Italian Spring Accelerometer (ISA)

• ISA is a high-sensitivity, three-axis mass-spring accelerometer designed to detect minute non-gravitational perturbations and perform the first in-situ measurement of a planetary gravity gradient.
• It integrates advanced mechanical, electrical, and thermal systems, achieving noise levels of ~1×10⁻⁹ m/s²/√Hz and a resolution of ~10⁻¹¹ m/s² within a ±5×10⁻⁴ m/s² dynamic range.
• ISA plays a pivotal role in precise orbit determination by enabling real-time data fusion with Ka-band radio tracking, effectively isolating external forces during critical mission phases.

The Italian Spring Accelerometer (ISA) is a high‐sensitivity, three‐axis mass‐spring accelerometer deployed on the Mercury Planetary Orbiter (MPO) of the ESA–JAXA BepiColombo mission. Designed to detect minute non‐gravitational perturbations and gravity gradients, ISA plays a crucial role in the BepiColombo Radio Science Experiment (BC-RSE), notably achieving the first direct in‐situ measurement of an extraterrestrial body's gravity gradient during the second Venus swing-by. ISA’s technical sophistication in mechanical, electrical, and thermal domains, along with advanced data fusion with Ka-band radio tracking, yields unprecedented measurement and orbit determination accuracy.

1. Mechanical and Electrical Architecture

ISA comprises three nominally identical one-dimensional sensing elements (SE0, SE1, SE2), each consisting of a trapezoidal proof-mass suspended from a rigid frame via a thin flexure (“blade”) spring. The proof-mass is equipped with capacitive pick-up electrodes on two opposing faces for displacement read-out, and four electrostatic actuation electrodes for centering and internal calibration. The overall mechanical system constitutes a simple harmonic oscillator with mass $m$ (nominally $\approx 0.02$ kg) and spring constant $k$ chosen such that the natural frequency %%%%3%%%% Hz.

The electrical design segregates the system into:

• ISA Detector Assembly (IDA): houses the sensing elements and front-end electronics (FEE), nested within thermal/shielding structures, with temperature controlled at $20^\circ$C $\pm 0.1^\circ$C.
• ISA Control Electronics (ICE): incorporates digital electronics, power converters, and data-handling interfaces. Digital feedback loop centers the proof-mass via controlled actuation voltages on electrodes.

Pick-up electrodes interface with low-noise capacitive-bridge electronics in the FEE. ICE communicates with the MPO on-board computer via SpaceWire and operates on a regulated 28 V supply.

2. Calibration, Reference Frames, and Reduction Procedures

ISA’s three sensing axes are not perfectly orthogonal. On-ground calibration produces an orthogonal “Instrument Line-of-Sight” frame (ISA_ILS) with origin at the center of mass of the Y-axis element. In-flight, raw acceleration signals $a_j$ from each element SE$_j$ undergo “vertex reduction” to yield a single acceleration vector $a_{ISA}$ at the ISA_ILS origin. This transformation accounts for the spatial offsets $r_j$ from MPO center of mass to each sensing element, as well as common-mode rotational and gravity-gradient corrections.

Key calibration metrics:

• Measurement band: $3 \times 10^{-5}$ Hz to $1 \times 10^{-1}$ Hz
• Noise-equivalent acceleration floor: $\sim 1 \times 10^{-9}$ m/s$^2$/√Hz (at 10 mHz)
• Calibration capability: $10^{-6}$ m/s$^2$ range, ppm-level accuracy
• Dynamic range: $\pm 5 \times 10^{-4}$ m/s$^2$ per axis
• Resolution: $\sim 10^{-11}$ m/s$^2$ (band-limited)

3. Integration on BepiColombo and Role in BC-RSE

The Detector Assembly is rigidly mounted on the MPO payload panel in a thermally optimized location, shielded by multilayer insulation, dedicated heaters, and sensors. ICE resides in the MPO avionics rack. ISA operates in conjunction with the Ka-band Transponder (KaT), enabling the BC-RSE (also referred to as MORE) to combine high-precision Doppler/range data with real-time vector accelerometry from ISA.

BC-RSE’s dynamic filter subtracts the non-gravitational perturbation force $F_{NGP} = m_{sc} \cdot a_{ISA}$ from spacecraft equations of motion, isolating pure gravitational dynamics, including relativistic effects. This methodology enables orbit determination accuracy better than 5 cm in range and $3 \times 10^{-5}$ in post-Newtonian $\gamma$ measurements.

