acceleration: In 1998, astronomers found that the red shifts of distant galaxies were smaller than predicted by Hubble's law. This fact implied that the expansion of the universe was slower in the past and that the rate of expansion has increased with time. The discovery of acceleration has caused cosmologists to revise their models and to posit the existence of "dark energy" to account for the acceleration.

adaptive optics: A system used in large telescopes to cancel the disturbing effect of the atmosphere on the image of a star or galaxy. Pioneered in the 1980s, adaptive optics are employed in the giant telescopes located in Chile and Hawaii.

al-Tusi couple: A geometric device used by the mathematician al-Tusi in which straight-line motion is produced by a combination of circular motions. Used in a planetary model to replace the equant. The al-Tusi couple also raised conceptual questions about the Aristotelian opposition of straight-line and circular motion.

annual parallax: Change in angular position of a star as observed from Earth during its annual orbit about the Sun. Also known as trigonometric parallax because the distance of the star can be determined in terms of astronomical units by trigonometry from the angle of parallax.

astronomical unit: The distance from the Earth to the Sun. Distances within the solar system are often measured in terms of astronomical units. Abbreviated to a.u.

big bang theory: The standard cosmological theory accepted by most scientists today. Posits that the universe began in primordial conditions of extremely high density and temperature approximately 13 billion years ago and that the universe has been expanding ever since.

blackbody: An ideal body that emits all the radiation that it absorbs. For a given temperature of the body, there is a characteristic graph giving the intensity of the emitted radiation as a function of the frequency of the radiation. The concept of a blackbody arose in 1900 in Planck's quantum theory. The microwave background radiation displays a characteristic graph for a blackbody at three degrees Kelvin, indicating its cosmic origin in the primordial big bang.

black hole: An object so dense that no radiation can escape its gravitational field. The term was introduced by Wheeler in 1968. It is believed that supermassive black holes lie at the centers of quasars and galaxies. celestial equator: The circle on the celestial sphere that is 90 degrees from the north celestial pole. The celestial equator is inclined at an angle of about 23 degrees to the ecliptic.

Cepheid variable: A type of variable star in which the period of variation is related to the absolute brightness or luminosity of the star. Named after the star 5 Cephei in the northern constellation of Cepheus. By comparing the absolute brightness of a star with its apparent brightness, one can determine its distance. Cepheid variables are an important tool for determining distances to stars and nearby galaxies.

charge-coupled device: An electronic device for recording the image of an object in a telescope. Such devices have replaced photography. Pioneered in astronomy in the 1970s, CCDs are used in today's digital cameras. cosmological constant: A constant introduced into the gravitational equations to produce a roughly static system in an extended system of masses. The presence of the constant corresponds to a repulsive tendency that acts over large distances. It was introduced by Neumann in 1896 and again by Einstein in 1917. With the discovery in 1998 that expansion is accelerating, cosmological models containing the cosmological constant have been a subject of renewed interest. The cosmological constant is sometimes known as the X constant because this was the notation used by Einstein. cosmological principle: The principle that the universe on a large scale looks the same from every point within it. The term was introduced by the British cosmologist Arthur Milne in the 1930s. Modern theories of cosmology of every stripe accept the cosmological principle.

dark matter: Matter that does not manifest itself in the form of electromagnetic radiation. Studies of the rotational motions of galaxies and clusters of galaxies have indicated the existence of large amounts of dark matter in the universe. Inflationary versions of the big bang theory also predict the existence of dark matter.

deferent: In Ptolemy's model for the motion of a planet the deferent is a large circle whose center is the Earth or a point near the Earth. The center of the planet's epicycle lies on the deferent. In the case of Venus and Mercury the epicycle center revolves on the deferent once each year. For Mars, Jupiter, and Saturn the epicycle center revolves on the deferent with a period characteristic of each planet.

diurnal parallax: The change in position of an object as observed from the surface and center of the Earth. The daily or diurnal motion of each of the planetary bodies—its rising and setting—occurs on a circle whose center is the center of the Earth. Because we observe the body from the surface of the Earth, at a substantial distance from the center, it appears to shift in direction during a 24-hour period. Only the Moon exhibits diurnal parallax that is large enough to be observable with the naked eye.

