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Monday, February 16, 2015

Light-year



From Wikipedia, the free encyclopedia


Light-year
Unit system astronomical units
Unit of length
Symbol ly 
Unit conversions
1 ly in ... ... is equal to ...
   metric (SI) units    9.4607×1015 m
   imperial & US units    5.8786×1012 mi
   astronomical units    6.3241×104 au
   0.3066 pc
A light-year (symbol: ly), sometimes written light year or lightyear, is a unit of length used informally to express astronomical distances. It is approximately 10 trillion kilometres (or about 6 trillion miles).[note 1] As defined by the International Astronomical Union (IAU), a light-year is the distance that light travels in vacuum in one Julian year.[1] Because it includes the word year, the term light-year is sometimes misinterpreted as a unit of time.

The light-year is most often used when expressing distances to stars and other distances on a galactic scale, especially in non-specialist and popular science publications. The unit usually used in professional astrometry is the parsec (symbol: pc, approximately 3.26 light-years; the distance at which one astronomical unit subtends an angle of one second of arc).[1]

Definitions

As defined by the IAU, the light-year is the product of the Julian year[note 2] (365.25 days as opposed to the 365.2425-day Gregorian year) and the speed of light (299792458 m/s).[note 3] Both these values are included in the IAU (1976) System of Astronomical Constants, used since 1984.[3] From this the following conversions can be derived.
1 light-year = 9460730472580800 metres (exactly)
9.461 petametres
5.878625 trillion miles
63241.077 astronomical units
0.306601 parsecs
Before 1984, the tropical year (not the Julian year) and a measured (not defined) speed of light were included in the IAU (1964) System of Astronomical Constants, used from 1968 to 1983.[4] The product of Simon Newcomb's J1900.0 mean tropical year of 31556925.9747 ephemeris seconds and a speed of light of 299792.5 km/s produced a light-year of 9.460530×1015 m (rounded to the seven significant digits in the speed of light) found in several modern sources[5][6][7] was probably derived from an old source such as C. W. Allen's 1973 Astrophysical Quantities reference work,[8] which was updated in 2000.[9][clarification needed]

Other high-precision values are not derived from a coherent IAU system. A value of 9.460536207×1015 m found in some modern sources[10][11] is the product of a mean Gregorian year (365.2425 days or 31556952 s) and the defined speed of light (299792458 m/s). Another value, 9.460528405×1015 m,[12][13] is the product of the J1900.0 mean tropical year and the defined speed of light.

History

The light-year unit appeared a few years after the first successful measurement of the distance to a star other than our Sun, by Friedrich Bessel in 1838. The star was 61 Cygni, and he used a 6.2-inch (160 mm) heliometer designed by Joseph von Fraunhofer. The largest unit for expressing distances across space at that time was the astronomical unit, equal to the radius of the Earth's orbit (1.50×108 km or 9.30×107 mi). In those terms, trigonometric calculations based on 61 Cygni's parallax of 0.314 arcseconds, showed the distance to the star to be 660000 astronomical units (9.9×1013 km or 6.1×1013 mi). Bessel added that light employs 10.3 years to traverse this distance.[14] He recognized that his readers would enjoy the mental picture of the approximate transit time for light, but he refrained from using the light-year as a unit. He may have resented expressing distances in light-years because it would deteriorate the accuracy of his parallax data due to multiplying with the uncertain parameter of the speed of light. The speed of light was not yet precisely known in 1838; its value changed in 1849 (Fizeau) and 1862 (Foucault). It was not yet considered to be a fundamental constant of nature, and the propagation of light through the aether or space was still enigmatic. The light-year unit appeared, however, in 1851 in a German popular astronomical article by Otto Ule.[15] The paradox of a distance unit name ending on year was explained by Ule by comparing it to a hiking road hour (Wegstunde). A contemporary German popular astronomical book also noticed that light-year is an odd name.[16] In 1868 an English journal labelled the light-year as a unit used by the Germans.[17] Eddington called the light-year an inconvenvient and irrelevant unit, which had sometimes crept from popular use into technical investigations.[18]

Although modern astronomers often prefer to use the parsec, light years are also popularly used to gauge the expanses of interstellar and intergalactic space.

