Astrology is a pseudoscience that claims to divine information about human affairs and terrestrial events by studying the movements and relative positions of celestial objects. Astrology has been dated to at least the 2nd millennium BCE, has its roots in calendrical systems used to predict seasonal shifts and to interpret celestial cycles as signs of divine communications. Many cultures have attached importance to astronomical events, some—such as the Hindus and the Maya—developed elaborate systems for predicting terrestrial events from celestial observations. Western astrology, one of the oldest astrological systems still in use, can trace its roots to 19th–17th century BCE Mesopotamia, from which it spread to Ancient Greece, the Arab world and Central and Western Europe. Contemporary Western astrology is associated with systems of horoscopes that purport to explain aspects of a person's personality and predict significant events in their lives based on the positions of celestial objects.
Throughout most of its history, astrology was considered a scholarly tradition and was common in academic circles in close relation with astronomy, alchemy and medicine. It was present in political circles and is mentioned in various works of literature, from Dante Alighieri and Geoffrey Chaucer to William Shakespeare, Lope de Vega, Calderón de la Barca. Following the end of the 19th century and the wide-scale adoption of the scientific method, astrology has been challenged on both theoretical and experimental grounds, has been shown to have no scientific validity or explanatory power. Astrology thus lost its academic and theoretical standing, common belief in it has declined. While polls have demonstrated that one quarter of American and Canadian people say they continue to believe that star and planet positions affect their lives, astrology is now recognized as a pseudoscience—a belief, incorrectly presented as scientific; the word astrology comes from the early Latin word astrologia, which derives from the Greek ἀστρολογία—from ἄστρον astron and -λογία -logia.
Astrologia passed into meaning'star-divination' with astronomia used for the scientific term. Many cultures have attached importance to astronomical events, the Indians and Maya developed elaborate systems for predicting terrestrial events from celestial observations. In the West, astrology most consists of a system of horoscopes purporting to explain aspects of a person's personality and predict future events in their life based on the positions of the sun and other celestial objects at the time of their birth; the majority of professional astrologers rely on such systems. Astrology has been dated to at least the 2nd millennium BCE, with roots in calendrical systems used to predict seasonal shifts and to interpret celestial cycles as signs of divine communications. A form of astrology was practised in the first dynasty of Mesopotamia. Vedāṅga Jyotiṣa, is one of earliest known Hindu texts on astrology; the text is dated between 1400 BCE to final centuries BCE by various scholars according to astronomical and linguistic evidences.
Chinese astrology was elaborated in the Zhou dynasty. Hellenistic astrology after 332 BCE mixed Babylonian astrology with Egyptian Decanic astrology in Alexandria, creating horoscopic astrology. Alexander the Great's conquest of Asia allowed astrology to spread to Ancient Rome. In Rome, astrology was associated with'Chaldean wisdom'. After the conquest of Alexandria in the 7th century, astrology was taken up by Islamic scholars, Hellenistic texts were translated into Arabic and Persian. In the 12th century, Arabic texts were translated into Latin. Major astronomers including Tycho Brahe, Johannes Kepler and Galileo practised as court astrologers. Astrological references appear in literature in the works of poets such as Dante Alighieri and Geoffrey Chaucer, of playwrights such as Christopher Marlowe and William Shakespeare. Throughout most of its history, astrology was considered a scholarly tradition, it was accepted in political and academic contexts, was connected with other studies, such as astronomy, alchemy and medicine.
At the end of the 17th century, new scientific concepts in astronomy and physics called astrology into question. Astrology thus lost its academic and theoretical standing, common belief in astrology has declined. Astrology, in its broadest sense, is the search for meaning in the sky. Early evidence for humans making conscious attempts to measure and predict seasonal changes by reference to astronomical cycles, appears as markings on bones and cave walls, which show that lunar cycles were being noted as early as 25,000 years ago; this was a first step towards recording the Moon's influence upon tides and rivers, towards organising a communal calendar. Farmers addressed agricultural needs with increasing knowledge of the constellations that appear in the different seasons—and used the rising of particular star-groups to herald annual floods or seasonal activities. By the 3rd millennium BCE, civilisations had sophisticated awareness of celestial cycles, may have oriented temples in alignment with heliacal risings of the stars.
