:: wikimiki.org ::

Open Cluster

Open cluster

An open cluster is a group of up to a few thousand stars that were formed from the same giant molecular cloud, and are still loosely gravitationally bound to each other. In contrast, globular clusters are very tightly bound by gravity. Open clusters are found only in spiral and irregular galaxies, in which active star formation is occurring. They are usually less than a few hundred million years old: they become disrupted by close encounters with other clusters and clouds of gas as they orbit the galactic centre, as well as losing cluster members through internal close encounters. Young open clusters may still be contained within the molecular cloud from which they formed, illuminating it to create an H II region. Over time, radiation pressure from the cluster will disperse the molecular cloud. Typically, about 10% of the mass of a gas cloud will coalesce into stars before radiation pressure drives the rest away. Open clusters are very important objects in the study of stellar evolution. Because the stars are all of very similar age and chemical composition, the effects of other more subtle variables on the properties of stars are much more easily studied than they are for isolated stars. chemical composition

Historical observations

The most prominent open clusters such as the Pleiades have been known and recognised as groups of stars since antiquity. Others were known as fuzzy patches of light, but had to wait until the invention of the telescope to be resolved into their constituent stars. Telescopic observations revealed two distinct types of clusters, one of which contained thousands of stars in a regular spherical distribution and was found preferentially towards the centre of the Milky Way, and the other of which consisted of a generally sparser population of stars in a more irregular shape and found all over the sky. Astronomers dubbed the former globular clusters, and the latter open clusters. Open clusters are also occasionally referred to as galactic clusters, because they are almost exclusively found in the plane of the Milky Way, as discussed below. It was realised early on that the stars in the open clusters were physically related. The Reverend John Michell calculated in 1767 that the probability of even just one group of stars like the Pleiades being the result of a chance alignment as seen from earth was just 1 in 496,000 . As astrometry became more accurate, cluster stars were found to share a common proper motion through space, while spectroscopic measurements revealed common radial velocities, thus showing that the clusters consist of stars born at the same time and bound together as a group. While open clusters and globular clusters form two fairly distinct groups, there may not be a great deal of difference in appearance between a very sparse globular cluster and a very rich open cluster. Some astronomers believe the two types of star clusters form via the same basic mechanism, with the difference being that the conditions which allowed the formation of the very rich globular clusters containing hundreds of thousands of stars no longer prevail in our galaxy.

Formation

star cluster.]] All stars are originally formed in multiple systems, because only a cloud of gas containing many times the mass of the Sun will be heavy enough to collapse under its own gravity, but such a heavy cloud cannot collapse into a single star. The formation of an open cluster begins with the collapse of part of a giant molecular cloud, a cold dense cloud of gas containing up to many thousands of times the mass of the Sun. Many factors may trigger the collapse of a giant molecular cloud (or part of it) and a burst of star formation which will result in an open cluster, including shock waves from a nearby supernova and gravitational interactions. Once a giant molecular cloud begins to collapse, star formation proceeds via successive fragmentations of the cloud into smaller and smaller clumps, resulting eventually in the formation of up to several thousand stars. In our own galaxy, the formation rate of open clusters is estimated to be one every few thousand years . Once star formation has begun, the hottest and most massive stars (known as OB stars) will emit copious amounts of ultraviolet radiation. This radiation rapidly ionizes the surrounding gas of the giant molecular cloud, forming an H II region. Stellar winds from the massive stars and radiation pressure begin to drive away the gases; after a few million years the cluster will experience its first supernovae, which will also expel gas from the system. After a few tens of millions of years, the cluster will be stripped of gas and no further star formation will take place. Typically, less than 10% of the gas originally in the cluster will form into stars before it is dissipated . It is common for two or more separate open clusters to form out of the same molecular cloud. In the Large Magellanic Cloud, both Hodge 301 and R136 are forming from the gases of the Tarantula Nebula, while in our own galaxy, tracing back the motion through space of the Hyades and Praesepe, two prominent nearby open clusters, suggests that they formed in the same cloud about 600 million years ago . Sometimes, two clusters born at the same time will form a binary cluster. The best known example in the Milky Way is the Double Cluster of h Persei and χ Persei, but at least 10 more double clusters are known to exist . Many more are known in the Small and Large Magellanic Clouds — they are easier to detect in external systems than in our own galaxy because projection effects can cause unrelated clusters within the Milky Way to appear close to each other.

Morphology and classification

projection effect.]] Open clusters range from very sparse clusters with only a few members to large agglomerations containing thousands of stars. They usually consist of quite a distinct dense core, surrounded by a more diffuse 'corona' of cluster members. The core is typically about 3–4 light years across, with the corona extending to about 20 light years from the cluster centre. Typical star densities in the centre of a cluster are about 1.5 stars per cubic light year (the stellar density near the sun is about 0.1 star per cubic light year) . Open clusters are often classified according to a scheme developed by Robert Trumpler in 1930. The Trumpler scheme gives a cluster a three part designation, with a Roman numeral from I-IV indicating its concentration and detachment from the surrounding star field (from strongly to weakly concentrated), an Arabic numeral from 1 to 3 indicating the range in brightness of members (from small to large range), and p, m or r to indication whether the cluster is poor, medium or rich in stars. An 'n' is appended if the cluster lies within nebulosity . Under the Trumpler scheme, the Pleiades are classified as I3rn (strongly concentrated and richly populated with nebulosity present), while the nearby Hyades are classified as II3m (more dispersed, and with fewer members).

Numbers and distribution

nebulosity There are over 1,000 known open clusters in our galaxy, but the true total may be up to ten times higher than that . In spiral galaxies, open clusters are invariably found in the spiral arms where gas densities are highest and so most star formation occurs, and clusters usually disperse before they have had time to travel beyond their spiral arm. Open clusters are strongly concentrated close to the galactic plane, with a scale height in our galaxy of about 180 light years, compared to a galactic radius of approximately 100,000 light years . In irregular galaxies, open clusters may be found throughout the galaxy, although their concentration is highest where the gas density is highest. Open clusters are not seen in elliptical galaxies: star formation ceased many millions of years ago in ellipticals, and so the open clusters which were originally present have long since dispersed. In our galaxy, the distribution of clusters depends on age, with older clusters being preferentially found at greater distances from the galactic centre. Tidal forces are stronger nearer the centre of the galaxy, increasing the rate of disruption of clusters, and also the giant molecular clouds which cause the disruption of clusters are concentrated towards the inner regions of the galaxy, so clusters in the inner regions of the galaxy tend to get dispersed at a younger age than their counterparts in the outer regions .

Stellar composition

Tidal force.]] Because open clusters tend to be dispersed before most of their stars reach the end of their lives, the light from them tends to be dominated by the young, hot blue stars. These stars are the most massive, and have the shortest lives of a few tens of millions of years. The older open clusters tend to contain more yellow stars. Some open clusters contain hot blue stars which seem to be much younger than the rest of the cluster. These blue stragglers are also observed in globular clusters, and in the very dense cores of globulars they are believed to arise when stars collide, forming a much hotter, more massive star. However, the stellar density in open clusters is much lower than that in globular clusters, and stellar collisions cannot explain the numbers of blue stragglers observed. Instead, it is thought that most of them probably originate when dynamical interactions with other stars cause a binary system to coalesce into one star . Once they have exhausted their supply of hydrogen through nuclear fusion, medium to low mass stars shed their outer layers to form a planetary nebula and evolve into white dwarfs. While most clusters become dispersed before a large proportion of their members have reached the white dwarf stage, the number of white dwarfs in open clusters is still generally much lower than would be expected, given the age of the cluster and the expected initial mass distribution of the stars. One possible explanation for the lack of white dwarfs is that when a red giant expels its outer layers to become a planetary nebula, a slight asymmetry in the loss of material could give the star a 'kick' of a few kilometres per second, enough to eject it from the cluster .

Eventual fate

kilometres per second is a very massive open cluster surrounded by an H II region.]] Many open clusters are inherently unstable, with a small enough mass that the escape velocity of the system is lower than the average velocity of the constituent stars. These clusters will rapidly disperse within a few million years. In many cases, the stripping away of the gas from which the cluster formed by the radiation pressure of the hot young stars reduces the cluster mass enough to allow rapid dispersal. Clusters which have enough mass to be gravitationally bound once the surrounding nebula has evaporated can remain distinct for many tens of millions of years, but over time internal and external processes tend also to disperse them. Internally, close encounters between members of the cluster will often result in the velocity of one being increased to beyond the escape velocity of the cluster, which results in the gradual 'evaporation' of cluster members. Externally, about every half-billion years or so an open cluster tends to be disturbed by external factors such as passing close to or through a molecular cloud. The gravitational tidal forces generated by such an encounter tend to disrupt the cluster. Eventually, the cluster becomes a stream of stars, not close enough to be a cluster but all related and moving in similar directions at similar speeds. The timescale over which a cluster disrupts depends on its initial stellar density, with more tightly packed clusters persisting for longer. Estimated cluster half lives, after which half the original cluster members will have been lost, range from 150–800 million years, depending on the original density . After a cluster has become gravitationally unbound, many of its constituent stars will still be moving through space on similar trajectories, in what is known as a stellar association, moving cluster or moving group . Several of the brightest stars in the 'Plough' of Ursa Major are former members of an open cluster which now form such an association - In this case, the Ursa Major moving group. Eventually their slightly different relative velocities will see them scattered throughout the galaxy. A larger cluster is then known as a stream, if we discover the similar velocities and ages of otherwise unrelated stars.

