Stellar parallax

Definition

Let a star be at distance $d$ from the Sun. Let $a$ be one astronomical unit, the mean distance from the Earth to the Sun. Place a segment of length $a$ at the Sun, perpendicular to the line from the Sun to the star. The annual parallax of the star is the angle $p$ that this segment subtends at the star, so $\tan p = a / d$ . The parsec is the distance $d$ at which $p = 1''$ .

Remarks

Since $p$ is tiny, $p \approx a/d$ in radians, so the distance in parsecs is $d = 1/p$ with $p$ in arcseconds. One parsec is about $206\,265$ astronomical units, or about $3.26$ light years. Example: Proxima Centauri has $p \approx 0.768''$ , so $d \approx 1.30$ pc. Over a year the direction of a star traces on the celestial sphere an ellipse with semi-major axis $p$ . Non-example: the yearly shift of the stars by aberration is not parallax; it has size about $20.5''$ for every star, whatever its distance. The shift by the rotation of the Earth, with the Earth's radius as base, is diurnal parallax, which matters for the Moon and planets.

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Celestial sphere concept
Stellar parallax definition

Tag	`DNH27B2PGR`
URI	`m2://DNH27B2PGR`
Kind	definition
Writing	W0 stub
MSC	85A04
Defines	Stellar parallax
Uses	Celestial sphere
Changed	3 November 2026

Stellar parallax

Definition

Remarks

Reading path

Further reading

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