Imagine that you’re looking at a tower in the middle distance: it’s straight ahead of you. Now walk 200 metres to your left: the tower is no longer straight ahead and you have to turn through an angle to face it. Go back to where you started and go 200 metres the other way: now you have to turn through an angle the opposite way to face the tower. That shift in angle as you move is parallax. If you measure the change in angle as you move and you know how far you moved, then you can work out the distance to the tower using trigonometry.
You can do this with stars. The Earth moves in its orbit, so we see the nearby stars at slightly different angles relative to the background stars according to where we are in the orbit.
The radius of the Earth’s orbit is very small compared to the distance to even the nearest star, so the parallaxes of stars are very small angles. It turns out that the nearest stars of all give a parallax of just over one second of arc – i.e. 1/3600 degree. The distance that gives one arcsecond of parallax is called a parallax-second, or “parsec”.
This is just about the only way to measure distances to stars directly, so professional astronomers use parsecs as the normal unit of distance.
A parsec is 3.26 light years. (Neither is a unit of time, whatever Han Solo said in Star Wars. George Lucas got a bit confused there.)
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