observational astronomy Observational astronomy is a division of astronomy that is concerned with recording data about the observable universe, in contrast with theoretical astronomy, which is mainly concerned with calculating the measurable implications of physical m ...

, culmination is the passage of a

celestial object An astronomical object, celestial object, stellar object or heavenly body is a naturally occurring physical object, physical entity, association, or structure that exists in the observable universe. In astronomy, the terms ''object'' and ''bod ...

(such as the

Sun The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...

, the

Moon The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...

, a

planet A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a you ...

, a

star A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...

constellation A constellation is an area on the celestial sphere in which a group of visible stars forms Asterism (astronomy), a perceived pattern or outline, typically representing an animal, mythological subject, or inanimate object. The origins of the e ...

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 f ...

) across the observer's

local meridian In astronomy, the meridian is the great circle passing through the celestial poles, as well as the zenith and nadir of an observer's location. Consequently, it contains also the north and south points on the horizon, and it is perpendicular ...

. These events were also known as meridian transits, used in

timekeeping Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, to co ...

and

navigation Navigation is a field of study that focuses on the process of monitoring and controlling the movement of a craft or vehicle from one place to another.Bowditch, 2003:799. The field of navigation includes four general categories: land navigation, ...

, and measured precisely using a

transit telescope In 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 obse ...

. During each day, every celestial object appears to move along a circular path on the

celestial sphere In astronomy and navigation, the celestial sphere is an abstract sphere that has an arbitrarily large radius and is concentric to Earth. All objects in the sky can be conceived as being projected upon the inner surface of the 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 retrograd ...

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 while the South Pole is in Antarctica. North and South poles are also defined ...

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 and a point or object. The exact definition and reference datum varies according to the context ...

(''A'') in degrees at its upper culmination is equal to 90 minus the observer's

latitude In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pol ...

(''L'') plus the object's

declination In astronomy, declination (abbreviated dec; symbol ''δ'') is one of the two angles that locate a point on the celestial sphere in the equatorial coordinate system, the other being hour angle. Declination's angle is measured north or south of the ...

(''δ''): .

Cases

Three cases are dependent on the observer's

(''L'') and the

(''δ'') of the

: *The object is above the

horizon The horizon is the apparent line that separates the surface of a celestial body from its sky when viewed from the perspective of an observer on or near the surface of the relevant body. This line divides all viewing directions based on whether i ...

even at its lower culmination; i.e. if (i.e. if in

absolute value In mathematics, the absolute value or modulus of a real number x, is the non-negative value without regard to its sign. Namely, , x, =x if is a positive number, and , x, =-x if x is negative (in which case negating x makes -x positive), an ...

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

colatitude In a spherical coordinate system, a colatitude is the complementary angle of a given latitude, i.e. the difference between a right angle and the latitude. Here Southern latitudes are defined to be negative, and as a result the colatitude is a non- ...

) 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.

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 object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a p ...

and

proper motion Proper motion is the 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 more dista ...

of Earth affect the period between successive upper culminations. Due to the

proper Proper may refer to: Mathematics * Proper map, in topology, a property of continuous function between topological spaces, if inverse images of compact subsets are compact * Proper morphism, in algebraic geometry, an analogue of a proper map for ...

and improper motions of the Sun, one

solar day A synodic day (or synodic rotation period or solar day) is the 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 day, which is ...

(the interval between like culminations of the Sun) is slightly longer than one

sidereal day Sidereal time (as a unit also sidereal day or sidereal rotation period) (sidereal ) 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 coord ...

(the interval between like culminations of any reference star). The

mean There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude and sign) of a given data set. For a data set, the ''arithme ...

difference is , since Earth takes 365.24219 days to complete one orbit around the Sun.

The Sun

From the

tropics The tropics are the regions of Earth surrounding the Equator. They are defined in latitude by the Tropic of Cancer in the Northern Hemisphere at N and the Tropic of Capricorn in the Southern Hemisphere at S. The tropics are also referred to ...

and

middle latitudes The middle latitudes (also called the mid-latitudes, sometimes midlatitudes, or moderate latitudes) are a spatial region on Earth located between the Tropic of Cancer (latitudes 23°26'22") to the Arctic Circle (66°33'39"), and Tropic of Caprico ...

