Einstein field equations
First published by Einstein in 1915 as a tensor equation, the EFE equate local spacetime curvature with the local energy and momentum within that spacetime. The relationship between the metric tensor and the Einstein tensor allows the EFE to be written as a set of partial differential equations when used in this way. The solutions of the EFE are the components of the metric tensor, the inertial trajectories of particles and radiation in the resulting geometry are calculated using the geodesic equation. As well as obeying local energy–momentum conservation, the EFE reduce to Newtons law of gravitation where the field is weak. Exact solutions for the EFE can only be found under simplifying assumptions such as symmetry, special classes of exact solutions are most often studied as they model many gravitational phenomena, such as rotating black holes and the expanding universe. Further simplification is achieved in approximating the actual spacetime as flat spacetime with a small deviation and these equations are used to study phenomena such as gravitational waves.
The EFE is an equation relating a set of symmetric 4 ×4 tensors. Each tensor has 10 independent components, although the Einstein field equations were initially formulated in the context of a four-dimensional theory, some theorists have explored their consequences in n dimensions. The equations in contexts outside of general relativity are still referred to as the Einstein field equations, the vacuum field equations define Einstein manifolds. Despite the simple appearance of the equations they are quite complicated. In fact, when written out, the EFE are a system of 10 coupled, nonlinear. The EFE can be written as G μ ν + Λ g μ ν =8 π G c 4 T μ ν. Using geometrized units where G = c =1, this can be rewritten as G μ ν + Λ g μ ν =8 π T μ ν. The expression on the left represents the curvature of spacetime as determined by the metric, the EFE can be interpreted as a set of equations dictating how matter/energy determines the curvature of spacetime. These equations, together with the equation, which dictates how freely-falling matter moves through space-time.
The above form of the EFE is the established by Misner, Thorne. The sign of the term would change in both these versions, if the metric sign convention is used rather than the MTW metric sign convention adopted here. Taking the trace with respect to the metric of both sides of the EFE one gets R − D2 R + D Λ =8 π G c 4 T where D is the spacetime dimension
Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure is the relative to the ambient pressure. Various units are used to express pressure, Pressure may be expressed in terms of standard atmospheric pressure, the atmosphere is equal to this pressure and the torr is defined as 1⁄760 of this. Manometric units such as the centimetre of water, millimetre of mercury, Pressure is the amount of force acting per unit area. The symbol for it is p or P, the IUPAC recommendation for pressure is a lower-case p. However, upper-case P is widely used. The usage of P vs p depends upon the field in one is working, on the nearby presence of other symbols for quantities such as power and momentum. Mathematically, p = F A where, p is the pressure, F is the normal force and it relates the vector surface element with the normal force acting on it. It is incorrect to say the pressure is directed in such or such direction, the pressure, as a scalar, has no direction.
The force given by the relationship to the quantity has a direction. If we change the orientation of the element, the direction of the normal force changes accordingly. Pressure is distributed to solid boundaries or across arbitrary sections of normal to these boundaries or sections at every point. It is a parameter in thermodynamics, and it is conjugate to volume. The SI unit for pressure is the pascal, equal to one newton per square metre and this name for the unit was added in 1971, before that, pressure in SI was expressed simply in newtons per square metre. Other units of pressure, such as pounds per square inch, the CGS unit of pressure is the barye, equal to 1 dyn·cm−2 or 0.1 Pa. Pressure is sometimes expressed in grams-force or kilograms-force per square centimetre, but using the names kilogram, kilogram-force, or gram-force as units of force is expressly forbidden in SI. The technical atmosphere is 1 kgf/cm2, since a system under pressure has potential to perform work on its surroundings, pressure is a measure of potential energy stored per unit volume.
