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(trigonometric parallax)
(angle due to different lines of sight)

Parallax is the angle between the apparent location of an object as seen from two different places: for example, given two distant trees in view, someone standing close to you might appear near one or the other tree depending upon where you are standing. This phenomenon is used to measure their distance to stars (stellar parallax), i.e., by measuring the angular distance between a nearer star and much more distant stars as the Earth moves. If a very small angle can be measured accurately, a distance to a nearby star can be determined.

For measuring distances to a star, the parallax used is the angle between viewing the star from Earth at two times, half a year apart, when the positions of the Earth differ by 2 AU (the baseline). The angle cited as parallax (parallax angle) is typically half this, the angle from two positions 1 AU apart, e.g., from the Sun and the Earth. A parsec is the distance of a star with this (1 AU) parallax angle of 1 arcsecond. Typical "rough" capabilities of telescopes (based upon the Rayleigh Criteria):

Instrument angular resolution distance
Ground-based telescope without adaptive optics 1 arcsecond 1 pc
With adoptive optics 50 milliarcseconds 20 pc
HST 50 milliarcseconds 20 pc
radio interferometer 5 milliarcseconds 200 pc
very-long-baseline interferometry (8000 km baseline) 1 milliarcsecond 1 kpc

(Note that astronomers have ways to do better than implied by the Rayleigh criteria, one such method being averaging many independent measurements.)

Secular parallax consists of using the Sun's motion to gain a longer baseline, but the fact that the target star also has such a motion limits the information that can be gained.

Further reading:

Referenced by pages:
All-Sky Compiled Catalogue (ASCC)
astronomical quantities
cosmic distance ladder
fixed star
galactic archaeology
General Catalogue of Trigonometric Parallaxes (GCTP)
Gould's Belt Distances Survey (GOBELINS)
Herschel Double Star Catalog (H)
mass-luminosity relation
gravitational microlensing
parsec (pc)
General Catalog of Trigonometric Parallaxes (GCTP)
radial velocity (RV)
spectroscopic parallax
stellar distance determination
stellar kinematics
stellar luminosity determination
stellar parameter determination
stellar radius determination
Transiting Exoplanet Survey Satellite (TESS)