Parsec (source code)
= Parsec
{title2=$\mathrm{pc}$}
{wiki}
The parsec is a distance unit defined by the exact convention
$$
1\,\mathrm{pc}=\frac{648000}{\pi}\,\mathrm{au}\simeq3.085677581\times10^{16}\,\mathrm m.
$$
The <astronomical unit> is exactly $149597870700\,\mathrm m$; one <arcsecond> is exactly $\pi/648000$ <radians>. The IAU resolution explicitly records the <parsec> convention. A megaparsec is one million <parsecs>. https://arxiv.org/pdf/1510.06262[IAU 2015 Resolution B2, note 4: Exact parsec convention]{ref}. https://www.esa.int/ESA_Multimedia/Images/2013/06/Measuring_stellar_distances_by_parallax[ESA: Astronomical-unit length]{ref}.
The familiar description "the distance giving one <arcsecond> of <stellar parallax>" uses the <small-angle approximation>. Exact <right triangle> geometry instead gives $\mathrm{au}/\tan(\pi/648000)$, slightly shorter than the conventional <parsec>. The relative difference is approximately $(\pi/648000)^2/3\simeq7.83\times10^{-12}$. This is negligible for the examples here, but distinguishing an exact unit convention from an approximate geometric interpretation prevents a misleading equality.
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