Center of mass
In physics, the center of mass of a distribution of mass in space is the unique point where the weighted relative position of the distributed mass sums to zero. This is the point to which a force may be applied to cause a linear acceleration without an angular acceleration. Calculations in mechanics are simplified when formulated with respect to the center of mass, it is a hypothetical point where entire mass of an object may be assumed to be concentrated to visualise its motion. In other words, the center of mass is the particle equivalent of a given object for application of Newton's laws of motion. In the case of a single rigid body, the center of mass is fixed in relation to the body, if the body has uniform density, it will be located at the centroid; the center of mass may be located outside the physical body, as is sometimes the case for hollow or open-shaped objects, such as a horseshoe. In the case of a distribution of separate bodies, such as the planets of the Solar System, the center of mass may not correspond to the position of any individual member of the system.
The center of mass is a useful reference point for calculations in mechanics that involve masses distributed in space, such as the linear and angular momentum of planetary bodies and rigid body dynamics. In orbital mechanics, the equations of motion of planets are formulated as point masses located at the centers of mass; the center of mass frame is an inertial frame in which the center of mass of a system is at rest with respect to the origin of the coordinate system. The concept of "center of mass" in the form of the center of gravity was first introduced by the great ancient Greek physicist and engineer Archimedes of Syracuse, he worked with simplified assumptions about gravity that amount to a uniform field, thus arriving at the mathematical properties of what we now call the center of mass. Archimedes showed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass.
In work on floating bodies he demonstrated that the orientation of a floating object is the one that makes its center of mass as low as possible. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes. Mathematicians who developed the theory of the center of mass include Pappus of Alexandria, Guido Ubaldi, Francesco Maurolico, Federico Commandino, Simon Stevin, Luca Valerio, Jean-Charles de la Faille, Paul Guldin, John Wallis, Louis Carré, Pierre Varignon, Alexis Clairaut. Newton's second law is reformulated with respect to the center of mass in Euler's first law; the center of mass is the unique point at the center of a distribution of mass in space that has the property that the weighted position vectors relative to this point sum to zero. In analogy to statistics, the center of mass is the mean location of a distribution of mass in space. In the case of a system of particles Pi, i = 1, …, n , each with mass mi that are located in space with coordinates ri, i = 1, …, n , the coordinates R of the center of mass satisfy the condition ∑ i = 1 n m i = 0.
Solving this equation for R yields the formula R = 1 M ∑ i = 1 n m i r i, where M is the sum of the masses of all of the particles. If the mass distribution is continuous with the density ρ within a solid Q the integral of the weighted position coordinates of the points in this volume relative to the center of mass R over the volume V is zero, ∭ Q ρ d V = 0. Solve this equation for the coordinates R to obtain R = 1 M ∭ Q ρ r d V, where M is the total mass in the volume. If a continuous mass distribution has uniform density, which means ρ is constant the center of mass is the same as the centroid of the volume; the coordinates R of the center of mass of a two-particle system, P1 and P2, with masses m1 and m2 is given by R = 1 m 1 + m 2. Let the percentage of the total mass divided between these two particles vary from 100% P1 and 0% P2 through 50% P1 and 50% P2 to 0% P1 and 100% P2 the center of mass R moves along the line from P1 to P2; the percentages of mass at each point can be viewed as projective coordinates of the point R on this line, are termed barycentric coordinates.
Another way of interpreting the process here is the mechanical balancing of moments about an arbitrary point. The numerator gives the total moment, balanced by an equivalent total force at the center of mass; this can be generalized
Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight, is measured by the angle or semi-angle of inclination between those two lines. Due to foreshortening, nearby objects show a larger parallax than farther objects when observed from different positions, so parallax can be used to determine distances. To measure large distances, such as the distance of a planet or a star from Earth, astronomers use the principle of parallax. Here, the term parallax is the semi-angle of inclination between two sight-lines to the star, as observed when Earth is on opposite sides of the Sun in its orbit; these distances form the lowest rung of what is called "the cosmic distance ladder", the first in a succession of methods by which astronomers determine the distances to celestial objects, serving as a basis for other distance measurements in astronomy forming the higher rungs of the ladder. Parallax affects optical instruments such as rifle scopes, binoculars and twin-lens reflex cameras that view objects from different angles.
