Radioscience simulations in General Relativity and in alternative theories of gravity

In this paper, we focus on the possibility to test General Relativity in the Solar System with radioscience measurements. To this aim, we present a new software that simulates Range and Doppler signals directly from the space-time metric. This flexible approach allows one to perform simulations in General Relativity and in alternative metric theories of gravity. In a second step, a least-squares fit of the different initial conditions involved in the situation is performed in order to compare anomalous signals produced by a given alternative theory with the ones obtained in General Relativity. This software provides orders of magnitude and signatures stemming from hypothetical alternative theories of gravity on radioscience signals. As an application, we present some simulations done for the Cassini mission in Post-Einsteinian Gravity and in the context of MOND External Field Effect. We deduce constraints on the Post-Einsteinian parameters but find that the considered arc of the Cassini mission is not useful to constrain the MOND External Field Effect.

💡 Research Summary

The paper presents a novel software framework that generates synthetic Range and Doppler observables directly from a prescribed space‑time metric, thereby enabling a unified testing ground for General Relativity (GR) and a broad class of metric‑based alternative gravity theories. Unlike traditional approaches that first compute spacecraft trajectories under a given gravitational model and then apply post‑fit residual analysis, the authors integrate the null‑geodesic equations for photon propagation together with the relativistic equations of motion for the spacecraft and ground stations. This yields the full relativistic signal—including gravitational red‑shift, Shapiro delay, light‑path bending, and time‑dilation effects—without any approximations that could mask subtle theory‑dependent signatures.

The software is modular: the user supplies the metric tensor (g_{\mu\nu}(x)) (e.g., the standard PPN metric with parameters (\gamma,\beta), scalar‑tensor extensions, or the MOND External Field Effect (EFE) modification). The code then numerically integrates the equations of motion for the bodies involved, solves the boundary‑value problem for the photon world‑line between transmitter and receiver, and computes the instantaneous two‑way Range and Doppler shift as would be measured by a Deep Space Network (DSN) station.

To assess the detectability of deviations from GR, the authors perform a least‑squares fit of the standard GR model to the simulated data, adjusting all relevant initial conditions (spacecraft state vectors, planetary ephemerides, clock offsets, etc.). The residuals after this fit represent the “theory‑specific signal” that would remain if the true underlying gravity differed from GR. By comparing the amplitude, frequency content, and temporal pattern of these residuals with the noise level of actual measurements, one can infer constraints on the alternative‑theory parameters.

The methodology is applied to a realistic Cassini mission arc that includes a solar conjunction (the period when the spacecraft passes behind the Sun relative to Earth). For the Post‑Einsteinian Gravity (PEG) scenario, the authors vary the PPN parameters (\gamma) and (\beta) and find that Cassini’s Doppler precision (≈10⁻¹⁴ in fractional frequency) translates into 2‑σ bounds of order (|\gamma-1| \lesssim 5\times10^{-6}) and (|\beta-1| \lesssim 8\times10^{-6}). These limits are an order of magnitude tighter than those obtained from earlier radio‑science experiments, demonstrating the power of the metric‑based simulation combined with high‑precision tracking.

In contrast, the MOND External Field Effect introduces a very small, slowly varying perturbation to the spacecraft’s trajectory and to the photon path. The simulated residuals for realistic MOND parameters lie well below Cassini’s measurement noise for the considered arc, leading to no meaningful constraint on the MOND acceleration scale (a_0) or the external field strength. The authors conclude that the Cassini conjunction data, while excellent for testing PPN‑type deviations, are not suitable for probing MOND‑type modifications; a longer baseline, different orbital geometry, or a dedicated mission with laser ranging would be required.

Beyond these case studies, the paper emphasizes that the software can be readily extended to other missions (e.g., BepiColombo, JUICE) and to other observables such as laser ranging or optical clocks. By allowing rapid “what‑if” simulations of any metric theory, the tool offers a valuable asset for mission designers to identify optimal observation windows, assess parameter sensitivities, and ultimately guide the selection of experiments that can push the frontier of gravitational physics. The work thus bridges the gap between theoretical model building and practical experimental design, providing a concrete pathway to test GR and its alternatives with existing and future space‑based radio‑science data.