In observational astronomy, culmination is the instant of time of the transit of a celestial object across the observer's local meridian. 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 rotationcreating two moments when it crosses the meridian. Except at the geographic poles, any celestial object passing through the meridian has an upper culmination, when it reaches its highest point above the horizon, and nearly twelve hours later, is followed by a lower culmination, when it reaches its lowest point. The time of culmination is often used to mean upper culmination. An object's altitude in degrees at its upper culmination is equal to 90 subtracted by the observer's latitude and added by the object's declination :.
Cases
Three cases are dependent on the observer's latitude and the declination of the celestial object:
The object is above the horizon even at its lower culmination; i.e. if
The object is below the horizon even at its upper culmination; i.e. if
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
The third case applies for objects in a part of the full sky equal to the cosine of the latitude. The first and second case each apply for half of the remaining sky.
Period of time
The period between one upper culmination and the next is about 24 hours, while the period between an upper one and a lower one is almost 12 hours. The orbital motion, Earth's rotation and proper motion of Earth affect the period between successive upper culminations. Due to the proper and improper motions of the Sun, one solar day is slightly longer than one sidereal day. The mean difference is 1/365.24219, since Earth takes 365.24219 days to complete one orbit around the Sun.
From the tropics and middle latitudes, the Sun is visible in the sky at its upper culmination and invisible at its lower culmination. When viewed from the region within either polar circle around the winter solstice of that hemisphere, 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° is added to and subtracted from the observer's latitude to find the solar altitudes at upper and lower culminations, respectively.
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° 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 due north.
