In
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 physica ...
, culmination is the passage of a
celestial object (such as the
Sun, 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 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 fa ...
) across the observer's
local meridian.
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.
During each day, every celestial object
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.
Except at the
geographic poles, 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 ...
(''L'') plus the object's
declination (''δ''): .
Cases
Three cases are dependent on 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 ...
(''L'') and the
declination (''δ'') of the
celestial object:
*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 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)
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,
Earth's rotation and
proper motion of Earth
affect the period between successive upper culminations. Due to the
proper and
improper motions of the Sun, one
solar day (the interval between like culminations of the Sun) is slightly longer than one
sidereal day (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 '' ar ...
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 refer ...
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 Cap ...
, 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
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 an ...
within either
polar circle 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 winter ...
of that hemisphere (the
December solstice 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), wh ...
in the
Antarctic), the Sun is below 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 ...
at both of its culminations.
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
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 ...
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, 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 a ...
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, ...
) 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 (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.
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
*
Meridian (astronomy)
*
Nadir
*
Satellite pass
An orbital pass (or simply pass) is the period in which a spacecraft is above the Horizontal coordinate system, local horizon, and thus available for Line-of-sight propagation, line-of-sight communication with a given ground station, satellite rec ...
*
Zenith
References
{{Reflist
Celestial mechanics
Spherical astronomy