Many animals, including humans, have two eyes with overlapping visual fields that use parallax to gain depth perception. In computer vision the effect is used for computer stereo vision, there is a device called a parallax rangefinder that uses it to find range, in some variations altitude to a target. A simple everyday example of parallax can be seen in the dashboard of motor vehicles that use a needle-style speedometer gauge; when viewed from directly in front, the speed may show 60. As the eyes of humans and other animals are in different positions on the head, they present different views simultaneously; this is the basis of stereopsis, the process by which the brain exploits the parallax due to the different views from the eye to gain depth perception and estimate distances to objects. Animals use motion parallax, in which the animals move to gain different viewpoints. For example, pigeons down to see depth; the motion parallax is exploited in wiggle stereoscopy, computer graphics which provide depth cues through viewpoint-shifting animation rather than through binocular vision.
Parallax arises due to change in viewpoint occurring due to motion of the observer, of the observed, or of both. What is essential is relative motion. By observing parallax, measuring angles, using geometry, one can determine distance. Astronomers use the word "parallax" as a synonym for "distance measurement" by other methods: see parallax #Astronomy. Stellar parallax created by the relative motion between the Earth and a star can be seen, in the Copernican model, as arising from the orbit of the Earth around the Sun: the star only appears to move relative to more distant objects in the sky. In a geostatic model, the movement of the star would have to be taken as real with the star oscillating across the sky with respect to the background stars. Stellar parallax is most measured using annual parallax, defined as the difference in position of a star as seen from the Earth and Sun, i. e. the angle subtended at a star by the mean radius of the Earth's orbit around the Sun. The parsec is defined as the distance.
Annual parallax is measured by observing the position of a star at different times of the year as the Earth moves through its orbit. Measurement of annual parallax was the first reliable way to determine the distances to the closest stars; the first successful measurements of stellar parallax were made by Friedrich Bessel in 1838 for the star 61 Cygni using a heliometer. Stellar parallax remains the standard for calibrating other measurement methods. Accurate calculations of distance based on stellar parallax require a measurement of the distance from the Earth to the Sun, now based on radar reflection off the surfaces of planets; the angles involved in these calculations are small and thus difficult to measure. The nearest star to the Sun, Proxima Centauri, has a parallax of 0.7687 ± 0.0003 arcsec. This angle is that subtended by an object 2 centimeters in diameter located 5.3 kilometers away. The fact that stellar parallax was so small that it was unobservable at the time was used as the main scientific argument against heliocentrism during the early modern age.
It is clear from Euclid's geometry that the effect would be undetectable if the stars were far enough away, but for various reasons such gigantic distances involved seemed implausible: it was one of Tycho's principal objections to Copernican heliocentrism that in order for it to be compatible with the lack of observable stellar parallax, there would have to be an enormous and unlikely void between the orbit of Saturn and the eighth sphere. In 1989, the satellite Hipparcos was launched for obtaining improved parallaxes and proper motions for over 100,000 nearby stars, increasing the reach of the method tenfold. So, Hipparcos is only able to measure parallax angles for stars up to about 1,600 light-years away, a little more than one percent of the diameter of the Milky Way Galaxy; the European Space Agency's Gaia mission, launched in December 2013, will be able to measure parallax angles to an accuracy of 10 microarcseconds, thus mapping nearby stars up to a distance of tens of thousands of ligh
In astronomy, the main sequence is a continuous and distinctive band of stars that appears on plots of stellar color versus brightness. These color-magnitude plots are known as Hertzsprung–Russell diagrams after their co-developers, Ejnar Hertzsprung and Henry Norris Russell. Stars on this band are known as main-sequence stars or dwarf stars; these are the most numerous true stars in the universe, include the Earth's Sun. After condensation and ignition of a star, it generates thermal energy in its dense core region through nuclear fusion of hydrogen into helium. During this stage of the star's lifetime, it is located on the main sequence at a position determined by its mass, but based upon its chemical composition and age; the cores of main-sequence stars are in hydrostatic equilibrium, where outward thermal pressure from the hot core is balanced by the inward pressure of gravitational collapse from the overlying layers. The strong dependence of the rate of energy generation on temperature and pressure helps to sustain this balance.