Usage of term

Distances expressed in light-years include those between stars in the same general area, such as those belonging to the same spiral arm or globular cluster. Galaxies themselves span from a few thousand to a few hundred thousand light-years in diameter, and are separated from neighbouring galaxies and galaxy clusters by millions of light-years. Distances to objects such as quasars and the Sloan Great Wall run up into the billions of light-years.

List of orders of magnitude for length
Scale (ly) Value Item
10−9 40.4×10−9 ly Reflected sunlight from the Moon's surface takes 1.2–1.3 seconds to travel the distance to the Earth's surface (travelling roughly 350000 to 400000 kilometres).
10−6 15.8×10−6 ly One astronomical unit (the distance from the Sun to the Earth). It takes approximately 499 seconds (8.32 minutes) for light to travel this distance.[19]
127×10−6 ly The Huygens probe lands on Titan off Saturn and transmits images from its surface 1.2 billion kilometres to the Earth.
10−3 2.04×10−3 ly The most distant space probe, Voyager 1, was about 18 light-hours away from the Earth as of October 2014.[20] It will take about 17500 years to reach one light-year (1.0×100 ly) at its current speed of about 17 km/s (38000 mph) relative to the Sun. On September 12, 2013, NASA scientists announced that Voyager 1 had entered the interstellar medium of space on August 25, 2012, becoming the first manmade object to leave the Solar System.[21]
100 1.6×100 ly The Oort cloud is approximately two light-years in diameter. Its inner boundary is speculated to be at 50000 AU, with its outer edge at 100000 au.
2.0×100 ly Maximum extent of the Sun's gravitational dominance (Hill sphere/Roche sphere, 125000 AU). Beyond this is the deep ex-solar gravitational interstellar medium.
4.22×100 ly The nearest known star (other than our Sun), Proxima Centauri, is about 4.22 light-years away.[22][23]
8.60×100 ly Sirius, the brightest star of the night sky. Twice as massive and 25 times more luminous than the Sun, it outshines more luminous stars due to its relative proximity.
11.90×100 ly HD 10700 e, an extrasolar candidate for a habitable planet. 6.6 times as massive as the earth, it is in the middle of the habitable zone of star Tau Ceti.[24][25]
20.5×100 ly Gliese 581, a red-dwarf star with several detectable exoplanets.
310×100 ly Canopus, second in brightness in the terrestrial sky only to Sirius, a type F supergiant 15000 times more luminous than the Sun.
103 26×103 ly The centre of our galaxy, the Milky Way, is about 26 kilolight-years away.[26][27]
100×103 ly The Milky Way is about 100000 light-years across.
165×103 ly R136a1, in the Large Magellanic Cloud, the most luminous star known at 8.7 million times the luminosity of the Sun, has an apparent magnitude 12.77, just brighter than 3C 273.
106 2.5×106 ly The Andromeda Galaxy is approximately 2.5 megalight-years away.
3×106 ly The Triangulum Galaxy (M33), at about 3 megalight-years away, is the most distant object visible to the naked eye.
59×106 ly The nearest large galaxy cluster, the Virgo Cluster, is about 59 megalight-years away.
150×106250×106 ly The Great Attractor lies at a distance of somewhere between 150 and 250 megalight-years (the latter being the most recent estimate).
109 1.2×109 ly The Sloan Great Wall (not to be confused with Great Wall and Her–CrB GW) has been measured to be approximately one gigalight-year distant.
2.4×109 ly 3C 273, optically the brightest quasar, of apparent magnitude 12.9, just dimmer than R136a1.
45.7×109 ly The comoving distance from the Earth to the edge of the visible universe is about 45.7 gigalight-years in any direction; this is the comoving radius of the observable universe. This is larger than the age of the universe dictated by the cosmic background radiation; see size of the universe: misconceptions for why this is possible.

