Editing Culmination

{{Short description|The passage of an astronomical body across the meridian}}

In [[observational astronomy]], '''culmination''' is the passage of a [[astronomical object|celestial object]] (such as the [[Sun]], the [[Moon]], a [[planet]], a [[star]], [[constellation]] or a [[deep-sky object]]) across the observer's [[meridian (astronomy)|local meridian]].<ref name="Hoskin1999">{{cite book | author = Michael Hoskin | date = 18 March 1999 | title = The Cambridge Concise History of Astronomy | publisher = Cambridge University Press | pages = | isbn = 978-0-521-57600-0 | url = https://books.google.com/books?id=9gZLXocOnSgC}}</ref>  These events are also known as '''meridian transits''', used in [[timekeeping]] and [[navigation]], and measured precisely using a [[transit telescope]].

During each day, every celestial object [[diurnal motion|appears to move]] along a circular path on the [[celestial sphere]] due to the [[Earth's rotation]] creating two moments when it crosses the meridian.<ref name="cgc">{{cite book |title=The Cambridge Guide to the Constellations |first=Michael E. |last=Bakich |publisher=[[Cambridge University Press]] |year=1995 |page=[https://archive.org/details/cambridgeguideto00baki/page/8 8] |isbn=0521449219 |url-access=registration |url=https://archive.org/details/cambridgeguideto00baki/page/8 }}</ref><ref name="fof">{{cite book |entry=Culmination |page=110 |title=The Facts on File Dictionary of Astronomy |first1=John |last1=Daintith |first2=William |last2=Gould |publisher=Infobase Publishing |year=2009 |isbn=978-1438109329}}</ref>  Except at the [[geographic pole]]s, any celestial object passing through the meridian has an '''upper culmination''', when it reaches its highest point (the moment when it is nearest to the [[zenith]]), and nearly twelve hours later, is followed by a '''lower culmination''', when it reaches its lowest point (nearest to the [[nadir]]). The time of ''culmination'' (when the object culminates) is often used to mean upper culmination.<ref name="cgc" /><ref name="fof" /><ref>{{cite book |entry=Meridian |page=993 |title=The National Encyclopaedia |edition=library |volume=8 |location=London, Edinburgh, and Glasgow |first=William |last=Mackenzie |issue=69 |publisher=Ludgate Hill, E.C. |year=1879–81}}</ref>

An object's [[altitude (astronomy)|altitude]] (''A'') in degrees at its upper culmination is equal to 90 minus the observer's [[latitude]] (''L'') plus the object's [[declination]] (''δ''): 
:{{math|''A'' {{=}} 90° − ''L'' + ''δ''}}.
This equation is the basis for the [[meridian altitude]] method for [[latitude determination]].

==Cases==
Three cases are dependent on the observer's [[latitude]] (''L'') and the [[declination]] (''δ'') of the [[celestial object]]:{{citation needed|date=November 2021}}
*The object is above the [[horizon]] even at its lower culmination; i.e. if {{math|<nowiki>|</nowiki> ''δ'' + ''L'' <nowiki>|</nowiki> > 90°}} (i.e. if in [[absolute value]] the declination is more than the colatitude, in the corresponding hemisphere)
*The object is below the horizon even at its upper culmination; i.e. if {{math|<nowiki>|</nowiki> ''δ'' − ''L'' <nowiki>|</nowiki> > 90°}} (i.e. if in absolute value the declination is more than the colatitude, in the opposite hemisphere)
*The upper culmination is above and the lower below the horizon, so the body is observed to rise and set daily; in the other cases (i.e. if in absolute value the declination is less than the [[colatitude]])

The third case applies for objects in a part of the full sky equal to the [[cosine]] of the latitude (at the equator it applies for all objects, because the sky turns around the horizontal north–south line; at the poles it applies for none, because the sky turns around the vertical line). The first and second case each apply for half of the remaining sky.{{citation needed|date=November 2021}}