It is therefore related to density and may be expressed in units such as joules per cubic metre. Similar pressures are given in kilopascals in most other fields, where the prefix is rarely used
Pallas, minor-planet designation 2 Pallas, is the second asteroid to have been discovered, and is one of the largest asteroids in the Solar System. With an estimated 7% of the mass of the belt, it is the third-most-massive asteroid. It is 512 kilometers in diameter, somewhat smaller than Vesta and it is likely a remnant protoplanet. When Pallas was discovered by the German astronomer Heinrich Wilhelm Matthäus Olbers on 28 March 1802, it was counted as a planet, the discovery of many more asteroids after 1845 eventually led to their reclassification. Pallass surface is most likely composed of a material, its spectrum. It was formerly considered a dwarf planet for its size. In 1801, the astronomer Giuseppe Piazzi discovered an object which he believed to be a comet. Shortly thereafter he announced his observations of this object, noting that the slow, uniform motion was uncharacteristic of a comet, suggesting it was a different type of object. This was lost from sight for months, but was recovered that year by the Baron von Zach and Heinrich W. M.
Olbers after a preliminary orbit was computed by Carl Friedrich Gauss. This object came to be named Ceres, and was the first asteroid to be discovered, a few months later, Olbers was again attempting to locate Ceres when he noticed another moving object in the vicinity. This was the asteroid Pallas, coincidentally passing near Ceres at the time, the discovery of this object created interest in the astronomy community. Before this point it had been speculated by astronomers that there should be a planet in the gap between Mars and Jupiter, unexpectedly, a second such body had been found. When Pallas was discovered, some estimates of its size were as high as 3,380 km in diameter, even as recently as 1979, Pallas was estimated to be 673 km in diameter, 26% greater than the currently accepted value. The orbit of Pallas was determined by Gauss, who found the period of 4.6 years was similar to the period for Ceres, Pallas has a relatively high orbital inclination to the plane of the ecliptic. In 1917, the Japanese astronomer Kiyotsugu Hirayama began to study asteroid motions, by plotting the mean orbital motion and eccentricity of a set of asteroids, he discovered several distinct groupings.
In a paper he reported a group of three associated with Pallas, which became named the Pallas family, after the largest member of the group. Since 1994 more than 10 members of family have been identified. The validity of this grouping was confirmed in 2002 by a comparison of their spectra and these resulted in the first accurate measurements of its diameter
X-radiation is a form of electromagnetic radiation. Most X-rays have a wavelength ranging from 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz, X-ray wavelengths are shorter than those of UV rays and typically longer than those of gamma rays. Spelling of X-ray in the English language includes the variants x-ray, xray, X-rays with high photon energies are called hard X-rays, while those with lower energy are called soft X-rays. Due to their ability, hard X-rays are widely used to image the inside of objects, e. g. in medical radiography. The term X-ray is metonymically used to refer to an image produced using this method. Since the wavelengths of hard X-rays are similar to the size of atoms they are useful for determining crystal structures by X-ray crystallography. By contrast, soft X-rays are easily absorbed in air, the length of 600 eV X-rays in water is less than 1 micrometer. There is no consensus for a definition distinguishing between X-rays and gamma rays, one common practice is to distinguish between the two types of radiation based on their source, X-rays are emitted by electrons, while gamma rays are emitted by the atomic nucleus.
This definition has problems, other processes can generate these high-energy photons. One common alternative is to distinguish X- and gamma radiation on the basis of wavelength, with radiation shorter than some arbitrary wavelength, such as 10−11 m and this criterion assigns a photon to an unambiguous category, but is only possible if wavelength is known. Occasionally, one term or the other is used in specific contexts due to precedent, based on measurement technique. Thus, gamma-rays generated for medical and industrial uses, for radiotherapy, in the ranges of 6–20 MeV. X-ray photons carry enough energy to ionize atoms and disrupt molecular bonds and this makes it a type of ionizing radiation, and therefore harmful to living tissue. A very high radiation dose over a period of time causes radiation sickness. In medical imaging this increased risk is generally greatly outweighed by the benefits of the examination. The ionizing capability of X-rays can be utilized in treatment to kill malignant cells using radiation therapy.
It is used for material characterization using X-ray spectroscopy, hard X-rays can traverse relatively thick objects without being much absorbed or scattered. For this reason, X-rays are widely used to image the inside of visually opaque objects, the most often seen applications are in medical radiography and airport security scanners, but similar techniques are important in industry and research
An oval is a closed curve in a plane which loosely resembles the outline of an egg. The term is not very specific, but in areas it is given a more precise definition. In common English, the term is used in a broader sense, the three-dimensional version of an oval is called an ovoid. The term oval when used to describe curves in geometry is not well-defined, many distinct curves are commonly called ovals or are said to have an oval shape. Generally, to be called an oval, a plane curve should resemble the outline of an egg or an ellipse, the adjectives ovoidal and ovate mean having the characteristic of being an ovoid, and are often used as synonyms for egg-shaped. In the theory of planes, an oval is a set of n +1 points in a projective plane of order n. An ovoid in the projective geometry PG is a set of q2 +1 points such that no three points are collinear. At each point of an all the tangent lines to the ovoid lie in a single plane. The shape of an egg is approximated by long half of a spheroid, joined to a short half of a roughly spherical ellipsoid.