Related units

Distances between objects within a star system tend to be small fractions of a light year, and are usually expressed in astronomical units. However, smaller units of length can similarly be formed usefully by multiplying units of time by the speed of light. For example, the light-second, useful in astronomy, telecommunications and relativistic physics, is exactly 299792458 metres or 131557600 of a light-year. Units such as the light-minute, light-hour and light-day are sometimes used in popular science publications. The light-month, roughly one-twelfth of a light-year, is also used occasionally for approximate measures.[28][29] The Hayden Planetarium specifies the light month more precisely as 30 days of light travel time.[30]

Metric prefixes are occasionally applied to the light-year. Thus one thousand, one million and one billion light-years are sometimes called a "kilolight-year", a "megalight-year" and a "gigalight-year" (abbreviated "kly", "Mly" and "Gly") respectively.

Light travels approximately one foot in a nanosecond; the term "light-foot" is sometimes used as an informal measure of time.


Scattering theory



From Wikipedia, the free encyclopedia


Top: the real part of a plane wave travelling upwards. Bottom: The real part of the field after inserting in the path of the plane wave a small transparent disk of index of refraction higher than the index of the surrounding medium. This object scatters part of the wave field, although at any individual point, the wave's frequency and wavelength remain intact.

In mathematics and physics, scattering theory is a framework for studying and understanding the scattering of waves and particles. Prosaically, wave scattering corresponds to the collision and scattering of a wave with some material object, for instance sunlight scattered by rain drops to form a rainbow. Scattering also includes the interaction of billiard balls on a table, the Rutherford scattering (or angle change) of alpha particles by gold nuclei, the Bragg scattering (or diffraction) of electrons and X-rays by a cluster of atoms, and the inelastic scattering of a fission fragment as it traverses a thin foil. More precisely, scattering consists of the study of how solutions of partial differential equations, propagating freely "in the distant past", come together and interact with one another or with a boundary condition, and then propagate away "to the distant future". The direct scattering problem is the problem of determining the distribution of scattered radiation/particle flux basing on the characteristics of the scatterer. The inverse scattering problem is the problem of determining the characteristics of an object (e.g., its shape, internal constitution) from measurement data of radiation or particles scattered from the object.

Since its early statement for radiolocation, the problem has found vast number of applications, such as echolocation, geophysical survey, nondestructive testing, medical imaging and quantum field theory, to name just a few.

Conceptual underpinnings

The concepts used in scattering theory go by different names in different fields. The object of this section is to point the reader to common threads.

Composite targets and range equations


Equivalent quantities used in the theory of scattering from composite specimens, but with a variety of units.

When the target is a set of many scattering centers whose relative position varies unpredictably, it is customary to think of a range equation whose arguments take different forms in different application areas. In the simplest case consider an interaction that removes particles from the "unscattered beam"at a uniform rate that is proportional to the incident flux I of particles per unit area per unit time, i.e. that
dIdx=QI
where Q is an interaction coefficient and x is the distance traveled in the target.

The above ordinary first-order differential equation has solutions of the form:
I=IoeQΔx=IoeΔxλ=Ioeσ(ηΔx)=IoeρΔxτ,
where Io is the initial flux, path length Δx ≡ x − xo, the second equality defines an interaction mean free path λ, the third uses the number of targets per unit volume η to define an area cross-section σ, and the last uses the target mass density ρ to define a density mean free path τ. Hence one converts between these quantities via Q = 1/λησρ/τ, as shown in the figure at left.

In electromagnetic absorption spectroscopy, for example, interaction coefficient (e.g. Q in cm−1) is variously called opacity, absorption coefficient, and attenuation coefficient. In nuclear physics, area cross-sections (e.g. σ in barns or units of 10−24 cm2), density mean free path (e.g. τ in grams/cm2), and its reciprocal the mass attenuation coefficient (e.g. in cm2/gram) or area per nucleon are all popular, while in electron microscopy the inelastic mean free path[1] (e.g. λ in nanometers) is often discussed[2] instead.

