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In
observational astronomy Observation is the active acquisition of information from a primary source. In living beings, observation employs the senses. In science, observation can also involve the perception and recording of data (information), data via the use of scienti ...
, culmination is the transit of a
celestial object In astronomy, an astronomical object or celestial object is a naturally occurring physical entity, association, or structure that exists in the observable universe. In astronomy, the terms ''object'' and ''body'' are often used interchange ...
(the
Sun The Sun is the star A star is an astronomical object consisting of a luminous spheroid of plasma (physics), plasma held together by its own gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many othe ...

Sun
, the
Moon The Moon is Earth's only natural satellite. At about one-quarter the diameter of Earth (comparable to the width of Australia (continent), Australia), it is the largest natural satellite in the Solar System relative to the size of its plane ...

Moon
, a
planet A planet is an astronomical body orbiting a star or Stellar evolution#Stellar remnants, stellar remnant that is massive enough to be Hydrostatic equilibrium, rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and ...

planet
, a
star A star is an astronomical object consisting of a luminous spheroid of plasma Plasma or plasm may refer to: Science * Plasma (physics), one of the four fundamental states of matter * Plasma (mineral) or heliotrope, a mineral aggregate * Quark ...

star
,
constellation A constellation is an area on the celestial sphere in which a group of visible stars forms a perceived outline or pattern, typically representing an animal, mythological person or creature, or an inanimate object. The origins of the earliest ...

constellation
or a
deep-sky object A deep-sky object (DSO) is any astronomical object that is not an individual star or Solar System object (such as Sun, Moon, planet, comet, etc.). The classification is used for the most part by amateur astronomers to denote visually observed faint ...
) across the observer's local meridian. These events were also known as meridian transits, used in timekeeping and navigation, and measured precisely using a
transit telescopeIn astronomy, a transit instrument is a small telescope with extremely precisely graduated telescope mount, mount used for the precise observation of star positions. They were previously widely used in astronomical observatory, astronomical observat ...
. During each day, every celestial object appears to move along a circular path on the
celestial sphere In astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and celestial event, phenomena. It uses ...

celestial sphere
due to the
Earth's rotation Earth's rotation or Earth's spin is the rotation of planet Earth around its own Rotation around a fixed axis, axis, as well as changes in the orientation (geometry), orientation of the rotation axis in space. Earth rotates eastward, in retrog ...
creating two moments when it crosses the meridian. Except at the
geographic pole A geographical pole or geographic pole is either of the two points on Earth where its axis of rotation intersects its surface. The North Pole lies in the Arctic Ocean The Arctic Ocean is the smallest and shallowest of the world's five m ...
s, any celestial object passing through the meridian has an upper culmination, when it reaches its highest point above the horizon, and nearly twelve hours later, is followed by a lower culmination, when it reaches its lowest point. The time of ''culmination'' (when the object culminates) is often used to mean upper culmination. An object's
altitude Altitude or height (also sometimes known as depth) is a distance measurement, usually in the vertical or "up" direction, between a reference datum Data (; ) are individual facts A fact is something that is truth, true. The usual t ...
(''A'') in degrees at its upper culmination is equal to 90 minus the observer's
latitude In geography Geography (from Greek: , ''geographia'', literally "earth description") is a field of science devoted to the study of the lands, features, inhabitants, and phenomena of the Earth and planets. The first person to use the ...

latitude
(''L'') plus the object's
declination In astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and celestial event, phenomena. It uses math ...
(''δ''): .


Cases

Three cases are dependent on the observer's
latitude In geography Geography (from Greek: , ''geographia'', literally "earth description") is a field of science devoted to the study of the lands, features, inhabitants, and phenomena of the Earth and planets. The first person to use the ...

latitude
(''L'') and the
declination In astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and celestial event, phenomena. It uses math ...
(''δ'') of the
celestial object In astronomy, an astronomical object or celestial object is a naturally occurring physical entity, association, or structure that exists in the observable universe. In astronomy, the terms ''object'' and ''body'' are often used interchange ...
: *The object is above the
horizon The horizon is the apparent line that separates the surface of a celestial body In astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that st ...

horizon
even at its lower culmination; i.e. if (i.e. if in
absolute value In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities an ...

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 (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
colatitudeIn a spherical coordinate system File:3D Spherical 2.svg, 240px, Spherical coordinates as often used in ''mathematics'': radial distance , azimuthal angle , and polar angle . The meanings of and have been swapped compared to the physics convent ...
) The third case applies for objects in a part of the full sky equal to the
cosine In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in al ...

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.


