The presented work analysed the ISA measurements campaign during the second Venus swing-by using a comparison of the acquired data with the expected tidal effects between S/C CoM and ISA sensors, evidencing ISA as the first accelerometer ever that took direct measurements of Gravity Gradients generated on a spacecraft from an extraterrestrial body. Furthermore, data analysis evidenced an unexpected and almost un-modellable NGP acting on the spacecraft resulting in an acceleration spike of about 3.5 × 10−6[m/s2] in a time interval of about 6 minutes around the Closest Approach. The dynamical analysis of ISA data and AOCS data (mainly the RWs torques) allowed to identify the axis and point of application of the force causing such an acceleration. The force was estimated to be applied close to the MPO radiator and the force direction to be almost opposite to the radiator normal, the authors than argue that it was a surface force to push the spacecraft along its +Y axis. The presence of that unexpected NGP is also supported by the communications that authors had with the MORE team and the ESOC flight dynamic department, from which can be drawn that the orbital trajectory estimation matches with very good accuracy the ISA accelerations measurements, in terms of ∆V transferred to the BepiColombo probe exit trajectory (ESOC private communication). The nature of such a force, and in particular the hypothesis of an out-gassing phenomenon, is deeply investigated in the companion paper of this work (U. De Filippis, ”Outgassing event detected by the Italian Spring Accelerometer during the second Venus flyby of BepiColombo”).

[Figure: Figure 12: 3 sigma formal standard deviation for the three components of the force application point compared with β angle]

[Figure: Figure 12 indicates the sensitivity of the converged solution respect to the variation of the observed data. As expected, Y coordinate is much more sensitive with respect to the X and Z, reflecting a bigger uncertainty in the solution. The same conclusion can be addressed empirically: if the force would be perfectly along the Y axis, wherever the force is applied on a straight line parallel to this axis it would produce the same torque, letting completely loosing sensitivity on the Y axis.]

2.3.2. Measured Delta V and orbit estimation comparison The numerical integration of the ISA measured signal and the expected one, provides the magnitude of the ∆V on the spacecraft centre of mass due to the unintended acceleration which is ∆V = 5.8 ± 0.4 × 10−4 m/s, where the uncertainty has been computed by integrating a sample of data where no signal was expected. This value is fully compatible with the analysis based on radio-data, which estimated an impulsive ∆V = 5.95 ± 2.71 × 10−4 m/s along +ˆysc centred at the peak of the ISA measured spike Del Vecchio et al. (2024). Previous analysis, made just after the Venus swing-by#2 by the ESA/ESOC flight dynamics department, proved that the orbit determination software during the swing-by added It is worthwhile to remark that the analysis of VSB2 data confirms that ISA like high-sensitivity accelerometers are key instruments for the spacecraft fine-dynamic and Precise Orbit reconstruction in the regime of small and very small accelerations, overcoming the need of modelling them that would be an extremely challenging and sometimes not feasible activity in such complex scenarios.