Parallax Distance

Parallax distance turns a tiny apparent shift in a nearby star’s position into an actual distance estimate. As Earth moves to opposite sides of its orbit, the star appears to move slightly against the distant background; the smaller the angle, the farther away the star is, which is why distance is inversely proportional to parallax. In the parsec system, 1 parsec is defined so that an object with a parallax of 1 arcsecond is exactly 1 parsec away, giving the simple relation d = 1/p when p is measured in arcseconds. This works because the geometry of the Earth-Sun baseline and the small-angle approximation make the parallax angle directly tied to the triangle’s distance.

Use this when converting an observed stellar parallax measurement into distance, especially in astrometry and introductory galactic astronomy. It is most appropriate for nearby stars whose parallaxes can be measured in arcseconds or milliarcseconds.

• Using degrees instead of arcseconds for p
• Forgetting that the formula gives distance in parsecs, not kilometres or light-years
• Confusing parallax with the full annual angular shift rather than the half-angle used in the parsec definition