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equinoxes and solstices on the earth 
A solstice is an astronomical event that happens twice each year as the Sun reaches its highest or lowest excursion relative to the celestial equator on the celestial sphere. As a result, on the day of the solstice the Sun appears to have reached its highest or lowest annual altitude in the sky above the horizon at local solar noon. The word solstice is derived from the Latin sol (sun) and sistere (to stand still), because at the solstices, the Sun stands still in declination; that is, the seasonal movement of the Sun's path (as seen from Earth) comes to a stop before reversing direction. The solstices, together with the equinoxes, are connected with the seasons. In many cultures the solstices mark either the beginning or the midpoint of winter and summer.
The term solstice can also be used in a broader sense, as the date (day) when this occurs. The day of the solstice is either the longest day of the year (in summer) or the shortest day of the year (in winter) for any place outside of the tropics.
Of the many ways in which solstice can be defined, one of the most common (and perhaps most easily understood) is by the astronomical phenomenon for which it is named, which is readily observable by anyone on Earth: a "sun-standing." This modern scientific word descends from a Latin scientific word in use in the late Roman republic of the 1st century BC: solstitium. Pliny uses it a number of times in his Natural History with the same meaning that it has today. It contains two Latin-language morphemes, sol, "sun", and -stitium, "stoppage." The Romans used "standing" to refer to a component of the relative velocity of the Sun as it is observed in the sky. Relative velocity is the motion of an object from the point of view of an observer in a frame of reference. From a fixed position on the ground, the sun appears to orbit around the Earth.
To an observer in an inertial frame of reference, the planet Earth is seen to rotate about an axis and revolve around the Sun in an elliptical path with the Sun at one focus. The Earth's axis is tilted with respect to the plane of the Earth's orbit and this axis maintains a position that changes little with respect to the background of stars. An observer on Earth therefore sees a solar path that is the result of both rotation and revolution.
The component of the Sun's motion seen by an earthbound observer caused by the revolution of the tilted axis – which, keeping the same angle in space, is oriented toward or away from the Sun – is an observed daily increment (and lateral offset) of the elevation of the Sun at noon for approximately six months and observed daily decrement for the remaining six months. At maximum or minimum elevation, the relative yearly motion of the Sun perpendicular to the horizon stops and reverses direction.
The maximum elevation occurs at the summer solstice and the minimum at the winter solstice. The path of the Sun, or ecliptic, sweeps north and south between the northern and southern hemispheres. The days are longer around the summer solstice and shorter around the winter solstice. When the Sun's path crosses the equator, the length of the nights at latitudes +L° and -L° are of equal length. This is known as an equinox. There are two solstices and two equinoxes in a tropical year.
The seasons occur because the Earth's axis of rotation is not perpendicular to its orbital plane (the “plane of the ecliptic”) but currently makes an angle of about 23.44° (called the "obliquity of the ecliptic"), and because the axis keeps its orientation with respect to an inertial frame of reference. As a consequence, for half the year the Northern Hemisphere is inclined toward the Sun while for the other half year the Southern Hemisphere has this distinction. The two moments when the inclination of Earth's rotational axis has maximum effect are the solstices.
At the northern solstice the subsolar point is further north than any other time: at latitude 23.44° north, known as the Tropic of Cancer. Similarly at the December Solstice the subsolar point is further south than any other time: at latitude 23.44° south, known as the Tropic of Capricorn. The subsolar point will cross every latitude between these two extremes exactly twice per year.
Also during the northern solstice, places on the Arctic Circle (latitude 66.56° north) will see the Sun just on the horizon during midnight, and all places north of it will see the Sun above horizon for 24 hours. That is the midnight sun or midsummer-night sun or polar day. On the other hand, places on the Antarctic Circle (latitude 66.56° south) will see the Sun just on the horizon during midday, and all places south of it will not see the Sun above horizon at any time of the day. That is the polar night. During the December Solstice, the effects on both hemispheres are just the opposite.
Animation of Earth as seen daily from the Sun looking at UTC+02:00, showing the solstice and changing seasons.
The concept of the solstices was embedded in ancient Greek celestial navigation. As soon as they discovered that the Earth is spherical they devised the concept of the celestial sphere, an imaginary spherical surface rotating with the heavenly bodies (ouranioi) fixed in it (the modern one does not rotate, but the stars in it do). As long as no assumptions are made concerning the distances of those bodies from Earth or from each other, the sphere can be accepted as real and is in fact still in use.
The stars move across the inner surface of the celestial sphere along the circumferences of circles in parallel planes perpendicular to the Earth's axis extended indefinitely into the heavens and intersecting the celestial sphere in a celestial pole. The Sun and the planets do not move in these parallel paths but along another circle, the ecliptic, whose plane is at an angle, the obliquity of the ecliptic, to the axis, bringing the Sun and planets across the paths of and in among the stars.*
The band of the Zodiac (zōdiakos kuklos, "zodiacal circle") is at an oblique angle (loksos) because it is positioned between the tropical circles and equinoctial circle touching each of the tropical circles at one point … This Zodiac has a determinable width (set at 8° today) … that is why it is described by three circles: the central one is called "heliacal" (hēliakos, "of the sun").
The term heliacal circle is used for the ecliptic, which is in the center of the zodiacal circle, conceived as a band including the noted constellations named on mythical themes. Other authors use Zodiac to mean ecliptic, which first appears in a gloss of unknown author in a passage of Cleomedes where he is explaining that the Moon is in the zodiacal circle as well and periodically crosses the path of the Sun. As some of these crossings represent eclipses of the Moon, the path of the Sun is given a synonym, the ekleiptikos (kuklos) from ekleipsis, "eclipse".