Scattered evidence suggests that the oldest known astrological references are copies of texts made in the ancient world. The Venus tablet of Ammisaduqa is thought to be compiled in Babylon around 1700 BCE. A scroll documenting an early use of electional astrology is doubtfully ascribed to the reign of the Sumerian ruler Gud
In astronomy, the meridian is the great circle passing through the celestial poles, as well as the zenith and nadir of an observer's location. It contains the north and south points on the horizon, it is perpendicular to the celestial equator and horizon. A celestial meridian is coplanar with the analogous terrestrial meridian projected onto the celestial sphere. Hence, the number of celestial meridians is infinite; the celestial meridian is undefined when the observer is at the geographical poles, since at these two points, the zenith and nadir are on the celestial poles, any great circle passing through the celestial poles passes through the zenith and nadir. There are several ways to divide the meridian into semicircles. In the horizontal coordinate system, the observer's meridian is divided into halves terminated by the horizon's north and south points; the observer's upper meridian passes through the zenith while the lower meridian passes through the nadir. Another way, the meridian is divided into the local meridian, the semicircle that contains the observer's zenith and both celestial poles, the opposite semicircle, which contains the nadir and both poles.
On any given day/night, a celestial object will appear to drift across, or transit, the observer's upper meridian as Earth rotates, since the meridian is fixed to the local horizon. At culmination, the object reaches its highest point in the sky. An object's right ascension and the local sidereal time can be used to determine the time of its culmination; the term meridian comes from the Latin meridies, which means both "midday" and "south", as the celestial equator appears to tilt southward from the Northern Hemisphere. Meridian Prime meridian Longitude Millar, William; the Amateur Astronomer's Introduction to the Celestial Sphere. Cambridge University Press
In navigation, dead reckoning is the process of calculating one's current position by using a determined position, or fix, advancing that position based upon known or estimated speeds over elapsed time and course. The corresponding term in biology, used to describe the processes by which animals update their estimates of position or heading, is path integration. Dead reckoning is subject to cumulative errors. Advances in navigational aids that give accurate information on position, in particular satellite navigation using the Global Positioning System, have made simple dead reckoning by humans obsolete for most purposes. However, inertial navigation systems, which provide accurate directional information, use dead reckoning and are widely applied. By analogy with their navigational use, the words dead reckoning are used to mean the process of estimating the value of any variable quantity by using an earlier value and adding whatever changes have occurred in the meantime; this usage implies that the changes are not known accurately.
The earlier value and the changes may be calculated quantities. The term "dead reckoning" was not used to abbreviate "deduced reckoning," nor is it a misspelling of the term "ded reckoning." The use of "ded" or "deduced reckoning" appeared much in history, no earlier than 1931. The original intention of "dead" in the term is not clear however. Whether it is used to convey "absolute" as in "dead ahead," reckoning using other objects that are "dead in the water," or using reckoning properly "you’re dead if you don’t reckon right," is not known. Dead reckoning can give the best available information on position, but is subject to significant errors as both speed and direction must be known at all instants for position to be determined accurately. For example, if displacement is measured by the number of rotations of a wheel, any discrepancy between the actual and assumed travelled distance per rotation, due to slippage or surface irregularities, will be a source of error; as each estimate of position is relative to the previous one, errors are cumulative, or compounding, multiplicatively or exponentially, if, the co-relationship of the quanta.
The accuracy of dead reckoning can be increased by using other, more reliable methods to get a new fix part way through the journey. For example, if one was navigating on land in poor visibility dead reckoning could be used to get close enough to the known position of a landmark to be able to see it, before walking to the landmark itself — giving a known start point — and setting off again. Localizing a static sensor node is not a difficult task because attaching a GPS device suffices the need of localization, but a mobile sensor node, which continuously change its geographical location with time is difficult to localize. Mobile sensor nodes within some particular domain for data collection can be used, i.e, sensor node attached to an animal within a grazing field or attached to a soldier on a battlefield. Within these scenarios a GPS device for each sensor node cannot be afforded; some of the reasons for this include cost and battery drainage of constrained sensor nodes. To overcome this problem a limited number of reference nodes within a field is employed.
These nodes continuously broadcast their locations and other nodes in proximity receive these locations and calculate their position using some mathematical technique like trilateration. For localization, at least three known reference locations are necessary to localize. Several localization algorithms based on Sequential Monte Carlo method have been proposed in literatures. Sometimes a node at some places receives only two known locations and hence it becomes impossible to localize. To overcome this problem, dead reckoning technique is used. With this technique a sensor node uses its previous calculated location for localization at time intervals. For example, at time instant 1 if node A calculates its position as loca_1 with the help of three known reference locations; this not only localizes a node in less time but localizes in positions where it is difficult to get three reference locations. In studies of animal navigation, dead reckoning is more known as path integration. Animals use it to estimate their current location based on their movements from their last known location.
