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116-449: Geodesy is the scientific discipline that deals with the measurement and representation of the earth , its gravitational field and geodynamic phenomena ( polar motion , earth tides , and crustal motion) in three-dimensional, time-varying space. The geoid is essentially the figure of the Earth abstracted from its topographic features. It is an idealized equilibrium surface of sea water,

232-608: A geocentric coordinate frame. One such frame is WGS84 , as well as frames by the International Earth Rotation and Reference Systems Service ( IERS ). GNSS receivers have almost completely replaced terrestrial instruments for large-scale base network surveys. To monitor the Earth's rotation irregularities and plate tectonic motions and for planet-wide geodetic surveys, methods of very-long-baseline interferometry (VLBI) measuring distances to quasars , lunar laser ranging (LLR) measuring distances to prisms on

348-406: A "reference frame" for the same. The ISO term for a datum transformation again is a "coordinate transformation". General geopositioning , or simply positioning, is the determination of the location of points on Earth, by myriad techniques. Geodetic positioning employs geodetic methods to determine a set of precise geodetic coordinates of a point on land, at sea, or in space. It may be done within

464-538: A century before, were first observed . In 2019, the international collaboration Event Horizon Telescope presented the first direct image of a black hole 's accretion disc . Modern science is commonly divided into three major branches : natural science , social science , and formal science . Each of these branches comprises various specialised yet overlapping scientific disciplines that often possess their own nomenclature and expertise. Both natural and social sciences are empirical sciences , as their knowledge

580-412: A complete definition. GRS80 chooses as these a {\displaystyle a} , G M {\displaystyle GM} , J 2 {\displaystyle J_{2}} and ω {\displaystyle \omega } , making the geometrical constant f {\displaystyle f} a derived quantity. The formula giving the eccentricity of

696-566: A coordinate system ( point positioning or absolute positioning ) or relative to another point ( relative positioning ). One computes the position of a point in space from measurements linking terrestrial or extraterrestrial points of known location ("known points") with terrestrial ones of unknown location ("unknown points"). The computation may involve transformations between or among astronomical and terrestrial coordinate systems. Known points used in point positioning can be GNSS continuously operating reference stations or triangulation points of

812-420: A country, usually documented by national mapping agencies. Surveyors involved in real estate and insurance will use these to tie their local measurements. In geometrical geodesy, there are two main problems: The solutions to both problems in plane geometry reduce to simple trigonometry and are valid for small areas on Earth's surface; on a sphere, solutions become significantly more complex as, for example, in

928-421: A discipline of applied mathematics . Geodynamical phenomena, including crustal motion, tides , and polar motion , can be studied by designing global and national control networks , applying space geodesy and terrestrial geodetic techniques, and relying on datums and coordinate systems . Geodetic job titles include geodesist and geodetic surveyor . Geodesy began in pre-scientific antiquity , so

1044-481: A discipline. Ideas on human nature, society, and economics evolved during the Enlightenment. Hume and other Scottish Enlightenment thinkers developed A Treatise of Human Nature , which was expressed historically in works by authors including James Burnett , Adam Ferguson , John Millar and William Robertson , all of whom merged a scientific study of how humans behaved in ancient and primitive cultures with

1160-411: A few of their scientific predecessors – Galileo , Kepler , Boyle , and Newton principally – as the guides to every physical and social field of the day. The 18th century saw significant advancements in the practice of medicine and physics; the development of biological taxonomy by Carl Linnaeus ; a new understanding of magnetism and electricity; and the maturation of chemistry as

1276-423: A greater role in knowledge creation and it was not until the 19th century that many of the institutional and professional features of science began to take shape, along with the changing of "natural philosophy" to "natural science". New knowledge in science is advanced by research from scientists who are motivated by curiosity about the world and a desire to solve problems. Contemporary scientific research

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1392-418: A higher-order network. Traditionally, geodesists built a hierarchy of networks to allow point positioning within a country. The highest in this hierarchy were triangulation networks, densified into the networks of traverses ( polygons ) into which local mapping and surveying measurements, usually collected using a measuring tape, a corner prism , and the red-and-white poles, are tied. Commonly used nowadays

1508-475: A highly stable universe where there could be little loss of resources. However, with the advent of the steam engine and the Industrial Revolution there was an increased understanding that not all forms of energy have the same energy qualities , the ease of conversion to useful work or to another form of energy. This realisation led to the development of the laws of thermodynamics , in which

1624-455: A hypothesis proves unsatisfactory it is modified or discarded. If the hypothesis survives testing, it may become adopted into the framework of a scientific theory , a validly reasoned , self-consistent model or framework for describing the behaviour of certain natural events. A theory typically describes the behaviour of much broader sets of observations than a hypothesis; commonly, a large number of hypotheses can be logically bound together by

1740-416: A large extent, Earth's shape is the result of rotation , which causes its equatorial bulge , and the competition of geological processes such as the collision of plates , as well as of volcanism , resisted by Earth's gravitational field. This applies to the solid surface, the liquid surface ( dynamic sea surface topography ), and Earth's atmosphere . For this reason, the study of Earth's gravitational field