Studying stellar evolution

Ursa Major moving group is older, and shows a lower turn off from the main sequence than that seen in M67.]] When a Hertzsprung-Russell diagram is plotted for an open cluster, most stars lie on the main sequence. The most massive stars have begun to evolve away from the main sequence and are becoming red giants, the position of the turn-off from the main sequence can be used to estimate the age of the cluster. Because the stars in an open cluster are all at roughly the same distance from Earth, and were born at roughly the same time from the same raw material, the differences in apparent brightness among cluster members is due only to their mass. This makes open clusters very useful in the study of stellar evolution, because when comparing one star to another, many of the variable parameters are fixed. The study of the abundances of lithium and beryllium in open cluster stars can give important clues about the evolution of stars and their interior structures. While hydrogen nuclei cannot fuse to form helium until the temperature reaches about 10 million K, lithium and beryllium are destroyed at temperatures of 2.5 million K and 3.5 million K respectively. This means that their abundances depend strongly on how much mixing occurs in stellar interiors. By studying their abundances in open cluster stars, variables such as age and chemical composition are fixed. Studies have shown that the abundances of these light elements are much lower than models of stellar evolution predict. While the reason for this underabundance is not yet fully understood, one possibility is that convection in stellar interiors can 'overshoot' into regions where radiation is normally the dominant mode of energy transport .

Open clusters and the astronomical distance scale

radiation.]] Determining the distances to astronomical objects is crucial to understanding them, but the vast majority of objects are too far away for their distances to be directly determined. Calibration of the astronomical distance scale relies on a sequence of indirect and sometimes uncertain measurements relating the closest objects for which distances can be directly measured to increasingly distant objects, and open clusters are a crucial step in this sequence. The closest open clusters can have their distance measured directly by one of two methods. First, the parallax (the small change in apparent position over the course of a year caused by the Earth moving from one side of its orbit around the Sun to the other) of stars in close open clusters can be measured, like other individual stars. Clusters such as the Pleiades, Hyades and a few others within about 500 light years are close enough for this method to be viable, and results from the Hipparcos position-measuring satellite yielded accurate distances for several clusters . The other direct method is the so-called 'moving cluster method'. This relies on the fact that the stars of a cluster share a common motion through space. Measuring the proper motions of cluster members and plotting their apparent motions across the sky will reveal that they converge on a vanishing point. The radial velocity of cluster members can be determined from Doppler shift measurements of their spectra, and once the radial velocity, proper motion and angular distance from the cluster to its vanishing point are known, simple trigonometry will reveal the distance to the cluster. The Hyades are the best known application of this method, which reveals their distance to be 46.3 parsecs . Once the distances to nearby clusters have been established, further techniques can extend the distance scale to more distant clusters. By matching the main sequence on the Hertzsprung-Russell diagram for a cluster at a known distance with that of a more distant cluster, the distance to the more distant cluster can be estimated. The nearest open cluster is the Hyades: the stellar association consisting of most of the Plough stars is at about half the distance of the Hyades, but is a stellar association rather than an open cluster as the stars are not gravitationally bound to each other. The most distant known open cluster in our galaxy is Berkeley 29, at a distance of about 15,000 parsecs . Open clusters are also easily detected in many of the galaxies of the Local Group. Accurate knowledge of open cluster distances is vital for calibrating the period-luminosity relationship shown by variable stars such as cepheid and RR Lyrae stars, which allows them to be used as standard candles. These luminous stars can be detected at great distances, and are then used to extend the distance scale to nearby galaxies in the Local Group.

References

# Michell J. (1767), An Inquiry into the probable Parallax, and Magnitude, of the Fixed Stars, from the Quantity of Light which they afford us, and the particular Circumstances of their Situation, Philosophical Transactions, v. 57, p. 234-264 # Battinelli P., Capuzzo-Dolcetta R. (1991), Formation and evolutionary properties of the Galactic open cluster system, Monthly Notices of the Royal Astronomical Society, v. 249, p. 76-83 # also see Battinelli P as previous reference. # Eggen O. J. (1960), Stellar groups, VII. The structure of the Hyades group, Monthly Notices of the Royal Astronomical Society, v. 120, p.540 # Subramaniam A., Gorti U., Sagar R., Bhatt H. C. (1995), Probable binary open star clusters in the Galaxy, Astronomy and Astrophysics, v.302, p.86 # Nilakshi S.R., Pandey A.K., Mohan V. (2002), A study of spatial structure of galactic open star clusters, Astronomy and Astrophysics, v. 383, p. 153-162 # Trumpler R.J. (1930), Preliminary results on the distances, dimensions and space distribution of open star clusters, Lick Observatory bulletin no. 420, Berkeley : University of California Press, p. 154-188 # Dias W.S., Alessi B.S., Moitinho A., Lépine J.R.D. (2002), New catalogue of optically visible open clusters and candidates, Astronomy and Astrophysics, v. 389, p. 871-873 # Janes K.A., Phelps R.L. (1980), The galactic system of old star clusters: The development of the galactic disk, The Astronomical Journal, v. 108, p. 1773-1785 # van den Bergh S., McClure R.D. (1980), Galactic distribution of the oldest open clusters, Astronomy & Astrophysics, v.88, p.360 # Andronov N., Pinsonneault M., Terndrup D. (2003), Formation of Blue Stragglers in Open Clusters, American Astronomical Society Meeting 203 # Fellhauer M., Lin D.N.C., Bolte M., Aarseth S.J., Williams K.A. (2003), The White Dwarf Deficit in Open Clusters: Dynamical Processes, The Astrophysical Journal, v. 595, pp. L53-L56 # de La Fuente M.R. (1998), Dynamical Evolution of Open Star Clusters, Publications of the Astronomical Society of the Pacific, v. 110, pp. 1117-1117 # VandenBerg, D.A., Stetson P.B. (2004), On the Old Open Clusters M67 and NGC 188: Convective Core Overshooting, Color-Temperature Relations, Distances, and Ages, Publications of the Astronomical Society of the Pacific, v. 116, pp. 997-1011 # Brown A.G.A. (2001), Open clusters and OB associations: a review, Revista Mexicana de Astronomía y Astrofísica, v. 11, p89-96 # Hanson R.B. (1975), A study of the motion, membership, and distance of the Hyades cluster, Astronomical Journal, v. 80, p. 379-401 # Bragaglia A., Held E.V., Tosi M. (2005), Radial velocities and membership of stars in the old, distant open cluster Berkeley 29, Astronomy and Astrophysics, v. 429, p. 881-886

External links

- [http://www.seds.org/messier/open.html Open Star Clusters @ SEDS Messier pages]
- [http://www.peripatus.gen.nz/Astronomy/OpeClu.html A general overview of open clusters]
- [http://www.armandocaussade.com/astronomy/open_and_globular.html Open and globular clusters overview]
- [http://zebu.uoregon.edu/~soper/Stars/movingcluster.html The moving cluster method]
- [http://www.nightskyinfo.com/open_clusters Open Clusters - Information and amateur observations] Category:Star clusters Category:Open clusters ja:散開星団

Star

:This article is about celestial bodies. A star is a massive body of plasma in outer space that is currently producing or has produced energy through nuclear fusion. Unlike a planet, from which most light is reflected, a star emits light because of its intense heat. Scientifically, stars are defined as self-gravitating spheres of plasma in hydrostatic equilibrium, which generate their own energy through the process of nuclear fusion. Small (dwarf) stars such as the Sun generally have essentially featureless disks with only small starspots. Larger (giant) stars have much bigger, much more obvious starspots, and also exhibit strong stellar limb-darkening (the brightness decreases towards the edge of the stellar disk). Stellar astronomy is the study of stars.

