## 4 Instrument Sensitivity, Accelerometer and Drag Compensation Assessment
### Accelerometer Selection and Drag Compensation Assessment  
The successive step concerns the selection of the suitable sensors compliant with the required accuracy specified in Table 5, demanding a ranging instrument able to capture the intersatellite distance variation with the resolution of few nanometers (described in Section 4.2). Focusing on low altitudes, the current intersatellite distance baseline has been set around 100 km (as per Section 4): for distances in the range of 70-100 km, the NGGM performance is relatively constant, and lengths > 100 km do not provide any benefit in terms of variable gravity field recovery [44]. The most suitable instruments with a performance better than \(10^{-11}\) m/s\({}^{2}\)/\(\surd\)Hz (in green in Table 5, bottom) are the GOCE GRADIO accelerometers, whose specifications are compared in Table 6 to the GRACE SuperSTAR accelerometer. Both instruments were developed by ONERA and are described in [45; 46]. The targeted differential nongravitational acceleration requirements can be only achieved taking into account the in-orbit lessons learned from GOCE. The performances of the GOCE GRADIO-class [47] accelerometers have been modeled considering the colored noise of the analog-to-digital-converter of the capacitive detector (of the proof-mass motion) at high frequency (>100 mHz), the estimated thermal drift at low frequency (<5 mHz) and the noise floor of 9.81\(\times 10^{-12}\) m/s\({}^{2}\)/\(\sqrt{\rm Hz}\) on the basis of the in-orbit measured noise. The full noise level of a single accelerometer has been assessed with a bottom-up approach, taking into account the following:  
- Accelerometer intrinsic measurement error;  
- Accelerometer coupling errors with the spacecraft;  
- Spacecraft-generated error (e.g., self-gravity effects);  
- Geometric transformation errors. These errors are combined linearly if correlated and with root square sum (RSS) if uncorrelated. The same is done for the companion satellite, and the combined differential nongravitational linear acceleration measurement can be computed as in Table 5 (bottom) according to the logic presented in Figure 9. \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **GOCE GRADIO** & **GRACE SuperSTAR** \\ \hline Mass (kg) & & \\ Volume (L) & 9.4 & 11.4 \\ Power consumption (W) & 10.6 & 13.7 \\ Range (m/s\({}^{2}\)) & 10.5 & 8 \\ Noise floor in MBW & \(6.6\times 10^{-6}\) & \(5\times 10^{-5}\) \\ (m/s\({}^{2}\)/\(\sqrt{\rm Hz}\)) & \(3\times 10^{-12}\) & \(10^{-10}\) \\ MBW (mHz) & 5–100 & 0.1–40 \\ Bias (m/s\({}^{2}\)) & \(1.3\times 10^{-7}\) & \(1.6\times 10^{-5}\) \\ Bias thermal sensitivity & \(7.9\times 10^{-11}\) & \(5.7\times 10^{-9}\) \\ (m/s\({}^{2}\)/\({}^{\circ}\)C) & \(18\times 10^{-6}\) & \(2.11\times 10^{-3}\) \\ Scale factor thermal sensitivity & & \\ (1/\({}^{\circ}\)C) & & \\ \hline \end{tabular}
\end{table} 
Table 6: GOCE GRADIO and GRACE SuperSTAR accelerometer specifications. Figure 9: Relative differential nongravitational linear acceleration measurement error tree budget. The noise floor of the differential nongravitational acceleration can be decreased to some extent by optimizing the instrument, allowing for a better exploitation of the laser ranging instrument in the millihertz region, where the accelerometer accuracy is the limiting factor [28; 29]. The new generation of MicroSTAR-class accelerometers, under development at ONERA [45], is a promising candidate for NGGM.