Search Results

The apparent change in direction of a celestial source of light caused by an observer's component of motion perpendicular to the impinging rays. In astronomy, aberration manifests, for example, as a star appearing aberrantly from what its true…

Technologies to optimize the performance of optical systems wherein controllable optical elements maintain a sharply focused image in the presence of wavefront aberrations. The practical development of adaptive optics started in the late 1960s. Main…

The interdisciplinary study that attempts to determine how much astronomy prehistoric people knew and how it influenced their lives. Archeoastronomy (Fig. 1) involves multiple disciplines: astronomy to chart the heavens, archeology to probe the…

One of the many hundreds of thousands of small planets (technically called minor planets) revolving around the Sun, mainly between the orbits of Mars and Jupiter. Asteroids are rocky bodies varying greatly in size from less than 10 meters across (33…

A kind of mathematics whose variables can only be True or False. A variable is called Boolean if it can only hold two possible values: True or False. The value True can be represented by the number one and False by zero. For example, if A is a…

Light emitted by a high-speed charged particle when the particle passes through a transparent, nonconducting, solid material at a speed greater than the speed of light in the material. The emission of Cerenkov radiation—also spelled Cherenkov—is…

The spinning of the Earth upon its planetary axis and movement of the Earth around the Sun. While appearing constant, the Earth's rate of rotation, where one complete rotation is measured as a day, and the rate of the Earth orbital motion around the…

One of the two places in the sky where the ecliptic crosses the celestial equator, or one of the two times of the year when the Sun crosses these points. The ecliptic is the great circle across the sky that marks the mean path of the Sun; the…

A mathematical system that details the properties and relationships of spatial objects such as points, lines, shapes, and planes. Euclidean geometry is also known as flat geometry or planar geometry, because planes in Euclidean geometry have the…

Planets beyond our solar system. For millennia, humankind has known about most of the major planets in our solar system because these worlds are visible to the naked eye. Exoplanets, however, were not indisputably known until 1995, when astronomers…

A large space telescope optimized for observations in infrared wavelengths through science operations in cryogenic conditions. Designed for addressing a range of astrophysical and cosmological questions, the James Webb Space Telescope, or JWST, in…

A space telescope mission dedicated to detecting exoplanets. The tenth mission launched under the National Aeronautics and Space Administration's (NASA's) Discovery Program, Kepler was the agency’s first mission dedicated to the search for planets…

The inverse function of an exponential function in mathematics. Stated less technically, a logarithm is the opposite of an exponent. Logarithms are used to solve equations in which the variable is an exponent. Historically, tables of logarithms…

The planet fourth outward from the Sun and the planet most like Earth in terms of geology, climate, and suitability for life. Mars is nicknamed the "Red Planet" for its reddish hue (Fig. 1). Besides Earth, Mars is the most-studied world in the solar…

A slow change in the direction of the axis of rotation of the Earth as well as a very small change in the orientation of the Earth's orbit around the Sun. As a consequence of the precession of equinoxes, both the celestial equator (the projection of…

A branch of mathematics involving numerical measures of how likely it is that a particular event will occur. A probability is a number between 0 and 1. An event that will never occur has a probability of zero, and an event that is certain to occur…

In medicine and health sciences, a value expected for an individual whose state of health is known and well described, and the interval of values broadly expected for a population, respectively. Results of clinical laboratory tests and other…

The second largest planet in the solar system and the sixth in order of distance from the Sun. The outermost planet known prior to 1781 CE, Saturn is surrounded by a system of rings far more extensive than any other in the solar system (Fig. 1), as…

The field of knowledge concerned with collecting, analyzing, and presenting data. Statistical methods are regularly used by researchers in the physical, biological, and social sciences, as well as engineers, business managers, government officials…

An instrument used to collect, measure, or analyze electromagnetic or other radiation from distant objects. A telescope overcomes the limitations of the human vision by increasing the ability to see faint objects and discern fine details. In…

