question: How come In the period of 24h, half the earth is always lit by the sunlight is true. when some regions of the earth get only six months nights and six months days?
comment: Because the Earth is tilted. The parts that are getting mostly darkness are tilted away while the parts that are getting mostly light are tilted toward the sun. It's 6 months each because the Earth is spinning around the Sun too, so the parts that are tilted away now will be tilted toward half a year and vice versa.
passages: In the region within either polar circle, the variation in daylight hours is so extreme that part of summer sees a period without night intervening between consecutive days, while part of winter sees a period without daytime intervening between consecutive nights.
  
  Section::::On other celestial bodies.
   Halvmörk's orbiting period (year) is a little over eight Earth years. Its orbit is extremely elliptic, and the inclination of its axis is 41°, so seasonal changes have an enormous effect on the weather. The rotational axis is inclined in the direction of the small axis of the orbit, so the periastron and the apastron coincide with the equinoxes.
   Nisan-years belongs to the Lunisolar calendar system, in which the lunar years and the solar years are synchronized by adding in an intercalary month in a leap year. Three ancient civilizations (Babylonia, China, and Israel) knew that by adding in seven intercalary months in nineteen years (called a Small Mahzor in the Jewish Talmudic Calendar, and the Metonic Cycle in non-Jewish context), the solar and the lunar years are basically synchronized. Since a tropical year is 365.2422 days, and a synodic month is averaged 29.53059 days, in nineteen years the solar and the lunar calendars will only differ by about two hours, or 1 part in 80,000.
   Secondly, the position of the Earth in its orbit around the Sun at the solstices, equinoxes, or other time defined relative to the seasons, slowly changes. For example, suppose that the Earth's orbital position is marked at the summer solstice, when the Earth's axial tilt is pointing directly toward the Sun. One full orbit later, when the Sun has returned to the same apparent position relative to the background stars, the Earth's axial tilt is not now directly toward the Sun: because of the effects of precession, it is a little way "beyond" this. In other words, the solstice occurred a little "earlier" in the orbit. Thus, the tropical year, measuring the cycle of seasons (for example, the time from solstice to solstice, or equinox to equinox), is about 20 minutes shorter than the sidereal year, which is measured by the Sun's apparent position relative to the stars. After about 26 000 years the difference amounts to a full year, so the positions of the seasons relative to the orbit are "back where they started". (Other effects also slowly change the shape and orientation of the Earth's orbit, and these, in combination with precession, create various cycles of differing periods; see also Milankovitch cycles. The magnitude of the Earth's tilt, as opposed to merely its orientation, also changes slowly over time, but this effect is not attributed directly to precession.)
   The length of a solar day varies through the year, and the accumulated effect produces seasonal deviations of up to 16 minutes from the mean. The effect has two main causes. First, Earth's orbit is an ellipse, not a circle, so the Earth moves faster when it is nearest the Sun (perihelion) and slower when it is farthest from the Sun (aphelion) (see Kepler's laws of planetary motion). Second, due to Earth's axial tilt (known as the "obliquity of the ecliptic"), the Sun's annual motion is along a great circle (the ecliptic) that is tilted to Earth's celestial equator. When the Sun crosses the equator at both equinoxes, the Sun's daily shift (relative to the background stars) is at an angle to the equator, so the projection of this shift onto the equator is less than its average for the year; when the Sun is farthest from the equator at both solstices, the Sun's shift in position from one day to the next is parallel to the equator, so the projection onto the equator of this shift is larger than the average for the year (see tropical year). In June and December when the sun is farthest from the celestial equator a given shift along the ecliptic corresponds to a large shift at the equator. So apparent solar days are shorter in March and September than in June or December.
   This cycle also occurs in the Gregorian calendar, but it is interrupted by years such as 1800, 1900, 2100, 2200, 2300 and 2500, which are divisible by four but which are common years. This interruption has the effect of skipping 16 years of the solar cycle between February 28 and March 1. Because the Gregorian cycle of 400 years has exactly 146,097 days, i.e. exactly 20,871 weeks, one can say that the Gregorian so-called solar cycle lasts 400 years.
   The mean calendar year of such a calendar approximates the sidereal year.
  
  Indian calendars like the Hindu calendar, Tamil calendar, Bengali calendar (non-revised) and Malayalam calendar are sidereal solar calendars. The Thai solar calendar, when based on the Hindu solar calendar was also a sidereal calendar. They are calculated on the basis of the apparent motion of the Sun through the twelve zodiacal signs rather than the tropical movement of the Earth.
  