Energy generated at the core is radiated away at the photosphere. The energy is carried by either radiation or convection, with the latter occurring in regions with steeper temperature gradients, higher opacity or both; the main sequence is sometimes divided into upper and lower parts, based on the dominant process that a star uses to generate energy. Stars below about 1.5 times the mass of the Sun fuse hydrogen atoms together in a series of stages to form helium, a sequence called the proton–proton chain. Above this mass, in the upper main sequence, the nuclear fusion process uses atoms of carbon and oxygen as intermediaries in the CNO cycle that produces helium from hydrogen atoms. Main-sequence stars with more than two solar masses undergo convection in their core regions, which acts to stir up the newly created helium and maintain the proportion of fuel needed for fusion to occur. Below this mass, stars have cores that are radiative with convective zones near the surface. With decreasing stellar mass, the proportion of the star forming a convective envelope increases.
Main-sequence stars below 0.4 M☉ undergo convection throughout their mass. When core convection does not occur, a helium-rich core develops surrounded by an outer layer of hydrogen. In general, the more massive a star is, the shorter its lifespan on the main sequence. After the hydrogen fuel at the core has been consumed, the star evolves away from the main sequence on the HR diagram, into a supergiant, red giant, or directly to a white dwarf. In the early part of the 20th century, information about the types and distances of stars became more available; the spectra of stars were shown to have distinctive features. Annie Jump Cannon and Edward C. Pickering at Harvard College Observatory developed a method of categorization that became known as the Harvard Classification Scheme, published in the Harvard Annals in 1901. In Potsdam in 1906, the Danish astronomer Ejnar Hertzsprung noticed that the reddest stars—classified as K and M in the Harvard scheme—could be divided into two distinct groups; these stars are either much brighter than the Sun, or much fainter.
To distinguish these groups, he called them. The following year he began studying star clusters, he published the first plots of color versus luminosity for these stars. These plots showed a continuous sequence of stars, which he named the Main Sequence. At Princeton University, Henry Norris Russell was following a similar course of research, he was studying the relationship between the spectral classification of stars and their actual brightness as corrected for distance—their absolute magnitude. For this purpose he used a set of stars that had reliable parallaxes and many of, categorized at Harvard; when he plotted the spectral types of these stars against their absolute magnitude, he found that dwarf stars followed a distinct relationship. This allowed the real brightness of a dwarf star to be predicted with reasonable accuracy. Of the red stars observed by Hertzsprung, the dwarf stars followed the spectra-luminosity relationship discovered by Russell. However, the giant stars are much brighter than so do not follow the same relationship.
Russell proposed that the "giant stars must have low density or great surface-brightness, the reverse is true of dwarf stars". The same curve showed that there were few faint white stars. In 1933, Bengt Strömgren introduced the term Hertzsprung–Russell diagram to denote a luminosity-spectral class diagram; this name reflected the parallel development of this technique by both Hertzsprung and Russell earlier in the century. As evolutionary models of stars were developed during the 1930s, it was shown that, for stars of a uniform chemical composition, a relationship exists between a star's mass and its luminosity and radius; that is, for a given mass and composition, there is a unique solution for determining the star's radius and luminosity. This became known as the Vogt–Russell theorem. By this theorem, when a star's chemical composition and its position on the main sequence is known, so too is the star's mass and radius. A refined scheme for stellar classification was published in 1943 by William Wilson Morgan and Philip Childs Keenan.
