The shadow square, also known as an altitude scale, [1] was an instrument used to determine the linear height of an object, in conjunction with the alidade, for angular observations. An early example was described in an Arabic treatise likely dating to 9th or 10th-century Baghdad. [2] Shadow squares are often found on the backs of astrolabes.
The main use of a shadow square is to measure the linear height of an object using its shadow. It does so by simulating the ratio between an object, generally a gnomon, and its shadow. If the Sun's ray is between 0 degrees and 45 degrees the umbra versa (Vertical axis) is used, between 45 degrees and 90 degrees the umbra recta (Horizontal axis) is used and when the Sun's ray is at 45 degrees its shadow falls exactly on the umbra media (y=x) [3] It was used during the time of medieval astronomy to determine the height of, and to track the movement of celestial bodies such as the Sun when more advanced measurement methods were not available. These methods can still be used today to determine the altitude, with reference to the horizon, of any visible celestial body.
A gnomon is used along with a shadow box commonly. A gnomon is a stick placed vertically in a sunny place so that it casts a shadow that can be measured. Studying the shadow of the gnomon provides information about the motion of the Sun. Gnomons were most likely independently discovered by many ancient civilizations, but it is known that they were used in the 5th century BC in Greece. Most likely for the measurement of the winter and summer solstices. "Herodotus says in his Histories written around 450 B.C., that the Greeks learned the use of the gnomon from the Babylonians. [4]
If a shadow of a human being is 4 feet long then what is the altitude of the sun? This problem can be solved through the use of the shadow box. The shadow box is divided in half, one half is calibrated by sixes the other by tens. Because it is a shadow cast by the human body the sixes are more convenient. By moving the alidade to the four (the same as the shadows length) and then reading the altitude scale shows the Sun is at an altitude of 56.3 degrees. [5]
The Shadow box can also be used with long shadows using a slightly modified method. If a human's shadow is 18 feet long, then what is the altitude of the Sun? Using the sixes side of the shadow box (using a human body as measurement) the longest shadow marked on a shadow box is six feet. This creates a problem any time the shadow is longer than the gnomon that casts it. By performing a simple calculation, by figuring out how tall a gnomon would be if it cast a six-foot shadow in the same situation, in this situation the gnomon would be only two feet tall in order to cast a six-foot shadow. If the shadow is longer than the gnomon, first turn the astrolabe upside down then set the alidade at two, the height of the projected gnomon, then read off the altitude from the altitude scale. It should read that the Sun is at 19 degrees above the horizon. [6]
A sextant is a doubly reflecting navigation instrument that measures the angular distance between two visible objects. The primary use of a sextant is to measure the angle between an astronomical object and the horizon for the purposes of celestial navigation.
The zodiac is a belt-shaped region of the sky that extends approximately 8° north and south of the ecliptic, which is the apparent path of the Sun across the celestial sphere over the course of the year. The orbital paths of the Moon and major planets are within the belt of the zodiac.
The zenith is an imaginary point directly "above" a particular location, on the celestial sphere. "Above" means in the vertical direction opposite to the gravity direction at that location (nadir). The zenith is the "highest" point on the celestial sphere.
A sundial is a horological device that tells the time of day when direct sunlight shines by the apparent position of the Sun in the sky. In the narrowest sense of the word, it consists of a flat plate and a gnomon, which casts a shadow onto the dial. As the Sun appears to move through the sky, the shadow aligns with different hour-lines, which are marked on the dial to indicate the time of day. The style is the time-telling edge of the gnomon, though a single point or nodus may be used. The gnomon casts a broad shadow; the shadow of the style shows the time. The gnomon may be a rod, wire, or elaborately decorated metal casting. The style must be parallel to the axis of the Earth's rotation for the sundial to be accurate throughout the year. The style's angle from horizontal is equal to the sundial's geographical latitude.
An astrolabe is an astronomical instrument dating to ancient times. It serves as a star chart and physical model of visible heavenly bodies. Its various functions also make it an elaborate inclinometer and an analog calculation device capable of working out several kinds of problems in astronomy. In its simplest form it is a metal disc with a pattern of wires, cutouts, and perforations that allows a user to calculate astronomical positions precisely. It is able to measure the altitude above the horizon of a celestial body, day or night; it can be used to identify stars or planets, to determine local latitude given local time, to survey, or to triangulate. It was used in classical antiquity, the Islamic Golden Age, the European Middle Ages and the Age of Discovery for all these purposes.