1856-407: A new non- teleological way. This implied a shift in the view of objects: objects were now considered as having no innate goals. Leibniz assumed that different types of things all work according to the same general laws of nature, with no special formal or final causes. During this time the declared purpose and value of science became producing wealth and inventions that would improve human lives, in

1972-513: A physical (real-world) realization of a coordinate system used for describing point locations. This realization follows from choosing (therefore conventional) coordinate values for one or more datum points. In the case of height data, it suffices to choose one datum point — the reference benchmark, typically a tide gauge at the shore. Thus we have vertical datums, such as the NAVD 88 (North American Vertical Datum 1988), NAP ( Normaal Amsterdams Peil ),

2088-458: A preference for one outcome over another. Eliminating the bias can be achieved through transparency, careful experimental design , and a thorough peer review process of the experimental results and conclusions. After the results of an experiment are announced or published, it is normal practice for independent researchers to double-check how the research was performed, and to follow up by performing similar experiments to determine how dependable

2204-456: A priori disciplines and because of this, there is disagreement on whether they constitute a science. Nevertheless, the formal sciences play an important role in the empirical sciences. Calculus , for example, was initially invented to understand motion in physics. Natural and social sciences that rely heavily on mathematical applications include mathematical physics , chemistry , biology , finance , and economics . Applied science

2320-482: A projection is UTM ( Universal Transverse Mercator ). Within the map plane, we have rectangular coordinates x and y . In this case, the north direction used for reference is the map north, not the local north. The difference between the two is called meridian convergence . It is easy enough to "translate" between polar and rectangular coordinates in the plane: let, as above, direction and distance be α and s respectively, then we have The reverse transformation

2436-400: A revolution in information technology and the rise of the global internet and mobile computing , including smartphones . The need for mass systematisation of long, intertwined causal chains and large amounts of data led to the rise of the fields of systems theory and computer-assisted scientific modelling . The Human Genome Project was completed in 2003 by identifying and mapping all of

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2552-461: A separate discipline from philosophy when Wilhelm Wundt founded the first laboratory for psychological research in 1879. During the mid-19th century Charles Darwin and Alfred Russel Wallace independently proposed the theory of evolution by natural selection in 1858, which explained how different plants and animals originated and evolved. Their theory was set out in detail in Darwin's book On

2668-592: A separate field because they rely on deductive reasoning instead of the scientific method or empirical evidence as their main methodology. Applied sciences are disciplines that use scientific knowledge for practical purposes, such as engineering and medicine . The history of science spans the majority of the historical record, with the earliest written records of identifiable predecessors to modern science dating to Bronze Age Egypt and Mesopotamia from around 3000 to 1200 BCE . Their contributions to mathematics, astronomy , and medicine entered and shaped

2784-481: A series expansion — see, for example, Vincenty's formulae . As defined in geodesy (and also astronomy ), some basic observational concepts like angles and coordinates include (most commonly from the viewpoint of a local observer): The reference surface (level) used to determine height differences and height reference systems is known as mean sea level . The traditional spirit level directly produces such (for practical purposes most useful) heights above sea level ;

2900-475: A set of basic assumptions that are needed to justify the scientific method: there is an objective reality shared by all rational observers; this objective reality is governed by natural laws ; these laws were discovered by means of systematic observation and experimentation. Mathematics is essential in the formation of hypotheses , theories , and laws, because it is used extensively in quantitative modelling, observing, and collecting measurements . Statistics

3016-463: A set of rules. It includes mathematics, systems theory , and theoretical computer science . The formal sciences share similarities with the other two branches by relying on objective, careful, and systematic study of an area of knowledge. They are, however, different from the empirical sciences as they rely exclusively on deductive reasoning, without the need for empirical evidence, to verify their abstract concepts. The formal sciences are therefore

3132-543: A single global, geocentric reference frame that serves as the "zero-order" (global) reference to which national measurements are attached. Real-time kinematic positioning (RTK GPS) is employed frequently in survey mapping. In that measurement technique, unknown points can get quickly tied into nearby terrestrial known points. One purpose of point positioning is the provision of known points for mapping measurements, also known as (horizontal and vertical) control. There can be thousands of those geodetically determined points in

3248-478: A single theory. Thus, a theory is a hypothesis explaining various other hypotheses. In that vein, theories are formulated according to most of the same scientific principles as hypotheses. Scientists may generate a model , an attempt to describe or depict an observation in terms of a logical, physical or mathematical representation, and to generate new hypotheses that can be tested by experimentation. While performing experiments to test hypotheses, scientists may have

3364-429: A strong awareness of the determining forces of modernity . Modern sociology largely originated from this movement. In 1776, Adam Smith published The Wealth of Nations , which is often considered the first work on modern economics. During the nineteenth century many distinguishing characteristics of contemporary modern science began to take shape. These included the transformation of the life and physical sciences;

3480-438: A unified theory in the early 20th-century when the modern synthesis reconciled Darwinian evolution with classical genetics . Albert Einstein 's theory of relativity and the development of quantum mechanics complement classical mechanics to describe physics in extreme length , time and gravity . Widespread use of integrated circuits in the last quarter of the 20th century combined with communications satellites led to