Star formation and evolution

Star formation occurs in molecular clouds, large regions of high density in the interstellar medium (though still less dense than the inside of an earthly vacuum chamber). Star formation begins with gravitational instability inside those clouds, often triggered by shockwaves from supernovae or collision of two galaxies (as in a starburst galaxy). High mass stars powerfully illuminate the clouds from which they formed. One example of such a nebula is the Orion Nebula. Stars spend about 90% of their lifetime fusing hydrogen to produce helium in high-temperature and high-pressure reactions near the core. Such stars are said to be on the main sequence. Small stars (called red dwarfs) burn their fuel very slowly and last tens to hundreds of billions of years. At the end of their lives, they simply become dimmer and dimmer, fading into black dwarfs. However, since the lifespan of such stars is greater than the current age of the universe (13.6 billion years), no black dwarfs exist yet. As most stars exhaust their supply of hydrogen, their outer layers expand and cool to form a red giant. In about 5 billion years, when the Sun is a red giant, it will be so large that it will consume both Mercury and Venus. Eventually the core is compressed enough to start helium fusion, and the star heats up and contracts. Larger stars will also fuse heavier elements, all the way to iron, which is the end point of the process. Since iron nuclei are more tightly bound than any heavier nuclei, they cannot be fused to release energy. Likewise, since they are more tightly bound than all lighter nuclei, energy cannot be released by fission. In old, very massive stars, a large core of inert iron will accumulate in the center of the star. An average-size star will then shed its outer layers as a planetary nebula. The core that remains will be a tiny ball of degenerate matter not massive enough for further fusion to take place, supported only by degeneracy pressure, called a white dwarf. These too will fade into black dwarfs over very long stretches of time. white dwarf In larger stars, fusion continues until an iron core accumulates that is too large to be supported by electron degeneracy pressure. This core will suddenly collapse as its electrons are driven into its protons, forming neutrons and neutrinos in a burst of inverse beta decay. The shockwave formed by this sudden collapse causes the rest of the star to explode in a supernova. Supernovae are so bright that they may briefly outshine the star's entire home galaxy. When they occur within the Milky Way, supernovae have historically been observed by naked-eye observers as "new stars" where none existed before. Eventually, most of the matter in a star is blown away by the explosion (forming nebulae such as the Crab Nebula) and what remains will be a neutron star (sometimes a pulsar or X-ray burster) or, in the case of the largest stars, a black hole. The blown-off outer layers of dying stars include heavy elements which may be recycled during new star formation. These heavy elements allow the formation of rocky planets. The outflow from supernovae and the stellar wind of large stars play an important part in shaping the interstellar medium.

Appearance and distribution of stars

All stars except the Sun appear to the human eye as shining points in the nighttime sky that twinkle because of the effect of the Earth's atmosphere. Interferometer telescopes are required in order to produce images of these objects. The Sun is also a star, but it is close enough to Earth to appear as a disk instead, and to provide daylight. Stars are not spread uniformly across the universe, but are typically grouped into galaxies. A typical galaxy contains hundreds of billions of stars. The majority of stars are gravitationally bound to other stars, forming binary stars. Larger groups called star clusters also exist. Astronomers estimate that there are at least 70 sextillion (7×10²²) stars in the known universe [http://news.bbc.co.uk/2/hi/science/nature/3085885.stm]. That is 70 000 000 000 000 000 000 000, or 230 billion times as many as the 300 billion in our own Milky Way. The nearest star to the Earth, apart from the Sun, is Proxima Centauri, which is 39.9 trillion kilometers, or 4.2 light years away (light from Proxima Centauri takes 4.2 years to reach Earth). Travelling at the orbit speed of the Space Shuttle (5 miles per second -- almost 30,000 kilometers per hour), it would take about 150,000 years to get there. Distances like this are typical inside galactic discs, where the Sun and Earth are located. Stars can be much closer to each other in the centres of galaxies and globular clusters, or much further apart in galactic halos.

Age and size of stars

galactic halo Many stars are between 1 billion and 10 billion years old. Some stars may even be close to 13.7 billion years old, which is the observed age of the universe. (See Big Bang theory and stellar evolution.) They range in size from the tiny neutron stars (which are actually dead stars) no bigger than a city, to supergiants like the North Star (Polaris) and Betelgeuse, in the Orion constellation, which have a diameter about 1,000 times larger than the Sun—about 1.6 billion kilometers. However, these have a much lower density than the Sun. One of the most massive stars known is η Carinae, with 100–150 times as much mass as the Sun. Recent work by Donald Figer, an astronomer at the Space Telescope Science Institute in Baltimore, Maryland, suggests that 150 solar masses is the upper limit of stars in the current era of the universe. He used the Hubble Space Telescope to observe about a thousand stars in the Arches cluster, a massive young star cluster near the core of the Milky Way, and found no stars over that limit despite a statistical expectation that there should be several. The reason for this limit is not precisely known, but the Eddington limit is part of the answer. The very first stars to form after the Big Bang may have been larger, up to 300 solar masses or more, due to the complete absence of elements heavier than lithium in their composition. This generation of supermassive star is long extinct, however, and currently only theoretical. With a mass only 93 times that of Jupiter, AB Doradus C, a companion to AB Doradus A, is the smallest known star undergoing nuclear fusion in its core. Smaller bodies are brown dwarfs, which occupy a poorly-defined grey area between stars and gas giants. The minimum mass a star can have is estimated to be in the vicinity of 75 Jupiters.

Star classification

There are different classifications of stars ranging from type W, which are very large and bright, to M, which is often just large enough to start ignition of the hydrogen. Some of the more common classifications are O, B, A, F, G, K, M, and can perhaps be more easily remembered using the mnemonic "Oh, Be A Fine Girl, Kiss Me" (variant: change "girl" to "guy"), invented by Annie Jump Cannon (1863-1941). There are many other mnemonics for star classification; the most frequent addition tacks "Right Now, Sweetheart" for the red dwarf sub-types R, N and S. The new types L and T have also been recently appended to the end of the OBAFGKM sequence to classify the coldest low-mass stars and brown dwarfs, prompting such additions as "Lovingly Tonight" to the mnemonic. Each letter has 10 subclassifications. Our Sun is a G2, which is very near the middle in terms of quantities observed. Most stars fall into the main sequence which is a description of stars based on their absolute magnitude and spectral type. The Sun is taken as the prototypical star (not because it is special in any way, but because it is the closest and most studied star we have), and most characteristics of other stars are usually given in solar units.
For example, the mass of the Sun is :M_Sun = 1.9891×10³⁰ kg The masses of other stars can be given in terms of M_Sun.

Naming of stars

Most stars are identified only by catalogue numbers; only a few have names as such. The names are either traditional names (mostly from Arabic), Flamsteed designations, or Bayer designations. The only body which has been recognized by the scientific community as having competence to name stars or other celestial bodies is the International Astronomical Union (IAU). A number of private companies (e.g. the "International Star Registry") purport to sell names to stars; however, these names are not recognized by the scientific community, nor used by them, and many in the astronomy community view these organizations as frauds preying on people ignorant of how stars are in fact named. See star designations for more information on how stars are named. For a list of traditional names, see the list of stars by constellation.

Energy production

The energy produced by stars radiates into space as electromagnetic radiation, as a stream of neutrinos from the star's core, and as a stream of particles from the star's outer layers (its stellar wind). The peak frequency of the light depends on the temperature of the outer layers of the star. Besides the emitted visible light, the ultraviolet and infrared components are typically significant. The apparent brightness of a star is measured by its apparent magnitude.

Nuclear fusion reaction pathways

A variety of different nuclear fusion reactions take place inside the cores of stars, depending upon their mass and composition (see Stellar nucleosynthesis). Stars begin as a cloud of mostly hydrogen with about 25% helium and heavier elements in smaller quantities. In the Sun, with a 10⁷ K core, hydrogen fuses to form helium in the proton-proton chain: :4¹H → 2²H + 2e⁺ + 2ν_e (4.0 MeV + 1.0 MeV) :2¹H + 2²H → 2³He + 2γ (5.5 MeV) :2³He → ⁴He + 2¹H (12.9 MeV) These reactions result in the overall reaction: :4¹H → ⁴He + 2e⁺ + 2γ + 2ν_e (26.7 MeV) In more massive stars, helium is produced in a cycle of reactions catalyzed by carbon, the carbon-nitrogen-oxygen cycle. In stars with cores at 10⁸ K and masses between 0.5 and 10 solar masses, helium can be transformed into carbon in the triple-alpha process: :⁴He + ⁴He + 92 keV → ^{8
-}Be :⁴He + ^{8
-}Be + 67 keV → ^{12
-}C :^{12
-}C → ¹²C + γ + 7.4 MeV For an overall reaction of: :3⁴He → ¹²C + γ + 7.2 MeV

Star mythology

As well as certain constellations and the Sun itself, stars as a whole have their own mythology. They were thought to be the souls of the dead, or gods/goddesses.