These are joined at the equator and sharing a principal axis of rotational symmetry, although the term egg-shaped usually implies a lack of reflection symmetry across the equatorial plane, it may refer to true prolate ellipsoids. It can be used to describe the 2-dimensional figure that, if revolved around its major axis, in technical drawing, an oval is a figure constructed from two pairs of arcs, with two different radii. The arcs are joined at a point in which lines tangential to both joining arcs lie on the line, thus making the joint smooth. Any point of an oval belongs to an arc with a constant radius, but in an ellipse, in common speech, oval means a shape rather like an egg or an ellipse, which may be two-dimensional or three-dimensional. It often refers to a figure that resembles two semicircles joined by a rectangle, like a cricket infield, speed skating rink or an athletics track, this is more correctly called a stadium or archaically, an oblong. Sometimes, it can refer to any rectangle with rounded corners.
The shape lends its name to many well-known places, ellipse Stadium Vesica piscis – a pointed oval
Due to the types of investigations involved, it is closely linked with Earth-based geology. The structures of the giant planets and their moons are examined, as is the make-up of the bodies of the Solar System, such as asteroids, the Kuiper Belt. He made important contributions to the field and the study of impact craters, asteroids, today many institutions are concerned with the study and communication of planetary sciences and planetary geology. The Visitor Center at Barringer Meteor Crater near Winslow, Arizona includes a Museum of planetary geology, the Geological Society of Americas Planetary Geology Division has been growing and thriving since May 1981 and has two mottos, One planet just isnt enough. And “The GSA Division with the biggest field area, Planetary geology uses a wide variety of standardised descriptor names for features. All planetary feature names recognised by the International Astronomical Union combine one of names with a possibly unique identifying name. The conventions which decide the more precise name are dependent on which planetary body the feature is on and this means that in some cases names may change as new imagery becomes available, or in other cases widely adopted informal names changed in line with the rules.
The standard names are chosen to consciously avoid interpreting the underlying cause of the feature, J. F. Bell III, B. A. Campbell, M. S. Robinson. Remote Sensing for the Earth Sciences, Manual of Remote Sensing, archived from the original on 2006-08-13
Iapetus is best known for its dramatic two-tone coloration. Discoveries by the Cassini mission in 2007 revealed several other unusual features, Iapetus was discovered by Giovanni Domenico Cassini, an Italian astronomer, in October 1671. He had discovered it on the side of Saturn and tried viewing it on the eastern side some months later. This was the case the year, when he was again able to observe it on the western side. Cassini finally observed Iapetus on the side in 1705 with the help of an improved telescope. Cassini correctly surmised that Iapetus has a bright hemisphere and a dark hemisphere, and this means that the bright hemisphere is visible from Earth when Iapetus is on the western side of Saturn, and that the dark hemisphere is visible when Iapetus is on the eastern side. The dark hemisphere was named Cassini Regio in his honour, Iapetus is named after the Titan Iapetus from Greek mythology. When first discovered, Iapetus was among four Saturnian moons labelled the Sidera Lodoicea by their discoverer Giovanni Cassini after King Louis XIV, astronomers fell into the habit of referring to them using Roman numerals, with Iapetus being Saturn V.
Once Mimas and Enceladus were discovered in 1789, the scheme was extended. And with the discovery of Hyperion in 1848, Iapetus became Saturn VIII, geological features on Iapetus are named after characters and places from the French epic poem The Song of Roland. Examples of names used include the craters Charlemagne and Baligant, the one exception is Cassini Regio, the dark region of Iapetus, named after the regions discoverer, Giovanni Cassini. The orbit of Iapetus is somewhat unusual, although it is Saturns third-largest moon, it orbits much farther from Saturn than the next closest major moon, Titan. It has the most inclined orbital plane of the regular satellites, the cause of this is unknown. From Iapetus, Saturn would appear to be 1°56 in diameter, the low density of Iapetus indicates that it is mostly composed of ice, with only a small amount of rocky materials. These features often lead it to be characterized as walnut-shaped, Iapetus is heavily cratered, and Cassini images have revealed large impact basins, at least five of which are over 350 km wide.
