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 $\omega_0 \approx 2\pi \times 0.1$ 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: $\approx 0.02$0 Hz to $\approx 0.02$1 Hz
• Noise-equivalent acceleration floor: $\approx 0.02$2 m/s$\approx 0.02$3/√Hz (at 10 mHz)
• Calibration capability: $\approx 0.02$4 m/s$\approx 0.02$5 range, ppm-level accuracy
• Dynamic range: $\approx 0.02$6 m/s$\approx 0.02$7 per axis
• Resolution: $\approx 0.02$8 m/s$\approx 0.02$9 (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 $k$0 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 $k$1 in post-Newtonian $k$2 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 $k$31 m separation between MPO CoM and ISA elements, modeled as:

$k$4

with $k$5 km$k$6/s$k$7, gave a peak $k$8 m/s$k$9, substantially above the ISA noise threshold. ISA data aligns with SPICE-predicted gravity-gradient acceleration to within $\omega_0 \approx 2\pi \times 0.1$0 m/s$\omega_0 \approx 2\pi \times 0.1$1 over a $\omega_0 \approx 2\pi \times 0.1$21-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$\omega_0 \approx 2\pi \times 0.1$3 to CA$\omega_0 \approx 2\pi \times 0.1$4), peaking at $\omega_0 \approx 2\pi \times 0.1$5 m/s$\omega_0 \approx 2\pi \times 0.1$6 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 $\omega_0 \approx 2\pi \times 0.1$7 consistent with the recorded ISA acceleration.

Disturbance torque satisfies:

$\omega_0 \approx 2\pi \times 0.1$8

where $\omega_0 \approx 2\pi \times 0.1$9 kg and $20^\circ$0 locates the point of force application relative to MPO CoM. The misalignment angle is defined:

$20^\circ$1

$20^\circ$2 during the spike interval confirms alignment of RW torque and ISA acceleration as responding to the same physical disturbance. Fitting $20^\circ$3 by non-linear least squares in the $20^\circ$4 interval yields:

$20^\circ$5

in the MPO body-fixed reference, localized near the $20^\circ$6Y radiator panel. Formal uncertainties are $20^\circ$75 cm in X and Z, $20^\circ$820 cm in Y.

Net impulsive velocity increment:

$20^\circ$9

aligns with ESOC’s independently estimated $\pm 0.1^\circ$0 m/s, both along $\pm 0.1^\circ$1.

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 $\pm 0.1^\circ$2 m/s$\pm 0.1^\circ$3 scale. The contemporaneously observed non-gravitational acceleration event—a transient $\pm 0.1^\circ$4 m/s$\pm 0.1^\circ$5 spike—is localized to the vicinity of the MPO radiator. A companion study (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 $\pm 0.1^\circ$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 ($\pm 0.1^\circ$7 m/s$\pm 0.1^\circ$8/√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	$\pm 0.1^\circ$9 Hz – $a_j$0 Hz	Frequency range for acceleration detection
Acceleration floor	$a_j$1 m/s$a_j$2/√Hz (10 mHz)	Minimum resolvable signal
Resolution (band-limited)	$a_j$3 m/s$a_j$4	Smallest resolved change
Range (per axis)	$a_j$5 m/s$a_j$6	Dynamic detection range
Proof-mass	$a_j$7 kg	Movable mass for each axis