  Section::::Non-solar calendars.
  
  The Islamic calendar, which is a purely lunar calendar and has a year, whose start drifts through the seasons and so is not a solar calendar.
   The axial tilt of the Earth results in seasons outside of the tropics. The change in the length of the day is the key signal for seasonal behavior (e.g. mating season) in non-tropical animals. The presence of light at night can result in "seasons out of time" , changing the behavior and thermoregulation of affected organisms. This effect can be deadly for small mammals in the winter, since when their body acts as if it's summer they don't maintain an adequate winter body temperature to survive winter nights.
  
  Section::::Natural light cycles.:Lunar cycles.
   The summer and winter solstices mark the shortest and longest nights, respectively. The closer a location is to either the North Pole or the South Pole, the wider the range of variation in the night's duration. Although daytime and night nearly equalize in length on the equinoxes, the ratio of night to day changes more rapidly at high latitudes than at low latitudes before and after an equinox. In the Northern Hemisphere, Denmark experiences shorter nights in June than India. In the Southern Hemisphere, Antarctica sees longer nights in June than Chile. Both hemispheres experience the same patterns of night length at the same latitudes, but the cycles are 6 months apart so that one hemisphere experiences long nights (winter) while the other is experiencing short nights (summer).
   Some variations in insolation are not due to solar changes but rather due to the Earth moving between its perihelion and aphelion, or changes in the latitudinal distribution of radiation. These orbital changes or Milankovitch cycles have caused radiance variations of as much as 25% (locally; global average changes are much smaller) over long periods. The most recent significant event was an axial tilt of 24° during boreal summer near the "Holocene climatic optimum".
   The duration of the "mean" calendar year of such a calendar approximates some form of the tropical year, usually either the mean tropical year or the vernal equinox year.
  
  The following are tropical solar calendars:
  
  BULLET::::- Ancient Armenian calendar
  
  BULLET::::- Gregorian calendar
  
  BULLET::::- Bengali calendar (National and official calendar in Bangladesh)
  
  BULLET::::- Iranian calendar (Jalāli calendar)
  
  BULLET::::- Indian national calendar (Saka calendar)
  
  Every one of these calendars has a year of 365 days, which is occasionally extended by adding an extra day to form a leap year, a method called "intercalation", the inserted day being "intercalary".
   In astronomical reckoning by hours of daylight alone, the solstices and equinoxes are in the "middle" of the respective seasons. Because of seasonal lag due to thermal absorption and release by the oceans, regions with a continental climate, which predominate in the Northern Hemisphere, often consider these four dates to be the "start" of the seasons as in the diagram, with the cross-quarter days considered seasonal midpoints. The length of these seasons is not uniform because of Earth's elliptical orbit and its different speeds along that orbit.
  
  Section::::Four-season calendar reckoning.
   Section::::Precession of solstices and equinoxes.
  
  The precession of solstices and equinoxes is the third factor that plays a role in Earth climate change that deals directly with the earth itself. The basis of the precession of solstices and equinoxes is that it causes the seasons to occur at different times in Earth's revolution around the sun throughout a cycle recurring about every 23,000 years.
   It has been noticed, and the Sothic cycle confirms, that Sirius does not move retrograde across the sky like other stars, a phenomenon widely known as the precession of the equinox. Professor Jed Buchwald wrote "Sirius remains about the same distance from the equinoxes—and so from the solstices—throughout these many centuries, despite precession." For the same reason, the helical rising or zenith of Sirius does not slip through the calendar at the precession rate of about one day per 71.6 years as other stars do but much slower. This remarkable stability within the solar year may be one reason that the Egyptians used it as a basis for their calendar. The coincidence of a heliacal rising of Sirius and the New Year reported by Censorinus occurred about the 20th of July, that is a month later after the summer solstice.
   In addition to the ecliptic longitude, cycles are also found by declination of the planets. On page 79, Gann wrote, “History shows that in 916 agriculture in the British Isles was at its lowest ebb and that there was great scarcity of wheat and corn. Very few people were engaged in tilling the soil on account of wars. The same conditions prevailed 1000 years later in 1916 and 1917, when this country was called on to furnish food to starving Europe and send men and money to save their armies from defeat.” Bonnie Hill explained that the common factor in 916 and 1916 is that geocentric Saturn was at maximum North declination in March. Since Saturn's sidereal year is 29.457 years, it is very uncommon for it to be at maximum North declination in March. Like the weather rules above, the astrological “sign” occurs in the spring.
   Section::::Setting.:Kirin Taq.
  
