Definitions

# vector space

In mathematics, a collection of objects called vectors, together with a field of objects (see field theory), known as scalars, that satisfy certain properties. The properties that must be satisfied are: (1) the set of vectors is closed under vector addition; (2) multiplication of a vector by a scalar produces a vector in the set; (3) the associative law holds for vector addition, u + (v + w) = (u + v) + w; (4) the commutative law holds for vector addition, u + v = v + u; (5) there is a 0 vector such that v + 0 = v; (6) every vector has an additive inverse (see inverse function), v + (−v) = 0; (7) the distributive law holds for scalar multiplication over vector addition, math.n(u + v) = math.nu + math.nv; (8) the distributive law also holds for vector multiplication over scalar addition, (math.m + math.n)v = math.mv + math.nv; (9) the associative law holds for scalar multiplication with a vector, (math.mmath.n)v = math.m(math.nv); and (10) there exists a unit vector 1 such that 1v = v. The set of all polynomials in one variable with real coefficients is an example of a vector space.

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Single entity that relates space and time in a four-dimensional structure, postulated by Albert Einstein in his theories of relativity. In the Newtonian universe it was supposed that there was no connection between space and time. Space was thought to be a flat, three-dimensional arrangement of all possible point locations, which could be expressed by Cartesian coordinates; time was viewed as an independent one-dimensional concept. Einstein showed that a complete description of relative motion requires equations that include time as well as the three spatial dimensions. He also showed that space-time is curved, which allowed him to account for gravitation in his general theory of relativity.

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Investigation of the universe beyond Earth's atmosphere by means of manned and unmanned spacecraft. Study of the use of rockets for spaceflight began early in the 20th century. Germany's research on rocket propulsion in the 1930s led to development of the V-2 missile. After World War II, the U.S. and the Soviet Union, with the aid of relocated German scientists, competed in the “space race,” making substantial progress in high-altitude rocket technology (see staged rocket). Both launched their first satellites (see Sputnik; Explorer) in the late 1950s (followed by other satellites and unmanned lunar probes) and their first manned space vehicles (see Vostok; Mercury) in 1961. A succession of longer and more complex manned space missions followed, most notably the U.S. Apollo program, including the first manned lunar landing in 1969, and the Soviet Soyuz and Salyut missions. Beginning in the 1960s, U.S. and Soviet scientists also launched unmanned deep-space probes for studies of the planets and other solar system objects (see Pioneer; Venera; Viking; Voyager; Galileo), and Earth-orbiting astronomical observatories (see, for example, Hubble Space Telescope), which permitted observation of cosmic objects from above the filtering and distorting effects of Earth's atmosphere. In the 1970s and '80s the Soviet Union concentrated on the development of space stations for scientific research and military reconnaissance (see Salyut; Mir). After the dissolution of the Soviet Union in 1991, Russia continued its space program, but on a reduced basis owing to economic constraints. In 1973 the U.S. launched its own space station (see Skylab), and since the mid 1970s it has devoted much of its manned space efforts to the space shuttle program and, more recently, to developing the International Space Station in collaboration with Russia and other countries.

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Soviet/Russian space station Mir, after completion in 1996. The date shown for each module is its elipsis

Manned artificial structure designed to revolve in a fixed orbit as a long-term base for astronomical observations, study of Earth's resources and environment, military reconnaissance, and investigations of materials and biological systems in weightless conditions. As of 2001, nine space stations have been placed in a low Earth orbit and occupied for varying lengths of time. The Soviet Union orbited the world's first space station, Salyut 1, designed for scientific studies, in 1971. From 1974 to 1982 five more Salyut stations—two outfitted for military reconnaissance—were successfully placed in orbit and occupied. In 1986 the U.S.S.R. launched the core module of Mir, a scientific station that was expanded with five additional modules over the next decade. The U.S. orbited its first space station in 1973; called Skylab, it was equipped as a solar observatory and medical laboratory. In 1998 the U.S. and Russia began the in-orbit construction of the International Space Station (ISS), a complex of laboratory and habitat modules that would ultimately involve contributions from at least 16 countries. In 2000 the ISS received its first resident crew.

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Sickness caused by contradiction between external data from the eyes and internal cues from the balance centre in the inner ear. For example, in seasickness the inner ear senses the ship's motion, but the eyes see the still cabin. This stimulates stress hormones and accelerates stomach muscle contraction, leading to dizziness, pallor, cold sweat, and nausea and vomiting. Minimizing changes of speed and direction may help, as may reclining, not turning the head, closing the eyes, or focusing on distant objects. Drugs can prevent or relieve motion sickness but may have side effects. Pressing an acupuncture point on the wrist helps some people.