The study of systems consisting of arbitrary sets of elements of unspecified type, together with certain operations satisfying prescribed lists of axioms. Abstract algebra has been developed since the mid-1920s and has become a basic idiom of…

An increase in the expansion rate of the universe, attributed to dark energy. In 1998, astronomers presented evidence that the universe's expansion is not slowing down, as would be expected due to the gravity from the abundances of matter strewn…

A statistical technique that partitions the total variation in experimental data into components assignable to specific sources. Analysis of variance is applicable to data for which (1) effects of sources are additive, (2) uncontrolled or…

The study of the universe and the objects in it through scientific investigation. The goal of astronomical research is to understand celestial objects and the nature and evolution of the cosmos (Fig. 1). Because much of contemporary astronomy uses…

The study of the stars, galaxies, and other objects outside of the Solar System, with attention to physical causes. Astrophysics developed in the late 19th century, taking over from the mere mapping of positions of objects that had been the…

A device that uses an internal resonance frequency of atoms (or molecules) to measure the passage of time. Atomic clocks (Fig. 1) are relied on internationally as the most accurate time and frequency standards with myriad uses in commerce, industry,…

The theory that the universe began in a hot, dense state and has since expanded and cooled. The big bang is the generally accepted cosmological theory for the origin, properties, and evolution of the universe (Fig. 1). Cosmology Universe 1 Timeline…

A discipline that combines biology, mathematics, and computer science to acquire, store, analyze, and disseminate complex biological data. The term bioinformatics was coined by Paulien Hogeweg and Ben Hesper in the early 1970s to describe the "the…

A region of spacetime exerting a gravitational field so strong that neither matter nor radiation can escape. Black holes are extreme cosmic objects predicted by German-born U.S. physicist Albert Einstein's theory of general relativity. Within a…

In its simplest form, a vector is a directed line segment. Physical quantities, such as velocity, acceleration, force, and displacement, are vector quantities, or simply vectors, because they can be represented by directed line segments. The algebra…

A natural and extremely useful extension of the familiar real numbers. They can be introduced formally as follows. Consider the two-dimensional real vector space consisting of all ordered pairs (a1, a2) of real numbers. Geometrically this space can…

A curve traced in the plane by a point on a circle that rolls, without slipping, on a line. If the line is the x axis of a rectangular coordinate system, at whose origin O the moving point P touches the axis, parametric equations of the cycloid are…

A branch of mathematics that deals with intrinsic properties of curves and surfaces in three-dimensional Euclidean space. The intrinsic properties are those which are independent of the geometrical object's orientation or location in space. The…

In arithmetic and algebra, the process of finding one of two factors of a number (or polynomial) when their product and one of the factors are given. The symbol ÷ now used mostly in elementary English and American arithmetics to denote division…

The number e usually defined as the limit approached by the expression as n approaches infinity. If the given expression is expanded by the binomial theorem, and if one uses the theorem that the limit of the quotient of two polynomials of equal…

A System that locates suitably equipped users by means of measurements made by electronic sensors. Typical measurements include distance or bearing from a vehicle to a known point, or direct determination of the present position of the vehicle in a…

A method of quantitative multivariate analysis with the goal of representing the interrelationships among a set of continuously measured variables (usually represented by their intercorrelations) by a number of underlying, linearly independent…

In algebra, the term "field" is used to designate an algebraic system or structure containing at least two elements and having two binary rules of composition: addition and multiplication (that is, if a and b are any two elements of the field, then…

A branch of mathematics concerned with the properties of space, including points, lines, curves, planes and surfaces in space, and figures bounded by them. Multiple kinds of geometry exist, dealing with everyday concepts such as lengths, angles, and…

A massive body producing distorted, magnified, or multiple images of more distant objects when its gravitational fields bend the paths of light rays. Examples of foreground bodies that can act as gravitational lenses of background objects include…

The largest visible-light observatory ever placed into space. The Hubble Space Telescope's orbit, some 612 km (380 mi) above Earth's surface (Fig. 1), keeps it beyond almost all of Earth's atmosphere, at a location where its view of the heavens is…

