parallaxes

Parallaxes are the apparent displacements of objects when viewed from different positions. The effect arises from the finite distance to the object and the geometry of the observer’s baseline. In astronomy, parallaxes are used to measure stellar distances by observing the tiny shift against distant background stars as the Earth (or a satellite) moves along its orbit.

Astronomical parallax: The annual or stellar parallax is the angle subtended by the Earth’s orbital baseline at the star. The parallax angle p is half the total apparent shift observed six months apart; the distance d to the star is related by d = 1/p when d is in parsecs and p is in arcseconds. This method directly ties angular measurements to distance without assumptions about luminosity or size.

Parsec: A parsec is the distance from which 1 astronomical unit subtends an angle of 1 arcsecond. It equals about 3.26 light-years. The term provides a practical unit for stellar distances derived from parallax measurements.

History: The first successful stellar parallax measurement was made by Friedrich Wilhelm Bessel in 1838 for the star 61 Cygni, confirming the method’s viability and inaugurating modern astrometry.

Modern measurements: Space-based astrometry has greatly improved accuracy. The Hipparcos satellite (1989–1993) measured parallaxes for about 100,000 stars with milliarcsecond precision. The Gaia mission (begun 2013) aims for microarcsecond accuracy and is mapping over a billion stars, refining the cosmic distance ladder and providing extensive kinematic data.

Other uses: Parallax also describes the apparent shift of nearby objects caused by the observer’s motion in everyday human vision, where disparities between the two eyes enable depth perception. In astronomy, parallax must be carefully modeled to separate genuine motion from instrumental and atmospheric effects.