1.
Jupiter
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Jupiter is the fifth planet from the Sun and the largest in the Solar System. It is a giant planet with a mass one-thousandth that of the Sun, Jupiter and Saturn are gas giants, the other two giant planets, Uranus and Neptune are ice giants. Jupiter has been known to astronomers since antiquity, the Romans named it after their god Jupiter. Jupiter is primarily composed of hydrogen with a quarter of its mass being helium and it may also have a rocky core of heavier elements, but like the other giant planets, Jupiter lacks a well-defined solid surface. Because of its rotation, the planets shape is that of an oblate spheroid. The outer atmosphere is visibly segregated into several bands at different latitudes, resulting in turbulence, a prominent result is the Great Red Spot, a giant storm that is known to have existed since at least the 17th century when it was first seen by telescope. Surrounding Jupiter is a faint planetary ring system and a powerful magnetosphere, Jupiter has at least 67 moons, including the four large Galilean moons discovered by Galileo Galilei in 1610. Ganymede, the largest of these, has a greater than that of the planet Mercury. Jupiter has been explored on several occasions by robotic spacecraft, most notably during the early Pioneer and Voyager flyby missions and later by the Galileo orbiter. In late February 2007, Jupiter was visited by the New Horizons probe, the latest probe to visit the planet is Juno, which entered into orbit around Jupiter on July 4,2016. Future targets for exploration in the Jupiter system include the probable ice-covered liquid ocean of its moon Europa, Earth and its neighbor planets may have formed from fragments of planets after collisions with Jupiter destroyed those super-Earths near the Sun. Astronomers have discovered nearly 500 planetary systems with multiple planets, Jupiter moving out of the inner Solar System would have allowed the formation of inner planets, including Earth. Jupiter is composed primarily of gaseous and liquid matter and it is the largest of the four giant planets in the Solar System and hence its largest planet. It has a diameter of 142,984 km at its equator, the average density of Jupiter,1.326 g/cm3, is the second highest of the giant planets, but lower than those of the four terrestrial planets. Jupiters upper atmosphere is about 88–92% hydrogen and 8–12% helium by percent volume of gas molecules, a helium atom has about four times as much mass as a hydrogen atom, so the composition changes when described as the proportion of mass contributed by different atoms. Thus, Jupiters atmosphere is approximately 75% hydrogen and 24% helium by mass, the atmosphere contains trace amounts of methane, water vapor, ammonia, and silicon-based compounds. There are also traces of carbon, ethane, hydrogen sulfide, neon, oxygen, phosphine, the outermost layer of the atmosphere contains crystals of frozen ammonia. The interior contains denser materials - by mass it is roughly 71% hydrogen, 24% helium, through infrared and ultraviolet measurements, trace amounts of benzene and other hydrocarbons have also been found
2.
Star
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A star is a luminous sphere of plasma held together by its own gravity. The nearest star to Earth is the Sun, many other stars are visible to the naked eye from Earth during the night, appearing as a multitude of fixed luminous points in the sky due to their immense distance from Earth. Historically, the most prominent stars were grouped into constellations and asterisms, astronomers have assembled star catalogues that identify the known stars and provide standardized stellar designations. However, most of the stars in the Universe, including all stars outside our galaxy, indeed, most are invisible from Earth even through the most powerful telescopes. Almost all naturally occurring elements heavier than helium are created by stellar nucleosynthesis during the stars lifetime, near the end of its life, a star can also contain degenerate matter. Astronomers can determine the mass, age, metallicity, and many properties of a star by observing its motion through space, its luminosity. The total mass of a star is the factor that determines its evolution. Other characteristics of a star, including diameter and temperature, change over its life, while the environment affects its rotation. A plot of the temperature of stars against their luminosities produces a plot known as a Hertzsprung–Russell diagram. Plotting a particular star on that allows the age and evolutionary state of that star to be determined. A stars life begins with the collapse of a gaseous nebula of material composed primarily of hydrogen, along with helium. When the stellar core is sufficiently dense, hydrogen becomes steadily converted into helium through nuclear fusion, the remainder of the stars interior carries energy away from the core through a combination of radiative and convective heat transfer processes. The stars internal pressure prevents it from collapsing further under its own gravity, a star with mass greater than 0.4 times the Suns will expand to become a red giant when the hydrogen fuel in its core is exhausted. In some cases, it will fuse heavier elements at the core or in shells around the core, as the star expands it throws a part of its mass, enriched with those heavier elements, into the interstellar environment, to be recycled later as new stars. Meanwhile, the core becomes a remnant, a white dwarf. Binary and multi-star systems consist of two or more stars that are bound and generally move around each other in stable orbits. When two such stars have a close orbit, their gravitational interaction can have a significant impact on their evolution. Stars can form part of a much larger gravitationally bound structure, historically, stars have been important to civilizations throughout the world
3.