In theoretical physics

In mathematical physics, scattering theory is a framework for studying and understanding the interaction or scattering of solutions to partial differential equations. In acoustics, the differential equation is the wave equation, and scattering studies how its solutions, the sound waves, scatter from solid objects or propagate through non-uniform media (such as sound waves, in sea water, coming from a submarine). In the case of classical electrodynamics, the differential equation is again the wave equation, and the scattering of light or radio waves is studied. In particle physics, the equations are those of Quantum electrodynamics, Quantum chromodynamics and the Standard Model, the solutions of which correspond to fundamental particles.

In regular quantum mechanics, which includes quantum chemistry, the relevant equation is the Schrödinger equation, although equivalent formulations, such as the Lippmann-Schwinger equation and the Faddeev equations, are also largely used. The solutions of interest describe the long-term motion of free atoms, molecules, photons, electrons, and protons. The scenario is that several particles come together from an infinite distance away. These reagents then collide, optionally reacting, getting destroyed or creating new particles. The products and unused reagents then fly away to infinity again. (The atoms and molecules are effectively particles for our purposes. Also, under everyday circumstances, only photons are being created and destroyed.) The solutions reveal which directions the products are most likely to fly off to and how quickly. They also reveal the probability of various reactions, creations, and decays occurring. There are two predominant techniques of finding solutions to scattering problems: partial wave analysis, and the Born approximation.

Elastic and inelastic scattering

The term "elastic scattering" implies that the internal states of the scattering particles do not change, and hence they emerge unchanged from the scattering process. In inelastic scattering, by contrast, the particles' internal state is changed, which may amount to exciting some of the electrons of a scattering atom, or the complete annihilation of a scattering particle and the creation of entirely new particles.

The example of scattering in quantum chemistry is particularly instructive, as the theory is reasonably complex while still having a good foundation on which to build an intuitive understanding. When two atoms are scattered off one another, one can understand them as being the bound state solutions of some differential equation. Thus, for example, the hydrogen atom corresponds to a solution to the Schrödinger equation with a negative inverse-power (i.e., attractive Coulombic) central potential. The scattering of two hydrogen atoms will disturb the state of each atom, resulting in one or both becoming excited, or even ionized, representing an inelastic scattering process.

The term "deep inelastic scattering" refers to a special kind of scattering experiment in particle physics.

The mathematical framework

In mathematics, scattering theory deals with a more abstract formulation of the same set of concepts.
For example, if a differential equation is known to have some simple, localized solutions, and the solutions are a function of a single parameter, that parameter can take the conceptual role of time. One then asks what might happen if two such solutions are set up far away from each other, in the "distant past", and are made to move towards each other, interact (under the constraint of the differential equation) and then move apart in the "future". The scattering matrix then pairs solutions in the "distant past" to those in the "distant future".

Solutions to differential equations are often posed on manifolds. Frequently, the means to the solution requires the study of the spectrum of an operator on the manifold. As a result, the solutions often have a spectrum that can be identified with a Hilbert space, and scattering is described by a certain map, the S matrix, on Hilbert spaces. Spaces with a discrete spectrum correspond to bound states in quantum mechanics, while a continuous spectrum is associated with scattering states. The study of inelastic scattering then asks how discrete and continuous spectra are mixed together.

An important, notable development is the inverse scattering transform, central to the solution of many exactly solvable models.

Spectroscopy



From Wikipedia, the free encyclopedia


Analysis of white light by dispersing it with a prism is an example of spectroscopy.

Spectroscopy /spɛkˈtrɒskəpi/ is the study of the interaction between matter and radiated energy.[1][2] Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, by a prism. Later the concept was expanded greatly to comprise any interaction with radiative energy as a function of its wavelength or frequency. Spectroscopic data is often represented by a spectrum, a plot of the response of interest as a function of wavelength or frequency.

Introduction

Spectroscopy and spectrography are terms used to refer to the measurement of radiation intensity as a function of wavelength and are often used to describe experimental spectroscopic methods. Spectral measurement devices are referred to as spectrometers, spectrophotometers, spectrographs or spectral analyzers.