Period of time

The period between one upper culmination and the next is about 24 hours, while the period between an upper one and a lower one is almost 12 hours. The
orbital motion In celestial mechanics, an orbit is the curved trajectory of an physical body, object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an satellite, artificial satellite around an object or pos ...
,
Earth's rotation Earth's rotation or Earth's spin is the rotation of planet Earth around its own Rotation around a fixed axis, axis, as well as changes in the orientation (geometry), orientation of the rotation axis in space. Earth rotates eastward, in retrog ...
and
proper motion Proper motion is the astrometry, astrometric measure of the observed changes in the apparent places of stars or other celestial objects in the sky, as seen from the center of mass of the Solar System, compared to the abstract background of the m ...

proper motion
of Earth affect the period between successive upper culminations. Due to the and improper motions of the Sun, one
solar day A synodic day (or synodic rotation period or solar day) is the rotation period, period for a celestial object to rotate once in relation to the star it is orbiting, and is the basis of solar time. The synodic day is distinguished from the sidereal ...
(the interval between like culminations of the Sun) is slightly longer than one
sidereal day Sidereal time () is a timekeeping system that astronomers use to locate celestial objects. Using sidereal time, it is possible to easily point a telescope to the proper coordinates in the night sky The term night sky, usually associated ...
(the interval between like culminations of any reference star). The
mean There are several kinds of mean in mathematics, especially in statistics. For a data set, the ''arithmetic mean'', also known as arithmetic average, is a central value of a finite set of numbers: specifically, the sum of the values divided by ...
difference is , since Earth takes 365.24219 days to complete one orbit around the Sun.


The Sun

From the
tropics The tropics are the region of Earth Earth is the third planet from the Sun and the only astronomical object known to harbour and support life. 29.2% of Earth's surface is land consisting of continents and islands. The remaining 70.8% ...

tropics
and
middle latitudes The middle latitudes (also called the mid-latitudes, sometimes midlatitudes, or moderate latitudes) are a spatial region on Earth Earth is the third planet from the Sun and the only astronomical object known to harbour and support life. 29 ...
, the
Sun The Sun is the star A star is an astronomical object consisting of a luminous spheroid of plasma (physics), plasma held together by its own gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many othe ...

Sun
is visible in the sky at its upper culmination (at
solar noon Noon (or midday) is 12 12-hour clock, o'clock in the daytime. It is written as 12 noon, 12:00 m. (for 12-hour clock, meridiem, literally 12:00 noon), 12 p.m. (for 12-hour clock, post meridiem, literally "after noon"), 12 pm, or 12:00 (using a 2 ...
) and invisible (below the horizon) at its lower culmination (at solar
midnight Midnight is the transition time from one day A day is approximately the period during which the Earth completes one rotation around its axis, which takes around 24 hours. A solar day is the length of time which elapses between the Sun reachin ...

midnight
). When viewed from the
region In geography Geography (from Ancient Greek, Greek: , ''geographia'', literally "earth description") is a field of science devoted to the study of the lands, features, inhabitants, and phenomena of the Earth and Solar System, planets. The ...
within either
polar circle A polar circle is a geographic term for a conditional circular line (arc) referring either to the Arctic Circle The Arctic Circle is one of the two s and the most northerly of the five major as shown on maps of . It marks the northernmo ...

polar circle
around the
winter solstice The winter solstice, also called the hibernal solstice, occurs when either of Earth's geographical pole, poles reaches its maximum axial tilt, tilt away from the Sun. This happens twice yearly, once in each hemisphere (Northern Hemisphere, Nort ...

winter solstice
of that hemisphere (the
December solstice The December solstice, also known as the southern solstice, is the solstice A solstice is an event that occurs when the Sun appears to reach its most northerly or southerly excursion relative to the celestial equator on the celestial sphe ...
in the
Arctic The Arctic ( or ) is a polar regions of Earth, polar region located at the northernmost part of Earth. The Arctic consists of the Arctic Ocean, adjacent seas, and parts of Alaska (United States), Canada, Finland, Greenland (Danish Realm, ...

Arctic
and the
June solstice The June solstice is the solstice on the Earth that occurs each year falling on 20–22 June according to the Gregorian calendar The Gregorian calendar is the calendar used in most of the world. It was introduced in October 1582 by Pope G ...
in the
Antarctic The Antarctic (US English or , UK English or and or ) is a around 's , opposite the region around the . The Antarctic comprises the continent of , the and other located on the or south of the . The Antarctic region includes the , wa ...

