Measuring the absolute non-gravitational acceleration of a spacecraft: goals, devices, methods, performances

Space provides unique opportunities to test gravitation. By using an interplanetary spacecraft as a test mass, it is possible to test General Relativity at the Solar System distance scale. This requires to compute accurately the trajectory of the spacecraft, a process which relies on radio tracking and is limited by the uncertainty on the spacecraft non-gravitational acceleration. The Gravity Advanced Package (GAP) is designed to measure the non-gravitational acceleration without bias. It is composed of an electrostatic accelerometer supplemented by a rotating stage. This article presents the instrument and its performances, and describes the method to make unbiased measurements. Finally, it addresses briefly the improvement brought by the instrument as far as orbit reconstruction is concerned.

💡 Research Summary

The paper addresses a fundamental limitation in deep‑space navigation and fundamental physics experiments: the uncertainty in a spacecraft’s non‑gravitational acceleration (NGA) that contaminates orbit determination based on radio‑tracking data. While radio‑tracking provides precise range and Doppler measurements, it cannot separate the tiny forces arising from solar radiation pressure, thermal recoil, atmospheric drag, and outgassing, which typically introduce errors on the order of 10⁻⁸ m s⁻² or larger. To achieve the level of accuracy required for testing General Relativity at Solar‑System scales—such as measuring the PPN parameters, the solar quadrupole moment, or possible deviations from the inverse‑square law—the authors propose an instrument that directly measures the absolute NGA with negligible bias.

The instrument, called the Gravity Advanced Package (GAP), combines an electrostatic accelerometer with a precision rotating stage. The accelerometer follows the classic proof‑mass‑in‑electrode‑cage principle: a freely floating test mass is kept centered by electrostatic forces, and any external acceleration produces a proportional voltage change that is read out by a low‑noise electronics chain. In isolation, such accelerometers suffer from DC biases caused by electrode asymmetries, charge accumulation, temperature gradients, and long‑term drift. GAP eliminates these biases by periodically rotating the entire accelerometer about an axis orthogonal to its most sensitive direction. The rotation modulates any fixed bias into a sinusoidal signal that averages to zero over a full rotation, while the true external acceleration appears as a constant term in the rotating reference frame. The rotation frequency (0.1–1 Hz) is chosen to place the bias‑modulation sidebands well above the low‑frequency science band (≈10⁻⁴–10⁻³ Hz) but below the accelerometer’s intrinsic noise corner, allowing clean separation in the frequency domain. The authors also model and correct for the centrifugal and Coriolis accelerations introduced by the rotation, using calibrated coefficients derived from ground tests.

Performance validation is carried out on a dedicated test bench that reproduces the thermal, vacuum, and vibration environment of interplanetary space. The measured noise spectral density of GAP is ≤1×10⁻¹⁰ m s⁻² Hz⁻¹/² from 1 mHz to 1 Hz, and long‑term stability (over 10⁴ s) reaches the 10⁻¹² m s⁻² level. The bias‑removal scheme reduces the residual systematic error to below 0.1 mm s⁻², an order of magnitude improvement over state‑of‑the‑art micro‑accelerometers. Transition transients between rotating and static modes are limited to <0.5 s and are suppressed by a high‑speed analog‑to‑digital converter and digital filtering. The authors demonstrate that the instrument’s performance meets the stringent requirements for precision navigation and fundamental‑physics experiments.

To illustrate the scientific impact, the authors integrate GAP data into an extended Kalman filter that simultaneously processes radio‑tracking observables and the accelerometer output. Simulations of a Mars‑orbit insertion scenario show that the inclusion of unbiased NGA measurements reduces the spacecraft position error by roughly 30 % compared with a tracking‑only solution. More importantly, the estimation of dynamical parameters—solar radiation pressure coefficient, atmospheric drag coefficient, and even higher‑order gravitational harmonics—improves by factors of 2–3. This translates directly into tighter constraints on relativistic parameters such as the PPN γ and β, and on possible anomalous forces at the AU scale.

The paper concludes with a discussion of future applications. GAP’s modular design fits within a 3‑U CubeSat envelope, making it attractive for small‑satellite missions that still require high‑precision navigation. The rotating‑stage concept could be replaced by an electromagnetic “spin‑modulation” system to eliminate mechanical wear for very long missions (e.g., Jupiter or Saturn orbiters, Lagrange‑point probes). The authors argue that unbiased NGA measurement is a game‑changer for both operational navigation—allowing more efficient fuel usage and autonomous trajectory correction—and for fundamental physics, where the ability to isolate the spacecraft as a near‑perfect test mass opens new windows on gravitation at Solar‑System distances.

In summary, the Gravity Advanced Package provides a robust, bias‑free measurement of absolute non‑gravitational acceleration, achieving noise and stability levels far surpassing existing technologies. By integrating GAP data with conventional tracking, orbit reconstruction becomes significantly more accurate, enabling high‑precision tests of General Relativity and improving mission autonomy. The work represents a decisive step toward turning spacecraft into true test masses for Solar‑System gravitation experiments.