Culmination
Encyclopedia
In astronomy, the culmination of a planet
, star
, constellation
, etc. is the altitude (or elevation angle) reached when the object transits over an observer's meridian
.
During a sidereal day, an astronomical object will cross the meridian twice: once at its upper culmination, when it is at its highest point as seen from the earth, and once at its lower culmination, its lowest point. Often, culmination is used to mean upper culmination.
The altitude
of an object in degrees at its upper culmination is equal to (90 − L + D), where L is the observer's latitude
and D is the object's declination
.
Generally, the sun is visible at its upper culmination (at noon) and not visible at its lower culmination (at midnight). But during winter near the North Pole
, the sun is below the horizon at both of its culminations. In most of the northern hemisphere, Polaris
, the "North Star", and the rest of the stars of the constellation Ursa Minor
can be seen to rotate around the celestial pole
and are all visible at both culminations, as long as the sky is dark enough.
These three examples illustrate all three cases, dependent on the latitude of the observer and the declination of the celestial body
.
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, the sky turns around the horizontal north-south line; at the poles it applies for none, the sky turns around the vertical line). The first and second case each apply for half of the remaining sky.
The time from one upper culmination to the next is approximately 24 hours, and from an upper to a lower culmination is approximately 12 hours. The movement of the Earth on its orbit and proper motion
of the celestial body affect the time between successive upper culminations of the body. Because of the proper
and improper motions of the sun, one solar day (the time between two upper culminations of the sun) is longer than one sidereal day (the time between two like culminations of any fixed star
). The mean
difference is 1/365.24219 because the Earth needs 365.24219 days for its orbit around the Sun. (see also sidereal day)
of 70° (from the sun to the pole) is added or subtracted from the observer's latitude to find the upper and lower culminations:
Planet
A planet is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.The term planet is ancient, with ties to history, science,...
, star
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...
, constellation
Constellation
In modern astronomy, a constellation is an internationally defined area of the celestial sphere. These areas are grouped around asterisms, patterns formed by prominent stars within apparent proximity to one another on Earth's night sky....
, etc. is the altitude (or elevation angle) reached when the object transits over an observer's meridian
Meridian (astronomy)
This article is about the astronomical concept. For other uses of the word, see Meridian.In the sky, a meridian is an imaginary great circle on the celestial sphere. It passes through the north point on the horizon, through the celestial pole, up to the zenith, through the south point on the...
.
During a sidereal day, an astronomical object will cross the meridian twice: once at its upper culmination, when it is at its highest point as seen from the earth, and once at its lower culmination, its lowest point. Often, culmination is used to mean upper culmination.
The altitude
Altitude
Altitude or height is defined based on the context in which it is used . As a general definition, altitude is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The reference datum also often varies according to the context...
of an object in degrees at its upper culmination is equal to (90 − L + D), where L is the observer's latitude
Latitude
In geography, the latitude of a location on the Earth is the angular distance of that location south or north of the Equator. The latitude is an angle, and is usually measured in degrees . The equator has a latitude of 0°, the North pole has a latitude of 90° north , and the South pole has a...
and D is the object's declination
Declination
In astronomy, declination is one of the two coordinates of the equatorial coordinate system, the other being either right ascension or hour angle. Declination in astronomy is comparable to geographic latitude, but projected onto the celestial sphere. Declination is measured in degrees north and...
.
Generally, the sun is visible at its upper culmination (at noon) and not visible at its lower culmination (at midnight). But during winter near the North Pole
North Pole
The North Pole, also known as the Geographic North Pole or Terrestrial North Pole, is, subject to the caveats explained below, defined as the point in the northern hemisphere where the Earth's axis of rotation meets its surface...
, the sun is below the horizon at both of its culminations. In most of the northern hemisphere, Polaris
Polaris
Polaris |Alpha]] Ursae Minoris, commonly North Star or Pole Star, also Lodestar) is the brightest star in the constellation Ursa Minor. It is very close to the north celestial pole, making it the current northern pole star....