References

- Cliff Pickover (2001) "The Stars of Heaven", Oxford University Press
- John Gribbin, Mary Gribbin (2001) "Stardust: Supernovae and Life — The Cosmic Connection", Yale University Press.

External links

- [http://www.mrao.cam.ac.uk/telescopes/coast/betel.html Images of starspots on the surface of Betelgeuse]
- [http://simbad.u-strasbg.fr/sim-fid.pl Find out what is known about any given star by entering its name or position]
- [http://www.enchantedlearning.com/subjects/astronomy/stars/startypes.shtml Star Classification] Category:Astronomical objects ko:항성 ms:Bintang ja:恒星 simple:Star th:ดาวฤกษ์

Giant Molecular Cloud

A dark nebula is a large cloud which appears as star-poor regions where the dust of interstellar medium seems to be concentrated. Dark nebulae can be seen if they obscure part of an emission or reflection nebula (eg. the Horsehead Nebula) or if they block out background stars (eg. the Coalsack Nebula). The form of such dark clouds is very irregular: they have no clearly defined outer boundaries and sometimes take on convoluted serpentine shapes. The largest dark nebulae are visible to the naked eye, appearing as dark patches against the brighter background of the Milky Way.

Astrophysics of dark nebulae

The hydrogen of these opaque dark clouds exists in the form of molecular hydrogen. The largest nebulae of this type, the so-called giant molecular clouds (GMC), are more than a million times as massive as the Sun. They contain much of the mass of the interstellar medium, are some 150 light-years across, and have an average density of 100 to 300 molecules per cubic centimetre and an internal temperature of only 7 to 15 K. Molecular clouds consist mainly of gas and dust but contain many stars as well. The cloud cores are completely hidden from view and would be undetectable except for the microwave emissions from their constituent molecules. This radiation is not absorbed by dust and readily escapes the cloud. The material within the clouds is clumped together in all sizes, with some clouds ranging down to the masses of individual stars, small clumps may extend about one light-year across. The clouds have an internal magnetic field that provides support against their own gravity. GMCs play an important role in galaxy dynamics: when a star passes near a GMC, the considerable gravity pull will perturb the star's orbit by a significant amount. After repeated near encounters, a middle-aged star will have significant velocity components in all directions, instead of an almost circular orbit like a newborn star (this is because the newborn star inherits the circular orbit of the GMC where it was born). This gives the astronomer another tool to estimate star ages, and helps to explain the thickness of the galactic disk. In the inner regions of dark nebulae important events take place, such as the formation of stars.

Gravity

Gravity is the force of attraction between massive particles. Weight is determined by the mass of an object and its location in a gravitational field. While a great deal is known about the properties of gravity, the ultimate cause of the gravitational force remains an open question. General relativity is the most successful theory of gravitation to date. It postulates that mass and energy curve space-time, resulting in the phenomenon known as gravity. The effect of the bending of spacetime is often misunderstood as most people seem to prefer to think of a falling object as accelerating when the facts do not support that assumption. Skydivers do not feel any acceleration (other than from wind resistance). Gravity is acceleration.

F=\dot=m\dot+\dotv\,\!

means (if the mass is unvarying) that there must be a force that causes a mass to accelerate. For a rocket ship, that is the rocket engine. For the earth, it is the compression of the mass between something on the surface of the earth and the earth's center of mass. The acceleration is in relation to spacetime in that the weight one feels is one's resistance to deviating from one's path in spacetime. The same holds true in the rocket ship except that a rocket engine supplies the force to accelerate an occupant from his spacetime path. There is no difference between the weight he feels because of gravity or the rocket.

Newton's law of universal gravitation

Newton's law of universal gravitation states the following: :Every object in the Universe attracts every other object with a force directed along the line of centers of mass for the two objects. This force is proportional to the product of their masses and inversely proportional to the square of the separation between the centers of mass of the two objects. Given that the force is along the line through the two masses, the law can be stated symbolically as follows. :

F = - G \frac

where: :F is the magnitude of the (repulsive) gravitational force between two objects :G is the gravitational constant, that is approximately : G = 6.67 × 10⁻¹¹ N m² kg^-2 :m₁ is the mass of first object :m₂ is the mass of second object :r is the distance between the objects It can be seen that this repulsive force F is always negative, and this means that the net attractive force is positive. The minus sign is used to hold the same value meaning as in the Coulomb's Law, where a positive force as result means repulsion between two charges. Thus gravity is proportional to the mass of each object, but has an inverse square relationship with the distance between the centres of each mass. Strictly speaking, this law applies only to point-like objects. If the objects have spatial extent, the force has to be calculated by integrating the force (in vector form, see below) over the extents of the two bodies. It can be shown that for an object with a spherically-symmetric distribution of mass, the integral gives the same gravitational attraction on masses outside it as if the object were a point mass.¹ This law of universal gravitation was originally formulated by Isaac Newton in his work, the Principia Mathematica (1687). Professor William Whewell of Cambridge University, author of History of the Inductive Sciences (1837) stated: ::The law of gravitation is indisputably and incomparably the greatest scientific discovery ever made, whether we look at the advance which it involved, the extent of the truth disclosed, or the fundamental and satisfactory nature of this truth. [In A Treasury of Science ed. Harlow Shapley et al, Harper & Bros. NY: 1946] The history of gravitation as a physical concept is considered in more detail below.

Vector form

below Newton's law of universal gravitation can be written as a vector equation to account for the direction of the gravitational force as well as its magnitude. In this formula, quantities in bold represent vectors. :

\mathbf_ =
 G 
 \, \mathbf_

\mathbf_ =
 - G 
 \, \mathbf_

where :F₁₂ is the force on object 1 due to object 2 :G is the gravitational constant :m₁ and m₂ are the masses of the objects 1 and 2 :r₂₁ = | r₂ − r₁ | is the distance between objects 2 and 1 :

\mathbf_ \equiv \frac

is the unit vector from object 2 to 1 It can be seen, that the vector form of the equation is the same as the scalar form, except for the vector value of F and the unit vector. Also, it can be seen that F₁₂ = − F₂₁. Gravitational acceleration is given by the same formula except for one of the factors m: :

\mathbf =
  G 
  \, \mathbf

Gravitational field

The gravitational field is a vector field that describes the gravitational force an object of given mass experiences in any given place in space. It is a generalization of the vector form, which becomes particularly useful if more than 2 objects are involved (such as a rocket between the Earth and the Moon). For 2 objects (e.g. object 1 is a rocket, object 2 the Earth), we simply write

\mathbf r

instead of

\mathbf r_

and

m

instead of

m_1

and define the gravitational field

\mathbf g(\mathbf r)

as: :

\mathbf g(\mathbf r) =
 G 
 \, \mathbf

so that we can write: :

\mathbf( \mathbf r) = m \mathbf g(\mathbf r)

This formulation is independent of the objects causing the field. The field has units of force divided by mass; in SI, this is N·kg⁻¹.

Problems with Newton's theory

Although Newton's formulation of gravitation is quite accurate for most practical purposes, it has a few problems:

Theoretical concerns

- There is no prospect of identifying the mediator of gravity. Newton himself felt the inexplicable action at a distance to be unsatisfactory (see "Newton's reservations" below).
- Newton's theory requires that gravitational force is transmitted instantaneously. Given classical assumptions of the nature of space and time, this is necessary to preserve the conservation of angular momentum observed by Johannes Kepler. However, it is in direct conflict with Einstein's theory of special relativity which places an upper limit—the speed of light in vacuum—on the velocity at which signals can be transmitted.

Disagreement with observation

- Newton's theory does not fully explain the precession of the perihelion of the orbit of the planet Mercury. There is a 43 arcsecond per century discrepancy between the Newtonian prediction (resulting from the gravitational tugs of the other planets) and the observed precession.
- The predicted deflection of light by gravity is only half as much as observations of this deflection, which were made after General Relativity was developed in 1915.
- The observed fact that gravitational and inertial masses are the same for all bodies is unexplained within Newton's system. General relativity takes this as a postulate. See equivalence principle.

