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Reverted edit by 36.74.38.114 (talk) to last version by Cyfal

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{{Short description|Spherical triangle used in astronavigation}}
{{More citations needed|date=January 2021}}
{{For|protractor triangles for navigation|Navigation protractor triangle}}
The '''navigational triangle''' or '''PZX triangle''' is a [[spherical triangle]] used in [[Celestial Navigation|astronavigation]] to determine the observer's position on the [[globe]].<ref>{{Cite book|last=Bowditch|first=Nathaniel|url=http://geocenter.survey.ntua.gr/main/labs/carto/academic/persons/bnakos_site_nafp/documentation/american_practical_navigator.pdf|title=The American Practical Navigator: An Epitome of Navigation|publisher=National Imagery and Mapping Agency|year=1802|edition=1995|location=Bethesda Maryland|pages=256}}</ref> It is composed of three reference points on the [[celestial sphere]]:

* P is the Celestial Pole (either [[North star|North]] or South). It is a fixed point.
* Z is the observer's [[zenith]], or their position on the celestial sphere.
* X is the position of a celestial body, such as the [[sun]], [[moon]], a [[Planets|planet]], or a [[star]].

The position of Z or X is described via its [[declination]]—the angular distance north or south of the equator (corresponding to its [[latitude]])—and the [[hour angle]]—the angle between its [[Meridian (geography)|meridian]] and the [[Greenwich meridian]] (corresponding to its [[longitude]]). If the observer knows the angles subtended by P, Z, and X, they can calculate their position on the globe. By measuring the angle of the celestial body in the sky, the observer can get the [[local hour angle]] (LHA) of X, which is the angle subtended at P between Z and X (the angle between the Z and X's [[Meridian (geography)|meridians]]) and calculate the longitude by subtracting from the Greenwich hour angle of the celestial body. Finding the latitude requires measuring the vertical angle (altitude) of X from the horizon using a sextant, the declination of X from a reference book, and a set of [[sight reduction]] Tables.

The sun, moon, and planets move relative to the celestial sphere, but only the stars' hour angles change with the rotation of the earth, completing a full 360 degrees every solar day.

==Gallery==
<gallery heights=250px widths=300px>
Первый астрономический треугольник.svg|PZX triangle. Due to the Russian-language source, the "X" point is marked as "R".
Второй астрономический треугольник.svg|RPM triangle. Here "M" is the celestial body ("X") and "R" is the ecliptic north pole; "P" is still the Earth rotational north pole. This is not for navigation, but for showing the difference between [[astronomical coordinate systems]] – ecliptic and equatorial in this case.
Третий астрономический треугольник.svg|GPR triangle. "R" is the body in question, "G" is the Earth's north pole, and "P" is the galactic north pole. This is not for navigation, but for showing the difference between astronomical coordinate systems – galactic and equatorial in this case.
</gallery>

==References==
{{reflist}}
*[https://web.archive.org/web/20070702205739/http://www.opensacandaga.com/navigation/Celestial2.htm Altitudes and the PZX] at opensacandaga.com
*[https://web.archive.org/web/20070913211911/http://www.icys.co.uk/celestial_navigation.htm CELESTIAL NAVIGATION] at icys.co.uk

[[Category:Spherical astronomy]]
[[Category:Navigation]]

Navigational triangle - Revision history

imported>C.Fred: Reverted edit by 36.74.38.114 (talk) to last version by Cyfal