3596-670: A variety of mechanisms: Geodynamics is the discipline that studies deformations and motions of Earth's crust and its solidity as a whole. Often the study of Earth's irregular rotation is included in the above definition. Geodynamical studies require terrestrial reference frames realized by the stations belonging to the Global Geodetic Observing System (GGOS ). Techniques for studying geodynamic phenomena on global scales include: [REDACTED] Geodesy at Wikibooks [REDACTED] Media related to Geodesy at Wikimedia Commons Science Science

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3712-454: Is approximately the same as the direction of the plumbline, i.e., local gravity, which is also the normal to the geoid surface. For this reason, astronomical position determination – measuring the direction of the plumbline by astronomical means – works reasonably well when one also uses an ellipsoidal model of the figure of the Earth. One geographical mile, defined as one minute of arc on the equator, equals 1,855.32571922 m. One nautical mile

3828-470: Is GPS, except for specialized measurements (e.g., in underground or high-precision engineering). The higher-order networks are measured with static GPS , using differential measurement to determine vectors between terrestrial points. These vectors then get adjusted in a traditional network fashion. A global polyhedron of permanently operating GPS stations under the auspices of the IERS is the basis for defining

3944-682: Is a systematic discipline that builds and organises knowledge in the form of testable hypotheses and predictions about the universe. Modern science is typically divided into two or three major branches: the natural sciences (e.g., physics , chemistry , and biology ), which study the physical world ; and the behavioural sciences (e.g., economics , psychology , and sociology ), which study individuals and societies. The formal sciences (e.g., logic , mathematics, and theoretical computer science ), which study formal systems governed by axioms and rules, are sometimes described as being sciences as well; however, they are often regarded as

4060-487: Is based on empirical observations and is capable of being tested for its validity by other researchers working under the same conditions. Natural science is the study of the physical world. It can be divided into two main branches: life science and physical science . These two branches may be further divided into more specialised disciplines. For example, physical science can be subdivided into physics, chemistry , astronomy , and earth science . Modern natural science

4176-439: Is becoming a central feature of computational contributions to science, for example in agent-based computational economics , random forests , topic modeling and various forms of prediction. However, machines alone rarely advance knowledge as they require human guidance and capacity to reason; and they can introduce bias against certain social groups or sometimes underperform against humans. Interdisciplinary science involves

4292-518: Is called physical geodesy . The geoid essentially is the figure of Earth abstracted from its topographical features. It is an idealized equilibrium surface of seawater , the mean sea level surface in the absence of currents and air pressure variations, and continued under the continental masses. Unlike a reference ellipsoid , the geoid is irregular and too complicated to serve as the computational surface for solving geometrical problems like point positioning. The geometrical separation between

4408-714: Is considered to be one of the most important publications in medicine and was used until the 18th century. By the eleventh century most of Europe had become Christian, and in 1088, the University of Bologna emerged as the first university in Europe. As such, demand for Latin translation of ancient and scientific texts grew, a major contributor to the Renaissance of the 12th century . Renaissance scholasticism in western Europe flourished, with experiments done by observing, describing, and classifying subjects in nature. In

4524-416: Is described by (apparent) sidereal time , which accounts for variations in Earth's axial rotation ( length-of-day variations). A more accurate description also accounts for polar motion as a phenomenon closely monitored by geodesists. In geodetic applications like surveying and mapping , two general types of coordinate systems in the plane are in use: One can intuitively use rectangular coordinates in

4640-717: Is determined to high precision by observation of satellite orbit perturbations. Its relationship with the geometric flattening is indirect. The relationship depends on the internal density distribution. The 1980 Geodetic Reference System (GRS 80) posited a 6 378 137  m semi-major axis and a 1 ⁄ 298.257222101 flattening. This system was adopted at the XVII General Assembly of the International Union of Geodesy and Geophysics ( IUGG ) in Canberra, Australia, 1979. The GRS 80 reference system

4756-399: Is given by: In geodesy, point or terrain heights are " above sea level " as an irregular, physically defined surface. Height systems in use are: Each system has its advantages and disadvantages. Both orthometric and normal heights are expressed in metres above sea level, whereas geopotential numbers are measures of potential energy (unit: m s ) and not metric. The reference surface is

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4872-542: Is highly collaborative and is usually done by teams in academic and research institutions , government agencies, and companies. The practical impact of their work has led to the emergence of science policies that seek to influence the scientific enterprise by prioritising the ethical and moral development of commercial products, armaments, health care, public infrastructure, and environmental protection . The word science has been used in Middle English since

4988-578: Is off by 200 ppm in the current definitions). This situation means that one kilometre roughly equals (1/40,000) * 360 * 60 meridional minutes of arc, or 0.54 nautical miles. (This is not exactly so as the two units had been defined on different bases, so the international nautical mile is 1,852 m exactly, which corresponds to rounding the quotient from 1,000/0.54 m to four digits). Various techniques are used in geodesy to study temporally changing surfaces, bodies of mass, physical fields, and dynamical systems. Points on Earth's surface change their location due to

5104-463: Is one minute of astronomical latitude. The radius of curvature of the ellipsoid varies with latitude, being the longest at the pole and the shortest at the equator same as with the nautical mile. A metre was originally defined as the 10-millionth part of the length from the equator to the North Pole along the meridian through Paris (the target was not quite reached in actual implementation, as it