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formally Space Transportation System (STS)

U.S. space shuttle orbiter.

Partially reusable rocket-launched vehicle developed by NASA to go into Earth orbit, transport people and cargo between Earth and orbiting spacecraft, and glide to a runway landing on Earth. The first flight of a space shuttle into orbit took place in 1981. The shuttle consists of a winged orbiter that carries crew and cargo; an expendable external tank of liquid fuel and oxidizer for the orbiter's three main rocket engines; and two large, reusable solid-propellant booster rockets. The orbiter lifts off vertically like an expendable launch vehicle but makes an unpowered descent similar to a glider. Each orbiter was designed to be reused up to 100 times. For manipulating cargo and other materials outside the orbiter, astronauts use a remotely controlled robot arm or exit the orbiter wearing spacesuits. On some missions, the shuttle carries a European-built pressurized research facility called Spacelab in its cargo bay. Between 1981 and 1985, four shuttle orbiters were put into service: Columbia (the first in orbit), Challenger, Discovery, and Atlantis. Challenger exploded in 1986 during launch, killing all seven astronauts aboard; it was replaced in 1992 by Endeavour. From 1995 to 1998, NASA conducted shuttle missions to the Russian space station Mir to prepare for the construction of the International Space Station (ISS). Beginning in 1998, the shuttle was used extensively to ferry components, supplies, and crews to the ISS. In 2003 Columbia disintegrated while returning from a space mission, claiming the lives of its seven-person crew.

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Branch of medicine, pioneered by Paul Bert, dealing with atmospheric flight (aviation medicine) and space flight (space medicine). Intensive preflight simulator training and attention to design of equipment and spacecraft promote the safety and effectiveness of humans exposed to the stresses of flight and can prevent some problems. The world's first unit for space research was established in the U.S. in 1948. Physicians trained in aerospace medicine are known as flight surgeons.

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Rocket system that boosts a spacecraft into Earth orbit or beyond Earth's gravitational pull. A wide variety of launch vehicles have been used to lift payloads ranging from satellites weighing a few pounds (or kilograms) to large modular components of space stations. Most launch vehicles are expendable (one-use) systems; many early ones were derived from intercontinental ballistic missiles (see ICBM). The Saturn V, which launched the spacecraft that carried humans to the Moon (see Apollo), had three stages (see staged rocket). The U.S. space shuttle system (from 1981) represents a significant departure from expendable launch vehicles in that it is partially reusable—its manned orbiting component is designed for numerous flights, and its solid rocket boosters can be recovered and refurbished.

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or space contraction

In relativity physics, the shortening of an object along the direction of its motion relative to an observer. Dimensions in other directions are not contracted. This concept was proposed by the Irish physicist George F. FitzGerald (1851–1901) in 1889 and later independently developed by Hendrik Antoon Lorentz. Significant at speeds approaching that of light, the contraction results from the properties of space and time, not from compression, cooling, or any similar physical disturbance. Seealso time dilation.

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In mathematics, a set of objects equipped with a concept of distance. The objects can be thought of as points in space, with the distance between points given by a distance formula, such that: (1) the distance from point A to point B is zero if and only if A and B are identical, (2) the distance from A to B is the same as from B to A, and (3) the distance from A to B plus that from B to C is greater than or equal to the distance from A to C (the triangle inequality). Two- and three-dimensional Euclidean spaces are metric spaces, as are inner product spaces, vector spaces, and certain topological spaces (see topology).

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in full National Aeronautics and Space Administration

Independent U.S. government agency established in 1958 for research and development of vehicles and activities for aeronautics and space exploration. Its goals include improving human understanding of the universe, the solar system, and Earth and establishing a permanent human presence in space. NASA, previously the National Advisory Committee for Aeronautics (NACA), was created largely in response to the Soviet Union's launch of Sputnik in 1957. Its organization was well under way in 1961, when Pres. John F. Kennedy proposed that the U.S. put a man on the Moon by the end of the 1960s (see Apollo). Later unmanned programs (e.g., Viking, Mariner, Voyager, Galileo) explored other planets and interplanetary space, and orbiting observatories (e.g., the Hubble Space Telescope) have studied the cosmos. NASA also developed and launched various satellites with Earth applications, such as Landsat and communications and weather satellites. It planned and developed the space shuttle and led the development and construction of the International Space Station.