Antarctic
), the Sun is below the
horizon The horizon is the apparent line that separates the surface of a celestial body In astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that st ...

horizon
at both of its culminations. Supposing that the
declination In astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and celestial event, phenomena. It uses math ...
of the Sun is +20° when it crosses the local meridian, then the
complementary angle In Euclidean geometry Euclidean geometry is a mathematical system attributed to Alexandria ) , name = Alexandria ( or ; ar, الإسكندرية ; arz, اسكندرية ; Coptic language, Coptic: Rakod ...
of 70° (from the Sun to the pole) is added to and subtracted from the observer's
latitude In geography Geography (from Greek: , ''geographia'', literally "earth description") is a field of science devoted to the study of the lands, features, inhabitants, and phenomena of the Earth and planets. The first person to use the ...

latitude
to find the solar altitudes at upper and lower culminations, respectively. *From 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 In Euclidean geometry Euclidean geometry is a mathematical system attributed to Alexandria Alexandria ( or ; ar, الإسكندرية ; arz, اسكندرية ; Coptic Coptic may refer to: Afro-Asia * Copts, an ethnoreligious group ma ...
being 58°) for the upper, and 52° − 70° = −18° for the lower. *From 80° north, the upper culmination is at 30° above the horizon due south, while the lower is at 10° above the horizon (
midnight sun The midnight sun is a natural phenomenon Types of natural phenomena include: Weather, fog, thunder, tornadoes; biological processes, decomposition, germination seedlings, three days after germination. Germination is the process by wh ...

midnight sun
) due north.


Circumpolar stars

From most of the
Northern Hemisphere The Northern Hemisphere is the half of Earth Earth is the third planet from the Sun and the only astronomical object known to harbour and support life. 29.2% of Earth's surface is land consisting of continents and islands. The remain ...

Northern Hemisphere
,
Polaris Polaris ( ), designated α Ursae Minoris ( Latinized to Alpha Ursae Minoris, abbreviated Alpha UMi, α UMi), commonly the North Star or Pole Star, is the brightest star of the constellation Ursa Minor. It is very close to the nort ...

Polaris
(the North Star) and the other stars of the
constellation A constellation is an area on the celestial sphere in which a group of visible stars forms a perceived outline or pattern, typically representing an animal, mythological person or creature, or an inanimate object. The origins of the earliest ...

constellation
Ursa Minor Ursa Minor (Latin: "Lesser Bear", contrasting with Ursa Major), also known as the Little Bear, is a constellation in the Northern Celestial Hemisphere, Northern Sky. Like the Great Bear, the tail of the Little Bear may also be seen as the handle ...

Ursa Minor
circles counterclockwise around the north
celestial pole The north and south celestial poles are the two imaginary points in the sky where Earth Earth is the third planet from the Sun and the only astronomical object known to harbour and support life. 29.2% of Earth's surface is land consis ...
and remain visible at both culminations (as long as the sky is clear and dark enough). In the
Southern Hemisphere The Southern Hemisphere is the half (hemisphere Hemisphere may refer to: * A half of a sphere As half of the Earth * A hemispheres of Earth, hemisphere of Earth ** Northern Hemisphere ** Southern Hemisphere ** Eastern Hemisphere ** Western He ...

Southern Hemisphere
there is no bright pole star, but the
constellation A constellation is an area on the celestial sphere in which a group of visible stars forms a perceived outline or pattern, typically representing an animal, mythological person or creature, or an inanimate object. The origins of the earliest ...

constellation
Octans Octans is a faint constellation A constellation is an area on the celestial sphere in which a group of visible stars forms a perceived outline or pattern, typically representing an animal, mythological person or creature, or an inanimate ...

Octans
circles clockwise around the south
celestial pole The north and south celestial poles are the two imaginary points in the sky where Earth Earth is the third planet from the Sun and the only astronomical object known to harbour and support life. 29.2% of Earth's surface is land consis ...
and remains visible at both culminations. Any astronomical objects that always remain above the local horizon, as viewed from the observer's latitude, are described as circumpolar.


See also

*
Celestial sphere In astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and celestial event, phenomena. It uses ...

Celestial sphere
*
Meridian (astronomy) In astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and celestial event, phenomena. It uses ...
*
Nadir The nadir (, ; ar, نظير, naẓīr, counterpart) is the direction pointing directly ''below'' a particular location; that is, it is one of two vertical direction In astronomy Astronomy (from el, ἀστρονομία, literally ...
* Satellite pass *
Zenith The zenith is an imaginary point directly "above" a particular location, on the imaginary celestial sphere. "Above" means in the vertical direction (plumb line) opposite to the gravity direction at that location (nadir). The zenith is the "high ...

Zenith


References

{{Reflist Celestial mechanics Spherical astronomy