5220-421: Is purely geometrical. The mechanical ellipticity of Earth (dynamical flattening, symbol J 2 ) can be determined to high precision by observation of satellite orbit perturbations . Its relationship with geometrical flattening is indirect and depends on the internal density distribution or, in simplest terms, the degree of central concentration of mass. The 1980 Geodetic Reference System ( GRS 80 ), adopted at

5336-451: Is the science of measuring and representing the geometry , gravity , and spatial orientation of the Earth in temporally varying 3D . It is called planetary geodesy when studying other astronomical bodies , such as planets or circumplanetary systems . Geodesy is an earth science and many consider the study of Earth's shape and gravity to be central to that science. It is also

5452-447: Is the search for solutions to practical problems using this knowledge. Most understanding comes from basic research, though sometimes applied research targets specific practical problems. This leads to technological advances that were not previously imaginable. Scientific research involves using the scientific method , which seeks to objectively explain the events of nature in a reproducible way. Scientists usually take for granted

5568-533: Is the successor to the natural philosophy that began in Ancient Greece . Galileo , Descartes , Bacon , and Newton debated the benefits of using approaches that were more mathematical and more experimental in a methodical way. Still, philosophical perspectives, conjectures , and presuppositions , often overlooked, remain necessary in natural science. Systematic data collection, including discovery science , succeeded natural history , which emerged in

5684-427: Is the use of the scientific method and knowledge to attain practical goals and includes a broad range of disciplines such as engineering and medicine. Engineering is the use of scientific principles to invent, design and build machines, structures and technologies. Science may contribute to the development of new technologies. Medicine is the practice of caring for patients by maintaining and restoring health through

5800-403: Is used to make falsifiable predictions, which are typically posted before being tested by experimentation. Disproof of a prediction is evidence of progress. Experimentation is especially important in science to help establish causal relationships to avoid the correlation fallacy , though in some sciences such as astronomy or geology, a predicted observation might be more appropriate. When

5916-410: Is used to summarise and analyse data, which allows scientists to assess the reliability of experimental results. In the scientific method an explanatory thought experiment or hypothesis is put forward as an explanation using parsimony principles and is expected to seek consilience  – fitting with other accepted facts related to an observation or scientific question. This tentative explanation

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6032-429: Is usually defined by its semi-major axis (equatorial radius) a {\displaystyle a} and either its semi-minor axis (polar radius) b {\displaystyle b} , aspect ratio ( b / a ) {\displaystyle (b/a)} or flattening f {\displaystyle f} , but GRS80 is an exception: four independent constants are required for

6148-632: The Byzantine empire and Arabic translations were done by groups such as the Nestorians and the Monophysites . Under the Caliphate , these Arabic translations were later improved and developed by Arabic scientists. By the 6th and 7th centuries, the neighbouring Sassanid Empire established the medical Academy of Gondeshapur , which is considered by Greek, Syriac, and Persian physicians as

6264-740: The Early Middle Ages (400 to 1000 CE), but in the Medieval renaissances ( Carolingian Renaissance , Ottonian Renaissance and the Renaissance of the 12th century ) scholarship flourished again. Some Greek manuscripts lost in Western Europe were preserved and expanded upon in the Middle East during the Islamic Golden Age , along with the later efforts of Byzantine Greek scholars who brought Greek manuscripts from

6380-609: The Proto-Italic language as * skije- or * skijo- meaning "to know", which may originate from Proto-Indo-European language as *skh 1 -ie , *skh 1 -io , meaning "to incise". The Lexikon der indogermanischen Verben proposed sciō is a back-formation of nescīre , meaning "to not know, be unfamiliar with", which may derive from Proto-Indo-European *sekH- in Latin secāre , or *skh 2 - , from *sḱʰeh2(i)- meaning "to cut". In

6496-561: The camera obscura and the telescope . At the start of the Renaissance, Roger Bacon , Vitello , and John Peckham each built up a scholastic ontology upon a causal chain beginning with sensation, perception, and finally apperception of the individual and universal forms of Aristotle. A model of vision later known as perspectivism was exploited and studied by the artists of the Renaissance. This theory uses only three of Aristotle's four causes: formal, material, and final. In

6612-446: The geoid , an equigeopotential surface approximating the mean sea level as described above. For normal heights, the reference surface is the so-called quasi-geoid , which has a few-metre separation from the geoid due to the density assumption in its continuation under the continental masses. One can relate these heights through the geoid undulation concept to ellipsoidal heights (also known as geodetic heights ), representing

6728-527: The geoids within their areas of validity, minimizing the deflections of the vertical over these areas. It is only because GPS satellites orbit about the geocenter that this point becomes naturally the origin of a coordinate system defined by satellite geodetic means, as the satellite positions in space themselves get computed within such a system. Geocentric coordinate systems used in geodesy can be divided naturally into two classes: The coordinate transformation between these two systems to good approximation

6844-424: The historical method , case studies , and cross-cultural studies . Moreover, if quantitative information is available, social scientists may rely on statistical approaches to better understand social relationships and processes. Formal science is an area of study that generates knowledge using formal systems . A formal system is an abstract structure used for inferring theorems from axioms according to

