# 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
Spatial aliasing is thought to be the biggest source of error, which increases as the time period of the gravity solutions increases (although temporal aliasing also exists, as for the other cases). Here, 6-day (as sub-cycle period) does not show important meaning. Possibly, the domination of spatial aliasing and the distribution of the geophysical signals with different strength over the globe h  
Figure 10: 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 CNR. Different colors stand for different \(\Omega\). The addition of cross-track measurement of Pendulum formation to only along-track measurement of GRACE-like formation brings the expectation that Pendulum formation should reduce the recovery error through its more isotropic sampling behavior. Figures 12-15 illustrate the gravity recovery of scenarios a and b of Table 2 of a Pendulum formation, respectively for \(L_{max}=32\), 64, CNR and MCNR. The average intersatellite distance of the two satellites in the formation is 100 km. For \(L_{max}=32\) in Figure 12, the recovery by \(\Omega=132^{\circ}\) is better than \(\Omega=116^{\circ}\). The recovery by \(\Omega=0^{\circ}\) is the worst and gets even worse at the longer periods. No significant difference is seen by the performance of the odd and even parities. In terms of global recovery, the 6 th day as sub-cycle period is not significantly important. Figure 11: 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 MCNR. Different colors stand for different \(\Omega\). Figure 12: Global error RMS in terms of geoid height for odd (solid line) and even (dashed line) parities (Pendulum 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 13 illustrates better performance in recovery quality by \(\Omega=132^{\circ}\) than \(\Omega=116^{\circ}\). After 5-day, the gravity recovery by \(\Omega=0^{\circ}\) is the worst, and gets even worse for the longer periods. No significant difference is seen by the performance of the odd and even parities, although the even parity performs only a bit better than the odd parity after 5-day. In terms of global recovery, the 6 th day as sub-cycle period is not significantly important, although it shows a small impact on the recovery by \(\Omega=0^{\circ}\) and \(\Omega=116^{\circ}\). Unlike the case of CNR by the GRACE-like formation, the errors for \(\Omega=116^{\circ}\) and \(\Omega=132^{\circ}\) in Figure 14 decrease by the longer period of the solutions. One may associate this error reduction to the less spatial aliasing. However, that is not the case for \(\Omega=0^{\circ}\). The question is then how the combination of isotropy and sampling plays role. Looking at the Figure 14, the \(\Omega=132^{\circ}\) scenario shows better performance than \(\Omega=116^{\circ}\) which outperforms \(\Omega=0^{\circ}\). Furthermore, the even parity performs a bit better than the odd parity. In terms of global recovery, the 6 th day as sub-cycle period is not significantly important. Figure 13: Global error RMS in terms of geoid height for odd (solid line) and even (dashed line) parities (Pendulum 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 Figure 15 (MCNR case), the error increases for all cases after 6-day solution. In this case, extracting a meaning for sub-cycle (6-day) is not straightforward. The odd parity outperforms the even parity at longer periods of solutions. The case \(\Omega=132^{\circ}\) usually performs better than the two other cases.