# Drag and Attitude Control for the Next Generation Gravity Mission
## 3 Drag and Attitude Control Role in the Measurement of the Non-Gravitational Accelerations
### The Candidate Accelerometer for NGGM  
In order to have the same level of performance along the three axes for linear accelerations and to provide three pure angular accelerations, ONERA has proposed the new concept of the accelerometer, named MicroSTAR, with a cubic proof mass (PM) surrounded by six identical electrode plates (Figure 10). The principle of measurement of MicroSTAR is identical to the previous accelerometers utilized on GOCE [28] or GFO [29]: the PM is suspended at the center of the electrode cage with electrostatic forces, with the control being ensured by a capacitive measurement of the motion of the PM with respect to the electrode cage. With the electrode cage being fixed inside the satellite, the electrostatic forces applied on the PM are representative of the relative acceleration of the PM with respect to the satellite at the accelerometer's location. For an accelerometer at the center of mass of the satellite, the linear accelerations measured by the instrument are the non-gravitational accelerations seen by the satellite. For an off-centered accelerometer, additional terms due to the angular motion of the satellite and the gravity gradient are present in the measurement, as described in Section 3.1. Figure 9: Error tree for the measurement of the non-gravitational differential acceleration along the satellite’s CoM-to-CoM direction. To achieve the performance required for the mission, the PM is made in Platinum Rhodium alloy (PtRh10), as for the GOCE accelerometer, with a gap between the PM and electrode of 300 \(\upmu\)m. A very thin gold wire of 5 \(\upmu\)m diameter polarizes the PM with a DC voltage Vp (polarization voltage) and a 100 kHz voltage Vd (detection voltage for capacitive detection). The PM is controlled with a digital control loop to take full benefit of the electrode redundancy and to facilitate the non-linearity calibration and correction, as was completed for the GOCE accelerometer. The accelerometer sensor head (ASH) with the accelerometer core and the front-end electronics unit (FEEU) with the sensitive analog functions (capacitive detection, actuation amplification, and readout chain) shall be located in a very stable thermal enclosure in order to achieve the performance at low frequency. A stability of 5 mK/\(\sqrt{\text{Hz}}\) for ASH and 10 mK/\(\sqrt{\text{Hz}}\) for the FEEU is required in addition to very low thermal sensitivity of the electronics functions. The interface and control unit (ICU) includes the software to control the PM along its six degrees of freedom, as well as to filter the accelerometer acceleration measurement before transferring the measurements to the on-board computer. It is foreseen to have two different outputs: one for the science processing with high resolution and lower range (1.2 \(\times\) 10\({}^{-5}\) m/s\({}^{2}\)) and one for the drag-free, attitude, and orbit control system (DFAOCS) with lower resolution but higher range (4.7 \(\times\) 10\({}^{-5}\) m/s\({}^{2}\)). Figure 11 shows the amplitude spectral density of the MicroSTAR measurement noise in the science output and in the DFAOCS output channel for the linear accelerations and the angular accelerations, derived from a worst-case analysis (WCA). Note that the X axis of the accelerometer is that on which the polarization gold wire is applied; therefore, it is slightly less sensitive than the other two (ultra-sensitive) Y and Z axes. On the spacecraft, the accelerometer is oriented with one of its ultra-sensitive axes nominally aligned to the flight direction. As explained in Section 3.1, the measurement performance of the relative non-gravitational acceleration depends not only on the accelerometer intrinsic noise, but also on the coupling of the accelerometer with the satellite environment. Indeed, due to the non-perfect geometry of the accelerometer parts or the non-perfect electronics components, the accelerometer is affected by a bias, a scale factor, a quadratic factor, and internal misalignments.