Animals such as ants and geese have been shown to track their locations continuously relative to a starting point and to return to it, an important skill for foragers with a fixed home. In marine navigation a "dead" reckoning plot does not take into account the effect of currents or wind. Aboard ship a dead reckoning plot is considered important in evaluating position information and planning the movement of the vessel. Dead reckoning begins with a known position, or fix, advanced, mathematically or directly on the chart, by means of recorded heading and time. Speed can be determined by many methods. Before modern instrumentation, it was determined aboard ship using a chip log. More modern methods include pit log referencing engine speed against a table of total displacement or referencing one's indicated airspeed fed by the pressure from a pitot tube; this measurement is converted to an equivalent airspeed based upon known atmospheric conditions and measured errors in the indicated airspeed system.
A naval vessel uses a device called a pit sword, which uses two sensors on a metal rod to measure the e
The horizon or skyline is the apparent line that separates earth from sky, the line that divides all visible directions into two categories: those that intersect the Earth's surface, those that do not. The true horizon is a theoretical line, which can only be observed when it lies on the sea surface. At many locations, this line is obscured by land, buildings, etc. and the resulting intersection of earth and sky is called the visible horizon. When looking at a sea from a shore, the part of the sea closest to the horizon is called the offing; the true horizon is horizontal. It surrounds the observer and it is assumed to be a circle, drawn on the surface of a spherical model of the Earth, its center is below sea level. Its distance from the observer varies from day to day due to atmospheric refraction, affected by weather conditions; the higher the observer's eyes are from sea level, the farther away is the horizon from the observer. For instance, in standard atmospheric conditions, for an observer with eye level above sea level by 1.70 metres, the horizon is at a distance of about 5 kilometres.
When observed from high standpoints, such as a space station, the horizon is much farther away and it encompasses a much larger area of Earth's surface. In this case, it becomes evident that the horizon more resembles an ellipse than a perfect circle when the observer is above the equator, that the Earth's surface can be better modeled as an ellipsoid than as a sphere; the word horizon derives from the Greek "ὁρίζων κύκλος" horizōn kyklos, "separating circle", where "ὁρίζων" is from the verb ὁρίζω horizō, "to divide", "to separate", which in turn derives from "ὅρος", "boundary, landmark". The distance to the visible horizon has long been vital to survival and successful navigation at sea, because it determined an observer's maximum range of vision and thus of communication, with all the obvious consequences for safety and the transmission of information that this range implied; this importance lessened with the development of the radio and the telegraph, but today, when flying an aircraft under visual flight rules, a technique called attitude flying is used to control the aircraft, where the pilot uses the visual relationship between the aircraft's nose and the horizon to control the aircraft.
A pilot can retain his or her spatial orientation by referring to the horizon. In many contexts perspective drawing, the curvature of the Earth is disregarded and the horizon is considered the theoretical line to which points on any horizontal plane converge as their distance from the observer increases. For observers near sea level the difference between this geometrical horizon and the true horizon is imperceptible to the naked eye. In astronomy the horizon is the horizontal plane through the eyes of the observer, it is the fundamental plane of the horizontal coordinate system, the locus of points that have an altitude of zero degrees. While similar in ways to the geometrical horizon, in this context a horizon may be considered to be a plane in space, rather than a line on a picture plane. One sees further along the Earth's curved surface than a simple geometric calculation allows for because of refraction error. If the ground, or water, surface is colder than the air above it, a cold, dense layer of air forms close to the surface, causing light to be refracted downward as it travels, therefore, to some extent, to go around the curvature of the Earth.
The reverse happens if the ground is hotter than the air above it, as happens in deserts, producing mirages. As an approximate compensation for refraction, surveyors measuring distances longer than 100 meters subtract 14% from the calculated curvature error and ensure lines of sight are at least 1.5 meters from the ground, to reduce random errors created by refraction. However, ignoring the effect of atmospheric refraction, distance to the true horizon from an observer close to the Earth's surface is about d ≈ 3.57 h, where d is in kilometres and h is height above sea level in metres. The constant 3.57 has units of km/m½. When d is measured in miles and h in feet, the distance is d ≈ 1.5 h ≈ 1.22 h. where the constant 1.22 has units of mi/ft½. In this equation Earth's surface is assumed to be spherical, with radius equal to about 6,371 kilometres. Assuming no atmospheric refraction and a spherical Earth with radius R=6,371 kilometres: For an observer standing on the ground with h = 1.70 metres, the horizon is at a distance of 4.7 kilometres.