4. Gravity-Gradient and Non-Gravitational Perturbation Measurements at Venus Swing-By

During the second Venus swing-by (VSB2), BepiColombo’s trajectory passed Venus at 550 km altitude (planetary radius 6051 km). The expected gravity gradient across the $\sim$1 m separation between MPO CoM and ISA elements, modeled as:

$$a_{GG}^j = \left(\frac{\mu_{Ven}}{R^3}\right) [3 (\hat{R} \otimes \hat{R}) - I_3] r_j$$

with $\mu_{Ven} = 3.2486 \times 10^5$ km$^3$/s$^2$, gave a peak $|a_{GG}| \approx 1.1 \times 10^{-6}$ m/s$^2$, substantially above the ISA noise threshold. ISA data aligns with SPICE-predicted gravity-gradient acceleration to within $\sim 10^{-8}$ m/s$^2$ over a $\pm$1-hour window, validating the first direct in-situ gravity gradient measurement due to a planetary body.

At closest approach (CA), a spurious acceleration spike was observed, lasting approximately 7 minutes (CA$-4'$ to CA$+3'$), peaking at $3.5 \times 10^{-6}$ m/s$^2$ predominantly along the Y-axis. The magnitude and profile could not be attributed to any modeled non-gravitational disturbance (solar pressure, albedo, IR emission, thermal recoil).

5. Attribution and Localization of the Non-Gravitational Event

Discrimination between instrument artifact and true external force leveraged contemporaneous Attitude and Orbit Control System (AOCS) reaction wheel torque telemetry. A clear deviation in commanded torques coincided with the acceleration spike, indicating compensation for a disturbance along $+Y_{body}$ consistent with the recorded ISA acceleration.

Disturbance torque satisfies:

$T_{dis} = m_{sc} (r_A \times a_{ISA})$

where $m_{sc} = 3991$ kg and $r_A$ locates the point of force application relative to MPO CoM. The misalignment angle is defined:

$$\beta = \arcsin \left( \frac{T_{dis} \cdot a_{ISA}}{|T_{dis}| |a_{ISA}|} \right)$$

$\beta \approx 0^\circ$ during the spike interval confirms alignment of RW torque and ISA acceleration as responding to the same physical disturbance. Fitting $r_A$ by non-linear least squares in the $\beta < 10^\circ$ interval yields:

$$r_A \approx [ +0.0235, -2.1841, -1.7233 ]\, \mathrm{m}$$

in the MPO body-fixed reference, localized near the $-$Y radiator panel. Formal uncertainties are $<$5 cm in X and Z, $<$20 cm in Y.

Net impulsive velocity increment:

$$\Delta V_{ISA} = \int a_{ISA}\, dt \approx (5.8 \pm 0.4) \times 10^{-4}\,\mathrm{m/s}$$

aligns with ESOC’s independently estimated $\Delta V_{radio} = (5.95 \pm 2.71) \times 10^{-4}$ m/s, both along $+Y_{body}$.

6. Scientific and Methodological Implications

ISA’s measurement at VSB2 constitutes the undisputed first direct in-situ detection of a planet’s tidal gravity gradient by a spacecraft accelerometer at the $10^{-6}$ m/s$^2$ scale. The contemporaneously observed non-gravitational acceleration event—a transient $\sim 3.5 \times 10^{-6}$ m/s$^2$ spike—is localized to the vicinity of the MPO radiator. A companion paper (De Filippis et al.) attributes the event to short-lived outgassing.

Combined ISA and AOCS analysis demonstrates the capacity of high-sensitivity accelerometry to isolate and quantify external forces producing $\Delta V \sim 0.6$ mm/s, which would otherwise confound precision orbit determination.

A plausible implication is that future missions demanding micrometer-per-second-level velocity accuracy should embed accelerometers of at least ISA-class sensitivity ($10^{-9}$ m/s$^2$/√Hz). Instrument mounting, thermal management, and shielding require stringent engineering to mitigate micro-thrusts and thermally driven outgassing effects.

ISA’s validation of the pseudo-drag-free BC-RSE strategy underscores the feasibility of achieving sub-ppm gravity-field and relativistic parameter sensitivity without recourse to complex drag-free platforms.

Table: Key Instrument Parameters

Parameter	Value	Description
Measurement band	$3 \times 10^{-5}$ Hz – $1 \times 10^{-1}$ Hz	Frequency range for acceleration detection
Acceleration floor	$\sim 1 \times 10^{-9}$ m/s$^2$/√Hz (10 mHz)	Minimum resolvable signal
Resolution (band-limited)	$\sim 10^{-11}$ m/s$^2$	Smallest resolved change
Range (per axis)	$\pm 5 \times 10^{-4}$ m/s$^2$	Dynamic detection range
Proof-mass	$\sim 0.02$ kg	Movable mass for each axis