A topological group with only countably many connected components whose identity component is open and is an analytic group. An analytic group or connected Lie group is a topological group with the additional structure of a smooth manifold such that…

That branch of mathematics which deals with solutions of systems of linear equations and the related geometric notions of vector spaces and linear transformations. It is fundamental in the theory of the calculus of functions of several variables and…

The small cluster of galaxies that contains the Milky Way Galaxy. The Local Group (see illustration) contains at least 80 galaxies, with two spiral galaxies, the Andromeda Galaxy and the Milky Way Galaxy being the largest, dominant members in terms…

The application of mathematics to biological systems. Just as physics underlies many engineering technologies, biology serves as a foundation for such disciplines as medicine, agriculture, animal husbandry, and environmental sciences, in which…

The study of the patterns and relationships that arise between abstract concepts. Though studied purely for its own sake, mathematics is the language with which all rigorous science is discussed. As the German-born U.S. theoretical physicist Albert…

The formation of nuclides present in the universe by various nuclear reactions. Theories of the origin of the chemical elements involve synthesis with charged and neutral particles (neutrons, protons, neutrinos, photons) and other nuclear building…

A ratio comparison of two quantities expressed by using 100 equal parts, or hundredths; symbolized %. There are three major uses of percent: part of a whole, rate, and comparison of any two quantities. Part of a whole The basic idea of percent is as…

A relatively large, rounded, celestial body that developed around a star and cannot sustain nuclear fusion reactors in its interior. Although humankind has known about the existence of planets in our solar system for centuries, recent discoveries…

The largest dwarf planet in the solar system and a member of the Kuiper Belt of icy objects mostly beyond the orbit of Neptune. Pluto (Fig. 1) was discovered on February 18, 1930, by U.S. astronomer Clyde W. Tombaugh at the Lowell Observatory in…

A natural object, not human-made, in orbit around at least one more massive object, called a primary, when this primary is not a star. An object orbiting a star, a pair of stars, a galaxy, or a black hole will not be referred to as a natural…

Collectively, the various biological sciences concerned with the study of organisms when exposed to the environment of space, or of a spacecraft beyond the immediate influence of Earth and its atmosphere. Space biology dates back to November 1957,…

A spherical, self-luminous, astronomical body that generates energy through thermonuclear fusion. Over 6000 stars can be seen in the night sky with the unaided eye, shining as fixed points due to their tremendous distances from Earth (Fig. 1). These…

A group of stars held together by mutual gravitational attraction. There are two basic morphological types: open clusters and globular clusters. Typical densities of field stars near the Sun are 0.1 star per cubic parsec. (One parsec equals 1.9 ×…

A device that automatically measures the angular separation of stellar observations with respect to a reference platform. It is also referred to as an astrotracker.By utilizing the star tracker in conjunction with a precise time reference…

A galaxy that is observed to be undergoing an unusually high rate of formation of stars. It is often defined as a galaxy that, if it continues to form stars at the currently observed rate, will exhaust its entire supply of star-forming material, the…

A magnetic field, far stronger than the Earth's magnetic field, which is possessed by many stars. Magnetic fields are important throughout the life cycle of a star. Initially, magnetic fields regulate how quickly interstellar clouds collapse into…

One of the categories into which stars may be classified, based on their place in the evolution of the galaxy that they occupy. The stellar component of the Milky Way Galaxy consists of three populations: the thin disk, the thick disk, and the halo.…

The spinning of stars, due to their angular momentum. Stars do not necessarily rotate as solid bodies, and their angular momentum may be distributed nonuniformly, depending on radius or latitude. However, it is nearly impossible to resolve the…

The assertion that under certain light restrictions the surface integral of (∇ × ℑ) · ν over a surface patch S is equal to the line integral of ℑ · τ taken around C, the boundary curve of S, provided the sense of transcription of C is right-handed…

An evolving star of luminosity class IV. Such a star is brighter than the main-sequence dwarfs and fainter than the true giants in its spectral class, lying between the two on the Hertzsprung-Russell diagram. The classic subgiants fall in a small…