6960-431: The materialistic sense of having more food, clothing, and other things. In Bacon's words , "the real and legitimate goal of sciences is the endowment of human life with new inventions and riches ", and he discouraged scientists from pursuing intangible philosophical or spiritual ideas, which he believed contributed little to human happiness beyond "the fume of subtle, sublime or pleasing [speculation]". Science during

7076-499: The prevention , diagnosis , and treatment of injury or disease. The applied sciences are often contrasted with the basic sciences , which are focused on advancing scientific theories and laws that explain and predict events in the natural world. Computational science applies computing power to simulate real-world situations, enabling a better understanding of scientific problems than formal mathematics alone can achieve. The use of machine learning and artificial intelligence

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7192-702: The tachymeter determines, electronically or electro-optically , the distance to a target and is highly automated or even robotic in operations. Widely used for the same purpose is the method of free station position. Commonly for local detail surveys, tachymeters are employed, although the old-fashioned rectangular technique using an angle prism and steel tape is still an inexpensive alternative. As mentioned, also there are quick and relatively accurate real-time kinematic (RTK) GPS techniques. Data collected are tagged and recorded digitally for entry into Geographic Information System (GIS) databases. Geodetic GNSS (most commonly GPS ) receivers directly produce 3D coordinates in

7308-487: The theory of impetus . His criticism served as an inspiration to medieval scholars and Galileo Galilei, who extensively cited his works ten centuries later. During late antiquity and the early Middle Ages , natural phenomena were mainly examined via the Aristotelian approach. The approach includes Aristotle's four causes : material, formal, moving, and final cause. Many Greek classical texts were preserved by

7424-465: The topographic surface of Earth — is also realizable. The locations of points in 3D space most conveniently are described by three cartesian or rectangular coordinates, X , Y , and Z . Since the advent of satellite positioning, such coordinate systems are typically geocentric , with the Z-axis aligned to Earth's (conventional or instantaneous) rotation axis. Before the era of satellite geodesy ,

7540-406: The 13th century, medical teachers and students at Bologna began opening human bodies, leading to the first anatomy textbook based on human dissection by Mondino de Luzzi . New developments in optics played a role in the inception of the Renaissance , both by challenging long-held metaphysical ideas on perception, as well as by contributing to the improvement and development of technology such as

7656-717: The 14th century in the sense of "the state of knowing". The word was borrowed from the Anglo-Norman language as the suffix -cience , which was borrowed from the Latin word scientia , meaning "knowledge, awareness, understanding". It is a noun derivative of the Latin sciens meaning "knowing", and undisputedly derived from the Latin sciō , the present participle scīre , meaning "to know". There are many hypotheses for science ' s ultimate word origin. According to Michiel de Vaan , Dutch linguist and Indo-Europeanist , sciō may have its origin in

7772-444: The 16th century by describing and classifying plants, animals, minerals, and other biotic beings. Today, "natural history" suggests observational descriptions aimed at popular audiences. Social science is the study of human behaviour and the functioning of societies. It has many disciplines that include, but are not limited to anthropology , economics, history, human geography , political science , psychology, and sociology. In

7888-633: The 3rd millennium BCE, the ancient Egyptians developed a decimal numbering system , solved practical problems using geometry , and developed a calendar . Their healing therapies involved drug treatments and the supernatural, such as prayers, incantations , and rituals. The ancient Mesopotamians used knowledge about the properties of various natural chemicals for manufacturing pottery , faience , glass, soap, metals, lime plaster , and waterproofing. They studied animal physiology , anatomy , behaviour , and astrology for divinatory purposes. The Mesopotamians had an intense interest in medicine and

8004-404: The Enlightenment was dominated by scientific societies and academies , which had largely replaced universities as centres of scientific research and development. Societies and academies were the backbones of the maturation of the scientific profession. Another important development was the popularisation of science among an increasingly literate population. Enlightenment philosophers turned to

8120-488: The GRS 80 reference ellipsoid. The geoid is a "realizable" surface, meaning it can be consistently located on Earth by suitable simple measurements from physical objects like a tide gauge . The geoid can, therefore, be considered a physical ("real") surface. The reference ellipsoid, however, has many possible instantiations and is not readily realizable, so it is an abstract surface. The third primary surface of geodetic interest —

8236-483: The GRS80 spheroid is: where and e ′ = e 1 − e 2 {\displaystyle e'={\frac {e}{\sqrt {1-e^{2}}}}} (so arctan ⁡ e ′ = arcsin ⁡ e {\displaystyle \arctan e'=\arcsin e} ). The equation is solved iteratively to give which gives Geodesy Geodesy or geodetics

8352-653: The Greek natural philosophy of classical antiquity , whereby formal attempts were made to provide explanations of events in the physical world based on natural causes, while further advancements, including the introduction of the Hindu–Arabic numeral system , were made during the Golden Age of India . Scientific research deteriorated in these regions after the fall of the Western Roman Empire during

8468-410: The Greek philosopher Leucippus and his student Democritus . Later, Epicurus would develop a full natural cosmology based on atomism, and would adopt a "canon" (ruler, standard) which established physical criteria or standards of scientific truth. The Greek doctor Hippocrates established the tradition of systematic medical science and is known as " The Father of Medicine ". A turning point in

