Measuring the Distance to the Stars
📐 Measuring the Earth
Question
How do we know how far away the stars are?
Hold your thumb up and close one eye, then the other: it appears to jump against the background. Stars do the same, but over six months, as the Earth moves 300 million km across its orbit. The shift is tiny - less than one arcsecond (1/3600 of a degree) for all but the nearest stars - so the first successful measurement waited until 1838, when Bessel measured 61 Cygni at 0.31 arcseconds.
The math
distance (parsecs) = 1 / parallax (arcseconds). 61 Cygni: 1/0.31 = 3.2 parsecs = 10.4 light-years. One parsec is 3.26 light-years. Today the Gaia satellite (at the Sun-Earth L2 point) measures parallaxes for ~2 billion stars to microarcsecond precision (1/1,000,000 of a degree); the baseline is the Earth's orbit (1 AU) - which is exactly what the parsec is defined from.
Why it matters
Parallax is the first rung of the cosmic distance ladder. Everything else - the size of the galaxy, the expansion of the universe, the age of the cosmos - is built on this one piece of geometry.