Supermassive black hole
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In the case of the Milky Way, the SMBH corresponds with the location of Sagittarius A*. Supermassive black holes have properties that distinguish them from lower-mass classifications, first, the average density of a supermassive black hole can be less than the density of water in the case of some supermassive black holes. This is because the Schwarzschild radius is proportional to mass. In addition, the forces in the vicinity of the event horizon are significantly weaker for massive black holes. Unlike with stellar mass black holes, one would not experience significant tidal force until very deep into the black hole, donald Lynden-Bell and Martin Rees hypothesized in 1971 that the center of the Milky Way galaxy would contain a supermassive black hole. Sagittarius A* was discovered and named on February 13 and 15,1974, by astronomers Bruce Balick and they discovered a radio source that emits synchrotron radiation, it was found to be dense and immobile because of its gravitation. This was, therefore, the first indication that a black hole exists in the center of the Milky Way. The origin of black holes remains an open field of research. Astrophysicists agree that once a black hole is in place in the center of a galaxy, it can grow by accretion of matter, there are, however, several hypotheses for the formation mechanisms and initial masses of the progenitors, or seeds, of supermassive black holes. The most obvious hypothesis is that the seeds are black holes of tens or perhaps hundreds of masses that are left behind by the explosions of massive stars. Yet another model involves a dense stellar cluster undergoing core-collapse as the heat capacity of the system drives the velocity dispersion in the core to relativistic speeds. Finally, primordial black holes may have been produced directly from external pressure in the first moments after the Big Bang, formation of black holes from the deaths of the first stars has been extensively studied and corroborated by observations. The other models for black hole formation listed above are theoretical, the difficulty in forming a supermassive black hole resides in the need for enough matter to be in a small enough volume. This matter needs to have very little angular momentum in order for this to happen, normally, the process of accretion involves transporting a large initial endowment of angular momentum outwards, and this appears to be the limiting factor in black hole growth. This is a component of the theory of accretion disks. Gas accretion is the most efficient and also the most conspicuous way in black holes grow. The majority of the growth of supermassive black holes is thought to occur through episodes of rapid gas accretion. Observations reveal that quasars were more frequent when the Universe was younger, indicating that supermassive black holes formed
4.
Fictitious force
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The force F does not arise from any physical interaction between two objects, but rather from the acceleration a of the non-inertial reference frame itself. As stated by Iro, Such an additional force due to relative motion of two reference frames is called a pseudo-force. Assuming Newtons second law in the form F = ma, fictitious forces are proportional to the mass m. A fictitious force on an object arises when the frame of reference used to describe the motion is accelerating compared to a non-accelerating frame. As a frame can accelerate in any way, so can fictitious forces be as arbitrary. Gravitational force would also be a force based upon a field model in which particles distort spacetime due to their mass. The role of forces in Newtonian mechanics is described by Tonnelat. To solve classical mechanics problems exactly in an Earth-bound reference frame, the Euler force is typically ignored because the variations in the angular velocity of the rotating Earth surface are usually insignificant. Both of the fictitious forces are weak compared to most typical forces in everyday life. For example, Léon Foucault was able to show that the Coriolis force results from the Earths rotation using the Foucault pendulum. If the Earth were to rotate a thousand times faster, people could easily get the impression that such forces are pulling on them. Other accelerations also give rise to forces, as described mathematically below. An example of the detection of a non-inertial, rotating reference frame is the precession of a Foucault pendulum, in the non-inertial frame of the Earth, the fictitious Coriolis force is necessary to explain observations. In an inertial frame outside the Earth, no such force is necessary. Figure 1 shows an accelerating car, when a car accelerates, a passenger feels like theyre being pushed back into the seat. In an inertial frame of reference attached to the road, there is no physical force moving the rider backward, however, in the riders non-inertial reference frame attached to the accelerating car, there is a backward fictitious force. We mention two possible reasons for the force to clarify its existence, Figure 1, to an observer at rest on an inertial reference frame, the car will seem to accelerate. In order for the passenger to stay inside the car, a force must be exerted on the passenger
5.