For an observer standing on the ground with h = 2 metres, the horizon is at a distance of 5 kilometres. For an observer standing on a hill or tower 100 feet above sea level, the horizon is at a distance of 12.2 miles. For an observer standing on a hill or tower 100 metres above sea level, the horizon is at a distance of 36 kilometres. For an observer standing on the roof of the Burj Khalifa, 828 metres from ground, about 834 metres above sea level, the horizon is at a distance of 103 kilometres. For an observe
Astronomy is a natural science that studies celestial objects and phenomena. It applies mathematics and chemistry in an effort to explain the origin of those objects and phenomena and their evolution. Objects of interest include planets, stars, nebulae and comets. More all phenomena that originate outside Earth's atmosphere are within the purview of astronomy. A related but distinct subject is physical cosmology, the study of the Universe as a whole. Astronomy is one of the oldest of the natural sciences; the early civilizations in recorded history, such as the Babylonians, Indians, Nubians, Chinese and many ancient indigenous peoples of the Americas, performed methodical observations of the night sky. Astronomy has included disciplines as diverse as astrometry, celestial navigation, observational astronomy, the making of calendars, but professional astronomy is now considered to be synonymous with astrophysics. Professional astronomy is split into theoretical branches. Observational astronomy is focused on acquiring data from observations of astronomical objects, analyzed using basic principles of physics.
Theoretical astronomy is oriented toward the development of computer or analytical models to describe astronomical objects and phenomena. The two fields complement each other, with theoretical astronomy seeking to explain observational results and observations being used to confirm theoretical results. Astronomy is one of the few sciences in which amateurs still play an active role in the discovery and observation of transient events. Amateur astronomers have made and contributed to many important astronomical discoveries, such as finding new comets. Astronomy means "law of the stars". Astronomy should not be confused with astrology, the belief system which claims that human affairs are correlated with the positions of celestial objects. Although the two fields share a common origin, they are now distinct. Both of the terms "astronomy" and "astrophysics" may be used to refer to the same subject. Based on strict dictionary definitions, "astronomy" refers to "the study of objects and matter outside the Earth's atmosphere and of their physical and chemical properties," while "astrophysics" refers to the branch of astronomy dealing with "the behavior, physical properties, dynamic processes of celestial objects and phenomena."
In some cases, as in the introduction of the introductory textbook The Physical Universe by Frank Shu, "astronomy" may be used to describe the qualitative study of the subject, whereas "astrophysics" is used to describe the physics-oriented version of the subject. However, since most modern astronomical research deals with subjects related to physics, modern astronomy could be called astrophysics; some fields, such as astrometry, are purely astronomy rather than astrophysics. Various departments in which scientists carry out research on this subject may use "astronomy" and "astrophysics" depending on whether the department is affiliated with a physics department, many professional astronomers have physics rather than astronomy degrees; some titles of the leading scientific journals in this field include The Astronomical Journal, The Astrophysical Journal, Astronomy and Astrophysics. In early historic times, astronomy only consisted of the observation and predictions of the motions of objects visible to the naked eye.
In some locations, early cultures assembled massive artifacts that had some astronomical purpose. In addition to their ceremonial uses, these observatories could be employed to determine the seasons, an important factor in knowing when to plant crops and in understanding the length of the year. Before tools such as the telescope were invented, early study of the stars was conducted using the naked eye; as civilizations developed, most notably in Mesopotamia, Persia, China and Central America, astronomical observatories were assembled and ideas on the nature of the Universe began to develop. Most early astronomy consisted of mapping the positions of the stars and planets, a science now referred to as astrometry. From these observations, early ideas about the motions of the planets were formed, the nature of the Sun and the Earth in the Universe were explored philosophically; the Earth was believed to be the center of the Universe with the Sun, the Moon and the stars rotating around it. This is known as the geocentric model of the Ptolemaic system, named after Ptolemy.