The largest, has a diameter of 580 km, its rim is extremely steep, Iapetus is known to support long-runout landslides or sturzstroms, possibly supported by ice sliding. In the 17th century, Giovanni Cassini observed that he could see Iapetus only on the west side of Saturn and he correctly deduced that Iapetus is locked in synchronous rotation about Saturn and that one side of Iapetus is darker than the other, conclusions confirmed by larger telescopes. The difference in colouring between the two Iapetian hemispheres is striking, the leading hemisphere and sides are dark with a slight reddish-brown coloring, while most of the trailing hemisphere and poles are bright
Atmosphere of Earth
The atmosphere of Earth is the layer of gases, commonly known as air, that surrounds the planet Earth and is retained by Earths gravity. The atmosphere of Earth protects life on Earth by absorbing solar radiation, warming the surface through heat retention. By volume, dry air contains 78. 09% nitrogen,20. 95% oxygen,0. 93% argon,0. 04% carbon dioxide, and small amounts of other gases. Air contains an amount of water vapor, on average around 1% at sea level. The atmosphere has a mass of about 5. 15×1018 kg, the atmosphere becomes thinner and thinner with increasing altitude, with no definite boundary between the atmosphere and outer space. The Kármán line, at 100 km, or 1. 57% of Earths radius, is used as the border between the atmosphere and outer space. Atmospheric effects become noticeable during atmospheric reentry of spacecraft at an altitude of around 120 km, several layers can be distinguished in the atmosphere, based on characteristics such as temperature and composition. The study of Earths atmosphere and its processes is called atmospheric science, early pioneers in the field include Léon Teisserenc de Bort and Richard Assmann.
The three major constituents of air, and therefore of Earths atmosphere, are nitrogen, water vapor accounts for roughly 0. 25% of the atmosphere by mass. The remaining gases are often referred to as gases, among which are the greenhouse gases, principally carbon dioxide, nitrous oxide. Filtered air includes trace amounts of other chemical compounds. Various industrial pollutants may be present as gases or aerosols, such as chlorine, fluorine compounds, sulfur compounds such as hydrogen sulfide and sulfur dioxide may be derived from natural sources or from industrial air pollution. In general, air pressure and density decrease with altitude in the atmosphere, temperature has a more complicated profile with altitude, and may remain relatively constant or even increase with altitude in some regions. In this way, Earths atmosphere can be divided into five main layers, excluding the exosphere, Earth has four primary layers, which are the troposphere, stratosphere and thermosphere. It extends from the exobase, which is located at the top of the thermosphere at an altitude of about 700 km above sea level, to about 10,000 km where it merges into the solar wind.
This layer is composed of extremely low densities of hydrogen and several heavier molecules including nitrogen, oxygen. The atoms and molecules are so far apart that they can travel hundreds of kilometers without colliding with one another, the exosphere no longer behaves like a gas, and the particles constantly escape into space. These free-moving particles follow ballistic trajectories and may migrate in and out of the magnetosphere or the solar wind, the exosphere is located too far above Earth for any meteorological phenomena to be possible
This page is about the measurement using water as a reference. For a general use of gravity, see relative density. See intensive property for the property implied by specific, Apparent specific gravity is the ratio of the weight of a volume of the substance to the weight of an equal volume of the reference substance. The reference substance is always water at its densest for liquids. Nonetheless, the temperature and pressure must be specified for both the sample and the reference, pressure is nearly always 1 atm. Temperatures for both sample and reference vary from industry to industry, in British beer brewing, the practice for specific gravity as specified above is to multiply it by 1000. Being a ratio of densities, specific gravity is a dimensionless quantity, Specific gravity varies with temperature and pressure and sample must be compared at the same temperature and pressure or be corrected to a standard reference temperature and pressure. Substances with a gravity of 1 are neutrally buoyant in water.
