# How was the parsec derived?

Mar 19, 2018

Parsec means 'Parallax of one arcsecond', or the distance to a star/object with a parallax of one arcsecon.

Using the diagram below, we can work out a parsec

The distance $S D$ is approximately one parsec.

$\tan \left(\angle E D S\right) = \frac{E S}{S D}$

SD=(ES)/(tan(/_EDS))=(1AU)/tan(1text("))

For small angles of $\theta$ $\tan \theta \approx \theta$

$1 \textrm{' '} = \frac{1}{3600} \text{th of a degree}$

$S D = \frac{1 A U}{\frac{1}{3600} \cdot \frac{\pi}{180}}$ (since we need radians)

$S D = \frac{648000}{\pi} A U \approx 206264.8062 A U$

$206264.8062 A U \approx 3.085677581 \cdot {10}^{16} m \approx 3.261563777 \text{ly}$