Figure 3 schematizes the HAA sensing elements as point masses, each associated with a sensing axis defined as the direction along which an external acceleration produces the maximum signal. Because the centers of gravity of the sensing elements do not coincide with the spacecraft's center of mass, the accelerometer is inherently sensitive to the gravity gradient generated by the Moon's gravitational field at the sensor locations. The expected signal can be computed using: 1aggi=μm|R0|33R0R0T-I3×3ri where μm is the Moon gravitational parameter, R0 is the position vector from JUICE center of mass to the Moon center of mass, and ri is the position vector from JUICE center of mass to the ith HAA sensing element.

In this work, only data collected by the Acc0 sensor are presented, as most of the relevant signals were detected along this axis, which was also the less noisy. Figure 4 shows the HAA calibrated data collected by the sensor Acc0 (black curve) compared with the expected gravity gradient signal (red curve). The HAA data calibration consisted of applying a low-pass filter with a cutoff frequency of fc=0.5 Hz to retain only frequencies within the instrument bandwidth. This was followed by a parabolic detrending procedure and a correction for thermal effects induced by temperature variations. The thermal compensation step was necessary because the instrument's thermal control system was not activated during the measurements. The correction was performed using the proof-mass thermometer readings, which were converted into equivalent acceleration signals and subsequently removed from the data. The temperature-to-acceleration conversion factor was estimated by minimizing the residuals of the calibrated acceleration after subtraction of the expected acceleration signal.

The HAA measurements show good agreement with the expected signal for most of the time, but it is evident how the black curve exhibits additional signatures, suggesting the presence of other perturbing phenomena.

The grey area corresponds to a solar eclipse experienced by the spacecraft from 20:36 to 21:08 UTC, also visible in the spacecraft ground track in Fig. 5 (blue dots). The abrupt temperature change in temperature during ingress/egress phases caused thermal snaps that are described in detail in the next section.

Due to the high solar array Sun aspect angle, α≈70°, the expected drop of solar radiation pressure acceleration during the eclipse was ∼ 10-8m s⁻², thus too close to the HAA measurement accuracy to be unambiguously detected. Also, the albedo pressure and infrared radiation emitted by the Moon were inducing accelerations well below the instrument's sensitivity ∼10-9 m s⁻². Instead, the sudden absence of solar radiation during the eclipse caused abrupt changes in the spacecraft surface temperatures and large thermal gradient between the front and rear surfaces induced thermoelastic distortions on the structure.

This phenomenon, known as thermal snap, can be described mathematically using (Eq. 2). The resulting quasi-static displacements can be expressed in terms of the temperature difference through the thickness of the considered structure (Johnston et al., 2000). These displacements are directly proportional to both the surface thermal expansion coefficient αCTE and inversely proportional the thickness h. The effect is magnified on the spacecraft solar array, due to their large surface area and small thickness, see Fig. 6. The term 1-ν2 contains the Poisson's coefficient ν and it's used to consider the structural response of a wide plate rather than a narrow beam. If the difference between front and back surface temperatures ΔT=Tf-Tb is not constant in time, the generic point of the solar array, with a distance x from the hinge, will be subject to an acceleration atst=d2ststdt2 acting along the solar array normal direction n, as described in Eq. (3). 2stst|x=-αCTE1-ν2ΔTtx2h2n3atst|x=d2ststdt2=-αCTE1-ν2d2ΔTtdt2x2h2n

Unfortunately, for the JUICE spacecraft only the solar array back surface temperature Tb can be retrieved from thermistors telemetry, while the front one Tf is available at a frequency of only one data point per month. For this reason, to reconstruct the ΔT curve during the eclipse we built a thermal mathematical model that describes the heat transmission from front to rear surfaces of the arrays. The solar array is modelled as a honeycomb aluminum core surrounded by two aluminum plates that exchanges heat via conduction through the core and via radiation from the plates towards internal surfaces and to the outer space. The front temperature can be estimated by solving the following system of equations (Van der Ha, 2010): 4QSUN/Ap-QAPR/Ap-σSBεSA,fTf4-kAalhTf-Tb-σSBεi1-Aal2-εiTf4-Tb4=Cp,fdTfdtσSBεSA,fTb4+kAalhTf-Tb+σSBεi1-Aal2-εiTf4-Tb4=Cp,bdTbdt with, 5QSUN=ApαSAcos⁡αtϕ1AUDs2 here, Cp,f and Cp,b are the thermal capacity of the front and back surfaces respectively, Ap is the area of the single panel, αSA is the absorptivity of the panel's front side, εSA,f and εSA,b are the emissivity of the panel's front and back sides, k is the conductivity of the aluminum honeycomb, Aal=ρhc/ρal is the net aluminum cross section defined as the ratio between the density of the honeycomb and the density of the aluminum, h is the panel's thickness, εi is the emissivity of the internal surfaces (assumed equal to 0.6) and σSB is the Stephan Boltzmann constant. It has been considered also the power extracted from each panel read by the array power regulator QAPR parameter, obtained from telemetry. The ϕ1AU and Ds are respectively the energy solar flux at one astronomical unit from the Sun and the spacecraft actual distance from the Sun.

