# Drag and Attitude Control for the Next Generation Gravity Mission
## 5 Conclusions  
In a mission based on the satellite-to-satellite tracking technique for monitoring at a high spatial and temporal resolution the variations of Earth's gravity field, the two fundamental observables (CoM-to-CoM distance variation and non-gravitational differential acceleration between the CoMs of the satellites) are equally important to achieve the final objectives. In Section 4.1, the importance of fulfilling the control requirements on the satellite's drag accelerations and attitude dynamics provided in Table 4 to achieve the measurement performance of the non-gravitational differential acceleration has been demonstrated. Without compensating at all the drag forces' variations in the MBW, the measurement performance is degraded with respect to the full drag-free control condition by about 100 times in the lowest part of the MBW for the orbit of the Bender constellation with the lower altitude (396 km). The degradation can be mitigated by compensating at least the largest component of the drag force along the flight direction. Conversely, without a fine stabilization of the satellite orientation along the satellite-to-satellite direction, the resulting performance degradation (again, about two orders of magnitude around 1 mHz) is independent of the orbital altitude. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Pointing** & **Drag Free** &
\begin{tabular}{c} **HIS Max. Res.** \\ **[SHD, km]** \\ \end{tabular} \\ \hline Fine & Full & 85 235 \\ Fine & X-axis & 85 235 \\ Fine & None & 81 245 \\ Coarse & Full & 80 250 \\ Coarse & X-axis & 80 250 \\ Coarse & None & 75 267 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Maximum spatial resolution of the different scenarios to fully observe the HIS signal, in spherical harmonic degree (SHD) and distance. Figure 21: Degree RMS of the error in the gravity field coefficients in terms of EWH resulting from the laser interferometer, the accelerometer, and associated drag-free and pointing regimes. The curves for X-axis and full drag-free for the coarse pointing (green and light blue lines) are overlapping. In terms of the influence of the instrument errors in the accuracy of the monthly gravity field models, the analysis conducted with linear perturbation theory (LTP), cf. Section 4.2, confirms that the only way to exploit the full capabilities of the accelerometer is to use drag-free control, either on the X-axis or for all directions combined with the fine pointing mode. This analysis predicts that the maximum achievable spatial resolution to completely observe the HIS signal of the ESA Earth system model is 235 km, since the laser interferometer can resolve signals with an amplitude of 0.2 mm EWH at SHD 85. This is also the only case where the errors caused by the accelerometer are below those of the laser interferometer for the complete SHD range. For all other cases, the accelerometer affects the lower degrees more severely and with decreasing intensity for higher degrees, up to SHDs 60-70. When the accelerometer operates in a satellite platform with coarse pointing, it needs the drag-free control (either on the X-axis or for all directions) to come close to the case of fine pointing coupled with no drag-free control, with a spatial resolution of 250 and 245 km, respectively (SHDs 80 and 81). In the case of coarse pointing and no drag-free control, the spatial resolution is predicted to be 267 km (SHD 75). Since our analysis tool cannot handle non-stationary noise, such as temporal aliasing, we expect these values to be optimistic, and they should be regarded as the upper limit for complete observability. The analysis of model errors with a more complex simulation approach will certainly lead to worse quality gravity field models. However, importantly, those results will also be proportional to the quality of the results found using the LPT, so our approach is adequate for instrument design, especially since it allowed us to perform a much larger number of simulations throughout the design process (not shown).