Daily observations of color can be related to spectroscopy. Neon lighting is a direct application of atomic spectroscopy. Neon and other noble gases have characteristic emission frequencies (colors). Neon lamps use collision of electrons with the gas to excite these emissions. Inks, dyes and paints include chemical compounds selected for their spectral characteristics in order to generate specific colors and hues. A commonly encountered molecular spectrum is that of nitrogen dioxide. Gaseous nitrogen dioxide has a characteristic red absorption feature, and this gives air polluted with nitrogen dioxide a reddish brown color. Rayleigh scattering is a spectroscopic scattering phenomenon that accounts for the color of the sky.

Spectroscopic studies were central to the development of quantum mechanics and included Max Planck's explanation of blackbody radiation, Albert Einstein's explanation of the photoelectric effect and Niels Bohr's explanation of atomic structure and spectra. Spectroscopy is used in physical and analytical chemistry because atoms and molecules have unique spectra. As a result, these spectra can be used to detect, identify and quantify information about the atoms and molecules. Spectroscopy is also used in astronomy and remote sensing on earth. Most research telescopes have spectrographs. The measured spectra are used to determine the chemical composition and physical properties of astronomical objects (such as their temperature and velocity).

Theory

One of the central concepts in spectroscopy is a resonance and its corresponding resonant frequency. Resonances were first characterized in mechanical systems such as pendulums. Mechanical systems that vibrate or oscillate will experience large amplitude oscillations when they are driven at their resonant frequency. A plot of amplitude vs. excitation frequency will have a peak centered at the resonance frequency. This plot is one type of spectrum, with the peak often referred to as a spectral line, and most spectral lines have a similar appearance.

In quantum mechanical systems, the analogous resonance is a coupling of two quantum mechanical stationary states of one system, such as an atom, via an oscillatory source of energy such as a photon. The coupling of the two states is strongest when the energy of the source matches the energy difference between the two states. The energy (E) of a photon is related to its frequency (ν) by E=hν where h is Planck's constant, and so a spectrum of the system response vs. photon frequency will peak at the resonant frequency or energy. Particles such as electrons and neutrons have a comparable relationship, the de Broglie relations, between their kinetic energy and their wavelength and frequency and therefore can also excite resonant interactions.

Spectra of atoms and molecules often consist of a series of spectral lines, each one representing a resonance between two different quantum states. The explanation of these series, and the spectral patterns associated with them, were one of the experimental enigmas that drove the development and acceptance of quantum mechanics. The hydrogen spectral series in particular was first successfully explained by the Rutherford-Bohr quantum model of the hydrogen atom. In some cases spectral lines are well separated and distinguishable, but spectral lines can also overlap and appear to be a single transition if the density of energy states is high enough.

Classification of methods

Spectroscopy is a sufficiently broad field that many sub-disciplines exist, each with numerous implementations of specific spectroscopic techniques. The various implementations and techniques can be classified in several ways.

Type of radiative energy

Types of spectroscopy are distinguished by the type of radiative energy involved in the interaction. In many applications, the spectrum is determined by measuring changes in the intensity or frequency of this energy. The types of radiative energy studied include:

Nature of the interaction

Types of spectroscopy can also be distinguished by the nature of the interaction between the energy and the material. These interactions include:[1]
  • Absorption occurs when energy from the radiative source is absorbed by the material. Absorption is often determined by measuring the fraction of energy transmitted through the material; absorption will decrease the transmitted portion.
  • Emission indicates that radiative energy is released by the material. A material's blackbody spectrum is a spontaneous emission spectrum determined by its temperature. Emission can also be induced by other sources of energy such as flames or sparks or electromagnetic radiation in the case of fluorescence.
  • Elastic scattering and reflection spectroscopy determine how incident radiation is reflected or scattered by a material. Crystallography employs the scattering of high energy radiation, such as x-rays and electrons, to examine the arrangement of atoms in proteins and solid crystals.
  • Impedance spectroscopy studies the ability of a medium to impede or slow the transmittance of energy. For optical applications, this is characterized by the index of refraction.
  • Inelastic scattering phenomena involve an exchange of energy between the radiation and the matter that shifts the wavelength of the scattered radiation. These include Raman and Compton scattering.
  • Coherent or resonance spectroscopy are techniques where the radiative energy couples two quantum states of the material in a coherent interaction that is sustained by the radiating field. The coherence can be disrupted by other interactions, such as particle collisions and energy transfer, and so often require high intensity radiation to be sustained. Nuclear magnetic resonance (NMR) spectroscopy is a widely used resonance method and ultrafast laser methods are also now possible in the infrared and visible spectral regions.

