Editing Parallax (section)

== Distance measurement ==
[[File:Telemetre parallaxe principe.svg|thumb|right|Parallax theory for finding naval distances. Once the triangle baseline length L and two angles at both sides of the baseline are known, all information of the triangle are determined, so the distance from the baseline to the naval object can be measured.]]

Parallax arises due to a change in viewpoint occurring due to the motion of the observer, of the observed, or both. What is essential is relative motion. By observing parallax, [[measurement|measuring]] [[angle]]s, and using [[geometry]], one can determine [[distance]].

[[Distance measurement]] by parallax is a special case of the principle of [[triangulation]], which states that, if one side length and two angles of a triangle are known, then the rest side lengths and the angle can be solved (i.e., the information of the triangle is fully determined). Thus, the careful measurement of the length of one baseline and two angles at the baseline edges can fix the scale of an entire triangulation network.

In astronomy, the triangle is extremely long and narrow, and by measuring both its shortest side length (the motion of the observer) and the small top angle (always less than 1 [[arcsecond]],<ref name="ZG44">{{harvnb|Zeilik|Gregory|1998|loc=p. 44}}.</ref> leaving the other two close to 90 degrees), the length of the long sides (in practice considered to be equal) can be determined. The distance ''d'' from the Sun to a star (measured in [[parsec]]s) is the [[Reciprocal (mathematics)|reciprocal]] of the parallax ''p'' (measured in [[arcsecond]]s): <math>d (\mathrm{pc}) = 1 / p (\mathrm{arcsec}).</math> For example, the distance from the Sun to [[Proxima Centauri]] is 1/0.7687&nbsp;=&nbsp;{{convert|1.3009|pc|ly}}, and a celestial object which distance is twice than this star has the half parallax 0.65045<ref name="apj118">{{cite journal | author=Benedict | title=Interferometric Astrometry of Proxima Centauri and Barnard's Star Using Hubble Space Telescope Fine Guidance Sensor 3: Detection Limits for Substellar Companions | journal=The Astronomical Journal | date=1999 | volume=118 | issue=2 | pages=1086–1100 | bibcode=1999AJ....118.1086B | doi=10.1086/300975 |arxiv = Astro-ph/9905318 | name-list-style=vanc | author2=G. Fritz | display-authors=2 | last3=Chappell | first3=D.W. | last4=Nelan | first4=E. | last5=Jefferys | first5=W.H. | last6=Van Altena | first6=W. | last7=Lee | first7=J. | last8=Cornell | first8=D. | last9=Shelus | first9=P.J. | s2cid=18099356 }}</ref>

On Earth, a [[coincidence rangefinder]] or parallax rangefinder can be used to find distance to a target. In [[surveying]], the problem of [[resection (surveying)|resection]] explores angular measurements from a known baseline for determining an unknown point's coordinates.