Parsec ↔ Light-year

Parsec: 1 pc ≈ 3.26 light-years

A parsec (parallax-second) is the distance at which 1 astronomical unit subtends 1 arcsecond, working out to roughly 3.086·10¹⁶ m, or 3.26 light-years. The formula is d(pc) = 1/p, with p being the stellar parallax in arcseconds. That parallax is the apparent angular shift of a nearby star against the distant background as Earth swings across its orbit. Take Proxima Centauri, the Sun's nearest neighbour: p ≈ 0.768″ gives d ≈ 1.30 pc ≈ 4.24 light-years. Typical Milky Way stars sit 0.1–100 kpc away, nearby galaxies land at Mpc scale, and quasars stretch out to Gpc. The Hipparcos mission (1989–1993) cataloged around 118,000 parallaxes; Gaia (2013–) has since measured over a billion at microarcsecond precision. Parallax sits at the bottom rung of the cosmic distance ladder, and every farther rung (Cepheids, supernovae) gets calibrated from it.

Applications

Cataloging stars and pinning down their distances comes first. Exoplanet detection relies on it too, since Doppler radial velocity needs the distance before it can yield a mass. Building the Hertzsprung–Russell diagram depends on it, because plotting luminosity against temperature means converting to absolute magnitudes through distance. Add mapping the structure of the Milky Way, plus calibrating the Cepheid period–luminosity relation and Type Ia supernovae for cosmological distances.

FAQ

Why use parsecs instead of light-years? The parsec falls straight out of the geometric measurement astronomers actually make, the parallax. Light-years show up a lot in popular writing, but getting one means multiplying the speed of light by time, an extra step nobody needs at the telescope.

What's the limit of the parallax method? From the ground you can't really get past ~100 pc. Hipparcos pushed that to ~1 kpc, and Gaia reaches ~10 kpc for bright stars and tens of kpc for the very brightest. Past that point, standard candles take over the job.

Are kpc and Mpc just multiples? That's all they are: 1 kpc = 1,000 pc, 1 Mpc = 10⁶ pc, 1 Gpc = 10⁹ pc. For scale, the observable universe has a radius of about 14 Gpc.