Gradient
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In mathematics, the gradient is a multi-variable generalization of the derivative. While a derivative can be defined on functions of a variable, for functions of several variables. The gradient is a function, as opposed to a derivative. If f is a differentiable, real-valued function of several variables, like the derivative, the gradient represents the slope of the tangent of the graph of the function. More precisely, the gradient points in the direction of the greatest rate of increase of the function, the components of the gradient in coordinates are the coefficients of the variables in the equation of the tangent space to the graph. The Jacobian is the generalization of the gradient for vector-valued functions of several variables, a further generalization for a function between Banach spaces is the Fréchet derivative. Consider a room in which the temperature is given by a field, T. At each point in the room, the gradient of T at that point will show the direction in which the temperature rises most quickly, the magnitude of the gradient will determine how fast the temperature rises in that direction. Consider a surface whose height above sea level at point is H, the gradient of H at a point is a vector pointing in the direction of the steepest slope or grade at that point. The steepness of the slope at point is given by the magnitude of the gradient vector. The gradient can also be used to measure how a scalar field changes in other directions, rather than just the direction of greatest change, suppose that the steepest slope on a hill is 40%. If a road goes directly up the hill, then the steepest slope on the road will also be 40%, if, instead, the road goes around the hill at an angle, then it will have a shallower slope. This observation can be stated as follows. If the hill height function H is differentiable, then the gradient of H dotted with a unit vector gives the slope of the hill in the direction of the vector. More precisely, when H is differentiable, the dot product of the gradient of H with a unit vector is equal to the directional derivative of H in the direction of that unit vector. The gradient of a function f is denoted ∇f or ∇→f where ∇ denotes the vector differential operator. The notation grad f is commonly used for the gradient. The gradient of f is defined as the vector field whose dot product with any vector v at each point x is the directional derivative of f along v. That is
6.
Tide
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Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon and the Sun and the rotation of the Earth. Some shorelines experience a semi-diurnal tide—two nearly equal high and low tides each day, other locations experience a diurnal tide—only one high and low tide each day. A mixed tide—two uneven tides a day, or one high, Tides vary on timescales ranging from hours to years due to a number of factors. To make accurate records, tide gauges at fixed stations measure water level over time, gauges ignore variations caused by waves with periods shorter than minutes. These data are compared to the level usually called mean sea level. Tidal phenomena are not limited to the oceans, but can occur in other systems whenever a gravitational field varies in time. For example, the part of the Earth is affected by tides. Tide changes proceed via the following stages, Sea level rises over several hours, covering the intertidal zone, the water rises to its highest level, reaching high tide. Sea level falls over several hours, revealing the intertidal zone, the water stops falling, reaching low tide. Oscillating currents produced by tides are known as tidal streams, the moment that the tidal current ceases is called slack water or slack tide. The tide then reverses direction and is said to be turning, slack water usually occurs near high water and low water. But there are locations where the moments of slack tide differ significantly from those of high, Tides are commonly semi-diurnal, or diurnal. The two high waters on a day are typically not the same height, these are the higher high water. Similarly, the two low waters each day are the low water and the lower low water. The daily inequality is not consistent and is small when the Moon is over the equator. From the highest level to the lowest, Highest Astronomical Tide – The highest tide which can be predicted to occur, note that meteorological conditions may add extra height to the HAT. Mean High Water Springs – The average of the two high tides on the days of spring tides, mean High Water Neaps – The average of the two high tides on the days of neap tides. Mean Sea Level – This is the sea level
7.
Tidal locking
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Tidal locking occurs when, over the course of an orbit, there is no net transfer of angular momentum between an astronomical body and its gravitational partner. This state can result from the gradient between two co-orbiting bodies, acting over a sufficiently long period of time. In the case where the orbital eccentricity is zero, tidal locking results in one hemisphere of the revolving object constantly facing its partner. For example, the side of the Moon always faces the Earth. A tidally locked body in synchronous rotation takes just as long to rotate around its own axis as it does to revolve around its partner, usually, only the satellite is tidally locked to the larger body. However, if both the difference between the two bodies and the distance between them are relatively small, each may be tidally locked to the other, this is the case for Pluto. This effect is employed to stabilize some artificial satellites, the possibility of lifeforms existing on tidally-locked planets has been debated. The change in rotation rate necessary to lock a body B to a larger body A is caused by the torque applied by As gravity on bulges it has induced on B by tidal forces. These distortions are known as tidal bulges, when B is not yet tidally locked, the bulges travel over its surface, with one of the two high tidal bulges traveling close to the point where body A is overhead. Smaller bodies also experience distortion, but this distortion is less regular, the material of B exerts resistance to this periodic reshaping caused by the tidal force. In effect, some time is required to reshape B to the equilibrium shape. Seen from a point in space, the points of maximum bulge extension are displaced from the axis oriented toward A. Because the bulges are now displaced from the A–B axis, As gravitational pull on the mass in them exerts a torque on B. The torque on the A-facing bulge acts to bring Bs rotation in line with its period, whereas the back bulge. However, the bulge on the A-facing side is closer to A than the bulge by a distance of approximately Bs diameter. The net resulting torque from both bulges, then, is always in the direction that acts to synchronize Bs rotation with its orbital period and this results in a raising of Bs orbit about A in tandem with its rotational slowdown. For the other case where B starts off rotating too slowly, the tidal locking effect is also experienced by the larger body A, but at a slower rate because Bs gravitational effect is weaker due to Bs smaller mass. For example, Earths rotation is gradually being slowed by the Moon, current estimations are that this has helped lengthen the Earth day from about 6 hours to the current 24 hours
8.
