Stellar parallax

Parallax is the apparent change in an object's direction when it is observed from different locations. A familiar example is a nearby finger seeming to move against a distant background when viewed first with one eye and then the other. In astronomy, Earth's orbital motion supplies a much larger observing baseline: measurements taken about six months apart view a star from opposite sides of Earth's orbit.

The nearby star appears to shift against the background of more distant stars. This angle can be used in a triangle with the known Earth–Sun baseline to calculate distance. By definition, a star with a parallax angle of one arcsecond is one parsec away; in general, d(parsecs) = 1/p(arcseconds). A smaller measured parallax corresponds to a greater distance.

The apparent displacement repeats with Earth's yearly orbit and is distinct from a star's proper motion, its actual gradual movement across the sky. Observers therefore measure positions over time and model the recurring parallax pattern separately from other motion. The angular shifts are very small, so accurate measurements require precise instruments and careful analysis.

For ground-based observations, atmospheric effects make extremely small angles difficult to measure. Space astrometry avoids atmospheric blurring and can observe stellar positions with much higher precision, extending the useful reach of parallax measurements.

The first successful measurements of stellar parallax for a small number of stars were made in the late 1830s by Friedrich Bessel, Wilhelm Struve and Thomas Henderson. The method established that stars lie at measurable, finite distances rather than all occupying the same remote celestial sphere.

Later space missions substantially expanded the number and precision of stellar measurements. ESA's Hipparcos mission made large catalogues of stellar positions and parallaxes. Gaia has used repeated measurements of stellar positions to determine parallaxes for a vastly larger sample, providing a geometric distance foundation for mapping the Milky Way.

Parallax is a direct geometric rung in astronomical distance measurement and is especially valuable for nearby stars. Distance estimates from parallax also help calibrate other methods used farther away. The method becomes more demanding as distance increases because the angle shrinks; uncertainties in a very small parallax can therefore produce large relative uncertainty in the inferred distance.

A parallax-based distance should be interpreted with its measurement uncertainty and, for very small or uncertain angles, suitable statistical methods. Parallax is not apparent brightness: a star can look bright or faint for reasons that do not by themselves establish its distance.