Sundial in the context of "Sidereal rotation period"

Ancient Chinese scientists and engineers made significant scientific innovations, findings and technological advances across various scientific disciplines including the natural sciences, engineering, medicine, military technology, mathematics, geology and astronomy.

Among the earliest inventions were the abacus, the sundial, and the Kongming lantern. The Four Great Inventions – the compass, gunpowder, papermaking, and printing – were among the most important technological advances, only known to Europe by the end of the Middle Ages 1000 years later. The Tang dynasty (AD 618–906) in particular was a time of great innovation. A good deal of exchange occurred between Western and Chinese discoveries up to the Qing dynasty.

The history of timekeeping devices dates back to when ancient civilizations first observed astronomical bodies as they moved across the sky. Devices and methods for keeping time have gradually improved through a series of new inventions, starting with measuring time by continuous processes, such as the flow of liquid in water clocks, to mechanical clocks, and eventually repetitive, oscillatory processes, such as the swing of pendulums. Oscillating timekeepers are used in modern timepieces. Sundials and water clocks were first used in ancient Egypt c. 1200 BC and later by the Babylonians, the Greeks and the Chinese. Incense clocks were being used in China by the 6th century. In the medieval period, Islamic water clocks were unrivalled in their sophistication until the mid-14th century. The hourglass, invented in Europe, was one of the few reliable methods of measuring time at sea.

In medieval Europe, purely mechanical clocks were developed after the invention of the bell-striking alarm, used to signal the correct time to ring monastic bells. The weight-driven mechanical clock controlled by the action of a verge and foliot was a synthesis of earlier ideas from European and Islamic science. Mechanical clocks were a major breakthrough, one notably designed and built by Henry de Vick in c. 1360, which established basic clock design for the next 300 years. Minor developments were added, such as the invention of the mainspring in the early 15th century, which allowed small clocks to be built for the first time.

Aristarchus of Samos (/ˌærəˈstɑːrkəs/; Ancient Greek: Ἀρίσταρχος ὁ Σάμιος, Aristarkhos ho Samios; c. 310 – c. 230 BC) was an ancient Greek astronomer and mathematician who presented the first known heliocentric model that placed the Sun at the center of the universe, with the Earth revolving around the Sun once a year and rotating about its axis once a day. He also supported the theory of Anaxagoras that the Sun was just another star.

He likely moved to Alexandria, and he was a student of Strato of Lampsacus, who later became the head of the Peripatetic school in Greece. According to Ptolemy, Aristarchus observed the summer solstice of 280 BC. Vitruvius writes that Aristarchus built two different sundials: one a flat disc; and one hemispherical. Aristarchus estimated the sizes of the Sun and Moon as compared to Earth, and the distances from the Earth to the Sun and to the Moon. His estimate that the Sun was 7 times larger than Earth (actually 109 times) brought about the further insight that the Sun's greater size made it the most natural central point of the universe, as opposed to Earth.

In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows. The hyperbola is one of the three kinds of conic section, formed by the intersection of a plane and a double cone. (The other conic sections are the parabola and the ellipse. A circle is a special case of an ellipse.) If the plane intersects both halves of the double cone but does not pass through the apex of the cones, then the conic is a hyperbola.

Besides being a conic section, a hyperbola can arise as the locus of points whose difference of distances to two fixed foci is constant, as a curve for each point of which the rays to two fixed foci are reflections across the tangent line at that point, or as the solution of certain bivariate quadratic equations such as the reciprocal relationship ${\displaystyle xy=1.}$ In practical applications, a hyperbola can arise as the path followed by the shadow of the tip of a sundial's gnomon, the shape of an open orbit such as that of a celestial object exceeding the escape velocity of the nearest gravitational body, or the scattering trajectory of a subatomic particle, among others.

A clock or chronometer is a device that measures and displays time. The clock is one of the oldest human inventions, meeting the need to measure intervals of time shorter than the natural units such as the day, the lunar month, and the year. Devices operating on several physical processes have been used over the millennia.

Some predecessors to the modern clock may be considered "clocks" that are based on movement in nature: A sundial shows the time by displaying the position of a shadow on a flat surface. There is a range of duration timers, a well-known example being the hourglass. Water clocks, along with sundials, are possibly the oldest time-measuring instruments. A major advance occurred with the invention of the verge escapement, which made possible the first mechanical clocks around 1300 in Europe, which kept time with oscillating timekeepers like balance wheels.

A solar term (or jiéqì, simplified Chinese: 节气; traditional Chinese: 節氣) is any of twenty-four moments in traditional Chinese lunisolar calendars that matches a particular astronomical event and signifies some natural phenomenon. The points are spaced 15° apart along the ecliptic and are used by lunisolar calendars to stay synchronized with the seasons, which is crucial for agrarian societies. The solar terms are also used to calculate intercalary months; which month is repeated depends on the position of the sun at the time.

According to the Book of Documents, the first determined term was Dongzhi (Winter Solstice) by Dan, the Duke of Zhou, while he was trying to locate the geological center of the Western Zhou dynasty, by measuring the length of the sun's shadow on an ancient type of sundial called tǔguī [ja] (土圭). Then four terms of seasons were set, which were soon evolved as eight terms; not until the Taichu Calendar of 104 BC were all twenty-four solar terms officially included in the Chinese calendar.

Sidereal time ("sidereal" pronounced /saɪˈdɪəriəl, sə-/ sy-DEER-ee-əl, sə-) is a system of timekeeping used especially by astronomers. Using sidereal time and the celestial coordinate system, it is easy to locate the positions of celestial objects in the night sky. Sidereal time is a "time scale that is based on Earth's rate of rotation measured relative to the fixed stars". A sidereal day (also known as the sidereal rotation period) represents the time for one rotation about the planet axis relative to the stars.

Viewed from the same location, a star seen at one position in the sky will be seen at the same position on another night at the same time of day (or night), if the day is defined as a sidereal day. This is similar to how the time kept by a sundial (Solar time) can be used to find the location of the Sun. Just as the Sun and Moon appear to rise in the east and set in the west due to the rotation of Earth, so do the stars. Both solar time and sidereal time make use of the regularity of Earth's rotation about its polar axis: solar time is reckoned according to the position of the Sun in the sky while sidereal time is based approximately on the position of the fixed stars on the theoretical celestial sphere.