Ring system
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A ring system is a disc or ring orbiting an astronomical object that is composed of solid material such as dust and moonlets, and is a common component of satellite systems around giant planets. A ring system around a planet is known as a planetary ring system. The most prominent planetary rings in the Solar System are those around Saturn, recent evidence suggests that ring systems may be found around other types of astronomical objects, including minor planets, moons, and brown dwarfs. Fainter planetary rings can form as a result of meteoroid impacts with moons orbiting around the planet or, in case of Saturns E-ring, the composition of ring particles varies, they may be silicate or icy dust. Larger rocks and boulders may also be present, and in 2007 tidal effects from eight moonlets only a few hundred meters across were detected within Saturns rings. The maximum size of a particle is determined by the specific strength of the material it is made of, its density. The tidal force is proportional to the average density inside the radius of the ring and it is also inversely proportional to the square of the orbital period of the ring. Sometimes rings will have shepherd moons, small moons orbit near the inner or outer edges of rings or within gaps in the rings. Jupiters ring system was the third to be discovered, when it was first observed by the Voyager 1 probe in 1979, and was observed more thoroughly by the Galileo orbiter in the 1990s. Its four main parts are a faint thick torus known as the halo, a thin, relatively bright main ring, the system consists mostly of dust. Saturns rings are the most extensive ring system of any planet in the solar system, Galileo Galilei first observed them in 1610, but they were not accurately described as a disk around Saturn until Christiaan Huygens did so in 1655. With help from the NASA/ESA/ASI Cassini mission, an understanding of the ring formation. The rings are not a series of tiny ringlets as many think and they consist mostly of water ice and trace amounts of rock, and the particles range in size from micrometers to meters. Uranus ring system lies between the level of complexity of Saturns vast system and the systems around Jupiter and Neptune. They were discovered in 1977 by James L. Elliot, Edward W. Dunham and they are dark and likely consist of water ice and some radiation-processed organics. The relative lack of dust is due to drag from the extended exosphere-corona of Uranus. The system around Neptune consists of five rings that, at their densest, are comparable to the low-density regions of Saturns rings. However, they are faint and dusty, much similar in structure to those of Jupiter
9.
Roche limit
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Inside the Roche limit, orbiting material disperses and forms rings whereas outside the limit material tends to coalesce. The term is named after Édouard Roche, who is the French astronomer who first calculated this theoretical limit in 1848, typically, the Roche limit applies to a satellites disintegrating due to tidal forces induced by its primary, the body about which it orbits. Some real satellites, both natural and artificial, can orbit within their Roche limits because they are held together by other than gravitation. Objects resting on the surface of such a satellite would be lifted away by tidal forces, a weaker satellite, such as a comet, could be broken up when it passes within its Roche limit. Indeed, almost all known planetary rings are located within their Roche limit, Saturns E-Ring, the Roche limit is not the only factor that causes comets to break apart. Splitting by thermal stress, internal gas pressure and rotational splitting are other ways for a comet to split under stress, the table below shows the mean density and the equatorial radius for selected objects in the Solar System. The equations for the Roche limits relate the minimum sustainable orbital radius to the ratio of the two objects densities and the Radius of the primary body, hence, using the data above, the Roche limits for these objects can be calculated. This has been done twice for each, assuming the extremes of the rigid and fluid body cases, the average density of comets is taken to be around 500 kg/m³. The table below gives the Roche limits expressed in kilometres and in primary radii, the mean radius of the orbit can be compared with the Roche limits. For convenience, the lists the mean radius of the orbit for each, excluding the comets, whose orbits are extremely variable. So, clearly these bodies are well outside their Roche limits by various factors, from 21 for the Moon as part of the Earth–Moon system, upwards to thousands for Earth, but how close are the Solar Systems other moons to their Roche limits. The table below gives each satellites closest approach in its orbit divided by its own Roche limit, again, both rigid and fluid body calculations are given. Note that Pan, Cordelia and Naiad, in particular, may be close to their actual break-up points. In practice, the densities of most of the satellites of giant planets are not known. In these cases, shown in italics, likely values have been assumed, the limiting distance to which a satellite can approach without breaking up depends on the rigidity of the satellite. At one extreme, a completely rigid satellite will maintain its shape until tidal forces break it apart, most real satellites would lie somewhere between these two extremes, with tensile strength rendering the satellite neither perfectly rigid nor perfectly fluid. The rigid-body Roche limit is a calculation for a spherical satellite. Irregular shapes such as those of tidal deformation on the body or the primary it orbits are neglected and it is assumed to be in hydrostatic equilibrium
10.
