In observational astronomy, culmination is the passage of a celestial object (such as the Sun, the Moon, a planet, 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) 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 telescope. 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 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 (''A'') in degrees at its upper culmination is equal to 90 minus the observer's latitude (''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 latitude (''L'') and the

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

The Sun

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 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 within either polar circle around the winter solstice 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 and the June solstice 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 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 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 are ...

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) 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 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

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.

References

{{Reflist Celestial mechanics Spherical astronomy

Cases

Period of time

The Sun

Circumpolar stars

See also

References