FACTOID # 26: Delaware is the latchkey kid capital of America, with 71.8% of households having both parents in the labor force.

 Home Encyclopedia Statistics States A-Z Flags Maps FAQ About

 WHAT'S NEW

SEARCH ALL

Search encyclopedia, statistics and forums:

(* = Graphable)

## Direct methods of distance determination GA_googleFillSlot("encyclopedia_square");

At the base of the ladder are fundamental distance measurements, in which distances are determined directly, with no physical assumptions about the nature of the object in question. These direct methods are:

Radar can (for practical reasons) only be used within the Solar System. For other uses, see Parallax (disambiguation). ... Triangulation can be used to find the distance from the shore to the ship. ... Wikibooks has a book on the topic of Trigonometry All of the trigonometric functions of an angle Î¸ can be constructed geometrically in terms of a unit circle centered at O. Trigonometry (from Greek trigÅnon triangle + metron measure[1]), informally called trig, is a branch of mathematics that deals with... Surveyor at work with a leveling instrument. ... The speed of light in vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness.[1] It is the speed of all electromagnetic radiation, including visible light, in a vacuum. ... For other uses, see Radar (disambiguation). ...

The precise measurement of stellar positions is part of the discipline of astrometry. Illustration of the use of optical wavelength interferometry to determine precise positions of stars. ...

### Parallax based metods

The most important fundamental distance measurements come from parallax. The Earth's motion around the sun causes small shifts in stellar positions. These shifts are angles in a right triangle, with 1 AU making the short leg of the triangle and the distance to the star being the long leg. One parsec is the distance of a star whose parallax is one arc second. Astronomers usually express distances in units of parsecs; light-years are used in popular media, but almost invariably values in light-years have been converted from numbers tabulated in parsecs in the original source. For other uses, see Parallax (disambiguation). ... A triangle. ... The astronomical unit (AU or au or a. ... A parsec is the distance from the Earth to an astronomical object which has a parallax angle of one arcsecond. ... A light-year, symbol ly, is the distance light travels in one year: exactly 9. ...

Because parallax becomes smaller for a greater stellar distance, useful distances can be measured only for stars whose parallax is larger than the precision of the measurement. In the 1990s, the Hipparcos mission obtained parallaxes for over a hundred thousand stars with a precision of about a milliarcsecond, providing useful distances for stars out to a few hundred parsecs. â€œAccuracyâ€ redirects here. ... For the band, see 1990s (band). ... Hipparcos (for High Precision Parallax Collecting Satellite) was an astrometry mission of the European Space Agency (ESA) dedicated to the measurement of stellar parallax and the proper motions of stars. ... A milliarcsecond (m, mas) , or a thoundsanth of an arcsecond. ...

Another fundamental distance method is statistical and secular parallax. This technique combines measurements of the motions and brightnesses of members of a selected, homogeneous group of stars in a statistical way to deduce an average distance to the group. It remains an important technique for the Cepheids and the RR Lyrae variables. RR Lyrae variables are variable stars often used as standard candles. ...

Moving cluster parallax is a technique where the motions of individual stars in a nearby star cluster (only open clusters are near enough for this technique to be useful) can be used to find the distance to the cluster. In particular the distance obtained for the Hyades has been an important step in the distance ladder. For other uses, see Parallax (disambiguation). ... The Pleiades is one of the most famous open clusters. ... The Hyades (Ã†Î¥Î¬Î´ÎµÏ‚ also known as Melotte 25 or Collinder 50 or Caldwell 41) is an open star cluster located in the constellation Taurus. ...

Other individual objects can have fundamental distance estimates made for them under special circumstances. If the expansion of a gas cloud, like a supernova remnant or planetary nebula, can be observed over time, then an expansion parallax distance to that cloud can be estimated. Binary stars which are both visual and spectroscopic binaries also can have their distance estimated by similar means. The common characteristic to these is that a measurement of angular motion is combined with a measurement of the absolute velocity (usually obtained via the Doppler effect). The distance estimate comes from computing how far away the object must be to make its observed absolute velocity appear with the observed angular motion. The Crab Nebula is an expanding cloud of gas created by the 1054 supernova. ... NGC 6543, The Cats Eye Nebula NGC 6853, The Dumbbell Nebula A planetary nebula is an astronomical object consisting of a glowing shell of gas and plasma formed by certain types of stars at the end of their lives. ... For the band of the same name, see: Binary Star (band) Hubble image of the Sirius binary system, in which Sirius B can be clearly distinguished (lower left). ... For the band of the same name, see: Binary Star (band) Hubble image of the Sirius binary system, in which Sirius B can be clearly distinguished (lower left). ... For the band of the same name, see: Binary Star (band) Hubble image of the Sirius binary system, in which Sirius B can be clearly distinguished (lower left). ... This article is about velocity in physics. ... A source of waves moving to the left. ...