One of the four fundamental operations of arithmetic and algebra. The first printed use of the symbol − to denote subtraction is in Johann Widman's Behennde und hüpsche Rechnung, Leipzig, 1489. Subtraction is often regarded as an operation inverse…

The star around which the Earth revolves and the source of our planet's light and heat. Containing 99.8% of the solar system's mass, the Sun holds all the system's planets and objects under its gravitational sway. The Sun measures 1.4 million km…

An instrument for telling time by the Sun. It is composed of a style that casts a shadow and a dial plate, which is the surface upon which hour lines are marked and upon which the shadow falls. The style lies parallel to Earth's axis. The…

A member of a class of evolved stars that occupy the top of the Hertzsprung-Russell diagram to the right of the main sequence. The absolute visual magnitudes (MV ) of supergiants range approximately between −4 and −10, and they are the largest and…

A system of convective cells, called supergranules, with diameters of about 30,000 km (20,000 mi) and lifetimes of 1 or 2 days, which cover the visible disk of the Sun, the photosphere. Smaller convection cells called granules, which are about 1500…

Proper motion of an astronomical object apparently exceeding the velocity of light, c. This phenomenon is relatively common in the nuclei of quasars, many of which exhibit systematic changes in their images over periods of months to years. In some…

A two-dimensional geometric figure (a collection of points) in three-dimensional space. The simplest example is a plane—a flat surface. Some other common surfaces are spheres, cylinders, and cones, the names of which are also used to describe the…

A double star system in the late stage of stellar evolution. A symbiotic star is a binary system and not a single star. The symbiotic phase represents a brief span in the life of the binary. Symbiotic stars are rare objects, and their distances are…

The alignment of three celestial objects within a solar system. Syzygy is most often used to refer to the alignment of the Sun, Earth, and Moon at the time of new or full moon. Although syzygy is strongly associated with these two lunar phases in…

A young low-mass star characterized by variability, the presence of hydrogen emission lines, and often other signatures of circumstellar gas and dust, including bright x-ray, ultraviolet, infrared, and radio emissions. T Tauri stars are named after…

A member of the rho-theta family of air navigation systems which define an aircraft's position by its distance and bearing to a single beacon. Such systems inherently answer the navigator's questions of “in what direction” and “how far,” without…

A term describing a relationship of two figures (usually of the same dimension) in the neighborhood of a common point. The figures are tangent at a point P if they touch at P but do not intersect in a sufficiently small neighborhood of P. To be more…

The Bull, a large zodiacal northern constellation prominent in the evening winter sky (see illustration). Taurus is usually said to be the form assumed by Zeus in Greek mythology in order to carry off the princess Europa. Zodiac Modern boundaries…

The systematic study of tensors which led to an extension and generalization of vectors, begun in 1900 by two Italian mathematicians, G. Ricci and T. Levi-Civita, following G. F. B. Riemann's proposal concerning a generalization of Euclidean…

A proposition arrived at by the methods of logical deduction from a set of basic postulates or axioms accepted as primitive and therefore not subject to deductive proof. So long as a theorem is part of a purely formal system, it is not meaningful to…

The branch of mathematics concerned with finding facts concerning the roots of algebraic equations and finding methods for obtaining them. The most important type of algebraic equation is the polynomial equation in one unknown which is an expression…

The largest moon of Saturn and the only satellite in the solar system with a substantial atmosphere, as well as the only object, besides Earth, known to host stable bodies of liquid on its surface. Titan, 5150 km (3200 mi) in diameter, is the second…

The study and application of topological transformation groups. Topological dynamics originated in the late-nineteenth-century investigations of the qualitative behavior of the solutions to the differential equations of classical mechanics by Henri…

The branch of mathematics that studies the qualitative properties of spaces, as opposed to the more delicate and refined geometric or analytic properties. While there are earlier results that belong to the field, the beginning of the subject as a…