The MK classification assigned each star a spectral type—based on the Harvard classification—and a luminosity class. The Harvard classification had been developed by assigning a different lett
In physics, in particular as measured by radiometry, radiant energy is the energy of electromagnetic and gravitational radiation. As energy, its SI unit is the joule; the quantity of radiant energy may be calculated by integrating radiant flux with respect to time. The symbol Qe is used throughout literature to denote radiant energy. In branches of physics other than radiometry, electromagnetic energy is referred to using E or W; the term is used when electromagnetic radiation is emitted by a source into the surrounding environment. This radiation may be invisible to the human eye; the term "radiant energy" is most used in the fields of radiometry, solar energy and lighting, but is sometimes used in other fields. In modern applications involving transmission of power from one location to another, "radiant energy" is sometimes used to refer to the electromagnetic waves themselves, rather than their energy. In the past, the term "electro-radiant energy" has been used; the term "radiant energy" applies to gravitational radiation.
For example, the first gravitational waves observed were produced by a black hole collision that emitted about 5.3×1047 joules of gravitational-wave energy. Because electromagnetic radiation can be conceptualized as a stream of photons, radiant energy can be viewed as photon energy – the energy carried by these photons. Alternatively, EM radiation can be viewed as an electromagnetic wave, which carries energy in its oscillating electric and magnetic fields; these two views are equivalent and are reconciled to one another in quantum field theory. EM radiation can have various frequencies; the bands of frequency present in a given EM signal may be defined, as is seen in atomic spectra, or may be broad, as in blackbody radiation. In the photon picture, the energy carried by each photon is proportional to its frequency. In the wave picture, the energy of a monochromatic wave is proportional to its intensity; this implies that if two EM waves have the same intensity, but different frequencies, the one with the higher frequency "contains" fewer photons, since each photon is more energetic.
When EM waves are absorbed by an object, the energy of the waves is converted to heat. This is a familiar effect, since sunlight warms surfaces that it irradiates; this phenomenon is associated with infrared radiation, but any kind of electromagnetic radiation will warm an object that absorbs it. EM waves can be reflected or scattered, in which case their energy is redirected or redistributed as well. Radiant energy is one of the mechanisms by which energy can leave an open system; such a system can be man-made, such as a solar energy collector, or natural, such as the Earth's atmosphere. In geophysics, most atmospheric gases, including the greenhouse gases, allow the Sun's short-wavelength radiant energy to pass through to the Earth's surface, heating the ground and oceans; the absorbed solar energy is re-emitted as longer wavelength radiation, some of, absorbed by the atmospheric greenhouse gases. Radiant energy is produced in the sun as a result of nuclear fusion. Radiant energy is used for radiant heating.
It can be generated electrically by infrared lamps, or can be absorbed from sunlight and used to heat water. The heat energy is emitted from a warm element and warms people and other objects in rooms rather than directly heating the air; because of this, the air temperature may be lower than in a conventionally heated building though the room appears just as comfortable. Various other applications of radiant energy have been devised; these include treatment and inspection and sorting, medium of control, medium of communication. Many of these applications involve a source of radiant energy and a detector that responds to that radiation and provides a signal representing some characteristic of the radiation. Radiant energy detectors produce responses to incident radiant energy either as an increase or decrease in electric potential or current flow or some other perceivable change, such as exposure of photographic film
John Wiley & Sons, Inc. branded as Wiley in recent years, is a global publishing company that specializes in academic publishing and instructional materials. The company produces books and encyclopedias, in print and electronically, as well as online products and services, training materials, educational materials for undergraduate and continuing education students. Founded in 1807, Wiley is known for publishing the For Dummies book series. In 2017, the company had a revenue of $1.7 billion. Wiley was established in 1807; the company was the publisher of such 19th century American literary figures as James Fenimore Cooper, Washington Irving, Herman Melville, Edgar Allan Poe, as well as of legal and other non-fiction titles. Wiley worked in partnership with Cornelius Van Winkle, George Long, George Palmer Putnam, Robert Halsted; the firm took its current name in 1865. Wiley shifted its focus to scientific and engineering subject areas, abandoning its literary interests. Charles Wiley's son John took over the business when his father died in 1826.
