# Impact of Groundtrack Pattern of a Single Pair Mission on the Gravity Recovery Quality
## 3 Results
### Global Gravity Recovery Solutions
#### 3.1.1 Two Scenarios for Comparisons  
Here, we choose two mission scenarios from Table 2 for more detailed comparison and investigation. The scenarios have been selected such that they have almost the same altitudes; therefore, the mission height difference does not affect the performance. However, scenario a is in an odd parity orbit, whereas scenario b is in the even parity. Both orbits have almost similar groundtrack gap  
Figure 5: Error RMS in terms of geoid height for the gravity solutions of the Table 1 mission scenarios for maximum spherical harmonic degree and order MCNR. Figure 6: The zoom-in graph of the Figure 5.  
evolution and same sub-cycle of 6 days (Figure 7), but different full repeat cycles (13 days vs. 31 days). The performance of the mission choices are studied for two different formation flights (GRACE-like and Pendulum) and different angles of right ascension of the ascending node (RAAN). The choices of RAAN for the simulation start date of 1 January 1996 correspond to:  
- \(\Omega=0^{\circ}\): Starting from a point in Pacific Ocean, west of South-America,  
- \(\Omega=116^{\circ}\): Starting from a point in West-Africa,  
- \(\Omega=132^{\circ}\): Starting from a point in East-Africa. \begin{table}
\begin{tabular}{c c c c c} \hline
**Scenario** & \(\beta\)**(\(\alpha\)rev./Day)** & **Parity (\(\beta-\alpha\))** & **Altitude (km)** & **Sub-Cycle (Days)** \\ \hline a & 206/13 & odd & 297.6 & 6 \\ b & 491/31 & even & 299.8 & 6 \\ \hline \end{tabular}
\end{table} 
Table 2: Selected scenarios for detailed comparisons. Figure 7: Gap evolution graphs for the repeat orbits of the Table 2 mission scenarios. The blue, red and black curves show the minimum, maximum and average unobserved gaps for each day, respectively. GRACE-like (Inline) Formation  
Figure 8 shows the gravity recovery of the GRACE-like scenarios a and b for \(L_{max}=32\). As we see in Figure 8, after the 5 th day, the gravity recovery by \(\Omega=132^{\circ}\) is better than \(\Omega=116^{\circ}\). The recovery by \(\Omega=0^{\circ}\) is the worst. The odd parity scenario a usually performs a bit better than the even parity scenario b. In terms of global recovery, the 6 th day as sub-cycle period is not significant. In case \(L_{max}=64\), Figure 9 shows that the performance of the odd parity scenario is better than the even parity scenario, but the impact of \(\Omega\) is not significant. Figure 8: Global error RMS in terms of geoid height for odd (solid line) and even (dashed line) parities (inline scenarios a and b of the Table 2, respectively) for the gravity solutions up to maximum spherical harmonic degree and order 32. Different colors stand for different \(\Omega\). Figure 9: Global error RMS in terms of geoid height for odd (solid line) and even (dashed line) parities (inline scenarios a and b of the Table 2, respectively) for the gravity solutions up to maximum spherical harmonic degree and order 64. Different colors stand for different \(\Omega\). In terms of global recovery, the 6 th day as sub-cycle period might be considered more significant for \(L_{max}=64\) than the case of \(L_{max}=32\). For \(L_{max}=\) CNR, the dominant effect is the different impacts of odd and even parities on the gravity solutions larger than 7-day (Figure 10). Moreover, the impact of \(\Omega\) can be seen (\(\Omega=132^{\circ}\) usually performs better than \(\Omega=116^{\circ}\), and \(\Omega=0^{\circ}\) is the worst). In terms of global recovery, the 6 th day as sub-cycle period has a significant influence. Afterwards, the error increases with the increase of time-interval of the solutions, which is very likely caused by the impact of temporal aliasing, since spatial aliasing is tried to be avoided (according to CNR). The case \(L_{max}=\) MCNR is shown in Figure 11. The figure shows that above 6-day solutions, the odd parity scenario performs better than the even parity. Surprisingly, \(\Omega=0^{\circ}\) performs almost the same as, or even better (for longer time solution) than, the others.