A new analysis shows that letting the orbit’s semi‑major axis a be a free parameter in a Bayesian Markov chain Monte Carlo algorithm does not change the inferred physics of wide binary stars. The algorithm, tested on the α‑Centauri AB‑Proxima system and a sample of 36 wide binaries, reproduces exactly the same posterior distributions for the effective gravitational parameter Γ and a as the older method that solves a from other orbital parameters.

The study starts by introducing a Bayesian MCMC routine where a can be free (with or without an empirical prior). Using both the α‑Centauri system and the Chae et al. sample, the authors find that the explicit‑a algorithm, when constrained by the observed sky‑plane separation s, produces posterior probability density functions indistinguishable from those obtained with the implicit‑a algorithm that derives a from a mathematical consistency relation.

Figures comparing the distributions of Γ and a for the binaries HD 189739/HD 189760 and α‑Centauri show excellent agreement between the two approaches. Even when a prior is applied, the shape of the inferred a distribution shifts only mildly, leaving the estimate of Γ unchanged.

However, the recovery of Γ is very sensitive to the uncertainties in radial velocity measurements. Adding arbitrary jitter errors can make a sample statistically consistent with Newtonian gravity, potentially biasing conclusions. This highlights the importance of careful error treatment and follow‑up observations when using wide binaries to test gravity.

Overall, the work demonstrates that the choice of parameterisation—explicit versus implicit for the semi‑major axis—has no effect on the scientific inference, provided the data are treated consistently.