Gaia DR3 astrometric-orbit cos i uncertainties are too small by a factor of 1.9 (68%: 1.6-2.35; s=1 rejected, p=1e-4) for 18 eclipsing binaries, if the eclipses limit |cos i| to (R1+R2)/r

Question: are the formal uncertainties of cos i in Gaia DR3 astrometric orbits correct? Method: an eclipsing binary has an orbit near edge-on. Thus its true |cos i| is less than a limit delta = (R1+R2)/r, where r is the separation at conjunction. We cross-matched the Gaia DR3 nss_two_body_orbit solutions with VSX, the TESS and Kepler eclipsing-binary catalogues and other sources. We kept the systems where the eclipse period agrees with the Gaia period (all within 2.7 %). We got 18 calibrators with periods of 4-624 d and G = 6-14. We calculated cos i and its linear uncertainty sigma from the Thiele-Innes constants and their covariance. We fitted one scale factor s for all sigma values. The likelihood uses a uniform true cos i in [-delta, delta]. Result: s = 1.92 (68 %: 1.59-2.35; 95 %: 1.35-2.93) with a conservative delta. A likelihood-ratio test rejects s = 1 (p = 1.3e-4). With s = 1, 5 of 18 systems are outside the central 95.4 % interval of the model (0.8 expected). With s = 1.92, no system is outside it. A nominal delta, delta = 0, a bootstrap and 11 other variants give s = 1.59-2.18. A constant extra error of 0.05 in cos i, added in quadrature, also fits the data. The data cannot tell between the two models. Near i = 90 deg, sigma(i) in radians is approximately sigma(cos i). Thus the inclination uncertainties of these orbits are also too small. This agrees with the factor of about 1.8 for Gaia conjunction times (Chopard-Vilhem 2026) and with the factors of 1.3-1.7 for the parallaxes of orbital solutions (Nagarajan & El-Badry 2024). Exploratory result: the excess scatter increases with RUWE (Spearman rho = 0.62). For a division at the median RUWE, s = 1.20 and 2.45, permutation p = 0.010. We selected RUWE after six tests, and RUWE also correlates with sigma. Thus this is only a hypothesis. Negative result: the Gaia DR3 eclipsing-binary table gave no period match with the orbits. Limitations: only 18 systems; only near edge-on orbits; without the three largest residuals, s = 1.59 (s = 1 rejected, p = 0.025). The package has all code, the query text, the input rows, the results and a one-command re-run. This re-run gave the result tables again, byte for byte.

Gaia DR3 · astrometric binaries · eclipsing binaries · orbital inclination · uncertainty calibration · error inflation factor · non-single stars · Thiele-Innes elements · nss_two_body_orbit · RUWE · profile likelihood · TESS eclipsing binaries · Kepler eclipsing binaries · VSX · Kepler-16