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Cutaway of the NASA Hubble Space Telescope, revealing the Optical Telescope Assembly, the heart of elipsis

Most sophisticated optical observatory ever placed into orbit around Earth. Because it is above Earth's obscuring atmosphere, it can obtain images much brighter, clearer, and more detailed than ground-based telescopes can. Named for Edwin Hubble, it was built under NASA supervision and deployed on a 1990 space-shuttle mission. The reflector telescope's mirror optics gather light from celestial objects and direct it to an array of cameras and spectrographs (see spectroscopy). A defect in the primary mirror initially caused it to produce fuzzy images; in 1993 another shuttle mission corrected this and other problems. Subsequent missions to the HST have been for maintenance, repairs, and instrument upgrades.

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French Agence Spatiale Européenne

Western European space and space-technology research organization headquartered in Paris. It was founded in 1975 from the merger of the European Launcher Development Organisation (ELDO) and the European Space Research Organisation (ESRO), both established in 1964. Members are Austria, Belgium, Britain, Denmark, Finland, France, Germany, Ireland, Italy, The Netherlands, Norway, Portugal, Spain, Sweden, and Switzerland. Canada, through a special cooperative agreement, participates in some projects. The ESA developed the Ariane series of space launch vehicles, and it supports a launch facility in French Guiana. It has launched a system of meteorological satellites (Meteosat) as well as the Giotto space probe, which examined the nucleus of Halley's Comet, and Hipparcos, a satellite that measured the parallaxes, positions, and proper motions of more than 100,000 stars. It is also a participant in the construction of the International Space Station.

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Space is the extent within which matter is physically extended and objects and events have positions relative to one another. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of the boundless four-dimensional continuum known as spacetime. In mathematics spaces with different numbers of dimensions and with different underlying structures can be examined. The concept of space is considered to be of fundamental importance to an understanding of the universe although disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework.

Many of the philosophical questions arose in the 17th century, during the early development of classical mechanics. In Isaac Newton's view, space was absolute - in the sense that it existed permanently and independently of whether there were any matter in the space. Other natural philosophers, notably Gottfried Leibniz, thought instead that space was a collection of relations between objects, given by their distance and direction from one another. In the 18th century, Immanuel Kant described space and time as elements of a systematic framework which humans use to structure their experience.

In the 19th and 20th centuries mathematicians began to examine non-Euclidean geometries, in which space can be said to be curved, rather than flat. According to Albert Einstein's theory of general relativity, space around gravitational fields deviates from Euclidean space. Experimental tests of general relativity have confirmed that non-Euclidean space provides a better model for explaining the existing laws of mechanics and optics.

## Philosophy of space

In the early 11th century, the Islamic philosopher and physicist, Ibn al-Haytham (also known as Alhacen or Alhazen), discussed space perception and its epistemological implications in his Book of Optics (1021). His experimental proof of the intromission model of vision led to changes in the way the visual perception of space was understood, contrary to the previous emission theory of vision supported by Euclid and Ptolemy. In "tying the visual perception of space to prior bodily experience, Alhacen unequivocally rejected the intuitiveness of spatial perception and, therefore, the autonomy of vision. Without tangible notions of distance and size for correlation, sight can tell us next to nothing about such things.

### Leibniz and Newton

In the seventeenth century, the philosophy of space and time emerged as a central issue in epistemology and metaphysics. At its heart, Gottfried Leibniz, the German philosopher-mathematician, and Isaac Newton, the English physicist-mathematician, set out two opposing theories of what space is. Rather than being an entity which independently exists over and above other matter, Leibniz held that space is no more than the collection of spatial relations between objects in the world: "space is that which results from places taken together. Unoccupied regions are those which could have objects in them and thus spatial relations with other places. For Leibniz, then, space was an idealised abstraction from the relations between individual entities or their possible locations and therefore could not be continuous but must be discrete. Space could be thought of in a similar way to the relations between family members. Although people in the family are related to one another, the relations do not exist independently of the people. Leibniz argued that space could not exist independently of objects in the world because that would imply that there would be a difference between two universes exactly alike except for the location of the material world in each universe. But since there would be no observational way of telling these universes apart then, according to the identity of indiscernibles, there would be no real difference between them. According to the principle of sufficient reason, any theory of space which implied that there could be these two possible universes, must therefore be wrong.

