# Drag and Attitude Control for the Next Generation Gravity Mission
## 4 Drag and Attitude Control Impacts on Mission Performance
### Implications on the Gravity Field Retrieval  
In order to assess the influence of the three drag-free cases and the two pointing regimes on the quality of the gravity field, we exploited the linear perturbation theory (LPT) [33] to propagate errors in the frequency domain to the Stokes coefficients, following the approach of [34]. In this way, the errors in the frequency domain are projected into the ground track coverage dictated by the orbital configuration of the constellation (i.e., both satellites), thus determining which gravity field coefficients are affected by those errors. This is an efficient method to evaluate the impact of colored noise from different sensors on the quality of the gravity field models [35]. As implied, this approach assumes the errors are stationary, which is adequate for instrument errors. Unfortunately, this approach is not capable of handling non-stationary errors, such as those resulting from temporal aliasing [36]. Although there are strategies to address temporal aliasing, e.g., [22; 37], these errors are still dominant in the error budget of II-SST satellites [20]. In any case, the level of temporal aliasing is dictated by the orbit configuration (namely their repeat period) and data processing choices on the ground. For this work, we have exploited the orbit configurations determined in [23] and note that data processing choices are irrelevant for the satellite design. For this reason, we chose the LPT to assess the impact of different design choices in the quality of the monthly gravity field. Figure 21 illustrates the cumulative degree RMS error of the three drag-free options and the two pointing regimes on the quality of the gravity field (cf. Figure 18, except for the \"NGGM requirement\" curve and Figure 20, yellow line), in terms of the equivalent water height (EWH) added to the \"goal\" case in Figure 3. This means the curves in Figure 21 include the errors from the laser interferometer, the accelerometer, and associated drag-free and pointing regimes. The first observation is that the full and X-axis drag-free cases (for both pointing regimes) are very similar, with some small differences in degrees 5-40 for the fine pointing regime and no obvious difference for the coarse pointing regime (i.e., the light blue and green lines are overlapping). For the fine pointing regime, the error amplitude below 40 degrees jumps up from full/X-axis drag-free to no drag-free by as much as it jumps from the latter to all coarse pointing cases. This means that the fine pointing regime has larger benefits to the quality of the gravity field than the drag-free options. As the degree increases, the differences between all six cases progressively reduce. This is because the errors in the laser interferometer (not shown) are dominant at degrees above 80; the exception is the fine pointing and full/X-axis drag-free cases, which are below the laser interferometer errors for degrees above 20. In other words, the full/X-axis drag-free capability is required to fully exploit the accuracy of the laser interferometer. Represented by the broken pink line is the so-called HIS signal, which contains the variability of the hydrological, icesheets, and solid-earth mass transport components, from [38]. This line represents one of the main signals to be observed by future gravimetry. As such, the intersection between the error curves and the HIS curve indicates the spherical harmonic degree (SHD), which can be directly translated to a spatial resolution, at which the signal-to-noise (SNR) is 1. For lower degrees (or lower spatial resolution), the HIS processes can be fully observed; above, this is not the case. Table 5 lists the values of the predicted spatial resolution for the cases considered in this study. As expected, the fine pointing and full/X-axis drag-free cases have the highest spatial resolution of 235 km and the coarse pointing with no drag-free control has the lowest at 267 km.