Newton's reservations

It's important to understand that while Newton was able to formulate his law of gravity in his monumental work, he was deeply uncomfortable with the notion of "action at a distance" which his equations implied. He never, in his words, "assigned the cause of this power". In all other cases, he used the phenomenon of motion to explain the origin of various forces acting on bodies, but in the case of gravity, he was unable to experimentally identify the motion that produces the force of gravity. Moreover, he refused to even offer a hypothesis as to the cause of this force on grounds that to do so was contrary to sound science. He lamented the fact that "philosophers have hitherto attempted the search of nature in vain" for the source of the gravitational force, as he was convinced "by many reasons" that there were "causes hitherto unknown" that were fundamental to all the "phenomena of nature". These fundamental phenomena are still under investigation and, though hypotheses abound, the definitive answer is yet to be found. While it is true that Einstein's hypotheses are successful in explaining the effects of gravitational forces more precisely than Newton's in certain cases, he too never assigned the cause of this power, in his theories. It is said that in Einstein's equations, "matter tells space how to curve, and space tells matter how to move", but this new idea, completely foreign to the world of Newton, does not enable Einstein to assign the "cause of this power" to curve space any more than the Law of Universal Gravitation enabled Newton to assign its cause. In Newton's own words: :I wish we could derive the rest of the phenomena of nature by the same kind of reasoning from mechanical principles; for I am induced by many reasons to suspect that they may all depend upon certain forces by which the particles of bodies, by some causes hitherto unknown, are either mutually impelled towards each other, and cohere in regular figures, or are repelled and recede from each other; which forces being unknown, philosophers have hitherto attempted the search of nature in vain. If science is eventually able to discover the cause of the gravitational force, Newton's wish could eventually be fulfilled as well. It should be noted that here, the word "cause" is not being used in the same sense as "cause and effect" or "the defendant caused the victim to die". Rather, when Newton uses the word "cause," he (apparently) is referring to an "explanation". In other words, a phrase like "Newtonian gravity is the cause of planetary motion" means simply that Newtonian gravity explains the motion of the planets. See Causality and Causality (physics).

Einstein's theory of gravitation

Einstein's theory of gravitation answered the problems with Newton's theory noted above. In a revolutionary move, his theory of general relativity (1915) stated that the presence of mass, energy, and momentum causes spacetime to become curved. Because of this curvature, the paths that objects in inertial motion follow can "deviate" or change direction over time. This deviation appears to us as an acceleration towards massive objects, which Newton characterized as being gravity. In general relativity however, this acceleration or free fall is actually inertial motion. So objects in a gravitational field appear to fall at the same rate due to their being in inertial motion while the observer is the one being accelerated. (This identification of free fall and inertia is known as the Equivalence principle.) The relationship between the presence of mass/energy/momentum and the curvature of spacetime is given by the Einstein field equations. The actual shapes of spacetime are described by solutions of the Einstein field equations. In particular, the Schwarzschild solution (1916) describes the gravitational field around a spherically symmetric massive object. The geodesics of the Schwarzschild solution describe the observed behavior of objects being acted on gravitationally, including the anomalous perihelion precession of Mercury and the bending of light as it passes the Sun. Arthur Eddington found observational evidence for the bending of light passing the Sun as predicted by general relativity in 1919. Subsequent observations have confirmed Eddington's results, and observations of a pulsar which is occulted by the Sun every year have permitted this confirmation to be done to a high degree of accuracy. There have also in the years since 1919 been numerous other tests of general relativity, all of which have confirmed Einstein's theory.

Units of measurement and variations in gravity

tests of general relativity. (ESA image)]] Gravitational phenomena are measured in various units, depending on the purpose. The gravitational constant is measured in newtons times metre squared per kilogram squared. Gravitational acceleration, and acceleration in general, is measured in metres per second squared or in non-SI units such as galileos, gees, or feet per second squared. The acceleration due to gravity at the Earth's surface is approximately 9.81 m/s², more precise values depending on the location. A standard value of the Earth's gravitational acceleration has been adopted, called g_n. When the typical range of interesting values is from zero to tens of metres per second squared, as in aircraft, acceleration is often stated in multiples of g_n. When used as a measurement unit, the standard acceleration is often called "gee", as g can be mistaken for g, the gram symbol. For other purposes, measurements in millimetres or micrometres per second squared (mm/s² or µm/s²) or in multiples of milligals or milligalileos (1 mGal = 1/1000 Gal), a non-SI unit still common in some fields such as geophysics. A related unit is the eotvos, which is a cgs unit of the gravitational gradient. Mountains and other geological features cause subtle variations in the Earth's gravitational field; the magnitude of the variation per unit distance is measured in inverse seconds squared or in eotvoses. Typical variations with time are 2 µm/s² (0.2 mGal) during a day, due to the tides, i.e. the gravity due to the Moon and the Sun. A larger variation in the effect of gravity occurs when we move from the equator to the poles. The effective force of gravity decreases as the distance from the equator decreases, due to the rotation of the Earth, and the resulting centrifugal force and flattening of the Earth. The centrifugal force causes an effective force 'up' which effectively counteracts gravity, while the flattening of the Earth causes the poles to be closer to the center of mass of the Earth. It is also related to the fact that the Earth's density changes from the surface of the planet to its centre. The sea-level gravitational acceleration is 9.780 m/s² at the equator and 9.832 m/s² at the poles, so an object will exert about 0.5% more force due to gravity at sea level at the poles than at sea level at the equator [http://curious.astro.cornell.edu/question.php?number=310].

Comparison with electromagnetic force

The gravitational interaction of protons is approximately a factor 10³⁶ weaker than the electromagnetic repulsion. This factor is independent of distance, because both interactions are inversely proportional to the square of the distance. Therefore on an atomic scale mutual gravity is negligible. However, the main interaction between common objects and the Earth and between celestial bodies is gravity, because at this scale matter is electrically neutral: even if in both bodies there were a surplus or deficit of only one electron for every 10¹⁸ protons and neutrons this would already be enough to cancel gravity (or in the case of a surplus in one and a deficit in the other: double the interaction). However, the main interactions between the charged particles in cosmic plasma (that makes up over 99% of the universe by volume), are electromagnetic forces. In terms of Planck units: the charge of a proton is 0.085, while the mass is only . From that point of view, the gravitational force is not small as such, but because masses are small. The relative weakness of gravity can be demonstrated with a small magnet picking up pieces of iron. The small magnet is able to overwhelm the gravitational interaction of the entire Earth. Similarly, when doing a chin-up, the electromagnetic interaction within your muscle cells is able to overcome the force induced by Earth on your entire body. Gravity is small unless at least one of the two bodies is large or one body is very dense and the other is close by, but the small gravitational interaction exerted by bodies of ordinary size can fairly easily be detected through experiments such as the Cavendish torsion bar experiment. Cavendish torsion bar experiment Further reading
- Jefimenko, Oleg D., "Causality, electromagnetic induction, and gravitation : a different approach to the theory of electromagnetic and gravitational fields". Star City [West Virginia] : Electret Scientific Co., c1992. ISBN 0917406095
- Heaviside, Oliver, "[http://www.as.wvu.edu/coll03/phys/www/Heavisid.htm A gravitational and electromagnetic analogy]". The Electrician, 1893.

Gravity and quantum mechanics

It is strongly believed that three of the four fundamental forces (the strong nuclear force, the weak nuclear force, and the electromagnetic force) are manifestations of a single, more fundamental force. Combining gravity with these forces of quantum mechanics to create a theory of quantum gravity is currently an important topic of research amongst physicists. General relativity is essentially a geometric theory of gravity. Quantum mechanics relies on interactions between particles, but general relativity requires no exchange of particles in its explanation of gravity. Scientists have theorized about the graviton (a messenger particle that transmits the force of gravity) for years, but have been frustrated in their attempts to find a consistent quantum theory for it. Many believe that string theory holds a great deal of promise to unify general relativity and quantum mechanics, but this promise has yet to be realized. It is notable that in general relativity gravitational radiation (which under the rules of quantum mechanics must be composed of gravitons) is only created in situations where the curvature of spacetime is oscillating, such as for co-orbiting objects. The amount of gravitational radiation emitted by the solar system and its planetary systems is far too small to measure. However, gravitational radiation has been indirectly observed as an energy loss over time in binary pulsar systems such as PSR1913+16). It is believed that neutron star mergers and black hole formation may create detectable amounts of gravitational radiation. Gravitational radiation observatories such as LIGO have been created to study the problem. No confirmed detections have been made of this hypothetical radiation, but as the science behind LIGO is refined and as the instruments themselves are endowed with greater sensitivity over the next decade, this may change.