Expansion parallaxes in particular can give fundamental distance estimates for objects very far away, because supernova ejecta have large expansion velocities and large sizes (compared to stars). Further, they can be observed with radio interferometers which can measure very small angular motions. These combine to mean that some supernovae in other galaxies have fundamental distance estimates[1]. Though valuable, such cases are quite rare, so they serve as important consistency checks on the distance ladder rather than workhorse steps by themselves. Interferometry is the applied science of combining two or more input points of a particular data type, such as optical measurements, to form a greater picture based on the combination of the two sources. ...

#### Astronomical unit

The use of the parallax method usually requires precise determination of the distance between the Earth and the Sun (the radius of the Earth's orbit), called the Astronomical Unit (AU). The astronomical unit (AU or au or a. ... The astronomical unit (AU or au or a. ...

Other astronomical distance measures build outward from this.

Historically, observations of transits of Venus were crucial in determining the AU; in the first half of the 20th Century, observations of asteroids were also important. Presently the AU is determined with high precision using radar measurements of Venus and other nearby planets and asteroids,[2] and by tracking interplanetary spacecraft in their orbits around the Sun through the Solar System. Kepler's Laws provide precise ratios of the sizes of the orbits of objects revolving around the Sun, but not a real measure of the orbits themselves. Radar provides a value in kilometers for the difference in two orbits' sizes, and from that and the ratio of the two orbit sizes, the size of Earth's orbit comes directly. The 2004 transit of Venus A transit of Venus across the Sun takes place when the planet Venus passes directly between the Sun and Earth, obscuring a small portion of the Suns disk. ... Asteroids is a popular vector-based video arcade game released in 1979 by Atari. ... Adjectives: Venusian or (rarely) Cytherean Atmosphere Surface pressure: 9. ... The Space Shuttle Discovery as seen from the International Space Station. ... Sol redirects here. ... This article is about the Solar System. ... Johannes Keplers primary contributions to astronomy/astrophysics were his three laws of planetary motion. ... A ratio is a quantity that denotes the proportional amount or magnitude of one quantity relative to another. ... â€œkmâ€ redirects here. ...

## Distance determination based on physical assumptions

With few exceptions, distances based on direct measurements are available only out to about a thousand parsecs, which is a modest portion of our own Galaxy. For distances beyond that, measures depend upon physical assumptions, that is, the assertion that one recognizes the object in question, and the class of objects is homogeneous enough that its members can be used for meaningful estimation of distance.

Almost all of these physical distance indicators are standard candles. These rely upon recognizing an object as belonging to some class, which has some known absolute magnitude, measuring its apparent magnitude, and using the inverse square law to infer the distance needed to make the "candle" appear at its observed brightness. Some means of accounting for interstellar extinction, which also makes objects appear fainter, is also needed. The difference between absolute and apparent magnitudes is called the distance modulus, and astronomical distances, especially intergalactic ones, are sometimes tabulated in this way. A standard candle is an astronomical object that has a known luminosity. ... In astronomy, absolute magnitude is the apparent magnitude, m, an object would have if it were at a standard luminosity distance away from us, in the absence of interstellar extinction. ... The apparent magnitude (m) of a star, planet or other celestial body is a measure of its apparent brightness as seen by an observer on Earth. ... In physics, an inverse-square law is any physical law stating that some quantity is inversely proportional to the square of the distance from a point. ... Extinction is a term used in astronomy to describe the absorption and scattering of light emitted by astronomical objects by matter (principally dust and gas) between the emitting object and the observer. ... The distance modulus is a way of expressing distances which is often used in astronomy to express the distance to galaxies and clusters of galaxies. ...

Physical distance indicators, used on progressively larger distance scales, include:

Two problems exist for any class of standard candle. The principal one is calibration, determining exactly what the absolute magnitude of the candle is. This includes defining the class well enough that members can be recognized, and finding enough members with well-known distances that their true absolute magnitude can be determined with enough accuracy. The second lies in recognizing members of the class, and not mistakenly using the standard candle calibration upon an object which does not belong to the class. At extreme distances, which is where one most wishes to use a distance indicator, this recognition problem can be quite serious. Hertzsprung-Russell diagram The main sequence of the Hertzsprung-Russell diagram is the curve where the majority of stars are located in this diagram. ... The Pleiades is one of the most famous open clusters. ... A Cepheid variable is a member of a particular class of variable stars, notable for a fairly tight correlation between their period of variability and absolute stellar luminosity. ... Artists conception of a white dwarf star accreting hydrogen from a larger companion A nova (pl. ... The galaxies of HCG 87, about four hundred million light-years distant. ... In astronomy, the Tully-Fisher relation, published by astronomers R. Brent Tully and J. Richard Fisher in 1977, is a standard candle that measures the distance to rotating spiral galaxies by the width of the galaxys spectral lines. ... Multiwavelength X-ray image of the remnant of Keplers Supernova, SN 1604. ... Redshift of spectral lines in the optical spectrum of a supercluster of distant galaxies (right), as compared with that of the Sun (left). ... Hubbles law is the statement in physical cosmology that the redshift in light coming from distant galaxies is proportional to their distance. ... Calibration refers to the process of determining the relation between the output (or response) of a measuring instrument and the value of the input quantity or attribute, a measurement standard. ...