A important early development was the beginning of mathematical and scientific astronomy, which began among the Babylonians, who laid the foundations for the astronomical traditions that developed in many other civilizations. The Babylonians discovered. Following the Babylonians, significant advances in astronomy were made in ancient Greece and the Hellenistic world. Greek astronomy is characterized from the start by seeking a rational, physical explanation for celestial phenomena. In the 3rd century BC, Aristarchus of Samos estimated the size and distance of the Moon and Sun, he proposed a model of the Solar System where the Earth and planets rotated around the Sun, now called the heliocentric model. In the 2nd century BC, Hipparchus discovered precession, calculated the size and distance of the Moon and inven
Encyclopædia Britannica, Eleventh Edition
The Encyclopædia Britannica, Eleventh Edition is a 29-volume reference work, an edition of the Encyclopædia Britannica. It was developed during the encyclopaedia's transition from a British to an American publication; some of its articles were written by the best-known scholars of the time. This edition of the encyclopedia, containing 40,000 entries, is now in the public domain, many of its articles have been used as a basis for articles in Wikipedia. However, the outdated nature of some of its content makes its use as a source for modern scholarship problematic; some articles have special value and interest to modern scholars as cultural artifacts of the 19th and early 20th centuries. The 1911 eleventh edition was assembled with the management of American publisher Horace Everett Hooper. Hugh Chisholm, who had edited the previous edition, was appointed editor in chief, with Walter Alison Phillips as his principal assistant editor. Hooper bought the rights to the 25-volume 9th edition and persuaded the British newspaper The Times to issue its reprint, with eleven additional volumes as the tenth edition, published in 1902.
Hooper's association with The Times ceased in 1909, he negotiated with the Cambridge University Press to publish the 29-volume eleventh edition. Though it is perceived as a quintessentially British work, the eleventh edition had substantial American influences, not only in the increased amount of American and Canadian content, but in the efforts made to make it more popular. American marketing methods assisted sales; some 14% of the contributors were from North America, a New York office was established to coordinate their work. The initials of the encyclopedia's contributors appear at the end of selected articles or at the end of a section in the case of longer articles, such as that on China, a key is given in each volume to these initials; some articles were written by the best-known scholars of the time, such as Edmund Gosse, J. B. Bury, Algernon Charles Swinburne, John Muir, Peter Kropotkin, T. H. Huxley, James Hopwood Jeans and William Michael Rossetti. Among the lesser-known contributors were some who would become distinguished, such as Ernest Rutherford and Bertrand Russell.
Many articles were carried over from some with minimal updating. Some of the book-length articles were divided into smaller parts for easier reference, yet others much abridged; the best-known authors contributed only a single article or part of an article. Most of the work was done by British Museum scholars and other scholars; the 1911 edition was the first edition of the encyclopædia to include more than just a handful of female contributors, with 34 women contributing articles to the edition. The eleventh edition introduced a number of changes of the format of the Britannica, it was the first to be published complete, instead of the previous method of volumes being released as they were ready. The print type was subject to continual updating until publication, it was the first edition of Britannica to be issued with a comprehensive index volume in, added a categorical index, where like topics were listed. It was the first not to include long treatise-length articles. Though the overall length of the work was about the same as that of its predecessor, the number of articles had increased from 17,000 to 40,000.
It was the first edition of Britannica to include biographies of living people. Sixteen maps of the famous 9th edition of Stielers Handatlas were translated to English, converted to Imperial units, printed in Gotha, Germany by Justus Perthes and became part this edition. Editions only included Perthes' great maps as low quality reproductions. According to Coleman and Simmons, the content of the encyclopedia was distributed as follows: Hooper sold the rights to Sears Roebuck of Chicago in 1920, completing the Britannica's transition to becoming a American publication. In 1922, an additional three volumes, were published, covering the events of the intervening years, including World War I. These, together with a reprint of the eleventh edition, formed the twelfth edition of the work. A similar thirteenth edition, consisting of three volumes plus a reprint of the twelfth edition, was published in 1926, so the twelfth and thirteenth editions were related to the eleventh edition and shared much of the same content.
However, it became apparent that a more thorough update of the work was required. The fourteenth edition, published in 1929, was revised, with much text eliminated or abridged to make room for new topics; the eleventh edition was the basis of every version of the Encyclopædia Britannica until the new fifteenth edition was published in 1974, using modern information presentation. The eleventh edition's articles are still of value and interest to modern readers and scholars as a cultural artifact: the British Empire was at its maximum, imperialism was unchallenged, much of the world was still ruled by monarchs, the tragedy of the modern world wars was still in the future, they are an invaluable resource for topics omitted from modern encyclopedias for biography and the history of science and technology. As a literary text, the encyclopedia has value as an example of early 20th-century prose. For example, it employs literary devices, such as pathetic fallacy, which are not as common in modern reference texts.