Experimental tests of theories

Today General Relativity is accepted as the standard description of gravitational phenomena. (Alternative theories of gravitation exist but are more complicated than General Relativity.) General Relativity is consistent with all currently available measurements of large-scale phenomena. For weak gravitational fields and bodies moving at slow speeds at small distances, Einstein's General Relativity gives almost exactly the same predictions as Newton's law of gravitation. Crucial experiments that justified the adoption of General Relativity over Newtonian gravity were the classical tests: the gravitational redshift, the deflection of light rays by the Sun, and the precession of the orbit of Mercury. More recent experimental confirmations of General Relativity were the (indirect) deduction of gravitational waves being emitted from orbiting binary stars, the existence of neutron stars and black holes, gravitational lensing, and the convergence of measurements in observational cosmology to an approximately flat model of the observable Universe, with a matter density parameter of approximately 30% of the critical density and a cosmological constant of approximately 70% of the critical density. The equivalence principle, the postulate of general relativity that presumes that inertial mass and gravitational mass are the same, is also under test. Past, present, and future tests are discussed in the equivalence principle section. Even to this day, scientists try to challenge General Relativity with more and more precise direct experiments. The goal of these tests is to shed light on the yet unknown relationship between Gravity and Quantum Mechanics. Space probes are used to either make very sensitive measurements over large distances, or to bring the instruments into an environment that is much more controlled than it could be on Earth. For example, in 2004 a dedicated satellite for gravity experiments, called Gravity Probe B, was launched to test general relativity's predicted frame-dragging effect, among others. Also, land-based experiments like LIGO and a host of "bar detectors" are trying to detect gravitational waves directly. A space-based hunt for gravitational waves, LISA, is in its early stages. It should be sensitive to low frequency gravitational waves from many sources, perhaps including the Big Bang. Speed of gravity: Einstein's theory of relativity predicts that the speed of gravity (defined as the speed at which changes in location of a mass are propagated to other masses) should be consistent with the speed of light. In 2002, the Fomalont-Kopeikin experiment produced measurements of the speed of gravity which matched this prediction. However, this experiment has not yet been widely peer-reviewed, and is facing criticism from those who claim that Fomalont-Kopeikin did nothing more than measure the speed of light in a convoluted manner. The Pioneer anomaly is an empirical observation that the positions of the Pioneer 10 and Pioneer 11 space probes differ very slightly from what would be expected according to known effects (gravitational or otherwise). The possibility of new physics has not been ruled out, despite very thorough investigation in search of a more prosaic explanation.

Recent Alternative theories

- Brans-Dicke theory of gravity
- Rosen bi-metric theory of gravity
- In the modified Newtonian dynamics (MOND), Mordehai Milgrom proposes a modification of Newton's Second Law of motion for small accelerations.

Historical Alternative theories

- Nikola Tesla challenged Albert Einstein's theory of relativity, announcing he was working on a Dynamic theory of gravity (which began between 1892 and 1894) and argued that a "field of force" was a better concept and focused on media with electromagnetic energy that fill all of space.
- In 1967 Andrei Sakharov proposed something similar, if not essentially identical. His theory has been adopted and promoted by Messrs. Haisch, Rueda and Puthoff who, among other things, explain that gravitational and inertial mass are identical and that high speed rotation can reduce (relative) mass. Combining these notions with those of T. T. Brown, it is relatively easy to conceive how field propulsion vehicles such as "flying saucers" could be engineered given a suitable source of power.
- Georges-Louis LeSage proposed a gravity mechanism, now commonly called LeSage gravity, based on a fluid-based explanation where a light gas fills the entire universe.

Self-gravitating system

A self-gravitating system is a system of masses kept together by mutual gravity. An example is a binary star.

Special applications of gravity

A height difference can provide a useful pressure in a liquid, as in the case of an intravenous drip or a water tower, and can even supply enough power for hydroelectricity. A weight hanging from a cable over a pulley provides a constant tension in the cable, also in the part on the other side of the pulley. pulley Dubuque, Iowa]] Molten lead, when poured into the top of a shot tower, will coalesce into a rain of spherical lead shot, first separating into droplets, forming molten spheres, and finally freezing solid, undergoing many of the same effects as meteoritic tektites, which will cool into spherical, or near-spherical shapes in free-fall. A fractionation tower can be used to manufacture some materials by separating out the material components based on their specific gravity.

Comparative gravities of different planets and Earth's moon

The standard acceleration due to gravity at the Earth's surface is, by convention, equal to 9.80665 metres per second squared. (The local acceleration of gravity varies slightly over the surface of the Earth; see gee for details.) This quantity is known variously as g_n, g_e (sometimes this is the normal equatorial value on Earth, 9.78033 m/s²), g₀, gee, or simply g (which is also used for the variable local value). The following is a list of the gravitational accelerations (in multiples of g) at the Sun, the surfaces of each of the planets in the solar system, and the Earth's moon : Note: The "surface" is taken to mean the cloud tops of the gas giants (Jupiter, Saturn, Uranus and Neptune) in the above table. It is usually specified as the location where the pressure is equal to a certain value (normally 75 kPa?). For the Sun, the "surface" is taken to mean the photosphere. Within the Earth, the gravitational field peaks at the core-mantle boundary, where it has a value of 10.7 m/s². For spherical bodies surface gravity in m/s² is 2.8 × 10⁻¹⁰ times the radius in m times the average density in kg/m³. When flying from Earth to Mars, climbing against the field of the Earth at the start is 100 000 times heavier than climbing against the force of the sun for the rest of the flight.

Mathematical equations for a falling body

These equations describe the motion of a falling body under acceleration g near the surface of the Earth. mantle Here, the acceleration of gravity is a constant, g, because in the vector equation above,

_

would be a constant vector, pointing straight down. In this case, Newton's law of gravitation simplifies to the law :F = mg The following equations ignore air resistance and the rotation of the Earth, but are usually accurate enough for heights not exceeding the tallest man-made structures. They fail to describe the Coriolis effect, for example. They are extremely accurate on the surface of the Moon, where the atmosphere is almost nil. Astronaut David Scott demonstrated this with a hammer and a feather. Galileo was the first to demonstrate and then formulate these equations. He used a ramp to study rolling balls, effectively slowing down the acceleration enough so that he could measure the time as the ball rolled down a known distance down the ramp. He used a water clock to measure the time; by using an "extremely accurate balance" to measure the amount of water, he could measure the time elapsed. ² :For Earth

\ g=9.8\, \mbox/\mbox^2 \quad

For other planets, multiply

\ g

by the ratio of the gravitational accelerations shown above. Note: "Average" means average in time. Note: Distance traveled, d, and time taken, t, must be in the same system of units as acceleration g. See dimensional analysis. To convert metres per second to kilometres per hour (km/h) multiply by 3.6, and to convert feet per second to miles per hour (mph) multiply by 0.68 (or, precisely, 15/22).

Gravitational potential

For any mass distribution there is a scalar field, the gravitational potential (a scalar potential), which is the gravitational potential energy per unit mass of a point mass, as function of position. It is

- G \int dm

where the integral is taken over all mass. Minus its gradient is the gravity field itself, and minus its Laplacian is the divergence of the gravity field, which is everywhere equal to -4πG times the local density. Thus when outside masses the potential satisfies Laplace's equation (i.e., the potential is a harmonic function), and when inside masses the potential satisfies Poisson's equation with, as right-hand side, 4πG times the local density.

Acceleration relative to the rotating Earth

The acceleration measured on the rotating surface of the Earth is not quite the same as the acceleration that is measured for a free-falling body because of the centrifugal force. In other words, the apparent acceleration in the rotating frame of reference is the total gravity vector minus a small vector toward the north-south axis of the Earth, corresponding to staying stationary in that frame reference.

History of gravitational theory

The first mathematical formulation of gravity was published in 1687 by Sir Isaac Newton. His law of universal gravitation was the standard theory of gravity until work by Albert Einstein and others on general relativity. Since calculations in general relativity are complicated, and Newtonian gravity is sufficiently accurate for calculations involving weak gravitational fields (e.g., launching rockets, projectiles, pendulums, etc.), Newton's formulae are generally preferred. Although the law of universal gravitation was first clearly and rigorously formulated by Isaac Newton, the phenomenon was observed and recorded by others. Even Ptolemy had a vague conception of a force tending toward the center of the Earth which not only kept bodies upon its surface, but in some way upheld the order of the universe. Johannes Kepler inferred that the planets move in their orbits under some influence or force exerted by the Sun; but the laws of motion were not then sufficiently developed, nor were Kepler's ideas of force sufficiently clear, to make a precise statement of the nature of the force. Christiaan Huygens and Robert Hooke, contemporaries of Newton, saw that Kepler's third law implied a force which varied inversely as the square of the distance. Newton's conceptual advance was to understand that the same force that causes a thrown rock to fall back to the Earth keeps the planets in orbit around the Sun, and the Moon in orbit around the Earth. Newton was not alone in making significant contributions to the understanding of gravity. Before Newton, Galileo Galilei corrected a common misconception, started by Aristotle, that objects with different mass fall at different rates. To Aristotle, it simply made sense that objects of different mass would fall at different rates, and that was enough for him. Galileo, however, actually tried dropping objects of different mass at the same time. Aside from differences due to friction from the air, Galileo observed that all masses accelerate the same. Using Newton's equation,

F = m a

, it is plain to us why: :

F = - = m_1a_1

The above equation says that mass

m_1

will accelerate at acceleration

a_1

under the force of gravity, but divide both sides of the equation by

m_1

and: :

a_1 =

Nowhere in the above equation does the mass of the falling body appear. When dealing with objects near the surface of a planet, the change in r divided by the initial r is so small that the acceleration due to gravity appears to be perfectly constant. The acceleration due to gravity on Earth is usually called g, and its value is about 9.82 m/s². Galileo didn't have Newton's equations, though, so his insight into gravity's proportionality to mass was invaluable, and possibly even affected Newton's formulation on how gravity works. However, across a large body, variations in

r

can create a significant tidal force.