Doppler effect: A shift in the length of waves emitted from a source moving with respect to the observer. If the source is approaching the observer, the wavelength increases, and if it is moving away from the observer, it decreases. Light from a receding source is shifted to the red, and light from an approaching source is shifted to the blue.

eccentric circle: A circle whose center is close to but does not coincide with the Earth. Such a circle is said to be situated eccentrically with respect to the Earth. Used by Hipparchus and Ptolemy to represent the motion of the Sun. ecliptic: The path traced by the Sun during its annual eastward circuit around the celestial sphere. The Moon and the planets also move eastward on the celestial sphere within a narrow band surrounding the ecliptic. elliptical geometry: A geometry different from Euclid's, characterized by the property that the angles of a triangle add up to more than 180 degrees. First discussed by Riemann in 1854, such a geometry is also known as Riemannian geometry. The surface of a sphere in which a line is defined as a great circle— the intersection of a plane through the center of the sphere and the surface—is a model for elliptical geometry. The first cosmological solutions of the field equations of general relativity by Einstein and Friedmann assumed that the universe was finite and that the geometry of space was elliptical. In such a world, light from a given source will eventually travel around a great circle in space and return to the source. Cosmologists today believe elliptical geometry is an unlikely choice as the geometry of space.

epicycle: In Ptolemy's model for planetary motion the planet revolves on a small circle called an epicycle whose center revolves on a larger circle known as the deferent.

equant: A device used by Ptolemy to account for small variations in planetary motion. The equant is a point offset from the center of the planetary deferent, the latter being situated eccentrically with respect to the Earth. The motion of the center of the epicycle on the deferent is uniform with respect to the equant. Hence neither the center of uniform angular motion nor the Earth itself is at the center of the deferent.

equivalence principle: The action of a uniform gravitational field on a system of bodies may be regarded as equivalent to the same system in which no force acts but in which the bodies are subjected to a uniform acceleration. Adoption of the equivalence principle was the first step in Einstein's development of the general theory of relativity.

Euclidean geometry: The traditional geometry of space that was described by Euclid of Alexandria around 300 b.c. In Euclidean geometry the angles of a triangle add up to 180 degrees and the relationship between the sides and diagonal of a triangle has the very simple Pythagorean form a2 + b2 = c2.

Euclidean geometry is currently favored by cosmologists as the geometry of the universe.

extragalactic: Until well into the twentieth century the word galaxy referred exclusively to the Milky Way galaxy. Hence any object that was outside of the Milky Way was said to be extragalactic. This meaning has persisted even as the term galaxy has been extended.

field equations: Equations that describe the action of gravity in Einstein's general theory of relativity. The field equations are written in terms of tensor notation using methods from a branch of mathematics known as differential geometry.

galaxy: The word comes from the Greek for "milky way" and originally referred to the Milky Way system of stars. With Hubble's discovery in 1925 that spiral nebulae and other white nebulae are star systems similar to the Milky Way and external to it, the word has come to refer to any of these large star systems. globular cluster: A spherically shaped cluster containing a very large number of stars. The galaxy is framed symmetrically by globular clusters. This fact was used by Shapley in 1920 to infer that the Sun is situated some distance away from the center of the Milky Way galaxy.

gravitational lens: An object whose gravitation bends the light from a more distance source. The image of a distant galaxy or quasar may be distorted, magnified, or multiplied as a result of the action of an intervening galaxy or cluster of galaxies lying along the line of sight to the more distant object. Gravitation lenses enable some of the most distant objects in the universe to be studied more closely than would be possible otherwise. They can also be used to determine the distance to the lensed object and therefore to determine the value of Hubble's constant.

gravitational wave: A rapid and sudden change in motion of a massive object will result in the propagation of gravitational waves, undulations in the gravitational field of the object that are propagated at the speed of light. Such waves are analyzed using the general theory of relativity. They have never been observed directly but have been inferred to exist from the observation of radio waves emitted by binary pulsars. Currently, there are large scientific projects in place to detect gravitational waves directly.

Great Attractor: An increase in density of matter at a distance of 150 million light-years in the directions of the constellations Hydra and Centaurus. In analyzing large numbers of galactic red shifts and distances during the 1980s, astronomers identified a departure from pure Hubble flow, leading them to infer the existence of what they called the Great Attractor. Its existence indicates that there is significant local inhomogeneity in the universe. Hertzsprung-Russell diagram: A graph in which the brightness of a star is plotted against surface temperature. For most stars, there is a linear relationship between brightness and surface temperature. There is also a class of bright red giants with a lower relative surface temperature. The H-R diagram is used to study the evolution of stars.

Hubble's constant: The constant H in Hubble's law, measured in units of kilometers per second per megaparsec. For every increase in distance of one megaparsec the recessional velocity of an object increases by H kilometers per second. Hubble's constant is currently believed to have a value of 70 with an uncertainty of ±15 percent.