The firm was successively named Wiley, Lane & Co. Wiley & Putnam, John Wiley; the company acquired its present name in 1876, when John's second son William H. Wiley joined his brother Charles in the business. Through the 20th century, the company expanded its publishing activities, the sciences, higher education. Since the establishment of the Nobel Prize in 1901, Wiley and its acquired companies have published the works of more than 450 Nobel Laureates, in every category in which the prize is awarded. One of the world's oldest independent publishing companies, Wiley marked its bicentennial in 2007 with a year-long celebration, hosting festivities that spanned four continents and ten countries and included such highlights as ringing the closing bell at the New York Stock Exchange on May 1. In conjunction with the anniversary, the company published Knowledge for Generations: Wiley and the Global Publishing Industry, 1807-2007, depicting Wiley's pivotal role in the evolution of publishing against a social and economic backdrop.
Wiley has created an online community called Wiley Living History, offering excerpts from Knowledge for Generations and a forum for visitors and Wiley employees to post their comments and anecdotes. In December 2010, Wiley opened an office in Dubai; the company has had an office in Beijing, since 2001, China is now its sixth-largest market for STEM content. Wiley established publishing operations in India in 2006, has established a presence in North Africa through sales contracts with academic institutions in Tunisia and Egypt. On April 16, 2012, the company announced the establishment of Wiley Brasil Editora LTDA in São Paulo, effective May 1, 2012. Wiley's scientific and medical business was expanded by the acquisition of Blackwell Publishing in February 2007; the combined business, named Scientific, Technical and Scholarly, publishes, in print and online, 1,400 scholarly peer-reviewed journals and an extensive collection of books, major reference works and laboratory manuals in the life and physical sciences and allied health, the humanities, the social sciences.
Through a backfile initiative completed in 2007, 8.2 million pages of journal content have been made available online, a collection dating back to 1799. Wiley-Blackwell publishes on behalf of about 700 professional and scholarly societies. Other major journals published include Angewandte Chemie, Advanced Materials, International Finance and Liver Transplantation. Launched commercially in 1999, Wiley InterScience provided online access to Wiley journals, major reference works, books, including backfile content. Journals from Blackwell Publishing were available online from Blackwell Synergy until they were integrated into Wiley InterScience on June 30, 2008. In December 2007, Wiley began distributing its technical titles through the Safari Books Online e-reference service. On February 17, 2012, Wiley announced the acquisition of Inscape Holdings Inc. which provides DISC assessments and training for interpersonal business skills. Wiley described the acquisition as complementary to the workplace learning products published under its Pfeiffer imprint, one that would help Wiley advance its digital delivery strategy and extend its global reach through Inscape's international distributor network.
On March 7, 2012, Wiley announced its intention to divest assets in the areas of travel, general interest, nautical and crafts, as well as the Webster's New World and CliffsNotes brands. The planned divestiture was aligned with Wiley's "increased strategic focus on content and services for research and professional practices, on lifelong learning through digital technology". On August 13, 2012, Wiley announced it entered into a definitive agreement to sell all of its travel assets, including all of its interests in the Frommer's brand, to Google Inc. On November 6, 2012, Houghton Mifflin Harcourt acquired Wiley's cookbooks and study guides. In 2013, Wiley sold its pets and general interest lines to Turner Publishing Company and its nautical line to Fernhurst Books. H
Newton's laws of motion
Newton's laws of motion are three physical laws that, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, its motion in response to those forces. More the first law defines the force qualitatively, the second law offers a quantitative measure of the force, the third asserts that a single isolated force doesn't exist; these three laws have been expressed in several ways, over nearly three centuries, can be summarised as follows: The three laws of motion were first compiled by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica, first published in 1687. Newton used them to investigate the motion of many physical objects and systems. For example, in the third volume of the text, Newton showed that these laws of motion, combined with his law of universal gravitation, explained Kepler's laws of planetary motion. A fourth law is also described in the bibliography, which states that forces add up like vectors, that is, that forces obey the principle of superposition.