Notes

- Note 1: Proposition 75, Theorem 35: p.956 - I.Bernard Cohen and Anne Whitman, translators: Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy. Preceded by A Guide to Newton's Principia, by I.Bernard Cohen. University of California Press 1999 ISBN 0-520-08816-6 ISBN 0-520-08817-4
- Note 2: See the works of Stillman Drake, for a comprehensive study of Galileo and his times, the Scientific Revolution.
- Max Born (1924), Einstein's Theory of Relativity (The 1962 Dover edition, page 348 lists a table documenting the observed and calculated values for the precession of the perihelion of Mercury, Venus, and Earth.)

References

-
-
-

External links

- [http://einstein.stanford.edu/ Gravity Probe B Experiment]
- [http://www.hkshum.net/whatisgravity/ What Is Gravity? - Aimed for Kids 8+ ]
- [http://www.intelligent-forces.com Intelligent Forces Theory] Satirical "Anti-Gravitationalism" website Category:Introductory physics Category:Celestial mechanics ko:중력 ja:重力 ms:Graviti

Globular clusters

A globular cluster is a spherical bundle of stars (star cluster) that orbits a galaxy as a satellite. Globular clusters are very tightly bound by gravity, which gives them their spherical shape, and extreme density (in relative terms) towards their core. satellite

General information

Globular clusters are composed of hundreds of thousands of old stars, similar to the bulge of a spiral galaxy but confined to a volume of only a few cubic parsecs. Globular clusters are fairly numerous; there are about 150 currently known globulars of the Milky Way (with perhaps 10-20 more undiscovered), and larger galaxies like Andromeda have more (Andromeda may have as many as 500). Some giant elliptical galaxies (e.g., M87) may have as many as 10 thousand globular clusters. These globular clusters orbit the galaxy out to large radii, 100 kiloparsecs or more. With a few notable exceptions, each globular cluster appears to have a definite age. That is, all the stars in the cluster formed at virtually the same time. It was the recognition of this fact, studying Hertzsprung-Russell diagrams of globulars, that led to the earliest understanding of stellar evolution. Some globular clusters (like Omega Centauri in our Milky Way, and G1 in M31) are truly massive clusters, with several million times the mass of our Sun. Such globular clusters may be the former nuclei of galaxies that once orbited their host galaxy, but were totally engulfed and tidally stripped of their stars save for the dense nucleus. However, most globular clusters are much smaller, having on the order of a few hundred thousand stars. Some globular clusters (like M15) have extremely massive cores which are expected to harbor black holes. In many galaxies (especially massive elliptical galaxies) there appear to be two populations of globular clusters, which appear to be of similar ages (nearly as old as the universe itself) but of different metal abundances. These subpopulations are generally known as "metal-poor" and "metal-rich", although the metallicities of the metal-rich clusters are generally less than that of the Sun. Many scenarios have been suggested to explain these subpopulations, including violent gas-rich galaxy mergers, the accretion of dwarf galaxies, and multiple phases of star formation in a single galaxy. In our Milky Way, the metal-poor clusters are associated with the halo and the metal-rich clusters with the Bulge. It was through the study of globular clusters that the Sun's position in the Milky Way galaxy became known. Until the 1930s, it was thought that the Sun was near the middle of the galaxy because the distribution of stars in the observable Milky Way appeared uniform. However, the distribution of globular clusters was strongly asymmetric. Assuming a roughly spherical distribution of globular clusters around the galaxy's center, one can estimate the direction from the Sun to the galactic center. By further estimating the distances to the clusters, the distance of the Sun to the galactic center can be estimated as well. It thus became clear that the part of the Milky Way seen from Earth was only a small part of the total galaxy, most of which was obscured by gas and dust. Globular clusters have a very high star density, and therefore close interactions and near-collisions of stars do sometimes occur. Some exotic classes of stars, such as blue stragglers, millisecond pulsars and low-mass X-ray binaries are much more common in globulars.

References

General resources

- [http://adswww.harvard.edu/ NASA Astrophysics Data System] has a collection of past articles, from all major astrophysics journals and many conference proceedings.
- [http://astro.u-strasbg.fr/scyon/ SCYON] is a newsletter dedicated to star clusters.
- [http://www.manybody.org/modest/ MODEST] is a loose collaboration of scientists working on star clusters.

Books

- Binney, James; Tremaine, Scott (1987). Galactic Dynamics, Princeton University Press, Princeton, New Jersey.
- Heggie, Douglas; Hut, Piet (2003). The Gravitational Million-Body Problem: A Multidisciplinary Approach to Star Cluster Dynamics, Cambridge University Press.
- Spitzer, Lyman (1987). Dynamical Evolution of Globular Clusters, Princeton University Press, Princeton, New Jersey.

Review Articles

- Elson, Rebecca; Hut, Piet; Inagaki, Shogo (1987). Dynamical evolution of globular clusters. Annual review of astronomy and astrophysics 25 565. [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1987ARA%26A..25..565E NASA ADS]
- Meylan, G.; Heggie, D. C. (1997). Internal dynamics of globular clusters. The Astronomy and Astrophysics Review 8 1. [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1997A%26ARv...8....1M NASA ADS]

External links

- [http://www.seds.org/messier/glob.html Globular Clusters], SEDS Messier pages
- [http://www.seds.org/~spider/spider/MWGC/mwgc.html Milky Way Globular Clusters]
- [http://physun.physics.mcmaster.ca/Globular.html Catalogue of Milky Way Globular Cluster Parameters] by William E. Harris, McMaster University, Ontario, Canada.
- [http://www.mporzio.astro.it/~marco/gc/ A galactic globular cluster database] by Marco Castellani, Rome Astronomical Observatory, Italy. Category:Star clusters Category:Globular clusters ja:球状星団

Spiral galaxy

A spiral galaxy is a type of galaxy in the Hubble sequence which is characterized by the following physical properties: Hubble sequence
- A considerable total angular momentum
- Composed of a central bulge surrounded by a disk
- The bulge resembles an elliptical galaxy, containing many old, so-called "Population II" stars, and usually a supermassive black hole at its center.
- The disk is a flat, rotating assembly consisting of interstellar matter, young "Population I" stars and open star clusters. Spiral galaxies are so named due to the bright arms of star formation within the disk that extend—roughly logarithmically—from the bulge. Though sometimes difficult to discern, such as in flocculent spirals, these arms distinguish spiral galaxies from their lenticular counterparts, which exhibit a disk structure but no evident spiral. The disks of spiral galaxies tend to be surrounded by large spheroid halos of Population II stars, many of which are concentrated in globular clusters that orbit the galactic center. Our galaxy, the Milky Way, has long been thought to be a spiral, with a Hubble sequence classification of Sbc (possibly SBb); recent research, however, suggests that it may in fact be a barred spiral.

Origin of the spiral structure

barred spiral simulating a spiral nebula (Birkeland's Fig. 262).]] Perhaps the first person to model a spiral nebula, was the Norwegian scientist and explorer Kristian Birkeland. Using his magnetised terrella to successfully model the aurora, he believed he was also able to simulate a spiral nebula. He wrote: :"Now we know that of the 120 000 nebulae scattered over the sky, at least half are of a spiral form. The most remarkable thing about them is that there are very often two spirals issuing symmetrically from two diametrically opposite parts of the nebula." :"We have previously seen how the continuous discharges round the magnetic cathode-globe in our experiments, could assume a shape that recalled Saturn's ring. These continuous discharges round the globe may, however, with higher gas-pressure in the almost exhausted vessel, take the form of two spirals, curved in the plane of the equator, issuing symmetrically from two diametrically opposite points on the globe." :"The accompanying figure (fig. 262) represents an experiment such as this with two such spirals. The photograph was obtained by accident, and I have seen still more interesting pictures appear, several of which I shall publish at some future time." The early pioneer of studies on the formation of the spiral arms was Bertil Lindblad. He realised that the idea of stars arranged permanently in a spiral shape was untenable due to the "winding dilemma". Since the speed of rotation of the galactic disk varies with distance from the centre of the galaxy, a radial arm (like a spoke) would quickly become curved as the galaxy rotates. The arm would, after a few galactic rotations, become increasingly curved and wind around the galaxy ever tighter. This is not what is observed. aurora The first acceptable theory was devised by C. C. Lin and Frank Shu in 1964. They suggested that the spiral arms were manifestations of spiral density waves. They assumed that the stars travel in slightly elliptical orbits and that the orientations of their orbits is correlated i.e. the ellipses vary in their orientation (one to another) in a smooth way with increasing distance from the galactic centre. This is illustrated in the diagram. It is clear that the elliptical orbits come close together in certain areas to give the effect of arms. Stars therefore do not remain forever in the position that we now see them in, but pass through the arms as they travel in their orbits. Alternative hypotheses that have been proposed involve waves of star formation moving about the galaxy; the bright stars produced by the star formation die out quickly, leaving darker regions behind the waves, and hence making the waves visible.

