# Drag and Attitude Control for the Next Generation Gravity Mission
## 3 Drag and Attitude Control Role in the Measurement of the Non-Gravitational Accelerations
### Drag Environment on NGGM Reference Orbits  
Atmospheric drag is the dominant source of non-gravitational accelerations for low-Earth orbits like those of the NGGM. The drag forces on the satellite depend on the atmospheric density, which in turn is affected by the solar activity, on the satellite's velocity relative to the atmosphere on the satellite geometry, on the accommodation factors, and on the temperature of its surfaces. * The atmospheric models utilized within the NGGM system study are:
* NRLMSISE-00 for neutral density estimation/predictions (consistent with ECSS E ST 10 04C Rev1 Space Environment standard);
* HWM-14 for winds;
* [PERSON]'s model for the high-frequency density/wind fluctuations [PERSON] (2016). The drag forces on the spacecraft are computed using the NGGM E2E e-MAGIC simulator, inherited from the end-to-end (E2E) simulator developed by Thales Alenia Space for the GOCE Mission and successfully validated against the flight data (see Figure 12). A remarkable result of this comparison is the fundamental role played by [PERSON]'s model for a correct reproduction of the drag force behavior in the frequency range from 1 mHz to 1 Hz (see Figure 13), which includes the measurement bandwidth of the NGGM. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Controlled Quantity** & **Requirement** & **Note** \\ \hline Non-gravitational linear & \(\leq\)10\({}^{-6}\) m/s\({}^{2}\) & Peak-to-peak limit, all axes \\ acceleration of satellite’s CoM & \(\leq\)5 \(\times\) 10\({}^{-9}\) m/s\({}^{2}\)/\(\sqrt{\mathrm{Hz}}\) & ASD limit in MBW, all axes \\ \hline Angular acceleration of the & \(\leq\)10\({}^{-6}\) rad/s\({}^{2}\) & Peak-to-peak limit, all axes \\ satellite around the CoM & \(\leq\)10\({}^{-8}\) rad/s\({}^{2}\)/\(\sqrt{\mathrm{Hz}}\) & ASD limit in MBW, all axes \\ \hline Angular rate of the satellite & \(\leq\)10\({}^{-4}\) rad/s & Peak-to-peak limit, X and Z axes \\ around the CoM & \(\leq\)1.2 \(\times\) 10\({}^{-3}\) rad/s & Peak-to-peak limit, Y (pitch) axis \\  & \(\leq\)10\({}^{-6}\) rad/s/\(\sqrt{\mathrm{Hz}}\) & ASD limit in MBW, all axes \\ \hline Satellite X-axis pointing in the & \(\leq\)2 \(\times\) 10\({}^{-5}\) rad & Peak-to-peak limit, around Y and Z 1 \\ satellite-to-satellite direction & \(\leq\)10\({}^{-5}\) rad/\(\sqrt{\mathrm{Hz}}\) & ASD limit in MBW, all axes \\ \hline \hline \end{tabular} \({}^{\dagger}\) Limit set by the pointing precision of the interferometer laser beam. Roll axis (X) is not constrained.  
\end{table} 
Table 4: Requirements on non-gravitational accelerations and attitude motion control for NGGM. Figure 12: Time history and amplitude spectral density of the drag force along the X-axis of GOCE measured in flight (black line) and computed by the E2E simulator (red line). Figure 13: Time history (**above**) and amplitude spectral density (**below**) of the drag force along the X-axis of NGGM computed with and without the [PERSON]’s atmospheric model. The dependency on the drag force module on the solar activity is clearly shown in the time series Figure 14 spanning 14 years from 2027 and computed for the two reference orbit altitudes of the NGGM considering the solar-flux (F\({}_{10.7}\)) and the geomagnetic index (A\({}_{\rm p}\)) predicted with the 50 th and 95 th percentile (i.e., the probability, expressed in percentage, that a variable X will be less than a given value) [31]. According to the predicted activity in solar cycle 26, the maximum is expected to occur around October 2034; the date comprised in the planned NGGM on-orbit lifetime. The three components of the uncompensated drag accelerations experienced by the satellite (expressed in its reference frame), computed along two orbits at the maximum of the predicted solar activity with the 95 th percentile, are provided in Figure 15 (time series) and Figure 16 (amplitude spectral density). Figure 14: Drag force module over 14 years from 2027 at 396 km and 492 km altitude, computed with 50 th percentile (**left**) and 95 th percentile (**right**) on F\({}_{10.7}\) and A\({}_{\rm p}\) prediction.