==Period of time==
{{see also|Sidereal time|Equation of time|Perturbation (astronomy)}}
The period between a culmination and the next is a [[sidereal day]], which is exactly 24 [[sidereal time|sidereal hours]] and 4 minutes less than 24 common [[solar hour]]s, while the period between an upper culmination and a lower one is 12 sidereal hours. The period between successive day to day (rotational) culminations is effected mainly by [[Earth's orbit]]al [[proper motion]], which produces the different lengths between the [[solar day]] (the interval between culminations of the Sun) and the sidereal day (the interval between culminations of any [[fixed stars|reference star]]) or the slightly more precise, [[precession]] unaffected, [[stellar day]].<ref name="US Naval Observatory Astronomical Applications Department 2023">{{cite web | title=Sidereal Time | website=US Naval Observatory Astronomical Applications Department | date=2023-06-02 | url=https://aa.usno.navy.mil/data/siderealtime | access-date=2023-06-02}}</ref> This results in culminations occurring every solar day at different times, taking a [[sidereal year]] (366.3 days), a year that is one day longer than the [[solar year]], for a culmination to reoccur. Therefore, only once every 366.3 solar days the culmination reoccurs at the same time of a solar day, while reoccurring every sidereal day.<ref name="Encyclopedia Britannica 1998">{{cite web | title=Calendar - Sidereal Day, Synodic Month, Tropical Year, Intercalation | website=Encyclopedia Britannica | date=1998-07-20 | url=https://www.britannica.com/science/calendar | access-date=2023-06-02}}</ref> The remaining small changes in the culmination period time from sidereal year to sidereal year is on the other hand mainly caused by [[Astronomical nutation|nutation]] (with a 18.6 years cycle), resulting in the longer time scale [[axial precession]] of Earth (with a 26,000 years cycle),<ref name="Oxford Reference 1999">{{cite web | title=apparent sidereal time | website=Oxford Reference | date=1999-02-22 | url=https://www.oxfordreference.com/display/10.1093/oi/authority.20110803095419792;jsessionid=3FA35A4692C474A698B5EFF99EDC87BC?rskey=xDQN4Z&result=5 | access-date=2023-06-02}}</ref><ref name="Buis Laboratory 2020">{{cite web | last=Buis | first=Alan | last2=Laboratory | first2=s Jet Propulsion | title=Milankovitch (Orbital) Cycles and Their Role in Earth's Climate – Climate Change: Vital Signs of the Planet | website=Climate Change: Vital Signs of the Planet | date=2020-02-27 | url=https://climate.nasa.gov/news/2948/milankovitch-orbital-cycles-and-their-role-in-earths-climate | access-date=2023-06-02}}</ref>  while [[apsidal precession]] and other mechanics have a much smaller impact on sidereal observation, impacting Earth's climate through the [[Milankovitch cycles]] significantly more. Though at such timescales stars themself change position, particularly those stars which have, as viewed from the [[Solar System]], a [[Proper motion#Stars with high proper motion|high proper motion]].

[[Stellar parallax]] appears to be a similar motion like all these apparent movements, but has only from non-averaged sidereal day to sidereal day a slight effect, returning to its original apparent position, completing a cycle every orbit, with a slight additional lasting change to the position due to the precessions. This phenomenon results from Earth changing position on its orbital path.

==The Sun==
{{main|Solar noon}}
{{See also|Sun path}}
From the [[tropics]] and [[middle latitudes]], the [[Sun]] is visible in the sky at its upper culmination (at [[solar noon]]) and invisible (below the horizon) at its lower culmination (at solar [[midnight]]). When viewed from the [[polar regions of Earth|region]] within either [[polar circle]] around the [[winter solstice]] of that hemisphere (the [[December solstice]] in the [[Arctic]] and the [[June solstice]] in the [[Antarctic]]), the Sun is below the [[horizon]] at both of its culminations.

Earth's [[subsolar point]] occurs at the point where the upper culmination of the Sun reaches the point's [[zenith]]. At this point, which moves around the [[tropics]] throughout the year, the Sun is perceived to be directly overhead.

We apply the previous equation, {{math|''A'' {{=}} 90° − ''L'' + ''δ''}}, in the following examples. 

Supposing that the [[declination]] of the Sun is +20° when it crosses the local meridian, then the [[complementary angle]] of 70° (from the Sun to the pole) is added to and subtracted from the observer's [[latitude]] to find the solar altitudes at upper and lower culminations, respectively.
*From [[52th parallel north|52° north]], the upper culmination is at 58° above the horizon due south, while the lower is at 18° below the horizon due north. This is calculated as 52° + 70° = 122° (the [[supplementary angle]] being 58°) for the upper, and 52° − 70° = −18° for the lower.
*From [[80th parallel north|80° north]], the upper culmination is at 30° above the horizon due south, while the lower is at 10° above the horizon ([[midnight sun]]) due north.

==Circumpolar stars==
{{main|Circumpolar star}}
From most of the [[Northern Hemisphere]], [[Polaris]] (the North Star) and the other stars of the [[constellation]] [[Ursa Minor]] circles counterclockwise around the north [[celestial pole]] and remain visible at both culminations (as long as the sky is clear and dark enough). In the [[Southern Hemisphere]] there is no bright pole star, but the [[constellation]] [[Octans]] circles clockwise around the south [[celestial pole]] and remains visible at both culminations.<ref name="Ridpath2004">{{cite book | editor = Ian Ridpath | author = Arthur Philip Norton | date = 2004 | title = Norton's Star Atlas and Reference Handbook, Epoch 2000.0 | edition = 20 | publisher = Pi Press | pages = | isbn = 978-0-13-145164-3 | oclc = 1085744128 | url = https://books.google.com/books?id=CnfvAAAAMAAJ}}</ref>

Any astronomical objects that always remain above the local horizon, as viewed from the observer's latitude, are described as [[circumpolar star|circumpolar]].<ref name="Ridpath2004"/>

==See also==
{{Wiktionary|culmination}}
*[[Celestial sphere]]
*[[Meridian (astronomy)]]
*[[Nadir]]
*[[Satellite pass]]
*[[Zenith]]

==References==
{{Reflist}}

[[Category:Celestial mechanics]]
[[Category:Spherical astronomy]]