Newton's laws are applied to objects which are idealised as single point masses, in the sense that the size and shape of the object's body are neglected to focus on its motion more easily. This can be done when the object is small compared to the distances involved in its analysis, or the deformation and rotation of the body are of no importance. In this way a planet can be idealised as a particle for analysis of its orbital motion around a star. In their original form, Newton's laws of motion are not adequate to characterise the motion of rigid bodies and deformable bodies. Leonhard Euler in 1750 introduced a generalisation of Newton's laws of motion for rigid bodies called Euler's laws of motion applied as well for deformable bodies assumed as a continuum. If a body is represented as an assemblage of discrete particles, each governed by Newton's laws of motion Euler's laws can be derived from Newton's laws. Euler's laws can, however, be taken as axioms describing the laws of motion for extended bodies, independently of any particle structure.
Newton's laws hold only with respect to a certain set of frames of reference called Newtonian or inertial reference frames. Some authors interpret the first law as defining. Other authors do treat the first law as a corollary of the second; the explicit concept of an inertial frame of reference was not developed until long after Newton's death. In the given interpretation mass, acceleration and force are assumed to be externally defined quantities; this is the most common, but not the only interpretation of the way one can consider the laws to be a definition of these quantities. Newtonian mechanics has been superseded by special relativity, but it is still useful as an approximation when the speeds involved are much slower than the speed of light; the first law states that if the net force is zero the velocity of the object is constant. Velocity is a vector quantity which expresses both the object's speed and the direction of its motion; the first law can be stated mathematically when the mass is a non-zero constant, as, ∑ F = 0 ⇔ d v d t = 0.
An object, at rest will stay at rest unless a force acts upon it. An object, in motion will not change its velocity unless a force acts upon it; this is known as uniform motion. An object continues to do. If it is at rest, it continues in a state of rest. If an object is moving, it continues to move without changing its speed; this is evident in space probes. Changes in motion must be imposed against the tendency of an object to retain its state of motion. In the absence of net forces, a moving object tends to move along a straight line path indefinitely. Newton placed the first law of motion to establish frames of reference for which the other laws are applicable; the first law of motion postulates the existence of at least one frame of reference called a Newtonian or inertial reference frame, relative to which the motion of a particle not subject to forces is a straight line at a constant speed. Newton's first law is referred to as the law of inertia. Thus, a condition necessary for the uniform motion of a particle relative to an inertial reference frame is that the total net force acting on it is zero.
In this sense, the first law can be restated as: In every material universe, the motion of a particle in a preferential reference frame Φ is determined by the action of forces whose total vanished for all times when and only when the velocity of the particle is constant in Φ. That is, a particle at rest or in uniform motion in the preferential frame Φ continues in that state unless compelled by forces to change it. Newton's first and second laws are valid only in an inertial reference frame. Any reference frame, in uniform motion with respect to an inertial frame is an in
In astronomy, luminosity is the total amount of energy emitted per unit of time by a star, galaxy, or other astronomical object. As a term for energy emitted per unit time, luminosity is synonymous with power. In SI units luminosity is measured in joules per second or watts. Values for luminosity are given in the terms of the luminosity of the Sun, L⊙. Luminosity can be given in terms of the astronomical magnitude system: the absolute bolometric magnitude of an object is a logarithmic measure of its total energy emission rate, while absolute magnitude is a logarithmic measure of the luminosity within some specific wavelength range or filter band. In contrast, the term brightness in astronomy is used to refer to an object's apparent brightness: that is, how bright an object appears to an observer. Apparent brightness depends on both the luminosity of the object and the distance between the object and observer, on any absorption of light along the path from object to observer. Apparent magnitude is a logarithmic measure of apparent brightness.
