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The oldest method of measuring the distance from our solar system to a distant star is the parallax method. To use this method, astronomers measure the right ascension on the sky of the star at two times of the year, half a year apart. The two measurements will differ by a small angle with respect to the most distant stars in that region of the sky. Exactly half this angle is the ''parallax angle'', having symbol ''p''. This is the angle that the star makes with the [[sun]] and the position of the [[earth]] at a right angle with that star.<ref name=Britannica3>"[https://www.britannica.com/eb/article-52809/star Star: Determining stellar distances]." ''Encyclopædia Britannica''. 2008. Encyclopædia Britannica Online. Accessed 24 Jan. 2019</ref> The distance s of the star, in astronomical units (AU), is:

The oldest method of measuring the distance from our solar system to a distant star is the parallax method. To use this method, astronomers measure the right ascension on the sky of the star at two times of the year, half a year apart. The two measurements will differ by a small angle with respect to the most distant stars in that region of the sky. Exactly half this angle is the ''parallax angle'', having symbol ''p''. This is the angle that the star makes with the [[sun]] and the position of the [[earth]] at a right angle with that star.<ref name=Britannica3>"[https://www.britannica.com/eb/article-52809/star Star: Determining stellar distances]." ''Encyclopædia Britannica''. 2008. Encyclopædia Britannica Online. Accessed 24 Jan. 2019</ref> The distance s of the star, in astronomical units (AU), is:

<math>\,\!s = \cot p</math>

:<math>s = \cot p</math>

In the range of the very small angles typically encountered, the cotangent of the angle measure (in radians) is very nearly equal to the reciprocal, and thus:

In the range of the very small angles typically encountered, the cotangent of the angle measure (in radians) is very nearly equal to the reciprocal, and thus:

<math>\,\!s \approx \frac {180 \times 3600}{p \times \pi}</math>

:<math>s \approx \frac {180 \times 3600}{p \times \pi}</math>

where p is measured in seconds of arc.

where p is measured in seconds of arc.

The cotangent of one second (1/3600 of a degree) of arc is approximately 206,264.81. No parallax angle for any star will be larger than one second. Therefore, astronomers initially defined a unit of stellar distance, the ''[[parsec]]'' (symbol pc), from this relationship. One parsec is the distance corresponding to a parallax angle of one second of arc. Hence:

The cotangent of one second (1/3600 of a degree) of arc is approximately 206,264.81. No parallax angle for any star will be larger than one second. Therefore, astronomers initially defined a unit of stellar distance, the ''[[parsec]]'' (symbol pc), from this relationship. One parsec is the distance corresponding to a parallax angle of one second of arc. Hence:

<math>1 pc \approx 206,264.81 AU</math>

:<math>1 \, \mathrm{pc} \approx 206,264.81 \, \mathrm{AU}</math>

However, the error of measurement of parallax angle is 0.005 arc seconds, and beyond a distance of 100 parsecs, this error becomes significant. 700 stars are near enough to measure their distances directly by using parallax.<ref name=Britannica3/> To measure distances further out than this, astronomers typically use absolute and relative magnitudes, or they apply [[Hubble Law|Hubble's Law]] to the star's estimated [[redshift]].

However, the error of measurement of parallax angle is 0.005 arc seconds, and beyond a distance of 100 parsecs, this error becomes significant. 700 stars are near enough to measure their distances directly by using parallax.<ref name=Britannica3/> To measure distances further out than this, astronomers typically use absolute and relative magnitudes, or they apply [[Hubble Law|Hubble's Law]] to the star's estimated [[redshift]].