Hubble's law: The red shift of an object such as a galaxy is linearly proportional to its distance from the Earth. Red shift is conventionally measured as the velocity of recession for the corresponding Doppler shift. The law is v = Hd, where v is the nominal recessional velocity of the object, d is its distance, and H is a constant known as Hubble's constant. If the red shift represents an actual recessional velocity—as most astronomers believe—then Hubble's law implies that the universe is expanding. In relativistic cosmology the motion of recession is understood to result from the expansion of space. At a certain distance the recessional velocity dominates any local or peculiar motions, giving rise to what is known as pure Hubble flow.

hyperbolic geometry: A geometry different from Euclid's characterized by the property that the angles of a triangle add up to less than 180 degrees. The functions describing the relationship between sides and angles in this geometry are the hyperbolic functions. Hyperbolic geometry was the first non-Euclidean geometry to be studied, with published accounts by Lobachevsky and Bolyai in the first part of the nineteenth century. In 1924 Friedmann constructed an infinite relativistic world model in which the geometry of space is hyperbolic. inertia: The tendency of a body in the absence of external forces to continue in uniform straight-line motion. The principle was the basis of the new physics of the seventeenth century that replaced traditional Aristotelian physics. inflation: In the big bang theory a very short-lived event involving exponential expansion of the whole universe in the first instant of the big bang. It is believed that inflation produced the homogeneity seen today in the microwave background radiation. It also explains the absence in the universe of a particle known as a magnetic monopole.

interferometer: A device that enables one to locate the position of a source by analyzing the interference patterns generated by a signal arriving at two different receivers. Very long base lines between receivers have been used in radio astronomy to provided unprecedented levels of resolution. island-universe theory: The white and oval-shaped nebulae such as M 31 and M 51 are autonomous star systems, or "island universes," similar to the Milky Way galaxy and external to it.

light-year: The distance light travels in one year. The nearest star is just over four light-years away. The galaxy is 100,000 light-years in diameter, and the Andromeda galaxy is 2.5 million light-years distant.

Mach's principle: The inertial properties of matter are determined by the distribution of matter throughout the universe. It influenced Einstein in adopting a form of what later became known as the cosmological principle as a basis for his cosmological solutions of the field equations.

Messier catalog: A catalog of 103 nebulae published by the French astronomer Charles Messier in 1781. The most prominent nebulae in the sky are identified by their Messier number. For example, M 31 is the Andromeda galaxy, and M 13 is the globular cluster in Hercules.

microwave background radiation: Radiation coming from all parts of the sky, possessing a temperature corresponding to a blackbody at three degrees Kelvin. The discovery of the microwave background radiation in 1965 was the event that confirmed (for most scientists) the big bang theory of the universe. The radiation is believed to have been emitted in the primordial bang that created the universe. The radiation is also known as the cosmic background radiation.

nebula: A fuzzy or milky object, from the Latin for "cloud." There are several different types of nebula, based on their appearance under telescopic examination: planetary nebulae, white nebulae (spiral and elliptical), reflection nebulae, globular clusters, and open clusters. The class of white nebulae consists of galaxies external to the Milky Way.

nesting principle: Adopted by Ptolemy in developing his planetary cosmology, the principle asserts that there are no empty spaces between the successive spherical shells within which the planets move. The principle enabled Ptolemy to determine the dimensions of the planetary system.

nucleosynthesis: Process in which the nuclei of elements fuse together and form heavier nuclei, releasing energy as they do so. The energy emitted by a star comes from thermonuclear fusion at the star's center. For stars on the main sequence of the H-R diagram, protons fuse to form helium nuclei. This process is known as the carbon-nitrogen cycle because carbon and nitrogen are formed temporarily at one step in the sequence of reactions.

Olber's paradox: If the sky is evenly populated by Sun-like stars and the universe is very large or infinite, then the total radiation reaching the Earth should be very large. The night sky should be bright, but paradoxically is not. Modern solutions of Olber's paradox use the fact that in the big bang model the amount of radiation reaching the Earth is constrained by the limited number and age of radiant bodies that have formed since the creation of the universe. opposition: If the Sun, Earth, and the planet lie in a straight line, then the planet is said to be in opposition. At opposition the planet reaches its highest point in the sky at midnight.

parsec: The distance of an object exhibiting an annual parallax of one second of arc. A parsec is approximately 3.26 light-years. The distances to galaxies are typically given in megaparsecs, or units of distance equaling one million parsecs.

perfect cosmological principle: The universe on a large scale is the same at all points in space and in time. Foundation of the steady state theory of the universe, developed by Bondi, Gold, and Hoyle in the 1940s and 1950s. photometry: The measurement of the brightness of stars and galaxies. Brightness is measured on the logarithmic magnitude scale, where each increase in magnitude corresponds to a 2.5-fold increase in brightness. Photometry has moved from optical methods, to photography, to highly sensitive electronic devices.