Those with SG greater than 1 are denser than water and will, disregarding surface tension effects and those with an SG less than 1 are less dense than water and will float on it. In scientific work, the relationship of mass to volume is expressed directly in terms of the density of the substance under study. It is in industry where specific gravity finds wide application, often for historical reasons. True specific gravity can be expressed mathematically as, S G true = ρ sample ρ H2 O where ρ sample is the density of the sample, the density of water varies with temperature and pressure as does the density of the sample. So it is necessary to specify the temperatures and pressures at which the densities or weights were determined and it is nearly always the case that measurements are made at 1 nominal atmosphere. For true specific gravity calculations, air pressure must be considered, temperatures are specified by the notation with T s representing the temperature at which the samples density was determined and T r the temperature at which the reference density is specified.
For example, SG would be understood to mean that the density of the sample was determined at 20°C and of the water at 4°C. Taking into account different sample and reference temperatures, we note that, while S G H2 O =1.000000, it is the case that S G H2 O =0.998203 /0.999840 =0.998363. Here, temperature is being specified using the current ITS-90 scale, on the previous IPTS-68 scale, the densities at 20 °C and 4 °C are 0.9982071 and 0.9999720 respectively, resulting in an SG value for water of 0.9982343. For example, in the industry, the Plato table lists sucrose concentration by weight against true SG
Vesta, minor-planet designation 4 Vesta, is one of the largest objects in the asteroid belt, with a mean diameter of 525 kilometres. It was discovered by the German astronomer Heinrich Wilhelm Olbers on 29 March 1807 and is named after Vesta, Vesta is the second-most-massive and second-largest body in the asteroid belt after the dwarf planet Ceres, and it contributes an estimated 9% of the mass of the asteroid belt. It is slightly larger than Pallas, though more massive. Vesta is the last remaining rocky protoplanet of the kind that formed the terrestrial planets, numerous fragments of Vesta were ejected by collisions one and two billion years ago that left two enormous craters occupying much of Vestas southern hemisphere. Debris from these events has fallen to Earth as howardite–eucrite–diogenite meteorites, Vesta is the brightest asteroid visible from Earth. Its maximum distance from the Sun is slightly greater than the distance of Ceres from the Sun. NASAs Dawn spacecraft entered orbit around Vesta on 16 July 2011 for an exploration and left orbit on 5 September 2012 en route to its final destination.
Researchers continue to examine data collected by Dawn for additional insights into the formation, Heinrich Olbers discovered Pallas in 1802, the year after the discovery of Ceres. He proposed that the two objects were the remnants of a destroyed planet and these orbital intersections were located in the constellations of Cetus and Virgo. Olbers commenced his search in 1802, and on 29 March 1807 he discovered Vesta in the constellation Virgo—a coincidence, because Ceres and Vesta are not fragments of a larger body. Because the asteroid Juno had been discovered in 1804, this made Vesta the fourth object to be identified in the region that is now known as the asteroid belt, the discovery was announced in a letter addressed to German astronomer Johann H. Schröter dated 31 March. Gauss decided on the Roman virgin goddess of home and hearth, Vesta was the fourth asteroid to be discovered, hence the number 4 in its formal designation. The name Vesta, or national variants thereof, is in use with two exceptions and China.
In Greek, the name adopted was the Hellenic equivalent of Vesta, Hestia, in English, in Chinese, Vesta is called the hearth-god star, 灶神星 zàoshénxīng, in contrast to the goddess Vesta, who goes by her Latin name. Upon its discovery, Vesta was, like Ceres, the symbol representing the altar of Vesta with its sacred fire and was designed by Gauss. In Gausss conception, this was drawn, in its modern form, after the discovery of Vesta, no further objects were discovered for 38 years, and the Solar System was thought to have eleven planets. However, in 1845, new asteroids started being discovered at a rapid pace and it soon became clear that it would be impractical to continue inventing new planetary symbols indefinitely, and some of the existing ones proved difficult to draw quickly. That year, the problem was addressed by Benjamin Apthorp Gould, who suggested numbering asteroids in their order of discovery, the fourth asteroid, acquired the generic symbol ④
In science and engineering, the weight of an object is usually taken to be the force on the object due to gravity. Weight is a vector whose magnitude, often denoted by an italic letter W, is the product of the m of the object. The unit of measurement for weight is that of force, which in the International System of Units is the newton. For example, an object with a mass of one kilogram has a weight of about 9.8 newtons on the surface of the Earth, in this sense of weight, a body can be weightless only if it is far away from any other mass. Although weight and mass are scientifically distinct quantities, the terms are often confused with other in everyday use. There is a tradition within Newtonian physics and engineering which sees weight as that which is measured when one uses scales. There the weight is a measure of the magnitude of the force exerted on a body. Typically, in measuring an objects weight, the object is placed on scales at rest with respect to the earth, thus, in a state of free fall, the weight would be zero.
