Culmination

Last updated January 13, 2024

In observational astronomy, culmination is the passage of a celestial object (such as the Sun, the Moon, a planet, a star, constellation or a deep-sky object) across the observer's local meridian.^[1] 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 due to the Earth's rotation creating two moments when it crosses the meridian.^[2]^[3] Except at the geographic poles, 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.^[2]^[3]^[4]

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 (δ):

A = 90° - L + δ

.

Cases

Three cases are dependent on the observer's latitude (L) and the declination (δ) of the celestial object:^{[ citation needed ]}

The object is above the horizon even at its lower culmination; i.e. if $| δ + L | > 90°$ (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 $| δ - L | > 90°$ (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 ]}

Period of time

The period between a culmination and the next is a sidereal day, which is exactly 24 sidereal hours and 4 minutes less than 24 common solar hours, 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 orbital 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 reference star) or the slightly more precise, precession unaffected, stellar day.^[5] 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.^[6] The remaining small changes in the culmination period time from sidereal year to sidereal year is on the other hand mainly caused by nutation (with a 18.6 years cycle), resulting in the longer time scale axial precession of Earth (with a 26,000 years cycle),^[7]^[8] 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 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

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 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.

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.^{[ citation needed ]}

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) due north.

Circumpolar stars

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.^[9]

Any astronomical objects that always remain above the local horizon, as viewed from the observer's latitude, are described as circumpolar.^{[ citation needed ]}^[9]

Related Research Articles

<span class="mw-page-title-main">Declination</span> Astronomical coordinate analogous to latitude

In astronomy, declination is one of the two angles that locate a point on the celestial sphere in the equatorial coordinate system, the other being hour angle. The declination angle is measured north (positive) or south (negative) of the celestial equator, along the hour circle passing through the point in question.

A solar equinox is a moment in time when the Sun crosses the Earth's equator, which is to say, appears directly above the equator, rather than north or south of the equator. On the day of the equinox, the Sun appears to rise "due east" and set "due west". This occurs twice each year, around 20 March and 23 September.

<span class="mw-page-title-main">Right ascension</span> Astronomical equivalent of longitude

Right ascension is the angular distance of a particular point measured eastward along the celestial equator from the Sun at the March equinox to the point in question above the Earth. When paired with declination, these astronomical coordinates specify the location of a point on the celestial sphere in the equatorial coordinate system.

A solstice is an event that occurs when the Sun reaches its most northerly or southerly excursion relative to the celestial equator on the celestial sphere. Two solstices occur annually, around June 21 and December 21. In many countries, the seasons of the year are determined by the solstices and the equinoxes.

<span class="mw-page-title-main">Celestial pole</span> Imaginary sky rotation points

The north and south celestial poles are the two points in the sky where Earth's axis of rotation, indefinitely extended, intersects the celestial sphere. The north and south celestial poles appear permanently directly overhead to observers at Earth's North Pole and South Pole, respectively. As Earth spins on its axis, the two celestial poles remain fixed in the sky, and all other celestial points appear to rotate around them, completing one circuit per day.

The equatorial coordinate system is a celestial coordinate system widely used to specify the positions of celestial objects. It may be implemented in spherical or rectangular coordinates, both defined by an origin at the centre of Earth, a fundamental plane consisting of the projection of Earth's equator onto the celestial sphere, a primary direction towards the vernal equinox, and a right-handed convention.

Sidereal time is a system of timekeeping used especially by astronomers. Using sidereal time and the celestial coordinate system, it is easy to locate the positions of celestial objects in the night sky. Sidereal time is a "time scale that is based on Earth's rate of rotation measured relative to the fixed stars".

A circumpolar star is a star that, as viewed from a given latitude on Earth, never sets below the horizon due to its apparent proximity to one of the celestial poles. Circumpolar stars are therefore visible from said location toward the nearest pole for the entire night on every night of the year. Others are called seasonal stars.

<span class="mw-page-title-main">Celestial equator</span> Projection of Earths equator out into space

The celestial equator is the great circle of the imaginary celestial sphere on the same plane as the equator of Earth. By extension, it is also a plane of reference in the equatorial coordinate system. In other words, the celestial equator is an abstract projection of the terrestrial equator into outer space. Due to Earth's axial tilt, the celestial equator is currently inclined by about 23.44° with respect to the ecliptic, but has varied from about 22.0° to 24.5° over the past 5 million years due to perturbation from other planets.

A lunar node is either of the two orbital nodes of the Moon, that is, the two points at which the orbit of the Moon intersects the ecliptic. The ascending node is where the Moon moves into the northern ecliptic hemisphere, while the descending node is where the Moon enters the southern ecliptic hemisphere.

In astronomy, a planisphere is a star chart analog computing instrument in the form of two adjustable disks that rotate on a common pivot. It can be adjusted to display the visible stars for any time and date. It is an instrument to assist in learning how to recognize stars and constellations. The astrolabe, an instrument that has its origins in Hellenistic astronomy, is a predecessor of the modern planisphere. The term planisphere contrasts with armillary sphere, where the celestial sphere is represented by a three-dimensional framework of rings.

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 to the celestial equator and horizon. Meridians, celestial and geographical, are determined by the pencil of planes passing through the Earth's rotation axis. For a location not at a geographical pole, there is a unique meridian plane in this axial-pencil through that location. The intersection of this plane with Earth's surface is the geographical meridian, and the intersection of the plane with the celestial sphere is the celestial meridian for that location and time.

