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Andrea M. Ghez measures stellar orbits around the supermassive black hole at the center of the Milky Way. Her team's Keck observations combined astrometry with radial velocities for the short-period star S0-2.

An angular orbit alone leaves a mass-distance degeneracy of an angular stellar orbit. Adding Doppler spectroscopy supplies a physical velocity scale, allowing central mass and Euclidean distance to be fitted together. Their 2008 analysis inferred roughly four million solar masses at a Euclidean distance of eight kiloparsecs, and examined how source confusion and assumptions about central motion affected the result.^[ref]

Orbital parallax infers a system's Euclidean distance by comparing the angular size of an orbit with its physical size. If an orbital fit gives a deprojected angular semimajor axis $\alpha$ in radians and spectroscopy gives the corresponding physical semimajor axis $a$, the small-angle approximation gives $d=a/\alpha$.

The scales must describe the same orbit. In a binary star, radial-velocity amplitudes, orbital period and eccentricity give physical projected orbital sizes; the astrometric geometry can supply the orbital inclination needed to remove that projection. The mass-distance degeneracy of an angular stellar orbit gives a worked example of why adding a physical velocity measurement changes what can be inferred.^[ref]