PX282 - A4 - parallax and parsecs

parallax

see PX158 - C1 - parallax

image: ESA

from the above diagram:

\sin p = \frac{r}{d}

if $r = 1 A U$ , and $p << 1 :$

p \approx \frac{r}{d}

units: $[arcseconds]$ or $[^{"}]$
$1^{"} = (\frac{1}{60 \times 60}) °$

parsec

short for parallax second
it is a measure of distance
an object at a distance of $1 p c$ subtends an angle of $1^{"}$ for the earth with $r = 1 A U$ , such that $1 p c = 3.09 \times 10^{16} m$