In 1917, using the pseudonym of S. S. Van Dine, the US art critic and author Willard Huntington Wright published Misinforming a Nation, a 200+
Earth radius is the distance from the center of Earth to a point on its surface. Its value ranges from 6,378 kilometres at the equator to 6,357 kilometres at a pole. Earth's radius can be defined in different ways; the surface to which a radius extends is chosen to be on an ellipsoid representing the shape of Earth. Like the surface, what point gets used for the center of Earth is a matter of definition and therefore contributes to the diverse ways of defining Earth's radius; when only one radius is stated, the International Astronomical Union prefers that it be the equatorial radius. The International Union of Geodesy and Geophysics gives three global average radii: the arithmetic mean of the radii of the ellipsoid. All three of those radii are about 6,371 kilometres. Many other ways to define Earth radius have been described; some appear below. A few definitions yield values outside the range between polar radius and equatorial radius because they include local or geoidal topology or because they depend on abstract geometrical considerations.
Earth's rotation, internal density variations, external tidal forces cause its shape to deviate systematically from a perfect sphere. Local topography increases the variance. Our descriptions of Earth's surface must be simpler than reality. Hence, we create models to approximate characteristics of Earth's surface relying on the simplest model that suits the need; each of the models in common use involve some notion of the geometric radius. Speaking, spheres are the only solids to have radii, but broader uses of the term radius are common in many fields, including those dealing with models of Earth; the following is a partial list of models of Earth's surface, ordered from exact to more approximate: The actual surface of Earth The geoid, defined by mean sea level at each point on the real surface A spheroid called an ellipsoid of revolution, geocentric to model the entire Earth, or else geodetic for regional work A sphereIn the case of the geoid and ellipsoids, the fixed distance from any point on the model to the specified center is called "a radius of the Earth" or "the radius of the Earth at that point".
It is common to refer to any mean radius of a spherical model as "the radius of the earth". When considering the Earth's real surface, on the other hand, it is uncommon to refer to a "radius", since there is no practical need. Rather, elevation above or below sea level is useful. Regardless of the model, any radius falls between the polar minimum of about 6,357 km and the equatorial maximum of about 6,378 km. Hence, the Earth deviates from a perfect sphere by only a third of a percent, which supports the spherical model in many contexts and justifies the term "radius of the Earth". While specific values differ, the concepts in this article generalize to any major planet. Rotation of a planet causes it to approximate an oblate ellipsoid/spheroid with a bulge at the equator and flattening at the North and South Poles, so that the equatorial radius a is larger than the polar radius b by aq; the oblateness constant q is given by q = a 3 ω 2 G M, where ω is the angular frequency, G is the gravitational constant, M is the mass of the planet.
For the Earth 1/q ≈ 289, close to the measured inverse flattening 1/f ≈ 298.257. Additionally, the bulge at the equator shows slow variations; the bulge had been decreasing, but since 1998 the bulge has increased due to redistribution of ocean mass via currents. The variation in density and crustal thickness causes gravity to vary across the surface and in time, so that the mean sea level differs from the ellipsoid; this difference is the geoid height, positive above or outside the ellipsoid, negative below or inside. The geoid height variation is under 110 m on Earth; the geoid height can change abruptly due to earthquakes or reduction in ice masses. Not all deformations originate within the Earth; the gravity of the Moon and Sun cause the Earth's surface at a given point to undulate by tenths of meters over a nearly 12-hour period. Given local and transient influences on surface height, the values defined below are based on a "general purpose" model, refined as globally as possible within 5 m of reference ellipsoid height, to within 100 m of mean sea level.
Additionally, the radius can be estimated from the curvature of the Earth at a point. Like a torus, the curvature at a point will be greatest in one direction and smallest perpendicularly; the corresponding radius of curvature depends on the location and direction of measurement from that point. A consequence is that a distance to the true horizon at the equator is shorter in the north/south direction than in the east-west direction. In summary, local variations in terrain prevent defining a single "precise" radius. One can only adopt an idealized model. Since the estimate by Eratosthenes, many models have been created; these models were based on regional topography, giving the best reference ellipsoid for the area under survey. As satellite remote sensing and the Global Positioning System ga