Model parameters were partly provided by the project (k,h,Ap,εSA,f,εSA,b,αSA) or estimated (CP,f,CP,b,αCTE,Aal) by matching the computed rear-side temperature with the corresponding measured data, collected in the same reference period. Figure 7 shows the computed front-side temperature (red curve) and rear-side temperature (blue curve), obtained by solving (Eq. 4, compared with the rear measured one (green curve). At this stage, Eq. (3) can be applied to compute the thermal snap acceleration induced by JUICE's solar array. To compare the modelled acceleration with the HAA measurements, the computed acceleration must be projected along the Acc0 sensitive axis and scaled by the ratio between the solar array mass and the total spacecraft mass MSC=5700 kg. Additionally, the relative displacement between the spacecraft center of mass and the solar array center of mass must be considered.

Table 2 reports the values of parameters, either assumed or estimated, used to model the thermal behavior of JUICE solar arrays.

Figure 8 shows the comparison between HAA Acc0 calibrated data after the removal of the Moon's gravity gradient signal and the computed thermal snap acceleration. This latter primarily occurred during the penumbra phase (yellow shadowed area), where the rapid transition from umbra condition (grey shadowed area) to the illuminated condition (white area), amplified both the thermal gradient and its second derivative. The computed quasi-static displacement of the solar array tip was estimated to be approximately 50 mm, corresponding to ∼0.3° of angular displacement. After the penumbra phase, HAA data shows a clear periodic signal easily explained by thermally induced vibrations of the solar array structure. This is confirmed by the amplitude spectral density (ASD) computed on HAA data after the spacecraft came back in full illumination (white area in Fig. 8), where we found that the dominant frequency closely matches the first out-of-plane mode of the solar array, as shown in Fig. 9. A similar phenomenon was observed at penumbra ingress; however, due to the slower transition from illumination to umbra, the perturbing signal was weaker, and the resulting displacement and corresponding acceleration detected by HAA were correspondingly smaller.

The first signal, identified by red circles in the Fig. 10, appears to be associated with spacecraft activity related to the Submilimetre Wave Instrument (SWI), the only one featuring a steerable component and active at the corresponding epochs: a telescope mounted on the same spacecraft plate as the HAA (+X vault). Personal communication with the SWI instrument team confirmed that at 20:41:58 UTC the telescope was rotated by 72° in the along-track direction to point toward the Moon (nadir position). A second rotation, in the opposite direction by 54°, was performed at 21:27 UTC to observe the Moon in a backward-looking configuration. These mechanical operations primarily excited resonance modes of the spacecraft's MAGboom structure (0.44, 0.46 and 2.6 Hz) and solar arrays (0.13, 0.21 and 0.89 Hz). The influence of these events on HAA data capability to support 3GM experiment has yet to be fully assessed. It is likely that dedicated tests will be required to thoroughly characterize possible interference issues.

The second SWI event is superimposed to another clearly visible low-frequency phenomenon occurred onboard the JUICE spacecraft. After the eclipse event, JUICE reached the Moon CA at 21:14:50 UTC and soon after crossed the terminator at 21:18:35 UTC. Figure 11 shows JUICE attitude during the terminator crossing. At that moment, the +Z and +X directions of JUICE were oriented toward the illuminated surface of the Moon, receiving most of the incoming heat due to lunar albedo and infrared radiation. One of the most plausible explanations for the effect is that the multilayer insulation (MLI) on the +Z vault may have accumulated frozen contaminants during the early cruise phase, as this surface is typically exposed to deep space. Given the combination of high incoming radiation and the low thermal inertia of the MLI, it is likely that its temperature increased rapidly, potentially triggering an outgassing event. A similar phenomenon was observed on the BepiColombo ESA–JAXA mission during a Venus swing-by (De Filippis et al., 2025).