(Another class of physical distance indicator is the standard ruler, but few of these are used at this time.) A standard ruler is an astronomical object that has a known size. ...

A succession of distance indicators, which is the distance ladder, is needed for determining distances to other galaxies. The reason is that objects bright enough to be recognized and measured at such distances are so rare that few or none are present nearby, so there are too few examples close enough with reliable trigonometric parallax to calibrate the indicator. For example, Cepheid variables, one of the best indicators for nearby spiral galaxies, cannot be satisfactorily calibrated by parallax alone. The situation is further complicated by the fact that different stellar populations generally do not have all types of stars in them. Cepheids in particular are massive stars, with short lifetimes, so they will only be found in places where stars have very recently been formed. Consequently, because elliptical galaxies usually have long ceased to have large-scale star formation, they will not have Cepheids. Instead, distance indicators whose origins are in an older stellar population (like novae and RR Lyrae variables) must be used. However, RR Lyrae variables are less luminous than Cepheids (so they cannot be seen as far away as Cepheids can), and novae are unpredictable and an intensive monitoring program — and luck during that program — is needed to gather enough novae in the target galaxy for a good distance estimate. It has been suggested that spiral nebula be merged into this article or section. ... The giant elliptical galaxy ESO 325-G004. ...

Because the more distant steps of the cosmic distance ladder depend upon the nearer ones, the more distant steps include the effects of errors in the nearer steps, both systematic and statistical ones. The result of these propagating errors means that distances in astronomy are rarely known to the same level of precision as measurements in the other sciences, and that the precision necessarily is poorer for more distant types of object. The word error has different meanings in different domains. ... In statistics, propagation of uncertainty (or propagation of error) is the effect of variables uncertainties (or errors) on the uncertainty of a function based on them. ...

Another concern, especially for the very brightest standard candles, is their "standardness": how homogeneous the objects are in their true absolute magnitude. For some of these different standard candles, the homogeneity is based on theories about the formation and evolution of stars and galaxies, and is thus also subject to uncertainties in those aspects. For the most luminous of distance indicators, the Type Ia supernovae, this homogeneity is known to be poor; however, no other class of object is bright enough to be detected at such large distances, so the class is useful simply because there is no real alternative. Media:Example. ... In astronomy, stellar evolution is the sequence of radical changes that a star undergoes during its lifetime (the time in which it emits light and heat). ...

The observational result of Hubble's Law, the proportional relationship between distance and the speed with which a galaxy is moving away from us (usually referred to as redshift) is a product of the cosmic distance ladder. Hubble observed that fainter galaxies are more redshifted. Finding the value of the Hubble constant was the result of decades of work by many astronomers, both in amassing the measurements of galaxy redshifts and in calibrating the steps of the distance ladder. Hubble's Law is the only means we have for estimating the distances of most quasars and other distant galaxies in which individual distance indicators cannot be seen. In mathematics, two quantities are called proportional if they vary in such a way that one of the quantities is a constant multiple of the other, or equivalently if they have a constant ratio. ... Redshift of spectral lines in the optical spectrum of a supercluster of distant galaxies (right), as compared with that of the Sun (left). ... Edwin Powell Hubble (November 20, 1889 â€“ September 28, 1953) was an American astronomer. ... The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ...

Results from FactBites:

 Cosmic distance ladder - Wikipedia, the free encyclopedia (181 words) The cosmic distance ladder refers to the methods by which astronomers determine the distances to celestial objects. At the base of the ladder are radar observations of Venus, which allow one to determine the distance between the Earth and Venus and by extension, the size of the orbit of the Earth. The field of astronomy which measures distances is known as astrometry.
 cosmic distance ladder (486 words) Distances within the Solar System are known to extreme accuracy by a variety methods, including the motions of the planets in the sky, radar, and timing of signals from interplanetary probes. Distances to stars within a couple of thousand light-years come from various geometrical methods; the most accurate values are those based on measurements of the annual parallax of about 10,000 nearby stars made by the Hipparcos satellite. Extragalactic distance indicators enable estimates to be made of the Hubble constant, a measure of the rate at which the universe as a whole is expanding.
More results at FactBites »

Share your thoughts, questions and commentary here