Newton took space to be more than relations between material objects and based his position on observation and experimentation. For a relationist there can be no real difference between inertial motion, in which the object travels with constant velocity, and non-inertial motion, in which the velocity changes with time, since all spatial measurements are relative to other objects and their motions. But Newton argued that since non-inertial motion generates forces, it must be absolute. He used the example of water in a spinning bucket to demonstrate his argument. Water in a bucket is hung from a rope and set to spin, starts with a flat surface. After a while, as the bucket continues to spin, the surface of the water becomes concave. If the bucket's spinning is stopped then the surface of the water remains concave as it continues to spin. The concave surface is therefore apparently not the result of relative motion between the bucket and the water. Instead, Newton argued, it must be a result of non-inertial motion relative to space itself. For several centuries the bucket argument was decisive in showing that space must exist independently of matter.

### Kant

In the eighteenth century the German philosopher Immanuel Kant developed a theory of knowledge in which knowledge about space can be both a priori and synthetic. According to Kant, knowledge about space is synthetic, in that statements about space are not simply true by virtue of the meaning of the words in the statement. In his work, Kant rejected the view that space must be either a substance or relation. Instead he came to the conclusion that space and time are not discovered by humans to be objective features of the world, but are part of an unavoidable systematic framework for organizing our experiences.

### Non-Euclidean geometry

Euclid's Elements contained five postulates which form the basis for Euclidean geometry. One of these, the parallel postulate has been the subject of debate among mathematicians for many centuries. It states that on any plane on which there is a straight line L1 and a point P not on L1, there is only one straight line L2 on the plane which passes through the point P and is parallel to the straight line L1. Until the 19th century, few doubted the truth of the postulate; instead debate centered over whether it was necessary as an axiom, or whether it was a theory which could be derived from the other axioms. Around 1830 though, the Hungarian János Bolyai and the Russian Nikolai Ivanovich Lobachevsky separately published treatises on a type of geometry which does not include the parallel postulate, called hyperbolic geometry. In this geometry, there are an infinite number of parallel lines which pass through the point P. Consequently the sum of angles in a triangle is less than 180o and the ratio of a circle's circumference to its diameter is greater than pi. In the 1850s, Bernhard Riemann developed an equivalent theory of elliptical geometry, in which there are no parallel lines which pass through P. In this geometry, triangles have more than 180o and circles have a ratio of circumference to diameter which is less than pi.

 Type of geometry Hyperbolic Euclidean Elliptical Number of parallels Sum of angles in a triangle Ratio of circumference to diameter of circle Measure of curvature Infinite < 180o > π < 0 1 180o π 0 0 > 180o < π > 0

### Gauss and Poincaré

Although there was a prevailing Kantian consensus at the time, once non-Euclidean geometries had been formalised, some began to wonder whether or not physical space is curved. Carl Friedrich Gauss, the German mathematician, was the first to consider an empirical investigation of the geometrical structure of space. He thought of making a test of the sum of the angles of an enormous stellar triangle and there are reports he actually carried out a test, on a small scale, by triangulating mountain tops in Germany.

Henri Poincaré, a French mathematician and physicist of the late 19th century introduced an important insight which attempted to demonstrate the futility of any attempt to discover by experiment which geometry applies to space. He considered the predicament which would face scientists if they were confined to the surface of an imaginary large sphere with particular properties, known as a sphere-world. In this world, the temperature is taken to vary in such a way that all objects expand and contract in similar proportions in different places on the sphere. With a suitable falloff in temperature, if the scientists try to use measuring rods to determine the sum of the angles in a triangle, they can be deceived into thinking that they inhabit a plane, rather than a spherical surface. In fact, the scientists cannot in principle determine whether they inhabit a plane or sphere and, Poincaré argued, the same is true for the debate over whether real space is Euclidean or not. For him, it was a matter of convention which geometry was used to describe space. Since Euclidean geometry is simpler than non-Euclidean geometry, he assumed the former would always be used to describe the 'true' geometry of the world.

### Einstein

In 1905, Albert Einstein published a paper on a special theory of relativity, in which he proposed that space and time be combined into a single construct known as spacetime. In this theory, the speed of light in a vacuum is the same for all observers - which has the result that two events that appear simultaneous to one particular observer will not be simultaneous to another observer if the observers are moving with respect to one another. Moreover, an observer will measure a moving clock to tick more slowly than one which is stationary with respect to them; and objects are measured to be shortened in the direction that they are moving with respect to the observer.

Over the following ten years Einstein worked on a general theory of relativity, which is a theory of how gravity interacts with spacetime. Instead of viewing gravity as a force field acting in spacetime, Einstein suggested that it modifies the geometric structure of spacetime itself. According to the general theory, time goes more slowly at places with lower gravitational potentials and rays of light bend in the presence of a gravitational field. Scientists have studied the behaviour of binary pulsars, confirming the predictions of Einstein's theories and Non-Euclidean geometry is usually used to describe spacetime.