The JUICE spacecraft attitude and orbit control system (AOCS) also detected this event. Figure 12 shows the unmodelled torque generated by the reaction wheels to maintain the commanded quasi-inertial attitude. The dominant torque component was observed along the +Y JUICE SPACECRAFT axis, while the main acceleration measured by HAA was along the -Z JUICE SPACECRAFT axis. Assuming that M=MSCr×a, where M is the unmodelled torque generated by the reaction wheels, r is the vector distance from the spacecraft center of mass and the outgassing location and a is the unmodelled acceleration measured by HAA, adopting the reasonable simplification that both torque and force acted predominantly along a single axis, the outgassing appears to have occurred approximately 50 cm from the spacecraft's center of mass, in the -X JUICE SPACECRAFT direction.

To further investigate the impact of the suspected outgassing event, we conducted an orbit determination analysis using Doppler data, collected during the Lunar gravity assist. The radiometric dataset consisted of X band two-way coherent Doppler data acquired by the ESTRACK ground stations at:

New Norcia on 19 August 2024, from 11:09 to 22:10 UTC, with an observed Doppler noise level of 0.035 mm s⁻¹ @60 s, and

Note that no 3GM's KaT operations were possible as it would have required a Ka band uplink signal, currently only available at Malargüe ground station. This analysis was performed with ESA's GODOT v1.11 software, using a setup adapted from radio science analyses (Cappuccio et al., 2025). In a first attempt we tried to solve for ΔVi components along all three spacecraft axes X, Y and Z, and the time event, but the reduced radiometric data set available for this analysis was not sufficient to fully decorrelate the three estimated impulses, resulting in a too large covariance matrix that was both consistent with estimates carried out by the Flight Dynamics (FD) team (Syndercombe et al., 2025) and null ΔVi. The estimated time of the outgassing event was 19 August 2024 21:26±42 s UTC. We had to accept to carry out a second constrained analysis in which ΔVy was kept null and we obtained a better statistical compatibility with FD solution. In summary, the analysis based solely on radiometric data provides only limited constraints on the characteristics of the outgassing event, which is detected with significantly greater sensitivity by the accelerometer measurements. Consequently, the HAA data were not included in the orbit determination process because it would not produce any significant effect on the orbital solution.

Indeed, along the +Z direction, HAA measurements are consistent with a ΔVy=-0.7 mm s⁻¹. Integrating a different portion of HAA data where no signals were detected, we associated to the outgassing impulse a maximum error of 0.1 mm s⁻¹. Along the +X direction, HAA measurements are strongly affected by the thermal disturbances, making the collected data unreliable. However, an upper bound for the ΔVx and ΔVy can be defined from the formal uncertainty of the orbit determination process. Considering 3σ formal uncertainties, an upper bound for the other components of the outgassing induced ΔV can be provided, |ΔVx|≤0.3 mm s⁻¹ and |ΔVy|≤5.4 mm s⁻¹.

After the outgassing, the spacecraft's momentum changed according to the push exerted by sublimated products. Using the conservation of momentum, the sublimated product's effective exit velocity Vsub and its mass msub can be related to the overall change in the spacecraft's velocity DV: 6msubVsub=MSCDV

The most plausible outgassing product is water ice, as also suggested by observations from different instrument teams during the flyby. Under this assumption, we can follow the same analysis made by Sandford et al. (2020), to estimate the mass of the outgassed products.

The effective exit velocity of the sublimated water vapor can be estimated by considering the theoretical maximum velocity for a sublimating gas, given by Bird (2002): 7Vlim=2γRTγ-1 where γ is the ratio of specific heat of water, R=461.5 J kg⁻¹ K⁻¹ is the specific gas constant, and T is the total temperature at zero velocity. For typical value of γ=1.33 and T=300 K, the Vlim=1000 m s⁻¹, However, this is only a physical maximum value, and the true value of the effective exit velocity is not easy to retrieve. Considering that the actual exit velocity Vsub can be up to Vsub=1/2Vlim=500 m s⁻¹, it's possible to give an estimate of the upper limit for the sublimated product's mass: 8msub=MSCDV/Vsub=8g

Note that the true value of the effective exit velocity may differ in relation to the sublimation dynamics. If Vsub=Vlim=1000 m s⁻¹, the outgassed mass became msub=4 g. Hence, is possible to assess that the sublimated products mass could be estimated within the range of [4–8] g.

Moreover, the estimation of sublimated particles along the other spacecraft axes is even more challenging. However, the accelerometer data provided indication that the outgassing components along those directions are significantly smaller than along the +Z JUICE SPACECRAFT axis.