Type of material

Spectroscopic studies are designed so that the radiant energy interacts with specific types of matter.

Atoms

Atomic spectroscopy was the first application of spectroscopy developed. Atomic absorption spectroscopy (AAS) and atomic emission spectroscopy (AES) involve visible and ultraviolet light.
These absorptions and emissions, often referred to as atomic spectral lines, are due to electronic transitions of outer shell electrons as they rise and fall from one electron orbit to another. Atoms also have distinct x-ray spectra that are attributable to the excitation of inner shell electrons to excited states.

Atoms of different elements have distinct spectra and therefore atomic spectroscopy allows for the identification and quantitation of a sample's elemental composition. Robert Bunsen and Gustav Kirchhoff discovered new elements by observing their emission spectra. Atomic absorption lines are observed in the solar spectrum and referred to as Fraunhofer lines after their discoverer. A comprehensive explanation of the hydrogen spectrum was an early success of quantum mechanics and explained the Lamb shift observed in the hydrogen spectrum led to the development of quantum electrodynamics.

Modern implementations of atomic spectroscopy for studying visible and ultraviolet transitions include flame emission spectroscopy, inductively coupled plasma atomic emission spectroscopy, glow discharge spectroscopy, microwave induced plasma spectroscopy, and spark or arc emission spectroscopy. Techniques for studying x-ray spectra include X-ray spectroscopy and X-ray fluorescence (XRF).

Molecules

The combination of atoms into molecules leads to the creation of unique types of energetic states and therefore unique spectra of the transitions between these states. Molecular spectra can be obtained due to electron spin states (electron paramagnetic resonance), molecular rotations, molecular vibration and electronic states. Rotations are collective motions of the atomic nuclei and typically lead to spectra in the microwave and millimeter-wave spectral regions; rotational spectroscopy and microwave spectroscopy are synonymous. Vibrations are relative motions of the atomic nuclei and are studied by both infrared and Raman spectroscopy. Electronic excitations are studied using visible and ultraviolet spectroscopy as well as fluorescence spectroscopy.

Studies in molecular spectroscopy led to the development of the first maser and contributed to the subsequent development of the laser.

Crystals and extended materials

The combination of atoms or molecules into crystals or other extended forms leads to the creation of additional energetic states. These states are numerous and therefore have a high density of states. This high density often makes the spectra weaker and less distinct, i.e., broader. For instance, blackbody radiation is due to the thermal motions of atoms and molecules within a material. Acoustic and mechanical responses are due to collective motions as well.

Pure crystals, though, can have distinct spectral transitions and the crystal arrangement also has an effect on the observed molecular spectra. The regular lattice structure of crystals also scatters x-rays, electrons or neutrons allowing for crystallographic studies.

Nuclei

Nuclei also have distinct energy states that are widely separated and lead to gamma ray spectra.
Distinct nuclear spin states can have their energy separated by a magnetic field, and this allows for NMR spectroscopy.

Other types

Other types of spectroscopy are distinguished by specific applications or implementations:

Applications


UVES is a high-resolution spectrograph on the Very Large Telescope.[9]

History

The history of spectroscopy began with Isaac Newton's optics experiments (1666–1672). Newton applied the word "spectrum" to describe the rainbow of colors that combine to form white light and that are revealed when the white light is passed through a prism. During the early 1800s, Joseph von Fraunhofer made experimental advances with dispersive spectrometers that enabled spectroscopy to become a more precise and quantitative scientific technique. Since then, spectroscopy has played and continues to play a significant role in chemistry, physics and astronomy.

Pluto

From Wikipedia, the free encyclopedia https://en.wikipedia.org/wiki/Pluto 134340 Pluto Pluto, imaged by the New Horizons spac...