The distance determined by luminosity measures can be somewhat ambiguous, is thus sometimes called the luminosity distance. In astronomy, luminosity is the amount of electromagnetic energy; when not qualified, the term "luminosity" means bolometric luminosity, measured either in the SI units, watts, or in terms of solar luminosities. A bolometer is the instrument used to measure radiant energy over a wide band by absorption and measurement of heating. A star radiates neutrinos, which carry off some energy, contributing to the star's total luminosity; the IAU has defined a nominal solar luminosity of 3.828×1026 W to promote publication of consistent and comparable values in units of the solar luminosity. While bolometers do exist, they cannot be used to measure the apparent brightness of a star because they are insufficiently sensitive across the electromagnetic spectrum and because most wavelengths do not reach the surface of the Earth. In practice bolometric magnitudes are measured by taking measurements at certain wavelengths and constructing a model of the total spectrum, most to match those measurements.
In some cases, the process of estimation is extreme, with luminosities being calculated when less than 1% of the energy output is observed, for example with a hot Wolf-Rayet star observed only in the infra-red. Bolometric luminosities can be calculated using a bolometric correction to a luminosity in a particular passband; the term luminosity is used in relation to particular passbands such as a visual luminosity of K-band luminosity. These are not luminosities in the strict sense of an absolute measure of radiated power, but absolute magnitudes defined for a given filter in a photometric system. Several different photometric systems exist; some such as the UBV or Johnson system are defined against photometric standard stars, while others such as the AB system are defined in terms of a spectral flux density. A star's luminosity can be determined from two stellar characteristics: size and effective temperature; the former is represented in terms of solar radii, R⊙, while the latter is represented in kelvins, but in most cases neither can be measured directly.
To determine a star's radius, two other metrics are needed: the star's angular diameter and its distance from Earth. Both can be measured with great accuracy in certain cases, with cool supergiants having large angular diameters, some cool evolved stars having masers in their atmospheres that can be used to measure the parallax using VLBI. However, for most stars the angular diameter or parallax, or both, are far below our ability to measure with any certainty. Since the effective temperature is a number that represents the temperature of a black body that would reproduce the luminosity, it cannot be measured directly, but it can be estimated from the spectrum. An alternative way to measure stellar luminosity is to measure the star's apparent brightness and distance. A third component needed to derive the luminosity is the degree of interstellar extinction, present, a condition that arises because of gas and dust present in the interstellar medium, the Earth's atmosphere, circumstellar matter.
One of astronomy's central challenges in determining a star's luminosity is to derive accurate measurements for each of these components, without which an accurate luminosity figure remains elusive. Extinction can only be measured directly if the actual and observed luminosities are both known, but it can be estimated from the observed colour of a star, using models of the expected level of reddening from the interstellar medium. In the current system of stellar classification, stars are grouped according to temperature, with the massive young and energetic Class O stars boasting temperatures in excess of 30,000 K while the less massive older Class M stars exhibit temperatures less than 3,500 K; because luminosity is proportional to temperature to the fourth power, the large variation in stellar temperatures produces an vaster variation in stellar luminosity. Because the luminosity depends on a high power of the stellar mass, high mass luminous stars have much shorter lifetimes; the most luminous stars are always young stars, no more than a few million years for the most extreme.
In the Hertzsprung–Russell diagram, the x-axis represents temperature or spectral type while the y-axis represents luminosity or magnitude. The vast majority of stars are found along the main sequence with blue Class O stars found at the top left of the chart while red Class M stars fall to the bottom right. Certain stars like Deneb and Betelgeuse are