Spaghettification
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In the most extreme cases, near black holes, the stretching is so powerful that no object can withstand it, no matter how strong its components. Within a small region the horizontal compression balances the vertical stretching so that small objects being spaghettified experience no net change in volume. Stephen Hawking describes the flight of an astronaut who, passing within a black holes event horizon, is stretched like spaghetti by the gravitational gradient from head to toe. The reason this happens would be because the gravity exerted from the singularity would be stronger at one end of your body from the other. If one were to fall into a black hole feet first, along with that, the right side of the body will be pulled to the left, and the left side of the body will be pulled to the right, horizontally compressing the person. However, the term spaghettification was established well before this, imagine four separate objects in the space above a planet, positioned in a diamond formation. The four objects follow the lines of the field, directed towards the celestial bodys centre. In accordance with the law, the lowest of the four objects experiences the biggest gravitational acceleration. Now imagine these four objects as connected parts of a larger object, a rigid body will resist distortion, and internal elastic forces develop as the body distorts to balance the tidal forces, so attaining mechanical equilibrium. If the tidal forces are too large, the body may yield and flow plastically before the forces can be balanced, or fracture. This gives F = μ l m/4r3, where μ is the standard gravitational parameter of the body, l is the length of the rod, m is rods mass. For non-uniform objects the tensile force is smaller if more mass is near the center, in addition, there is a horizontal compression force toward the center. For massive bodies with a surface, the force is largest near the surface, and this maximum value is only dependent on the object. For example, for a rod with a mass of 1 kg and a length of 1 m, and a body with the average density of the Earth. Due to the density, the tidal force near the surface of a white dwarf is much stronger. Moreover, a hole has no surface to stop a fall. Thus, the object is stretched into a thin strip of matter. The point at which tidal forces destroy an object or kill a person depend on the black holes size
11.
Lunar theory
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Lunar theory attempts to account for the motions of the Moon. There are many irregularities in the Moons motion, and many attempts have been made to account for them, after centuries of being problematic, lunar motion is now modeled to a very high degree of accuracy. Lunar theory has a history of over 2000 years of investigation and its more modern developments have been used over the last three centuries for fundamental scientific and technological purposes, and are still being used in that way. The Moon has been observed for millennia, over these ages, various levels of care and precision have been possible, according to the techniques of observation available at any time. There is a long history of lunar theories, it stretches from the times of the Babylonian and Greek astronomers. The history can be considered to fall into three parts, from ancient times to Newton, the period of classical physics, and modern developments, of Babylonian astronomy, practically nothing was known to historians of science before the 1880s. Surviving ancient writings of Pliny had made mention of three astronomical schools in Mesopotamia – at Babylon, Uruk and Hipparenum. Since then, knowledge of the subject, still fragmentary, has had to be built up by painstaking analysis of deciphered texts, mainly in form, on tablets from Babylon. This system involved calculating daily stepwise changes of speed, up or down, with a minimum. The basis of these appears to have been arithmetical rather than geometrical. The Babylonians appear to have interested in calendars, new moons. Some time between the years 500 BC and 400 BC they identified and began to use the 19-year cyclic relation between lunar months and solar years now known as the Metonic cycle. e, the mean period for the phases of the Moon. This same value was used by Hipparchos and Ptolemy, was used throughout the Middle Ages, and still forms the basis of the Hebrew calendar. The mean lunar velocity relative to the stars they estimated at 13°1035 per day, giving a corresponding month of 27.321598 days, the draconitic month, i. e. g. of 27.212204 days, to compare with a modern value of 27. The Babylonian estimate for the month was adopted for the greater part of two millennia by Hipparchus, Ptolemy and medieval writers. Prominent in these geometrical lunar theories were combinations of circular motions – applications of the theory of epicycles, the circle acted as a deferent, carrying an epicycle along which the Moon was assumed to move in a retrograde direction. The center of the epicycle moved at a rate corresponding to the change in Moons longitude. This epicycle approximately provided for what was recognized as the elliptical inequality, the equation of the center
12.
Equipotential
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Equipotential or isopotential in mathematics and physics refers to a region in space where every point in it is at the same potential. This usually refers to a potential, although it can also be applied to vector potentials. An equipotential of a potential function in n-dimensional space is typically an dimensional space. The del operator illustrates the relationship between a field and its associated scalar potential field. Note that an equipotential region might be referred as being of equipotential or simply be called an equipotential, an equipotential region of a scalar potential in three-dimensional space is often an equipotential surface, but it can also be a three-dimensional region in space. The gradient of the potential is everywhere perpendicular to the equipotential surface. Electrical conductors offer an intuitive example, thus, an equipotential would contain both points a and b as they have the same potential. Extending this definition, an isopotential is the locus of all points that are of the same potential, in gravity, a hollow sphere has a three-dimensional equipotential region inside, with no gravity. In electrostatics a conductor is an equipotential region. In the case of a conductor, the equipotential region includes the space inside. A ball will not be accelerated by the force of gravity if it is resting on a flat, horizontal surface, equipotential surface Potential gradient Isopotential map Scalar potential Electric Field Applet
13.
