= Orbital parallax
<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.<Measuring Distance and Properties of the Milky Way's Central Supermassive Black Hole with Stellar Orbits by Andrea M. Ghez and others>[Abstract: combined angular and radial-velocity orbit measurements and simultaneous mass–distance inference]{ref}
Back to article page
