# Culmination

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[citation needed].

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[citation needed].

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. Such stars, which never set at the observer's location, are described as being circumpolar.

These three examples illustrate all three cases, dependent on the latitude of the observer and the declination of the celestial body.

• 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, 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, 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)[citation needed]. The 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 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 angle 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 sun), in the north.