Nadir
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The nadir, is the direction pointing directly below a particular location, that is, it is one of two vertical directions at a specified location, orthogonal to a horizontal flat surface there. Since the concept of being below is itself somewhat vague, scientists define the nadir in more rigorous terms. Specifically, in astronomy, geophysics and related sciences, the nadir at a point is the local vertical direction pointing in the direction of the force of gravity at that location. The direction opposite of the nadir is the zenith, the word is also used figuratively to mean the lowest point of a persons spirits, or the quality of an activity or profession. The term nadir can also be used to represent the lowest point reached by a body during its apparent orbit around a given point of observation. This can be used to describe the location of the Sun, the sun is said to be at the nadir at a location when it is at the zenith at the locations antipode and the sun is 90 degrees below the horizon. In oncology, the nadir is used to represent the lowest level of a blood cell count while a patient is undergoing chemotherapy. A diagnosis of neutropenic nadir after chemotherapy typically lasts 7–10 days
14.
Field (physics)
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In physics, a field is a physical quantity, typically a number or tensor, that has a value for each point in space and time. For example, on a map, the surface wind velocity is described by assigning a vector to each point on a map. Each vector represents the speed and direction of the movement of air at that point, as another example, an electric field can be thought of as a condition in space emanating from an electric charge and extending throughout the whole of space. When a test electric charge is placed in this electric field, physicists have found the notion of a field to be of such practical utility for the analysis of forces that they have come to think of a force as due to a field. In the modern framework of the theory of fields, even without referring to a test particle, a field occupies space, contains energy. This led physicists to consider electromagnetic fields to be a physical entity, the fact that the electromagnetic field can possess momentum and energy makes it very real. A particle makes a field, and a field acts on another particle, in practice, the strength of most fields has been found to diminish with distance to the point of being undetectable. One consequence is that the Earths gravitational field quickly becomes undetectable on cosmic scales, a field has a unique tensorial character in every point where it is defined, i. e. a field cannot be a scalar field somewhere and a vector field somewhere else. For example, the Newtonian gravitational field is a vector field, moreover, within each category, a field can be either a classical field or a quantum field, depending on whether it is characterized by numbers or quantum operators respectively. In fact in this theory an equivalent representation of field is a field particle, to Isaac Newton his law of universal gravitation simply expressed the gravitational force that acted between any pair of massive objects. In the eighteenth century, a new quantity was devised to simplify the bookkeeping of all these gravitational forces and this quantity, the gravitational field, gave at each point in space the total gravitational force which would be felt by an object with unit mass at that point. The development of the independent concept of a field began in the nineteenth century with the development of the theory of electromagnetism. In the early stages, André-Marie Ampère and Charles-Augustin de Coulomb could manage with Newton-style laws that expressed the forces between pairs of electric charges or electric currents. However, it became more natural to take the field approach and express these laws in terms of electric and magnetic fields. The independent nature of the field became more apparent with James Clerk Maxwells discovery that waves in these fields propagated at a finite speed, Maxwell, at first, did not adopt the modern concept of a field as fundamental quantity that could independently exist. Instead, he supposed that the field expressed the deformation of some underlying medium—the luminiferous aether—much like the tension in a rubber membrane. If that were the case, the velocity of the electromagnetic waves should depend upon the velocity of the observer with respect to the aether. Despite much effort, no evidence of such an effect was ever found
15.
Saturn
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Saturn is the sixth planet from the Sun and the second-largest in the Solar System, after Jupiter. It is a gas giant with a radius about nine times that of Earth. Although it has only one-eighth the average density of Earth, with its larger volume Saturn is just over 95 times more massive, Saturn is named after the Roman god of agriculture, its astronomical symbol represents the gods sickle. Saturns interior is composed of a core of iron–nickel and rock. This core is surrounded by a layer of metallic hydrogen, an intermediate layer of liquid hydrogen and liquid helium. Saturn has a yellow hue due to ammonia crystals in its upper atmosphere. Saturns magnetic field strength is around one-twentieth of Jupiters, the outer atmosphere is generally bland and lacking in contrast, although long-lived features can appear. Wind speeds on Saturn can reach 1,800 km/h, higher than on Jupiter, sixty-two moons are known to orbit Saturn, of which fifty-three are officially named. This does not include the hundreds of moonlets comprising the rings, Saturn is a gas giant because it is predominantly composed of hydrogen and helium. It lacks a definite surface, though it may have a solid core, Saturns rotation causes it to have the shape of an oblate spheroid, that is, it is flattened at the poles and bulges at its equator. Its equatorial and polar radii differ by almost 10%,60,268 km versus 54,364 km, Jupiter, Uranus, and Neptune, the other giant planets in the Solar System, are also oblate but to a lesser extent. Saturn is the planet of the Solar System that is less dense than water—about 30% less. Although Saturns core is considerably denser than water, the specific density of the planet is 0.69 g/cm3 due to the atmosphere. Jupiter has 318 times the Earths mass, while Saturn is 95 times the mass of the Earth, together, Jupiter and Saturn hold 92% of the total planetary mass in the Solar System. On 8 January 2015, NASA reported determining the center of the planet Saturn, the temperature, pressure, and density inside Saturn all rise steadily toward the core, which causes hydrogen to transition into a metal in the deeper layers. Standard planetary models suggest that the interior of Saturn is similar to that of Jupiter, having a rocky core surrounded by hydrogen. This core is similar in composition to the Earth, but more dense, in 2004, they estimated that the core must be 9–22 times the mass of the Earth, which corresponds to a diameter of about 25,000 km. This is surrounded by a liquid metallic hydrogen layer, followed by a liquid layer of helium-saturated molecular hydrogen that gradually transitions to a gas with increasing altitude
16.
