Anomalous orbits are found when minimum-χ2 estimation is applied to synthetic Gaia data for orbits with astrometric signatures comparable to the single-scan measurement error (Pourbaix 2002, A&A, 385, 686). These orbits are nearly parabolic, edge-on, and their major axes align with the line-of-sight to the observer. Such orbits violate the Copernican principle (CPr) and as such could be rejected. However, the preferred alternative is to develop a statistical technique that incorporates the CPr as a fundamental postulate. This can be achieved in a Bayesian context by defining a Copernican prior. Pourbaix’s anomalous orbits then no longer arise. Instead, the selected orbits have a somewat higher χ2 but do not violate the CPr. The problem of detecting a weak additional orbit in an astrometric binary with a well-determined orbit is also treated.
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