# Directly testing gravity with Proxima Centauri

## TL;DR

This paper proposes a method to test gravity theories by observing the orbit of Proxima Centauri with high-precision astrometry over about a decade, potentially distinguishing between Newtonian and Milgromian dynamics.

## Contribution

It introduces a feasible observational strategy using upcoming astrometric missions to test gravity in low acceleration regimes through Proxima Centauri's orbit.

## Key findings

- High-precision astrometry can differentiate gravity models within 10 years.
- Radial velocity measurements need improvement to reduce uncertainties.
- Long-period planets could mimic MOND signals under specific conditions.

## Abstract

The wide binary orbit of Proxima Centauri around $\alpha$ Centauri A and B differs significantly between Newtonian and Milgromian dynamics (MOND). By combining previous calculations of this effect with mock observations generated using a Monte Carlo procedure, we show that this prediction can be tested using high precision astrometry of Proxima Centauri. This requires ${\approx 10}$ years of observations at an individual epoch precision of $0.5 \, \mu$as, within the design specifications of the proposed Theia mission. In general, the required duration should scale as the 2/5 power of the astrometric precision. A long-period planet could produce a MOND-like astrometric signal, but only if it has a particular ratio of mass to separation squared and a sky position close to the line segment connecting Proxima Centauri with $\alpha$ Centauri. Uncertainties in perspective effects should be small enough for this test if the absolute radial velocity of Proxima Centauri can be measured to within ${\approx 10}$ m/s, better than the present accuracy of 32 m/s. We expect the required improvement to become feasible using radial velocity zero points estimated from larger samples of close binaries, with the Sun providing an anchor. We demonstrate that possible astrometric microlensing of Proxima Centauri is unlikely to affect the results. We also discuss why it should be possible to find sufficiently astrometrically stable reference stars. Adequately addressing these and other issues would enable a decisive test of gravity in the currently little explored low acceleration regime relevant to the dynamical discrepancies in galactic outskirts.