In this second sense of weight, terrestrial objects can be weightless, ignoring air resistance, the famous apple falling from the tree, on its way to meet the ground near Isaac Newton, is weightless. Further complications in elucidating the various concepts of weight have to do with the theory of relativity according to gravity is modelled as a consequence of the curvature of spacetime. In the teaching community, a debate has existed for over half a century on how to define weight for their students. The current situation is that a set of concepts co-exist. Discussion of the concepts of heaviness and lightness date back to the ancient Greek philosophers and these were typically viewed as inherent properties of objects. Plato described weight as the tendency of objects to seek their kin. To Aristotle weight and levity represented the tendency to restore the order of the basic elements, earth, fire. He ascribed absolute weight to earth and absolute levity to fire, archimedes saw weight as a quality opposed to buoyancy, with the conflict between the two determining if an object sinks or floats.
The first operational definition of weight was given by Euclid, who defined weight as, weight is the heaviness or lightness of one thing, compared to another, operational balances had, been around much longer. According to Aristotle, weight was the cause of the falling motion of an object
In physics, redshift happens when light or other electromagnetic radiation from an object is increased in wavelength, or shifted to the red end of the spectrum. Some redshifts are an example of the Doppler effect, familiar in the change of apparent pitches of sirens, a redshift occurs whenever a light source moves away from an observer. Finally, gravitational redshift is an effect observed in electromagnetic radiation moving out of gravitational fields. However, redshift is a common term and sometimes blueshift is referred to as negative redshift. Knowledge of redshifts and blueshifts has been applied to develop several terrestrial technologies such as Doppler radar and radar guns, Redshifts are seen in the spectroscopic observations of astronomical objects. Its value is represented by the letter z, a special relativistic redshift formula can be used to calculate the redshift of a nearby object when spacetime is flat. However, in contexts, such as black holes and Big Bang cosmology. Special relativistic and cosmological redshifts can be understood under the umbrella of frame transformation laws, the history of the subject began with the development in the 19th century of wave mechanics and the exploration of phenomena associated with the Doppler effect.
The effect is named after Christian Doppler, who offered the first known physical explanation for the phenomenon in 1842, the hypothesis was tested and confirmed for sound waves by the Dutch scientist Christophorus Buys Ballot in 1845. Doppler correctly predicted that the phenomenon should apply to all waves, before this was verified, however, it was found that stellar colors were primarily due to a stars temperature, not motion. Only was Doppler vindicated by verified redshift observations, the first Doppler redshift was described by French physicist Hippolyte Fizeau in 1848, who pointed to the shift in spectral lines seen in stars as being due to the Doppler effect. The effect is called the Doppler–Fizeau effect. In 1868, British astronomer William Huggins was the first to determine the velocity of a moving away from the Earth by this method. In 1871, optical redshift was confirmed when the phenomenon was observed in Fraunhofer lines using solar rotation, about 0.1 Å in the red. In 1887, Vogel and Scheiner discovered the annual Doppler effect, in 1901, Aristarkh Belopolsky verified optical redshift in the laboratory using a system of rotating mirrors.
The word does not appear unhyphenated until about 1934 by Willem de Sitter, perhaps indicating that up to point its German equivalent. Beginning with observations in 1912, Vesto Slipher discovered that most spiral galaxies, Slipher first reports on his measurement in the inaugural volume of the Lowell Observatory Bulletin. Three years later, he wrote a review in the journal Popular Astronomy, Slipher reported the velocities for 15 spiral nebulae spread across the entire celestial sphere, all but three having observable positive velocities