Ellipsoid
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An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation. An ellipsoid is a surface, that is a surface that may be defined as the zero set of a polynomial of degree two in three variables. Among quadric surfaces, an ellipsoid is characterized by any of the two following properties, every planar cross section is either an ellipse, or is empty, or is reduced to a single point. It is bounded, which means that it may be enclosed in a large sphere. An ellipsoid has three perpendicular axes of symmetry which intersect at a center of symmetry, called the center of the ellipsoid. The line segments that are delimited on the axes of symmetry by the ellipsoid are called the principal axes, if the three axes have different lengths, the ellipsoid is said to be tri-axial or scalene, and the axes are uniquely defined. If two of the axes have the length, then the ellipsoid is an ellipsoid of revolution. In this case, the ellipsoid is invariant under a rotation around the third axis, if the third axis is shorter, the ellipsoid is an oblate spheroid, if it is longer, it is prolate spheroid. If the three axes have the length, the ellipsoid is a sphere. The points, and lie on the surface, the line segments from the origin to these points are called the semi-principal axes of the ellipsoid, because a, b, c are half the length of the principal axes. They correspond to the axis and semi-minor axis of an ellipse. If a = b > c, one has an oblate spheroid, if a = b < c, one has a prolate spheroid, if a = b = c, one has a sphere. It is easy to check, The intersection of a plane, remark, The contour of an ellipsoid, seen from a point outside the ellipsoid or from infinity, is in any case a plane section, hence an ellipse. The ellipsoid may be parameterized in several ways, which are simpler to express when the ellipsoid axes coincide with coordinate axes. A common choice is x = a cos cos , y = b cos sin , z = c sin and these parameters may be interpreted as spherical coordinates. More precisely, π /2 − θ is the polar angle, and φ is the azimuth angle of the point of the ellipsoid. More generally, an arbitrarily oriented ellipsoid, centered at v, is defined by the x to the equation T A =1. The eigenvectors of A define the axes of the ellipsoid and the eigenvalues of A are the reciprocals of the squares of the semi-axes
17.
Oval
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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 also refer to true prolate ellipsoids. It can also 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 also often refers to a figure that resembles two semicircles joined by a rectangle, like a cricket infield, speed skating rink or an athletics track, however, 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
18.
Barycenter
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The barycenter is the center of mass of two or more bodies that are orbiting each other, or the point around which they both orbit. It is an important concept in such as astronomy and astrophysics. The distance from a center of mass to the barycenter can be calculated as a simple two-body problem. In cases where one of the two objects is more massive than the other, the barycenter will typically be located within the more massive object. Rather than appearing to orbit a center of mass with the smaller body. This is the case for the Earth–Moon system, where the barycenter is located on average 4,671 km from the Earths center, when the two bodies are of similar masses, the barycenter will generally be located between them and both bodies will follow an orbit around it. This is the case for Pluto and Charon, as well as for many binary asteroids and it is also the case for Jupiter and the Sun, despite the thousandfold difference in mass, due to the relatively large distance between them. In astronomy, barycentric coordinates are non-rotating coordinates with the origin at the center of mass of two or more bodies, the International Celestial Reference System is a barycentric one, based on the barycenter of the Solar System. In geometry, the barycenter is synonymous with centroid, the geometric center of a two-dimensional shape. The barycenter is one of the foci of the orbit of each body. This is an important concept in the fields of astronomy and astrophysics. If a is the distance between the centers of the two bodies, r1 is the axis of the primarys orbit around the barycenter. When the barycenter is located within the massive body, that body will appear to wobble rather than to follow a discernible orbit. The following table sets out some examples from the Solar System, figures are given rounded to three significant figures. If Jupiter had Mercurys orbit, the Sun–Jupiter barycenter would be approximately 55,000 km from the center of the Sun, but even if the Earth had Eris orbit, the Sun–Earth barycenter would still be within the Sun. To calculate the motion of the Sun, you would need to sum all the influences from all the planets, comets, asteroids. If all the planets were aligned on the side of the Sun. The calculations above are based on the distance between the bodies and yield the mean value r1
19.