A surface obtained by rotating a circle about a line that lies in the plane of the circle but that has no points in common with the circle (see illustration). The equations x = u cos v, y = u sin v, z = [r2 − (u − b)2]1/2, b > r > 0, represent the…

A plane curve for which the length of any tangent between the curve and a fixed line is constant c. If the x axis is the fixed line, its differential equation is Eq. (1). 1 With ψ, the inclination of the tangent, as pa­ram­eter, this yields Eqs.…

The passage of one astronomical object across another. The term "transit" implies that the foreground object is smaller than the background object (Fig. 1). A related term, "eclipse," implies that the foreground object hides a background object that…

The study of triangles and the trigonometric functions. One common use for trigonometry is to measure heights and distances that are awkward or impossible to measure by ordinary means. Surveyors use it to find heights of mountains and distances…

Asteroids located near the equilateral Lagrangian stability points of a Sun-planet system (Fig. 1). As shown by J. L. Lagrange in 1772, these are two of the five stable points in the circular, restricted, three-body system, the other three points…

The Great Bear, a circumpolar constellation for observers at mid-northern latitudes or higher latitudes (see illustration). Part of this constellation is the prominent asterism (star pattern) known as the Big Dipper, whose bowl of four stars is…

The Little Bear, a circumpolar constellation from northern latitudes (see illustration). Part of this constellation is the prominent asterism (star pattern) known as the Little Dipper, whose stars are fainter than the corresponding stars of the Big…

A term that became part of mathematical language during the development of analytic geometry (no equivalent word is found in the writings of Archimedes and other Greek mathematicians), and which is frequently not defined in modern works, apparently…

A star with a detectable change in brightness that is often accompanied by other physical changes. Every star varies in brightness sometime during its life, usually in the early stages (while it is forming) or in the late stages (close to its…

A mathematical element used to describe quantities having magnitude and direction. It can be represented by a directed line segment. Many physical quantities, for example, velocity, acceleration, and force, are vectors. Vectors are widely used in…

The fifth brightest of all stars and the third brightest in the northern sky. It will be the north polar star in about 12,000 years. In moving through the Milky Way Galaxy, the Sun is generally heading toward the position now occupied by Vega. At a…

The Maiden or the Virgin, the largest zodiacal constellation and the second-largest constellation in the sky. Virgo (see illustration) is a southern constellation, visible in the summer evening sky from midnorthern latitudes. Virgo contains the…

The nearest large cluster of galaxies and one of the best studied. It dominates the distribution of bright galaxies in the sky, forming a conspicuous clump in the distribution of easily visible elliptical and spiral galaxies. The clump lies mostly…

A theorem in classical mechanics which relates the kinetic energy of a system to the virial of Clausius, as defined below. The theorem can be generalized to quantum mechanics and has widespread application. It connects the average kinetic and…

An instrument designed to collect and detect x-rays emitted from a source outside the Earth's atmosphere and to resolve the x-rays into an image. X-rays are part of the electromagnetic spectrum, between ultraviolet light and gamma rays. This x-ray…

A whole number, 0, representing the number of things in a group with no objects. In mathematics, zero (see illustration) is conceptually used both as a number and as a value of a variable. Mathematics A typical depiction of the number "0" as an…

A discipline that combines the means to know the location and heading of an aircraft with respect to some map or coordinate system, with guidance which means steering the aircraft along some desired path toward a destination. The construction of the…

The branch of mathematics dealing with the solution of equations. These equations involve unknowns, or variables, along with fixed numbers from a specified system (Fig. 1). The origins of algebra were based on the need to develop equations that…

The study of zero sets of polynomial equations. Examples of zero sets of polynomial equations studied in algebraic geometry are the parabola y − x2 = 0, thought of as sitting in the (x, y)-plane, and the locus of all points (t, t2, t3, t4), which is…

The closest spiral galaxy to the Milky Way Galaxy. The name of the Andromeda Galaxy (Fig. 1) derives from its appearance in the constellation of Andromeda. The galaxy is also known as M31 and NGC 224, based on its entries in two widely used…