Editing Stellar parallax (section)

=== Derivation ===
For a [[right triangle]],
: <math>\tan p = \frac {1\,\text{au}} {d} ,</math>
where <math>p</math> is the parallax, {{convert|1|au|km | abbr=on | sigfig=4 }} is approximately the average distance from the Sun to Earth, and <math>d</math> is the distance to the star.
Using [[small-angle approximation]]s (valid when the angle is small compared to 1 [[radian]]),
: <math>\tan x \approx x\text{ radians} = x \cdot \frac {180} {\pi} \text{ degrees} = x \cdot 180  \cdot \frac {3600} {\pi} \text{ arcseconds} ,</math>
so the parallax, measured in arcseconds, is
:<math>p'' \approx \frac {1 \text{ au}} {d} \cdot 180 \cdot \frac{3600} {\pi} .</math>
If the parallax is 1", then the distance is
:<math>d = 1 \text{ au}  \cdot 180 \cdot \frac {3600} {\pi} \approx 206,265 \text{ au} \approx 3.2616 \text{ ly} \equiv 1 \text{ parsec} .</math>
This ''defines'' the [[parsec]], a convenient unit for measuring distance using parallax. Therefore, the distance, measured in parsecs, is simply <math>d = 1 / p</math>, when the parallax is given in arcseconds.<ref>Similar derivations are in most astronomy textbooks. See, e.g., {{harvnb|Zeilik|Gregory|1998|loc=§ 11-1}}.</ref>