, the "North Star", and the rest of the stars of the constellation Ursa Minor
Ursa Minor
Ursa Minor , also known as the Little Bear, is a constellation in the northern sky. Like the Great Bear, the tail of the Little Bear may also be seen as the handle of a ladle, whence the name Little Dipper...
can be seen to rotate around the celestial pole
Celestial pole
The north and south celestial poles are the two imaginary points in the sky where the Earth's axis of rotation, indefinitely extended, intersects the imaginary rotating sphere of stars called the celestial sphere...
and are all visible at both culminations, as long as the sky is dark enough.
These three examples illustrate all three cases, dependent on the latitude of the observer and the declination of the celestial body
Celestial Body
Celestial Body is a Croatian film directed by Lukas Nola. It was released in 2000....
.
- the object is above the horizonHorizonThe horizon is the apparent line that separates earth from sky, the line that divides all visible directions into two categories: those that intersect the Earth's surface, and those that do not. At many locations, the true horizon is obscured by trees, buildings, mountains, etc., and the resulting...
even at its lower culmination: it is circumpolarCircumpolar starA circumpolar star is a star that, as viewed from a given latitude on Earth, never sets , due to its proximity to one of the celestial poles...
; i.e. if |declination + latitude| > 90° (i.e. if in absolute valueAbsolute valueIn mathematics, the absolute value |a| of a real number a is the numerical value of a without regard to its sign. So, for example, the absolute value of 3 is 3, and the absolute value of -3 is also 3...
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 |declination − latitude| > 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 colatitudeColatitudeIn spherical coordinates, colatitude is the complementary angle of the latitude, i.e. the difference between 90° and the latitude.-Astronomical use:The colatitude is useful in astronomy because it refers to the zenith distance of the celestial poles...
)
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, the sky turns around the horizontal north-south line; at the poles it applies for none, the sky turns around the vertical line). The first and second case each apply for half of the remaining sky.
The time from one upper culmination to the next is approximately 24 hours, and from an upper to a lower culmination is approximately 12 hours. The movement of the Earth on its orbit and proper motion
Proper motion
The proper motion of a star is its angular change in position over time as seen from the center of mass of the solar system. It is measured in seconds of arc per year, arcsec/yr, where 3600 arcseconds equal one degree. This contrasts with radial velocity, which is the time rate of change in...
of the celestial body affect the time between successive upper culminations of the body. Because of the proper
Proper motion
The proper motion of a star is its angular change in position over time as seen from the center of mass of the solar system. It is measured in seconds of arc per year, arcsec/yr, where 3600 arcseconds equal one degree. This contrasts with radial velocity, which is the time rate of change in...
and improper motions of the sun, one solar day (the time between two upper culminations of the sun) is longer than one sidereal day (the time between two like culminations of any fixed star
Fixed star
The fixed stars are celestial objects that do not seem to move in relation to the other stars of the night sky. Hence, a fixed star is any star except for the Sun. A nebula or other starlike object may also be called a fixed star. People in many cultures have imagined that the stars form pictures...
). The mean
Mean
In statistics, mean has two related meanings:* the arithmetic mean .* the expected value of a random variable, which is also called the population mean....
difference is 1/365.24219 because the Earth needs 365.24219 days for its orbit around the Sun. (see also sidereal day)
Example: the Sun
Suppose on a given summer day the declination of the sun is +20°. The complementary angleComplementary angles
In geometry, complementary angles are angles whose measures sum to 90°. If the two complementary angles are adjacent their non-shared sides form a right angle....
of 70° (from the sun to the pole) is added or subtracted from the observer's latitude to find the upper and lower culminations:
- At a latitude of 52°N, the upper culmination is at 58°, in the south, and the lower culmination is −18°, below the horizon, in the north. This is calculated as 52°+70°=122° (the supplementary angleSupplementary anglesSupplementary angles are pairs of angles that add up to 180 degrees. Thus the supplement of an angle of x degrees is an angle of degrees....
being 58°) for the upper, and 52°-70°=−18° for the lower. - At a latitude of 80°N the upper culmination is at 30°, in the south, and the lower at 10°, also above the horizon (midnight sunMidnight sunThe midnight sun is a natural phenomenon occurring in summer months at latitudes north and nearby to the south of the Arctic Circle, and south and nearby to the north of the Antarctic Circle where the sun remains visible at the local midnight. Given fair weather, the sun is visible for a continuous...
), in the north.