8584-633: The Kronstadt datum, the Trieste datum, and numerous others. In both mathematics and geodesy, a coordinate system is a "coordinate system" per ISO terminology, whereas the International Earth Rotation and Reference Systems Service (IERS) uses the term "reference system" for the same. When coordinates are realized by choosing datum points and fixing a geodetic datum, ISO speaks of a "coordinate reference system", whereas IERS uses

8700-458: The Milesian school, which was founded by Thales of Miletus and later continued by his successors Anaximander and Anaximenes , were the first to attempt to explain natural phenomena without relying on the supernatural . The Pythagoreans developed a complex number philosophy and contributed significantly to the development of mathematical science. The theory of atoms was developed by

8816-584: The Moon, and satellite laser ranging (SLR) measuring distances to prisms on artificial satellites , are employed. Gravity is measured using gravimeters , of which there are two kinds. First are absolute gravimeter s, based on measuring the acceleration of free fall (e.g., of a reflecting prism in a vacuum tube ). They are used to establish vertical geospatial control or in the field. Second, relative gravimeter s are spring-based and more common. They are used in gravity surveys over large areas — to establish

8932-555: The Origin of Species , published in 1859. Separately, Gregor Mendel presented his paper, " Experiments on Plant Hybridization " in 1865, which outlined the principles of biological inheritance, serving as the basis for modern genetics. Early in the 19th century John Dalton suggested the modern atomic theory , based on Democritus's original idea of indivisible particles called atoms . The laws of conservation of energy , conservation of momentum and conservation of mass suggested

9048-556: The XVII General Assembly of the International Union of Geodesy and Geophysics ( IUGG ), posited a 6,378,137 m semi-major axis and a 1:298.257 flattening. GRS 80 essentially constitutes the basis for geodetic positioning by the Global Positioning System (GPS) and is thus also in widespread use outside the geodetic community. Numerous systems used for mapping and charting are becoming obsolete as countries increasingly move to global, geocentric reference systems utilizing

9164-472: The advent of writing systems in early civilisations like Ancient Egypt and Mesopotamia , creating the earliest written records in the history of science in around 3000 to 1200 BCE . Although the words and concepts of "science" and "nature" were not part of the conceptual landscape at the time, the ancient Egyptians and Mesopotamians made contributions that would later find a place in Greek and medieval science: mathematics, astronomy, and medicine. From

9280-398: The combination of two or more disciplines into one, such as bioinformatics , a combination of biology and computer science or cognitive sciences . The concept has existed since the ancient Greek period and it became popular again in the 20th century. Scientific research can be labelled as either basic or applied research. Basic research is the search for knowledge and applied research

9396-414: The coordinate systems associated with a geodetic datum attempted to be geocentric , but with the origin differing from the geocenter by hundreds of meters due to regional deviations in the direction of the plumbline (vertical). These regional geodetic datums, such as ED 50 (European Datum 1950) or NAD 27 (North American Datum 1927), have ellipsoids associated with them that are regional "best fits" to

9512-610: The course of tens of thousands of years, taking different forms around the world, and few details are known about the very earliest developments. Women likely played a central role in prehistoric science, as did religious rituals . Some scholars use the term " protoscience " to label activities in the past that resemble modern science in some but not all features; however, this label has also been criticised as denigrating, or too suggestive of presentism , thinking about those activities only in relation to modern categories. Direct evidence for scientific processes becomes clearer with

9628-505: The discovery of radioactivity by Henri Becquerel and Marie Curie in 1896, Marie Curie then became the first person to win two Nobel Prizes . In the next year came the discovery of the first subatomic particle, the electron . In the first half of the century the development of antibiotics and artificial fertilisers improved human living standards globally. Harmful environmental issues such as ozone depletion , ocean acidification , eutrophication , and climate change came to

9744-526: The dying Byzantine Empire to Western Europe at the start of the Renaissance . The recovery and assimilation of Greek works and Islamic inquiries into Western Europe from the 10th to 13th century revived " natural philosophy ", which was later transformed by the Scientific Revolution that began in the 16th century as new ideas and discoveries departed from previous Greek conceptions and traditions. The scientific method soon played

9860-596: The earliest medical prescriptions appeared in Sumerian during the Third Dynasty of Ur . They seem to have studied scientific subjects which had practical or religious applications and had little interest in satisfying curiosity. In classical antiquity , there is no real ancient analogue of a modern scientist. Instead, well-educated, usually upper-class, and almost universally male individuals performed various investigations into nature whenever they could afford

9976-476: The figure of the geoid over these areas. The most accurate relative gravimeters are called superconducting gravimeter s, which are sensitive to one-thousandth of one-billionth of Earth-surface gravity. Twenty-some superconducting gravimeters are used worldwide in studying Earth's tides , rotation , interior, oceanic and atmospheric loading, as well as in verifying the Newtonian constant of gravitation . In

10092-462: The free energy of the universe is seen as constantly declining: the entropy of a closed universe increases over time. The electromagnetic theory was established in the 19th century by the works of Hans Christian Ørsted , André-Marie Ampère , Michael Faraday , James Clerk Maxwell , Oliver Heaviside , and Heinrich Hertz . The new theory raised questions that could not easily be answered using Newton's framework. The discovery of X-rays inspired

