During a sidereal day, an astronomical object crosses the meridian twice: once at its upper culmination, when it is approximately at its highest point as seen from the Earth, and once at its lower culmination, its approximately lowest point. Often, culmination is used to mean upper culmination.
The three cases are dependent on the observer's latitude 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, because the sky turns around the horizontal north-south line; at the poles it applies for none, because 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 between 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. 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)