Culmination
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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.
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).
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°.
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.
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 265.2425 days for its orbit around the Sun. (see also sidereal 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.
In general use, culmination refers to completion or fulfillment.