  Kirin Taq is, in many respects, the polar opposite to the Dominions. Where the Dominions enjoys near-constant fair weather, Kirin Taq is a land beset by twilight due to its sun existing in a perpetual eclipse. Without the day/night cycle the denizens of the Dominions use to record the passage of time, the Kirins have resorted to utilising elements of the local flora and geology - namely the bioluminescent Glimmer Plant and Glowstones - in order to achieve the same goal.
   Chinese seasons are based on observations of the sun and stars. Many Chinese calendrical systems have started the new year on the second new moon after the winter solstice.
   Because the Earth's axis is tilted relative to its orbital plane, sunlight is incident at different angles at different times of the year. In June the Northern Hemisphere is tilted towards the sun, so at any given Northern Hemisphere latitude sunlight falls more directly on that spot than in December (see Effect of sun angle on climate). This effect causes seasons. Over thousands to hundreds of thousands of years, changes in Earth's orbital parameters affect the amount and distribution of solar energy received by the Earth and influence long-term climate. (See Milankovitch cycles).
   According to Livy, the king of Rome Numa Pompilius (753-673 BC) inserted intercalary months in such a way that "in the twentieth year the days should fall in with the same position of the sun from which they had started." As "the twentieth year" takes place nineteen years after "the first year", this seems to indicate that the Metonic cycle was applied to Numa's calendar.
  
  Apollo was said to have visited the Hyperboreans once every 19 years, presumably at the high point of the cycle.
   In effect, this means that the "tropical year" on the Moon is only 347 days long. This is called the draconic year or eclipse year. The "seasons" on the Moon fit into this period. For about half of this draconic year, the Sun is north of the lunar equator (but at most 1.543°), and for the other half, it is south of the lunar equator. Obviously, the effect of these seasons is minor compared to the difference between lunar night and lunar day. At the lunar poles, instead of usual lunar days and nights of about 15 Earth days, the Sun will be "up" for 173 days as it will be "down"; polar sunrise and sunset takes 18 days each year. "Up" here means that the centre of the Sun is above the horizon. Lunar polar sunrises and sunsets occur around the time of eclipses (solar or lunar). For example, at the Solar eclipse of March 9, 2016, the Moon was near its descending node, and the Sun was near the point in the sky where the equator of the Moon crosses the ecliptic. When the Sun reaches that point, the centre of the Sun sets at the lunar north pole and rises at the lunar south pole.
   Section::::Months.:Month names.
  
  There are 12 months in the Hindu lunar calendar (). If the transits of the Sun through various constellations (Rāśi) are used, then we get solar months, which do not shift with reference to the Gregorian calendar. In practice, solar months are mostly referred as Rāśi (not months). The solar months (Rāśi) along with the corresponding Hindu seasons and Gregorian months are:
  
  Section::::Months.:Months and approximate correspondence.
   Until 2009 it was thought that 28 cycles had spanned the 309 years between 1699 and 2008, giving an average length of 11.04 years, but research then showed that the longest of these (1784–1799) may actually have been two cycles. If so then the average length would be only around 10.7 years. Since observations began cycles as short as 9 years and as long as 14 years have been observed, and if the cycle of 1784–1799 is double then one of the two component cycles had to be less than 8 years in length. Significant amplitude variations also occur.
   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 (the interval between like culminations of the Sun) is slightly longer than one sidereal day (the interval between like culminations of any reference star). The mean difference is 1/365.24219, since Earth takes 365.24219 days to complete one orbit around the Sun.
   The effect of axial tilt is observable as the change in day length and altitude of the Sun at solar noon (the Sun's culmination) during the year. The low angle of Sun during the winter months means that incoming rays of solar radiation are spread over a larger area of the Earth's surface, so the light received is more indirect and of lower intensity. Between this effect and the shorter daylight hours, the axial tilt of the Earth accounts for most of the seasonal variation in climate in both hemispheres.
  
  Section::::Causes and effects.:Elliptical Earth orbit.
   Section::::Four-season calendar reckoning.:Solar.
  
  Solar timing is based on insolation in which the solstices and equinoxes are seen as the midpoints of the seasons. It was the method for reckoning seasons in medieval Europe, especially by the Celts, and is still ceremonially observed in Ireland and some East Asian countries. Summer is defined as the quarter of the year with the greatest insolation and winter as the quarter with the least.
  