The two solstices can be distinguished by different pairs of names, depending on which feature one wants to stress.
The traditional East Asian calendars divide a year into 24 solar terms (節氣). Xiàzhì (pīnyīn) or Geshi (rōmaji) (Chinese and Japanese: 夏至; Korean: 하지(Haji); Vietnamese: Hạ chí; literally: "summer's extreme") is the 10th solar term, and marks the summer solstice. It begins when the Sun reaches the celestial longitude of 90° (around June 21) and ends when the Sun reaches the longitude of 105° (around July 7). Xiàzhì more often refers in particular to the day when the Sun is exactly at the celestial longitude of 90°.
Dōngzhì (pīnyīn) or Tōji (rōmaji) (Chinese and Japanese: 冬至; Korean: 동지(Dongji); Vietnamese: Đông chí; literally: "winter's extreme") is the 22nd solar term, and marks the winter solstice. It begins when the Sun reaches the celestial longitude of 270° (around December 22 ) and ends when the Sun reaches the longitude of 285° (around January 5). Dōngzhì more often refers in particular to the day when the Sun is exactly at the celestial longitude of 270°.
The solstices (as well as the equinoxes) mark the middle of the seasons in East Asian calendars. Here, the Chinese character 至 means "extreme", so the terms for the solstices directly signify the summits of summer and winter.
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The term solstice can also be used in a wider sense, as the date (day) that such a passage happens. The solstices, together with the equinoxes, are connected with the seasons. In some languages they are considered to start or separate the seasons; in others they are considered to be centre points (in England, in the Northern Hemisphere, for example, the period around the northern solstice is known as midsummer, and Midsummer's Day is 24 June, about three days after the solstice itself). Similarly 25 December is the start of the Christmas celebration, and is the day the Sun begins to return to the Northern Hemisphere.
Many cultures celebrate various combinations of the winter and summer solstices, the equinoxes, and the midpoints between them, leading to various holidays arising around these events. For the southern solstice, Christmas is the most popular holiday to have arisen. In addition, Yalda, Saturnalia, Karachun, Hanukkah, Kwanzaa and Yule (see winter solstice for more) are also celebrated around this time. For the northern solstice, Christian cultures celebrate the feast of St. John from June 23 to 24 (see St. John's Eve, Ivan Kupala Day, Midsummer), while Neopagans observe Midsummer, also known as Litha. For the vernal (spring) equinox, several spring-time festivals are celebrated, such as the Persian Nowruz, the observance in Judaism of Passover and in most Christian churches of Easter. The autumnal equinox has also given rise to various holidays, such as the Jewish holiday of Sukkot. At the midpoints between these four solar events, cross-quarter days are celebrated.
In the southern tip of South America, the Mapuche people celebrate We Tripantu (the New Year) a few days after the northern solstice, on June 24. Further north the Atacama people formerly celebrated this date with a noise festival, to call the Sun back. Further east, the Aymara people celebrate their New Year on June 21. A particularly beautiful and significant celebration occurs at sunrise when the sun shines right through the Gate of the Sun in Tiwanaku. Other Aymara New Year feasts occur throughout Bolivia, including at the site of El Fuerte de Samaipata.
In many cultures the solstices and equinoxes traditionally determine the midpoint of the seasons, which can be seen in the celebrations called midsummer and midwinter. Along this vein, the Japanese celebrate the start of each season with an occurrence known as Setsubun. The cumulative cooling and warming that result from the tilt of the planet become most pronounced after the solstices, leading to the more recent custom of using them to mark the beginning of summer and winter in most countries of Central and Northern Europe, as well as in Canada, the USA and New Zealand.
In the Hindu calendar, two sidereal solstices are named Makara Sankranti which marks the start of Uttarayana and Karkat Sankranti which marks the start of Dakshinayana. The former occurs around January 14 each year, while the latter occurs around July 14 each year. These mark the movement of the Sun along a sidereally fixed zodiac (precession is ignored) into Makara, the zodiacal sign which corresponds with Capricorn, and into Karkat, the zodiacal sign which corresponds with Cancer, respectively.
Unlike the equinox, the solstice time is not easy to determine. The changes in Solar declination become smaller as the sun gets closer to its maximum/minimum declination. The days before and after the solstice, the declination speed is less than 30 arcseconds per day which is less than 1⁄60 of the angular size of the sun, or the equivalent to just 2 seconds of right ascension.
This difference is hardly detectable with indirect viewing based devices like sextant equipped with a vernier, and impossible with more traditional tools like a gnomon or an astrolabe. It is also hard to detect the changes on sunrise/sunset azimuth due to the atmospheric refraction changes. Those accuracy issues render it impossible to determine the solstice day based on observations made within the 3 (or even 5) days surrounding the solstice without the use of more complex tools.
Ptolemy used an approximation method based on interpolation, which is still used by some amateurs. This method consists of recording the declination angle at noon during some days before and after the solstice, trying to find two separate days with the same declination. When those two days are found, the halfway time between both noons is estimated solstice time. An interval of 45 days has been postulated, as the best one to achieve up to a quarter-day precision, in the solstice determination.
Using the current official IAU constellation boundaries — and taking into account the variable precession speed and the rotation of the ecliptic — the solstices shift through the constellations as follows (expressed in astronomical year numbering in which the year 0 = 1 BC, -1 = 2 BC, etc.):
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