Distances to stars and their sizes

As the Earth moves along its orbit, a nearby star traces a small ellipse once a year against the distant stars. The annual parallax π is the angle at which the radius of the Earth’s orbit (1 AU) is seen from the star. The distance is d = 1 / π, with π in arcseconds and d in parsecs; 1 pc is the distance to a star whose parallax is 1″. Bessel first measured a stellar parallax in 1838, for 61 Cygni (≈ 0.3″, i.e. ≈ 11 light-years); Struve (Vega) and Henderson (Alpha Centauri) did so at about the same time. Proxima Centauri has π ≈ 0.77″ (≈ 1.3 pc). From the ground, π could be measured down to ≈ 0.01″ (≈ 100 pc); the Hipparcos satellite (1989–1993) measured ≈ 118,000 stars, and Gaia (operating 2013–2025) has measured more than a billion stars very accurately. Parallax is often given in milliarcseconds (mas): d (pc) = 1000 / π(mas).