Hold your thumb at arm’s length and close one eye, then the other. Your thumb shifts against the background. That’s parallax — and it’s the same principle astronomers use to measure the distance to stars.

Stellar parallax

As Earth orbits the Sun, nearby stars appear to shift slightly against the distant background. The baseline is the diameter of Earth’s orbit: 2 AU (about 300 million km).

The parallax angle $p$ is half the total angular shift over six months. Distance and parallax are inversely related:

$$d = \frac{1}{p}$$

where $d$ is in parsecs and $p$ is in arcseconds. One parsec = the distance at which 1 AU subtends 1 arcsecond = 3.26 light-years.

Watch the nearby star (yellow) shift against the fixed background as Earth orbits. More distant stars show smaller parallax angles.

The precision revolution

Hipparcos (ESA, 1989–1993): Measured parallaxes to ~1 milliarcsecond (mas) accuracy, giving reliable distances to stars within ~100 parsecs (~300 light-years). Catalogue of 118,000 stars.

Gaia (ESA, 2013–present): Measures parallaxes to ~10 microarcseconds ($\mu$as) — 100× better than Hipparcos. Reliable distances to stars across the Milky Way. DR3 (2022) contains 1.8 billion sources. Gaia has revolutionised our understanding of the galaxy’s structure, dynamics, and history.

The nearest star, Proxima Centauri, has a parallax of 768 mas (distance: 1.30 pc = 4.24 light-years). At 10 kpc (30,000 light-years — across the galaxy), the parallax is just 0.1 mas. Even Gaia struggles beyond ~10 kpc.

The cosmic distance ladder

Parallax is the first rung of the cosmic distance ladder — the foundation on which all other distance measurements rest:

1. Parallax (direct geometry): up to ~10 kpc with Gaia
2. Standard candles (Cepheid variables, RR Lyrae): their intrinsic brightness is known → compare with apparent brightness → distance
3. Type Ia supernovae: brighter standard candles, visible in distant galaxies
4. Hubble’s law (redshift): for the most distant objects, recession velocity ∝ distance

Each rung is calibrated against the one below it. Errors compound upward — which is why the parallax foundation matters so much. Every improvement in parallax precision recalibrates the entire ladder.