In astronomy, the culmination, at a given point, of a planet, star, constellation, etc. is the time within the diurnal motion when it appears on an observer's meridian; in other words, its highest point, when it is closest to the zenith. A planet (from the Greek πλανήτης, planētēs which means wanderer or more forcefully vagrant, tramp) is an object in orbit around a star that is not a star in its own right. ... The Pleiades star cluster A star is any massive gaseous body in outer space, just like the Sun. ... Orion is a remarkable constellation, visible from most places on the globe (but not always the whole year long). ... Diurnal motion is an astronomical term referring to the apparent daily motion of stars in orbit around the Earth, caused by the Earths rotation around its axis. ... Meridian is: Meridian (astronomy): an imaginary circle perpendicular to the horizon. ... This article is about an astronomy term. ...

Sometimes, one differentiates between upper culmination, which is the time described above, while the lower culmination is the time when the object in question passes the meridian another time, at its lowest point (i.e. closest to the nadir or farthest from the zenith). In astronomy, the nadir is the, obviously invisible, point on the sky vertically downward, i. ... This article is about an astronomy term. ...

The altitudes are the latitude on Earth of the point of observation, plus or minus the distance from the object to the celestial pole. Here 110° corresponds to 70° and -100° to -80°, etc. The azimuth of both is the same, or if we had to do exactly one of the latter conversions, the azimuths differ 180°. Altitude is the elevation of an object from a known level or datum, called zero level. ... Latitude, denoted by the Greek letter φ, gives the location of a place on Earth north or south of the Equator. ... For other uses of the word pole, see Pole (disambiguation). ... Azimuth is the horizontal component of a direction (compass direction), measured around the horizon from the North point, toward the East, i. ...

For a given latitude we can distinguish three cases:

• the object is above the horizon even at its lower culmination: it is circumpolar; i.e. if |declination + latitude| > 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 |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; 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, 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 apply each for half of the remaining sky. Horizon The horizon is the line that separates earth from sky. ... Circumpolar stars are those stars which are located near the celestial poles of the celestial sphere, i. ... The graph of the absolute value function In mathematics, the absolute value (or modulus) of a real number is its numerical value without regard to its sign. ...

The time from one upper culmination to the next is 24 hours, of course, and from an upper to a lower culmination it is 12 hours. However, that is only roughly true due to the movement of the Earth on its orbit and possible proper movements of the object (if it is a planet or a moon).

The precise effect of the movement of the Earth in its movement is that one solar day (i.e. the time between two like culminations of the Sun) is longer than one sidereal day (the time between two like culmination of any fixed star). The mean difference is 1/365.2425 because the Earth needs 365.2425 days for its orbit around the Sun. (see also sidereal day) A sun is the star at the center of a solar system. ... A fixed star is a celestial object that does not seem to move (in comparison to the other stars of the night sky). ... In statistics, mean has two related meanings: the average in ordinary English, which is more correctly called the arithmetic mean, to distinguish it from geometric mean or harmonic mean. ... On a prograde planet like the Earth, the sidereal day is shorter than the solar day. ...

The Sun, examples

Suppose at some day the declination of the Sun is +20°, then at a latitude of 52°N, where the celestial pole is at an altitude of 52°, we add or subtract the distance from the Sun to the pole, which is 70°. We get the upper culmination at 122°, is 58° in the south, and the lower at -18°, below the horizon, in the north.

At a latitude of 80°N we get the upper culmination at 30°, in the south, and the lower at 10°, also above the horizon (midnight sun), in the north. The midnight sun at Nordkapp, Norway The midnight sun is a phenomenon occurring in latitudes north of the arctic circle and south of the antarctic circle where the sun is continuously visible for at least 24 hours. ...

In general use, culmination refers to completion or fulfillment.