How parallax measures a distance
A nearby star appears to shift against the distant background stars as Earth moves around the Sun. Six months apart, the baseline is 2 AU, and the geometry is a triangle thin enough to apply the small-angle approximation:
distance (parsec) = 1 ÷ p (arcseconds)
The unit is self-defining. A star with a parallax of exactly 1 arcsecond is, by definition, 1 parsec away — the name is "parallax of one arcsecond".
Worked example: Barnard's Star has the largest parallax of any star, about 0.547 arcsec. Distance = 1 ÷ 0.547 = 1.83 parsec = about 5.96 light years. That makes it the closest star to the Sun after the Alpha Centauri system, and its high proper motion gives it away: it has covered more sky in human history than almost any other star.
The error grows as the square of the distance
This is the practical limit of the method and it is not gentle. If the parallax is measured to 1% precision, the distance is known to 1% — but only because both numbers are small. At larger distances the parallax becomes a small difference between two larger quantities, and the relative error explodes:
- 0.1 arcsec → 10 pc, error ±0.1 pc
- 0.01 arcsec → 100 pc, error ±1 pc
- 0.001 arcsec → 1,000 pc, error ±10 pc
- 0.0001 arcsec → 10,000 pc, error ±100 pc
That last row is why ground-based parallax effectively stops around a few thousand parsecs, and why the space Gaia mission matters so much: by measuring a billion stars with a metre-class telescope, it pushed the reliable limit to around 100,000 parsecs and produced distances to galaxies two and a half million light years away.
Beyond parallax
For anything more distant, distance is inferred from brightness, and that requires knowing the intrinsic luminosity. Main-sequence stars follow a tight mass–luminosity relation, so a star's spectrum gives its mass and therefore its expected output — then distance follows from how dim it actually looks:
distance ∝ √(observed flux ratio)
The other two workhorse methods are variable stars (Cepheids and RR Lyrae have a period that correlates with luminosity) and Type Ia supernovae (standard candles whose peak brightness is remarkably uniform). All three are calibrated using nearby parallaxes, which is why the parallax scale remains the foundation even where it is not directly used.
Reading a published distance honestly
A quoted distance is an estimate with an uncertainty, and the uncertainty is often the interesting part. "Sirius is 8.6 light years away" compresses a measurement good to about ±0.1 light years, and the two numbers do not carry the same weight. The light travel time inherits the same relative error, which is why "Proxima Centauri, 4.2465 ly" implies a light that left in early 2022 and arrives in mid-2026 — accurate to a few days, and the precision is genuine, not decorative.