \\ \hline Global & \(3.3108\times 10^{-4}\) & \(3.1546\times 10^{-4}\) & \(3.1345\times 10^{-4}\) & \(3.4147\times 10^{-4}\) & \(2.9978\times 10^{-4}\) & \(2.8446\times 10^{-4}\) \\ Regional: & \(1.5001\times 10^{-5}\) & \(8.0113\times 10^{-6}\) & \(1.2389\times 10^{-5}\) & \(1.3820\times 10^{-5}\) & \(7.1328\times 10^{-6}\) & \(1.2389\times 10^{-5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Error RMS in terms of geoid height for global and regional (West-Africa) 6-day recovery up to \(L_{max}=32\) of the scenario (a) inline and Pendulum formations. The smallest values in global and regional cases for each inline and Pendulum formation are written in blue. Figure 18: Groundtrack patterns over West-Africa after 6 days. **Left**: Scenario (a), and **right**: Scenario (b). From top to bottom: \(\Omega=0^{\circ}\), \(116^{\circ}\) and \(132^{\circ}\).