In the celestial equatorial coordinate system Σ(α, δ) in astronomy, polar distance (PD) is an angular distance of a celestial object on its meridian measured from the celestial pole, similar to the way declination is measured from the celestial equator.

Many astronomical phenomena viewed from the planet Mars are the same as or similar to those seen from Earth; but some are quite different. For example, because the atmosphere of Mars does not contain an ozone layer, it is also possible to make UV observations from the surface of Mars.

Spherical astronomy, or positional astronomy, is a branch of observational astronomy used to locate astronomical objects on the celestial sphere, as seen at a particular date, time, and location on Earth. It relies on the mathematical methods of spherical trigonometry and the measurements of astrometry.

Meridian altitude is a method of celestial navigation to calculate an observer's latitude. It notes the altitude angle of an astronomical object above the horizon at culmination.

A lunar standstill or lunistice is when the Moon reaches its furthest north or furthest south point during the course of a month. The declination at lunar standstill varies in a cycle 18.6 years long between 18.134° and 28.725°, due to lunar precession. These extremes are called the minor and major lunar standstills.

Daytime as observed on Earth is the period of the day during which a given location experiences natural illumination from direct sunlight. Daytime occurs when the Sun appears above the local horizon, that is, anywhere on the globe's hemisphere facing the Sun. In direct sunlight the movement of the sun can be recorded and observed using a sundial that casts a shadow that slowly moves during the day. Other planets and natural satellites that rotate relative to a luminous primary body, such as a local star, also experience daytime, but this article primarily discusses daytime on Earth.

Sun path, sometimes also called day arc, refers to the daily and seasonal arc-like path that the Sun appears to follow across the sky as the Earth rotates and orbits the Sun. The Sun's path affects the length of daytime experienced and amount of daylight received along a certain latitude during a given season.

This glossary of astronomy is a list of definitions of terms and concepts relevant to astronomy and cosmology, their sub-disciplines, and related fields. Astronomy is concerned with the study of celestial objects and phenomena that originate outside the atmosphere of Earth. The field of astronomy features an extensive vocabulary and a significant amount of jargon.

References

↑ Michael Hoskin (18 March 1999). The Cambridge Concise History of Astronomy. Cambridge University Press. ISBN 978-0-521-57600-0.
1 2 Bakich, Michael E. (1995). The Cambridge Guide to the Constellations . Cambridge University Press. p. 8. ISBN 0521449219.
1 2 Daintith, John; Gould, William (2009). "Culmination". The Facts on File Dictionary of Astronomy. Infobase Publishing. p. 110. ISBN 978-1438109329.
↑ Mackenzie, William (1879–81). "Meridian". The National Encyclopaedia. Vol. 8 (library ed.). London, Edinburgh, and Glasgow: Ludgate Hill, E.C. p. 993.
↑ "Sidereal Time". US Naval Observatory Astronomical Applications Department. 2023-06-02. Retrieved 2023-06-02.
↑ "Calendar - Sidereal Day, Synodic Month, Tropical Year, Intercalation". Encyclopedia Britannica. 1998-07-20. Retrieved 2023-06-02.
↑ "apparent sidereal time". Oxford Reference. 1999-02-22. Retrieved 2023-06-02.
↑ Buis, Alan; Laboratory, s Jet Propulsion (2020-02-27). "Milankovitch (Orbital) Cycles and Their Role in Earth's Climate – Climate Change: Vital Signs of the Planet". Climate Change: Vital Signs of the Planet. Retrieved 2023-06-02.
1 2 Arthur Philip Norton (2004). Ian Ridpath (ed.). Norton's Star Atlas and Reference Handbook, Epoch 2000.0 (20 ed.). Pi Press. ISBN 978-0-13-145164-3. OCLC 1085744128.

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.

[Hoskin1999-1] Michael Hoskin (18 March 1999). The Cambridge Concise History of Astronomy. Cambridge University Press. ISBN 978-0-521-57600-0.

[cgc-2] 1 2 Bakich, Michael E. (1995). The Cambridge Guide to the Constellations . Cambridge University Press. p. 8. ISBN 0521449219.

[fof-3] 1 2 Daintith, John; Gould, William (2009). "Culmination". The Facts on File Dictionary of Astronomy. Infobase Publishing. p. 110. ISBN 978-1438109329.

[4] Mackenzie, William (1879–81). "Meridian". The National Encyclopaedia. Vol. 8 (library ed.). London, Edinburgh, and Glasgow: Ludgate Hill, E.C. p. 993.

[US_Naval_Observatory_Astronomical_Applications_Department_2023-5] "Sidereal Time". US Naval Observatory Astronomical Applications Department. 2023-06-02. Retrieved 2023-06-02.

[Encyclopedia_Britannica_1998-6] "Calendar - Sidereal Day, Synodic Month, Tropical Year, Intercalation". Encyclopedia Britannica. 1998-07-20. Retrieved 2023-06-02.

[Oxford_Reference_1999-7] "apparent sidereal time". Oxford Reference. 1999-02-22. Retrieved 2023-06-02.

[Buis_Laboratory_2020-8] Buis, Alan; Laboratory, s Jet Propulsion (2020-02-27). "Milankovitch (Orbital) Cycles and Their Role in Earth's Climate – Climate Change: Vital Signs of the Planet". Climate Change: Vital Signs of the Planet. Retrieved 2023-06-02.

[Ridpath2004-9] 1 2 Arthur Philip Norton (2004). Ian Ridpath (ed.). Norton's Star Atlas and Reference Handbook, Epoch 2000.0 (20 ed.). Pi Press. ISBN 978-0-13-145164-3. OCLC 1085744128.

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]