PX158 - C1 - parallax

an object with spatial extent, $l$ , at a distance, $d$
$\tan α = \frac{l}{d}$ , $α$ in radians

\tan α = α + \frac{1}{3} α^{3} + \frac{2}{15} α^{5} + . . .

for small $α$ , $\tan α \approx α$ :

∴ α = \frac{l}{d}

- $l$ and $d$ must be in the same units; $α$ in radians

$p =$ angle of parallax
$d >> 1 A U$
$$d = \frac{1 , AU}{p}$$
where, $p$ is in $a r c s e c o n d s$ , and $d$ will be in $p a r s e c s$

parsec = parallax-arcsecond
in 1836, bessel measured the parallax for a star called "61 Cyg", and found $p = {0.31}^{"}$ :

d = \frac{1}{0.31} \approx 3.2 p c