References

- Kristian Birkeland, "[http://www.catastrophism.com/texts/birkeland/ On Possible Electric Phenomena in Solar Systems and Nebulae]" (Section 2. Chapter VI), (1908) in The Norwegian Aurora Polaris Expedition 1902-1903

Examples

- Andromeda
- Triangulum
- Whirlpool

External links

- [http://www.seds.org/messier/spir.html Spiral Galaxies @ SEDS Messier pages]
- ja:渦巻銀河

Irregular galaxy

An irregular galaxy is a galaxy that does not fall into the Hubble classification for galaxies. These are galaxies that feature neither spiral nor elliptical morphology. They are often chaotic in appearance, with neither a nuclear bulge or any trace of spiral arm structure. Collectively they are thought to make up about a quarter of all galaxies. There are two major Hubble types of irregular galaxies:
- An Irr-I galaxy (Irr I) is an irregular galaxy that features some structure but not enough to place it cleanly into the Hubble sequence. de Vaucouleurs subtypes this into galaxies that have some spiral structure Sm, and those that do not Im.
- An Irr-II galaxy (Irr II) is an irregular galaxy that does not appear to feature any structure that can place it into the Hubble sequence. A third classification of irregular galaxies are the dwarf irregulars, labelled as dI or dIrrs. This type of galaxy is now thought to be important to understand the overall evolution of galaxies, as they tend to have a low level of metallicity and relatively high levels of gas, and are thought to be similar to the earliest galaxies that populated the Universe. They may represent a local (and therefore more recent) version of the faint blue galaxies known to exist in deep field galaxy surveys. Some irregular galaxy are small spiral galaxies that are being distorted by the gravity of a larger neighbour. The Magellanic Cloud galaxies were once classified as irregular galaxies, but have since been found to contain barred spiral structures, and have been since re-classified as "SBm", a fourth type of barred spiral galaxy.

Examples

- IC 1613
- Irregular Galaxy IC 10
- Leo A
- Messier 82 (The Cigar Galaxy)
- NGC 1569
- NGC 3109
- Pegasus Dwarf Irregular Galaxy
- Phoenix Dwarf
- Sculptor Dwarf Irregular Galaxy
- Sextans A
- Wolf-Lundmark-Melotte

Radiation pressure

Radiation pressure is the pressure exerted upon any surface exposed to electromagnetic radiation. If absorbed, the pressure is the energy flux density divided by the speed of light. If the radiation is totally reflected, the radiation pressure is doubled. For example, the radiation of the Sun at the Earth has an energy flux density of 1370 W/m², so the radiation pressure is 4.6 μPa (absorbed) (see also Climate model).

Discovery

The fact that electromagnetic radiation exerts a pressure upon any surface exposed to it was deduced theoretically by James Clerk Maxwell in 1871, and proven experimentally by Lebedev in 1900 and by Nichols and Hull in 1901. The pressure is very feeble, but can be detected by allowing the radiation to fall upon a delicately poised vane of reflective metal (Nichols radiometer).

Theory

It may be shown by electromagnetic theory, by quantum theory, or by thermodynamics, making no assumptions as to the nature of the radiation, that the pressure against a surface exposed in a space traversed by radiation uniformly in all directions is equal to 1/3 the total radiant energy per unit volume within that space. For black body radiation, in equilibrium with the exposed surface, the energy density is, in accordance with the Stefan-Boltzmann law, equal to σT⁴/3c; in which σ is the Stefan-Boltzmann constant, c is the speed of light, and T is the absolute temperature of the space. One third of this energy is equal to 6.305×10⁻¹⁷T⁴ J/m³K⁴, which is therefore equal to the pressure in pascals.

In interplanetary space

For example, at the boiling point of water (T = 373.15 K), the pressure only amounts to 3 micropascals (about 2 pounds force per square mile). If the radiation is directional (in interplanetary space, the overwhelming proportion of the energy flux comes from the Sun alone), the radiation pressure is tripled, to σT⁴/c; if the body is a perfect reflector, the pressure can be doubled again, to 2σT⁴/c. A solar sail at the distance where the equivalent radiation temperature is the boiling point of water could thus achieve about 22 µPa, or nearly 13 lbf/sq mi. Such feeble pressures are, nevertheless, able to produce marked effects upon minute particles like gas ions and electrons, and are important in the theory of electron emission from the Sun, of cometary material, and so on (see also: Yarkovsky effect, YORP effect).

In stellar interiors

In stellar interiors the temperatures are very high. Stellar models predict a temperature of 15 MK in the center of the Sun and at the cores of supergiant stars the temperature may exceed 1 GK. As the radiation pressure scales as the fourth power of the temperature, it becomes important at these high temperatures. In the Sun, radiation pressure is still quite small when compared to the gas pressure. In the heaviest stars, radiation pressure is the dominant pressure component.

Solar sails

Solar sails, a proposed method of spacecraft propulsion, would utilize radiation pressure from the Sun as a motive force. Private spacecraft Cosmos 1 was to have used this form of propulsion.

Radiation pressure in acoustics

In acoustics, radiation pressure is the unidirectional pressure force exerted at an interface between two media due to the passage of a sound wave.

References

- van Nostrand Scientific Encyclopedia (3rd edition) Category:Celestial mechanics

Chemical element

A chemical element, often called simply element, is a chemical substance that canot be divided or changed into other chemical substances by any ordinary chemical technique. The smallest unit of this kind of chemical substances is an atom. An element is a class of substances that contain the same number of protons in all its atoms.

Chemistry terminology

Earlier an element or pure element was defined as a substance which "cannot be further broken down into another compound with different chemical properties" -- which should be taken to mean it consists of atoms of one element. However, due to allotropy, the isotope effect, and the confusion with the more useful term referring to the general class of atoms (irrespective of what compound it may be in), this usage is in disfavor amongst contemporary chemists, and sees restricted, mostly historical, use. This definition was motivated by the observation that these elements could not be dissociated by chemical means into other compounds. For example, water could be converted into hydrogen and oxygen, but hydrogen and oxygen could not be further decomposed, thus "elemental". There are also many counterexamples (for example "elemental oxygen" (O₂) can be decomposed by solely chemical means into oxygen ions and atoms which have drastically different chemical properties). The remainder of this article will concern itself with the first definition.

Description

The atomic number of an element, Z, is equal to the number of protons which defines the element. For example, all carbon atoms contain 6 protons in their nucleus, so for carbon Z=6. These atoms may have different amounts of neutrons, and are known as isotopes of the element. The atomic ma

Open cluster

Historical observations

Formation

Morphology and classification

Numbers and distribution

Stellar composition

Eventual fate

Studying stellar evolution

Open clusters and the astronomical distance scale

References

Further reading

External links

Star

Star formation and evolution

Appearance and distribution of stars

Age and size of stars

Star classification

Naming of stars

Energy production

Nuclear fusion reaction pathways

Star mythology

References

See also

Related lists

External links

Giant Molecular Cloud

Astrophysics of dark nebulae

See also

Gravity

Newton's law of universal gravitation

Vector form

Gravitational field

Problems with Newton's theory

Theoretical concerns

Disagreement with observation

Newton's reservations

Einstein's theory of gravitation

Units of measurement and variations in gravity

Comparison with electromagnetic force

Gravity and quantum mechanics

Experimental tests of theories

Recent Alternative theories

Historical Alternative theories

Self-gravitating system

Special applications of gravity

Comparative gravities of different planets and Earth's moon

Mathematical equations for a falling body

Gravitational potential

Acceleration relative to the rotating Earth

History of gravitational theory

Notes

See also

References

External links

Globular clusters

General information

See also

References

General resources

Books

Review Articles

External links

Spiral galaxy

Origin of the spiral structure

References

Examples

See also

External links

Irregular galaxy

Examples

See also

Radiation pressure

Discovery

Theory

In interplanetary space

In stellar interiors

Solar sails

Radiation pressure in acoustics

References

Chemical element