A gnomon is the part of a sundial that casts a shadow. The term is used for a variety of purposes in mathematics and other fields.
Theon of Alexandria was a Greek scholar and mathematician who lived in Alexandria, Egypt. He edited and arranged Euclid's Elements and wrote commentaries on works by Euclid and Ptolemy. His daughter Hypatia also won fame as a mathematician.
An alidade or a turning board is a device that allows one to sight a distant object and use the line of sight to perform a task. This task can be, for example, to triangulate a scale map on site using a plane table drawing of intersecting lines in the direction of the object from two or more points or to measure the angle and horizontal distance to the object from some reference point's polar measurement. Angles measured can be horizontal, vertical or in any chosen plane.
The Jantar Mantar, Jaipur is a collection of 19 astronomical instruments built by the Rajput king Sawai Jai Singh, the founder of Jaipur, Rajasthan. The monument was completed in 1734. It features the world's largest stone sundial, and is a UNESCO World Heritage Site. It is near City Palace and Hawa Mahal. The instruments allow the observation of astronomical positions with the naked eye. The observatory is an example of the Ptolemaic positional astronomy which was shared by many civilizations.
Medieval Islamic astronomy comprises the astronomical developments made in the Islamic world, particularly during the Islamic Golden Age, and mostly written in the Arabic language. These developments mostly took place in the Middle East, Central Asia, Al-Andalus, and North Africa, and later in the Far East and India. It closely parallels the genesis of other Islamic sciences in its assimilation of foreign material and the amalgamation of the disparate elements of that material to create a science with Islamic characteristics. These included Greek, Sassanid, and Indian works in particular, which were translated and built upon.
Babylonian astronomy was the study or recording of celestial objects during the early history of Mesopotamia.
An equatorium is an astronomical calculating instrument. It can be used for finding the positions of the Moon, Sun, and planets without arithmetic operations, using a geometrical model to represent the position of a given celestial body.
Gaocheng Astronomical Observatory, also known as the Dengfeng Observatory, is an observatory in Duke of Zhou's shrine, Gaocheng Town, near Dengfeng in Henan province, China. This site has a long tradition of astronomical observations, from the time of the Western Zhou up to the early Yuan dynasty. There is also a gnomon used for the Da Yan calendar in 729 AD and the great observatory of the Yuan Dynasty. As part of the "Dengfeng Historic Monuments of Dengfeng 'in the Center of Heaven and Earth'" the observatory was listed as a UNESCO World Heritage Site in 2010.
The mariner's astrolabe, also called sea astrolabe, was an inclinometer used to determine the latitude of a ship at sea by measuring the sun's noon altitude (declination) or the meridian altitude of a star of known declination. Not an astrolabe proper, the mariner's astrolabe was rather a graduated circle with an alidade used to measure vertical angles. They were designed to allow for their use on boats in rough water and/or in heavy winds, which astrolabes are ill-equipped to handle. It was invented by the Portuguese people, a nation known for its maritime prowess that dominated the sea for multiple centuries. In the sixteenth century, the instrument was also called a ring.
A quadrant is an instrument used to measure angles up to 90°. Different versions of this instrument could be used to calculate various readings, such as longitude, latitude, and time of day. Its earliest recorded usage was in ancient India in Rigvedic times by Rishi Atri to observe a solar eclipse. It was then proposed by Ptolemy as a better kind of astrolabe. Several different variations of the instrument were later produced by medieval Muslim astronomers. Mural quadrants were important astronomical instruments in 18th-century European observatories, establishing a use for positional astronomy.
The ancient Egyptians were one of the first cultures to widely divide days into generally agreed-upon equal parts, using early timekeeping devices such as sundials, shadow clocks, and merkhets . Obelisks were also used by reading the shadow that they make. The clock was split into daytime and nighttime, and then into smaller hours.
Astronomical rings, also known as Gemma's rings, are an early astronomical instrument. The instrument consists of three rings, representing the celestial equator, declination, and the meridian.
Shadows is a software package for the calculation and drawing of sundials and astrolabes, available as a freeware in its base level.
Earth's circumference is the distance around Earth. Measured around the equator, it is 40,075.017 km (24,901.461 mi). Measured passing through the poles, the circumference is 40,007.863 km (24,859.734 mi).