Platonic axiom: The motion of all celestial bodies is circular and uniform (constant angular motion). The basic axiom of Greek mathematical astronomy, it dominated the study of planetary motions up to the time of Kepler. Platonic solid: A polyhedron that is convex (no indentations) and in which each face is a congruent regular polygon. Euclid showed around 300 b.c. that there are only five such solids, the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. Kepler constructed a heliocentric cosmology by fitting the six planetary orbits within a nested sequence of the Platonic solids.

precession: The slow movement in a westward direction of the two points of intersection of the celestial equator and the ecliptic.

proper motion: Real as opposed to apparent motion of a star. In proper motions the stars are actually moving in space. First detected by Halley in 1718. Proper motions were one of the first subjects studied in stellar astronomy, indicative of the beginning of an interest in the universe beyond the solar system. pulsar: A rapidly rotating neutron star that emits radio waves along the ends of an axis inclined to its axis of rotation. The radio waves are received on the Earth as a sequence of pulses. Study of a pulsar-star binary system in the late 1970s led to the detection of what were inferred to be gravitational waves. quasar: A quasi-stellar radio source, an extremely luminous and very distant object. The first quasars to be discovered were energetic emitters of radio waves and possessed extremely large red shifts. Radio-silent quasar-like objects were subsequently found. The existence of quasars has been used as evidence that the universe is evolutionary.

red shift: A shift to lower frequency in the spectrum of a star or galaxy. For optical spectra a shift to the red. A red shift may result from the action of gravitation on the emitted light. Most often, it is caused by the motion of the light source away from the Earth. The recessional velocity of an object may be peculiar (arising from its motion through space relative to the Earth) or cosmological (arising from the expansion of space according to the general theory of relativity). Cosmological red shifts are described by Hubble's law and are very large, increasing linearly with distance.

reflector: A telescope in which the light from a source is reflected and focused by a primary mirror. The focused image is examined by an eyepiece, spectroscope, or photometric receiver. Reflecting telescopes today are the largest optical instruments in astronomy and are the main instruments used to study faint and distant objects. Hubble's law was discovered through observations of nebulae made with the Hooker 100-inch (250 centimeter) reflector at the Mount Wilson Observatory in southern California.

refractor: A telescope in which the light from a source passes through a main objective lens and is focused and examined by an eyepiece, spectroscope, or photometric receiver. Because the objective lens can only be supported around its circumference, the size of refractors is limited.

retrograde motion: The planets move eastward along the ecliptic, except for certain periods, when they move backward for a while before resuming their forward motion. The backward motion is called retrograde motion. spectroscopy: The study of spectra. Spectroscopy gives information about the chemical constitution, temperature, and motion of a star or nebula. spiral nebula: A nebula possessing a spiral structure. First identified by Lord Rosse in 1840, spiral nebulae were found to be external galaxies similar to the Milky Way galaxy.

statistical parallax: Other things being equal, the size of proper motion in a star is inversely proportional to its distance. By measuring the average proper motion of a group of stars, one obtains an estimate of the distance to this group. If the stars are relatively close together and their number is large, the estimate will be very accurate. Distances measured in this way are said to be obtained by the method of statistical parallax.

steady state theory: A theory of an expanding universe that supposes that the average density of matter remains constant in time. As the universe expands, new atoms are created in space, compensating for the decrease in density that would otherwise occur. The universe is in a steady state, unchanging on a large scale in both space and time.

stellar aberration: The apparent direction of starlight received by an observer on Earth is affected by the motion of the Earth as it moves about the Sun. First discovered in the 1720s, aberration confirmed that light propagates with finite velocity.

supernova: A star that suddenly appears and shines for a short period of time with a brightness many millions of times the brightness of a normal star. Such an event results from a sudden and massive explosion in the star and has causes related to changes in energy processes within the star. zone of avoidance: A region centered around the equator of the Milky Way characterized by the absence of spiral and other white nebulae. Many nineteenth-century astronomers believed that the existence of the zone indicated that the nebulae were systemically connected to the Milky Way galaxy and so were not external island universes. Curtis showed in the first part of the twentieth century that many galaxies contain bands of obscuring dust and gas in their equatorial regions. The presence of such matter in the Milky Way explains the zone of avoidance.

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