, the

is visible in the sky at its upper culmination (at

solar noon Noon (or midday) is 12 o'clock in the daytime. It is written as 12 noon, 12:00 m. (for meridiem, literally 12:00 noon), 12 p.m. (for post meridiem, literally "after noon"), 12 pm, or 12:00 (using a 24-hour clock) or 1200 (military time). Solar ...

) and invisible (below the horizon) at its lower culmination (at solar

midnight Midnight is the transition time from one day to the next – the moment when the date changes, on the local official clock time for any particular jurisdiction. By clock time, midnight is the opposite of noon, differing from it by 12 hours. ...

). When viewed from the

region In geography, regions, otherwise referred to as zones, lands or territories, are areas that are broadly divided by physical characteristics (physical geography), human impact characteristics (human geography), and the interaction of humanity and t ...

within either

polar circle A polar circle is a geographic term for a conditional circular line (arc) referring either to the Arctic Circle or the Antarctic Circle. These are two of the keynote circles of latitude (parallels). On Earth, the Arctic Circle is currently ...

around the

winter solstice The winter solstice, also called the hibernal solstice, occurs when either of Earth's poles reaches its maximum tilt away from the Sun. This happens twice yearly, once in each hemisphere ( Northern and Southern). For that hemisphere, the winte ...

of that hemisphere (the

December solstice The December solstice, also known as the southern solstice, is the solstice that occurs each December – typically on 21 December, but may vary by one day in either direction according to the Gregorian calendar. In the Northern Hemisphere, the ...

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 Canada (Yukon, Northwest Territories, Nunavut), Danish Realm (Greenla ...

and the

June solstice The June solstice is the solstice on Earth that occurs annually between 20 and 22 June according to the Gregorian calendar. In the Northern Hemisphere, the June solstice is the summer solstice (the day with the longest period of daylight), whil ...

in the

Antarctic The Antarctic ( or , American English also or ; commonly ) is a polar region around Earth's South Pole, opposite the Arctic region around the North Pole. The Antarctic comprises the continent of Antarctica, the Kerguelen Plateau and other ...

), the Sun is below the

at both of its culminations. Supposing that the

of the Sun is +20° when it crosses the local meridian, then the

complementary angle In Euclidean geometry, an angle is the figure formed by two rays, called the '' sides'' of the angle, sharing a common endpoint, called the ''vertex'' of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles ar ...

of 70° (from the Sun to the pole) is added to and subtracted from the observer's

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 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 that occurs in the summer months in places north of the Arctic Circle or south of the Antarctic Circle, when the Sun remains visible at the local midnight. When the midnight sun is seen in the Arctic, t ...

) due north.

Circumpolar stars

From most of the

Northern Hemisphere The Northern Hemisphere is the half of Earth that is north of the Equator. For other planets in the Solar System, north is defined as being in the same celestial hemisphere relative to the invariable plane of the solar system as Earth's Nort ...

Polaris Polaris is a star in the northern circumpolar constellation of Ursa Minor. It is designated α Ursae Minoris ( Latinized to ''Alpha Ursae Minoris'') and is commonly called the North Star or Pole Star. With an apparent magnitude that ...

(the North Star) and the other stars of the

Ursa Minor Ursa Minor (Latin: 'Lesser Bear', contrasting with Ursa Major), also known as the Little Bear, is a constellation located in the far northern sky. As with the Great Bear, the tail of the Little Bear may also be seen as the handle of a ladle, h ...

circles counterclockwise around the north

celestial pole The north and south celestial poles are the two points in the sky where Earth's rotation around a fixed axis, axis of rotation, indefinitely extended, intersects the celestial sphere. The north and south celestial poles appear permanently dire ...

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

Octans Octans () is a faint constellation located in the deep Southern Sky. Its name is Latin for the eighth part of a circle, but it is named after the octant, a navigational instrument. Devised by French astronomer Nicolas Louis de Lacaille in 1752 ...

circles clockwise around the south

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 Circumpolar may refer to: * Antarctic region ** Antarctic Circle ** the Antarctic Circumpolar Current ** Subantarctic ** List of Antarctic and subantarctic islands ** Antarctic Convergence ** Antarctic Circumpolar Wave ** Antarctic Ocean * Arctic ...

References

{{Reflist Celestial mechanics Spherical astronomy

Cases

Period of time

The Sun

Circumpolar stars

See also

References