10208-425: The frequent use of precision instruments; the emergence of terms such as "biologist", "physicist", and "scientist"; an increased professionalisation of those studying nature; scientists gaining cultural authority over many dimensions of society; the industrialisation of numerous countries; the thriving of popular science writings; and the emergence of science journals. During the late 19th century, psychology emerged as

10324-401: The future, gravity and altitude might become measurable using the special-relativistic concept of time dilation as gauged by optical clocks . Geographical latitude and longitude are stated in the units degree, minute of arc, and second of arc. They are angles , not metric measures, and describe the direction of the local normal to the reference ellipsoid of revolution. This direction

10440-530: The genes of the human genome . The first induced pluripotent human stem cells were made in 2006, allowing adult cells to be transformed into stem cells and turn into any cell type found in the body. With the affirmation of the Higgs boson discovery in 2013, the last particle predicted by the Standard Model of particle physics was found. In 2015, gravitational waves , predicted by general relativity

10556-412: The geoid and a reference ellipsoid is called geoidal undulation , and it varies globally between ±110 m based on the GRS 80 ellipsoid. A reference ellipsoid, customarily chosen to be the same size (volume) as the geoid, is described by its semi-major axis (equatorial radius) a and flattening f . The quantity f = ⁠ a − b / a ⁠ , where b is the semi-minor axis (polar radius),

10672-444: The geoid-ellipsoid separation, N . It varies globally between ±110 m . A reference ellipsoid , customarily chosen to be the same size (volume) as the geoid, is described by its semi-major axis (equatorial radius) a and flattening f . The quantity f  = ( a − b )/ a , where b is the semi-minor axis (polar radius), is a purely geometrical one. The mechanical ellipticity of the earth (dynamical flattening, symbol J 2 )

10788-399: The global scale, or engineering geodesy ( Ingenieurgeodäsie ) that includes surveying — measuring parts or regions of Earth. For the longest time, geodesy was the science of measuring and understanding Earth's geometric shape, orientation in space, and gravitational field; however, geodetic science and operations are applied to other astronomical bodies in our Solar System also. To

10904-430: The height of a point above the reference ellipsoid . Satellite positioning receivers typically provide ellipsoidal heights unless fitted with special conversion software based on a model of the geoid. Because coordinates and heights of geodetic points always get obtained within a system that itself was constructed based on real-world observations, geodesists introduced the concept of a "geodetic datum" (plural datums ):

11020-431: The heliocentric model. The printing press was widely used to publish scholarly arguments, including some that disagreed widely with contemporary ideas of nature. Francis Bacon and René Descartes published philosophical arguments in favour of a new type of non-Aristotelian science. Bacon emphasised the importance of experiment over contemplation, questioned the Aristotelian concepts of formal and final cause, promoted

11136-562: The history of early philosophical science was Socrates ' example of applying philosophy to the study of human matters, including human nature, the nature of political communities, and human knowledge itself. The Socratic method as documented by Plato 's dialogues is a dialectic method of hypothesis elimination: better hypotheses are found by steadily identifying and eliminating those that lead to contradictions. The Socratic method searches for general commonly-held truths that shape beliefs and scrutinises them for consistency. Socrates criticised

11252-557: The idea that science should study the laws of nature and the improvement of all human life. Descartes emphasised individual thought and argued that mathematics rather than geometry should be used to study nature. At the start of the Age of Enlightenment , Isaac Newton formed the foundation of classical mechanics by his Philosophiæ Naturalis Principia Mathematica , greatly influencing future physicists. Gottfried Wilhelm Leibniz incorporated terms from Aristotelian physics , now used in

11368-405: The inverse problem, the azimuths differ going between the two end points along the arc of the connecting great circle . The general solution is called the geodesic for the surface considered, and the differential equations for the geodesic are solvable numerically. On the ellipsoid of revolution, geodesics are expressible in terms of elliptic integrals, which are usually evaluated in terms of

11484-514: The late 20th century active recruitment of women and elimination of sex discrimination greatly increased the number of women scientists, but large gender disparities remained in some fields. The discovery of the cosmic microwave background in 1964 led to a rejection of the steady-state model of the universe in favour of the Big Bang theory of Georges Lemaître . The century saw fundamental changes within science disciplines. Evolution became

11600-412: The mean sea level surface in the absence of currents, air pressure variations etc. and continued under the continental masses. The geoid, unlike the ellipsoid, is irregular and too complicated to serve as the computational surface on which to solve geometrical problems like point positioning. The geometrical separation between it and the reference ellipsoid is called the geoidal undulation , or more usually

11716-500: The more economical use of GPS instruments for height determination requires precise knowledge of the figure of the geoid , as GPS only gives heights above the GRS80 reference ellipsoid. As geoid determination improves, one may expect that the use of GPS in height determination shall increase, too. The theodolite is an instrument used to measure horizontal and vertical (relative to the local vertical) angles to target points. In addition,

