a temperature much greater that the surfaces pointing -Y. During the cruise, at a Sun-spacecraft distance comparable with the Venus orbit, the delta average temperature between the two spacecraft sides can be kept around 120 K. Looking at thermistors onboard the spacecraft, we knew that the Venus albedo heated the -Y side of the MCS, increasing the temperature of of about 30 K. In terms of acceleration, considering that ISA is a relative 8 accelerometer, the changes of acceleration in its frequency band can be only addressed to the 30 K variation, since the +Y side of the MCS did not change significantly its temperature.

We can conclude that this effect is well below the instrument sensitivity.
2.2. Gravity Gradients measurement Figure 8 shows the calibrated acceleration detected by ISA (solid lines) over-imposed to the expected calculated accelerations (dotted lines) that, as expressed in the previous paragraph, can be considered mainly the gravity gradients signals expected at each ISA sensing elements. ISA team, by got the executed attitude and the most accurate final trajectory using the BepiColombo operational SPICE kernels,precisely simulated the expected Gravity Gradient signal experienced by each accelerometer sensing elements. The equation for the Venus field monopole effect is used:
� 3 ˆR0 ˆR
�
T
aj GG = µg |R0|3
rj ISA,
0 −I3×3
(2) where µg = GMg is the Venus standard gravitational coefficient, R0 is the vector linking the CoM of MCS with the Venus center, ˆR0 is its unit vector, the I3×3 is a 3x3 identity matrix and rj
ISA
is the vector of the j-nth accelerometer (Acc0 = +X ISA directed, Acc1 = Y ISA directed, Acc2 = Z ISA directed) from the MCS CoM. The CoM position used in our simulations has been taken from the ESA/ESOC manoeuvre file. The figure 8 undoubtedly unveils that the simulated Gravity Gradient signal agrees with the ISA measured data. Hence, for the first time, a direct measurement of the Gravity gradient was carried out for an extraterrestrial body.
2.3. Unexpected Non Gravitational Perturbation The figure (8) also shows that in the period from CA−4′ to CA+3′ a spike acceleration, magnified along Acc1 (Y ISA directed and hence very close to Y MCS), but visible in all the channels, caused the measurement to deviate, by order of magnitude, from the expected signals. Occurring at the CA, the spike appeared in coincidence with
the direct albedo acceleration and the Planetary Infrared radiation pressure expected maximum, making impossible to distinguish them among data. This spike soon was considered completely unexpected because it did not match in amplitude and behaviour to any of the predicted accelerations listed in the previous section. At this point, ISA team wondered if this signal was a real physical acceleration acting on the spacecraft or an artifact introduced by the instrument.
2.3.1. On board net torque analysis To understand if ISA measured an artifact or the whole spacecraft experienced a real external acceleration, the team looked for in the Attitude-Orbit-Control-System (AOCS) data for signatures indicating a torque caused by an external force acting on the MCS. Since, as described in 1.4, the commanded attitude was quasi-inertial and the +Y Axis always pointed towards the Sun, the main torque compensation of the AOCS should have been the gravity gradient torque. So, linking the spacecraft moment of inertia, trajectory and attitude, the expected gravity gradient torque was calculated using the following equation:
� (3)
TGG = 3n2 ˆRB 0 × � J ˆRB
where n is the spacecraft mean motion, J is the spacecraft moment of inertia and ˆRB 0 is the Venus-spacecraft direction. Figure 9 shows the gravity gradient estimated torques (dashed lines) around the MCS body axis, computed using the equation above, overimposed to the torque effectively commanded by the AOCS (solid lines). It is clear that the curves are compatible everywhere except for the time span [13:49:30 UTC, 13:53:20 UTC] = [CA −2′, CA + 1′] when the unexpected acceleration spike, described in the previous paragraph, was detected. The misalignment is visible on the three axes, but is clearly highlighted on the MCS + X axis. This circumstance let the ISA team argue that exactly at the time of the spike in acceleration detected by ISA, BepiColombo AOCS compensated a torque to keep the spacecraft at the commanded attitude, mainly around the S/C+ˆxsc axis:

[Figure: Figure 8: ISA measured calibrated accelerations during the second Venus flyby.]