How parallax measures the distance to stars
Why a tiny yearly wobble reveals how far away a star is, what a parsec really means, and the limits of the method.
The geometry behind the wobble
Hold a finger at arm's length and blink one eye then the other, and the finger jumps against the background. Astronomers do the same with the whole Earth orbit as their two viewpoints, six months apart. A nearby star shifts against the distant background stars, and half of that annual shift is the parallax angle. Because the baseline, the Earth to Sun distance, is known precisely, the angle and simple trigonometry give the distance.
Why the parsec makes the math simple
The parsec was invented to make this calculation trivial. It is defined as the distance at which one astronomical unit appears one arcsecond wide, so the messy tangent collapses into a clean reciprocal. Distance in parsecs is just one divided by the parallax in arcseconds. A star at one arcsecond sits at one parsec, at half an arcsecond it doubles to two parsecs, and at a tenth of an arcsecond it reaches ten parsecs. No trig tables required.
From parsecs to light years and AU
Different audiences prefer different units, so the result is also shown as light years and astronomical units. One parsec equals about 3.261564 light years, the distance light covers in that many years, and 206264.806 astronomical units. Those factors come straight from the geometry: 206265 is roughly the number of arcseconds in a radian, which is why it appears in the AU conversion. Multiplying the parsec distance by each factor gives the other two views of the same separation.
The limits of parallax
Parallax is the first rung of the cosmic distance ladder and it only reaches so far. The farther a star, the smaller its angle, until the shift disappears into measurement noise. From the ground, atmospheric blurring caps the useful range at a few hundred parsecs. Space telescopes such as Hipparcos and Gaia removed that blur and now chart millions of stars out to thousands of parsecs. For anything more distant, astronomers switch to standard candles like Cepheid variables that are themselves calibrated using nearby parallax stars.