## Mathematics

In modern mathematics, spaces are frequently described as different types of manifolds which are spaces that locally approximate to Euclidean space and where the properties are defined largely on local connectedness of points that lie on the manifold.

## Physics

### Classical mechanics

Space is one of the few fundamental quantities in physics, meaning that it cannot be defined via other quantities because nothing more fundamental is known at the present. On the other hand, it can be related to other fundamental quantities. Thus, similar to other fundamental quantities (like time and mass), space can be explored via measurement and experiment.

### Astronomy

Astronomy is the science involved with the observation, explanation and measuring of objects in outer space.

### Relativity

Before Einstein's work on relativistic physics, time and space were viewed as independent dimensions. Einstein's discoveries have shown that due to relativity of motion our space and time can be mathematically combined into one object — spacetime. It turns out that distances in space or in time separately are not invariant with respect to Lorentz coordinate transformations, but distances in Minkowski space-time along space-time intervals are — which justifies the name.

In addition, time and space dimensions should not be viewed as exactly equivalent in Minkowski space-time. One can freely move in space but not in time. Thus, time and space coordinates are treated differently both in special relativity (where time is sometimes considered an imaginary coordinate) and in general relativity (where different signs are assigned to time and space components of spacetime metric).

Furthermore, from Einstein's general theory of relativity, it has been shown that space-time is geometrically distorted- curved -near to gravitationally significant masses.

Experiments are ongoing to attempt to directly measure gravitational waves. This is essentially solutions to the equations of general relativity which describe moving ripples of spacetime. Indirect evidence for this has been found in the motions of the Hulse-Taylor binary system.

### Cosmology

Relativity theory lead to the cosmological question of what shape the universe is, and where space came from. It appears that space was created in the Big Bang and has been expanding ever since. The overall shape of space is not known, but space is known to be expanding very rapidly which is evident due to the Hubble expansion.

## Spatial measurement

The measurement of physical space has long been important. Although earlier societies had developed measuring systems, the International System of Units, (SI), is now the most common system of units used in the measuring of space, and is almost universally used within science.

Currently, the standard space interval, called a standard meter or simply meter, is defined as the distance traveled by light in a vacuum during a time interval of exactly 1/299,792,458 of a second. This definition coupled with present definition of the second is based on the special theory of relativity, that our space-time is a Minkowski space.

## Geography

Geography is the branch of science concerned with identifying and describing the Earth, utilizing spatial awareness to try and understand why things exist in specific locations. Cartography is the mapping of spaces to allow better navigation, for visualization purposes and to act as a locational device. Geostatistics apply statistical concepts to collected spatial data in order to create an estimate for unobserved phenomena.

Geographical space is often considered as land, and can have a relation to ownership usage (in which space is seen as property or territory). While some cultures assert the rights of the individual in terms of ownership, other cultures will identify with a communal approach to land ownership, while still other cultures such as Australian Aboriginals, rather than asserting ownership rights to land, invert the relationship and consider that they are in fact owned by the land. Spatial planning is a method of regulating the use of space at land-level, with decisions made at regional, national and international levels. Space can also impact on human and cultural behavior, being an important factor in architecture, where it will impact on the design of buildings and structures, and on farming.

Ownership of space is not restricted to land. Ownership of airspace and of waters is decided internationally. Other forms of ownership have been recently asserted to other spaces — for example to the radio bands of the electromagnetic spectrum or to cyberspace.

Public space is a term used to define areas of land as collectively owned by the community, and managed in their name by delegated bodies; such spaces are open to all. While private property is the land culturally owned by an individual or company, for their own use and pleasure.

Abstract space is a term used in geography to refer to a hypothetical space characterized by complete homogeneity. When modeling activity or behavior, it is a conceptual tool used to limit extraneous variables such as terrain.

## In psychology

The way in which space is perceived is an area which psychologists first began to study in the middle of the 19th century, and it is now thought by those concerned with such studies to be a distinct branch within psychology. Psychologists analyzing the perception of space are concerned with how recognition of an object's physical appearance or its interactions are perceived.

Other, more specialized topics studied include amodal perception and object permanence. The perception of surroundings is important due to its necessary relevance to survival, especially with regards to hunting and self preservation as well as simply one's idea of personal space.

Several space-related phobias have been identified, including agoraphobia (the fear of open spaces), astrophobia (the fear of celestial space), claustrophobia (the fear of enclosed spaces), and cenophobia (the fear of empty spaces).