11832-626: The most important medical center of the ancient world. The House of Wisdom was established in Abbasid -era Baghdad , Iraq , where the Islamic study of Aristotelianism flourished until the Mongol invasions in the 13th century. Ibn al-Haytham , better known as Alhazen, used controlled experiments in his optical study. Avicenna 's compilation of the Canon of Medicine , a medical encyclopaedia,

11948-672: The notion that the only function of the eye is perception, and shifted the main focus in optics from the eye to the propagation of light. Kepler is best known, however, for improving Copernicus' heliocentric model through the discovery of Kepler's laws of planetary motion . Kepler did not reject Aristotelian metaphysics and described his work as a search for the Harmony of the Spheres . Galileo had made significant contributions to astronomy, physics and engineering. However, he became persecuted after Pope Urban VIII sentenced him for writing about

12064-450: The older type of study of physics as too purely speculative and lacking in self-criticism . Aristotle in the 4th century BCE created a systematic program of teleological philosophy. In the 3rd century BCE, Greek astronomer Aristarchus of Samos was the first to propose a heliocentric model of the universe, with the Sun at the centre and all the planets orbiting it. Aristarchus's model

12180-611: The past, science was a synonym for "knowledge" or "study", in keeping with its Latin origin. A person who conducted scientific research was called a "natural philosopher" or "man of science". In 1834, William Whewell introduced the term scientist in a review of Mary Somerville 's book On the Connexion of the Physical Sciences , crediting it to "some ingenious gentleman" (possibly himself). Science has no single origin. Rather, systematic methods emerged gradually over

12296-507: The plane for one's current location, in which case the x -axis will point to the local north. More formally, such coordinates can be obtained from 3D coordinates using the artifice of a map projection . It is impossible to map the curved surface of Earth onto a flat map surface without deformation. The compromise most often chosen — called a conformal projection — preserves angles and length ratios so that small circles get mapped as small circles and small squares as squares. An example of such

12412-573: The public's attention and caused the onset of environmental studies . During this period scientific experimentation became increasingly larger in scale and funding . The extensive technological innovation stimulated by World War I , World War II , and the Cold War led to competitions between global powers , such as the Space Race and nuclear arms race . Substantial international collaborations were also made, despite armed conflicts. In

12528-453: The seminal encyclopaedia Natural History . Positional notation for representing numbers likely emerged between the 3rd and 5th centuries CE along Indian trade routes. This numeral system made efficient arithmetic operations more accessible and would eventually become standard for mathematics worldwide. Due to the collapse of the Western Roman Empire , the 5th century saw an intellectual decline and knowledge of Greek conceptions of

12644-525: The sixteenth century Nicolaus Copernicus formulated a heliocentric model of the Solar System, stating that the planets revolve around the Sun, instead of the geocentric model where the planets and the Sun revolve around the Earth. This was based on a theorem that the orbital periods of the planets are longer as their orbs are farther from the centre of motion, which he found not to agree with Ptolemy's model. Johannes Kepler and others challenged

12760-422: The sky to a traveler headed South. In English , geodesy refers to the science of measuring and representing geospatial information , while geomatics encompasses practical applications of geodesy on local and regional scales, including surveying . In German , geodesy can refer to either higher geodesy ( höhere Geodäsie or Erdmessung , literally "geomensuration") — concerned with measuring Earth on

12876-405: The social sciences, there are many competing theoretical perspectives, many of which are extended through competing research programs such as the functionalists , conflict theorists , and interactionists in sociology. Due to the limitations of conducting controlled experiments involving large groups of individuals or complex situations, social scientists may adopt other research methods such as

12992-476: The time. Before the invention or discovery of the concept of phusis or nature by the pre-Socratic philosophers , the same words tend to be used to describe the natural "way" in which a plant grows, and the "way" in which, for example, one tribe worships a particular god. For this reason, it is claimed that these men were the first philosophers in the strict sense and the first to clearly distinguish "nature" and "convention". The early Greek philosophers of

13108-462: The very word geodesy comes from the Ancient Greek word γεωδαισία or geodaisia (literally, "division of Earth"). Early ideas about the figure of the Earth held the Earth to be flat and the heavens a physical dome spanning over it. Two early arguments for a spherical Earth were that lunar eclipses appear to an observer as circular shadows and that Polaris appears lower and lower in

13224-484: The world deteriorated in Western Europe. During the period, Latin encyclopaedists such as Isidore of Seville preserved the majority of general ancient knowledge. In contrast, because the Byzantine Empire resisted attacks from invaders, they were able to preserve and improve prior learning. John Philoponus , a Byzantine scholar in the 500s, started to question Aristotle's teaching of physics, introducing

13340-484: Was originally used by the World Geodetic System 1984 (WGS 84). The reference ellipsoid of WGS 84 now differs slightly due to later refinements. The numerous other systems which have been used by diverse countries for their maps and charts are gradually dropping out of use as more and more countries move to global, geocentric reference systems using the GRS80 reference ellipsoid. The reference ellipsoid

13456-511: Was widely rejected because it was believed to violate the laws of physics, while Ptolemy's Almagest , which contains a geocentric description of the Solar System , was accepted through the early Renaissance instead. The inventor and mathematician Archimedes of Syracuse made major contributions to the beginnings of calculus . Pliny the Elder was a Roman writer and polymath, who wrote

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