# Drag and Attitude Control for the Next Generation Gravity Mission
## 2 NGGM Objectives, Measurement Technique, and Fundamental Observables
### User's Need and Objectives of the Next Generation Gravity Mission
Acceleration measurement errors (e.g., temperature-induced bias drifts), the relatively high and variable altitude (i.e., natural orbit decay), and the one-dimensional near North-South sampling away from the poles are known to affect the GRACE and GFO gravity model quality. Improvements to the spacecraft design (thermal control, attitude measurement, and control) can help to reduce systematic errors. Beyond that, however, the errors are dominated by the aliasing due to the coarse temporal sampling, limited to a monthly resolution in GRACE and GFO. Even a substantially improved instrument such as the LRI cannot be fully exploited due to the uncertainties in the aliasing reduction modeling of high-frequency ocean and atmospheric mass variations [20]. A future gravity mission dedicated to monitoring mass changes in the Earth system, as studied in the context of a Next Generation Gravity Mission [8], will therefore require improvements in the instrumentation, the spacecraft (disturbing accelerations), and the mission design (sampling). In particular, a single satellite pair must evolve in a dual-pair \"Bender constellation\" [21] with a controlled orbit altitude to reduce the aliasing errors by increasing the temporal resolution from one month to one week or less, while providing a homogenous spatial resolution high enough for the investigation of the phenomena of interest. Notably, by choosing the optimal orbit constellations for the two pairs of satellites (i.e., the orbit periods, inclinations, repeat cycles and sub-cycles, the relative orientation of the lines of nodes, etc. ), high frequency mass variations will be observable and temporal aliasing errors from under-sampling will not be the limiting factor anymore [22]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Thematic Field**} & \multirow{2}{*}{
\begin{tabular}{c} **Geophysical Phenomena/** \\ **Events/Quantities** \\ \end{tabular} } & \multirow{2}{*}{**Time Scale 1**} & \multirow{2}{*}{**Resolution**} & \multicolumn{2}{c}{**Gravity Signal**} \\  & & & & & **(cm of EWH 3)** & \\ \cline{5-8}  & & & **km** & **SH 2 Max. Degree** & **Threshold** & **Goal** \\ \hline \multirow{5}{*}{Solid Earth} & \multirow{2}{*}{Natural hazards} & D & 300 & \(\mathrm{SHD}_{\mathrm{max}}=67\) & 6 cm & 0.6 cm \\ \cline{3-8}  & & L & \(150\) & \(\mathrm{SHD}_{\mathrm{max}}=133\) & \(5\) cm/yr & 0.5 cm/yr \\ \cline{2-8}  & & Evolution of Earth’s crust & M & 180 & \(\mathrm{SHD}_{\mathrm{max}}=111\) & 18 cm & 1.8 cm \\ \cline{3-8}  & & under external or & internal forcing & L & 150 & \(\mathrm{SHD}_{\mathrm{max}}=133\) & 5 cm/yr & 0.5 cm/yr \\ \cline{2-8}  & & Natural resources exploitation & D & 300 & \(\mathrm{SHD}_{\mathrm{max}}=67\) & 6 cm & 0.6 cm \\ \cline{2-8}  & & L & 150 & \(\mathrm{SHD}_{\mathrm{max}}=133\) & 5 cm/yr & 0.5 cm/yr \\ \cline{2-8}  & & Deep interior properties and dynamics & M & 180 & \(\mathrm{SHD}_{\mathrm{max}}=111\) & 18 cm & 1.8 cm \\ \cline{2-8}  & & L & 150 & \(\mathrm{SHD}_{\mathrm{max}}=133\) & 5 cm/yr & 0.5 cm/yr \\ \hline \hline \end{tabular}  
* D: daily to weekly; M: monthly (seasonal to inter-annual), L: long-term trend. 2 SHD\({}_{\mathrm{max}}=\) maximum degree of geopotential spherical harmonic corresponding to that spatial resolution. 3 EWH = equivalent water height.  
\end{table} 
Table 1: _Cont._