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 in radians and spectroscopy gives the corresponding physical semimajor axis , the small-angle approximation gives .
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]
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