Centripetal force
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A centripetal force is a force that makes a body follow a curved path. Its direction is orthogonal to the motion of the body. Isaac Newton described it as a force by which bodies are drawn or impelled, or in any way tend, in Newtonian mechanics, gravity provides the centripetal force responsible for astronomical orbits. One common example involving centripetal force is the case in which a body moves with uniform speed along a circular path, the centripetal force is directed at right angles to the motion and also along the radius towards the centre of the circular path. The mathematical description was derived in 1659 by the Dutch physicist Christiaan Huygens, the direction of the force is toward the center of the circle in which the object is moving, or the osculating circle. The speed in the formula is squared, so twice the speed needs four times the force, the inverse relationship with the radius of curvature shows that half the radial distance requires twice the force. Expressed using the orbital period T for one revolution of the circle, the rope example is an example involving a pull force. The centripetal force can also be supplied as a push force, newtons idea of a centripetal force corresponds to what is nowadays referred to as a central force. Another example of centripetal force arises in the helix that is traced out when a particle moves in a uniform magnetic field in the absence of other external forces. In this case, the force is the centripetal force that acts towards the helix axis. Below are three examples of increasing complexity, with derivations of the formulas governing velocity and acceleration, uniform circular motion refers to the case of constant rate of rotation. Here are two approaches to describing this case, assume uniform circular motion, which requires three things. The object moves only on a circle, the radius of the circle r does not change in time. The object moves with constant angular velocity ω around the circle, therefore, θ = ω t where t is time. Now find the velocity v and acceleration a of the motion by taking derivatives of position with respect to time, consequently, a = − ω2 r. negative shows that the acceleration is pointed towards the center of the circle, hence it is called centripetal. While objects naturally follow a path, this centripetal acceleration describes the circular motion path caused by a centripetal force. The image at right shows the relationships for uniform circular motion. In this subsection, dθ/dt is assumed constant, independent of time, consequently, d r d t = lim Δ t →0 r − r Δ t = d ℓ d t
20.
Tidal heating
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Tidal heating occurs through the tidal friction processes, orbital and rotational energy are dissipated as heat in either the surface ocean or interior of a planet or satellite. Io, a moon of Jupiter, is the most volcanically active body in the system, evidenced by active volcanos. Ios heating is a result of the tug between Jupiter and the other Galilean moons, the eccentricity of Ios orbit causes the height of Ios tidal bulge to vary significantly over the course of an orbit, the friction from this tidal flexing then heats up its interior. A similar but weaker process is theorised to have melted the lower layers of the ice surrounding the mantle of Jupiters next large moon. Saturns moon Enceladus is similarly thought to have a water ocean beneath its icy crust. The water vapor geysers which eject material from Enceladus are thought to be powered by friction generated within this moons shifting ice crust, im is the imaginary portion of the second order Love number which measures the efficiency of body dissipation within the satellite. This imaginary portion is a function of the satellites bulk shear modulus and these in turn are dependent upon temperature and melting of the satellites interior. Cryovolcano Tidal acceleration Tidal locking Tidal heating of Io
21.
Io (moon)
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Io /ˈaɪ. oʊ/ is the innermost of the four Galilean moons of the planet Jupiter. It is the fourth-largest moon, has the highest density of all the moons and it was discovered in 1610 and was named after the mythological character Io, a priestess of Hera who became one of Zeuss lovers. With over 400 active volcanoes, Io is the most geologically active object in the Solar System, several volcanoes produce plumes of sulfur and sulfur dioxide that climb as high as 500 km above the surface. Ios surface is dotted with more than 100 mountains that have been uplifted by extensive compression at the base of Ios silicate crust. Some of these peaks are taller than Mount Everest, unlike most satellites in the outer Solar System, which are mostly composed of water ice, Io is primarily composed of silicate rock surrounding a molten iron or iron-sulfide core. Most of Ios surface is composed of extensive plains coated with sulfur, Ios volcanism is responsible for many of its unique features. Numerous extensive lava flows, several more than 500 km in length, the materials produced by this volcanism make up Ios thin, patchy atmosphere and Jupiters extensive magnetosphere. Ios volcanic ejecta also produce a large torus around Jupiter. Io played a significant role in the development of astronomy in the 17th and 18th centuries and it was discovered in January 1610 by Galileo Galilei, along with the other Galilean satellites. This discovery furthered the adoption of the Copernican model of the Solar System, the development of Keplers laws of motion, and the first measurement of the speed of light. In 1979, the two Voyager spacecraft revealed Io to be a geologically active world, with numerous volcanic features, large mountains, the Galileo spacecraft performed several close flybys in the 1990s and early 2000s, obtaining data about Ios interior structure and surface composition. These spacecraft also revealed the relationship between Io and Jupiters magnetosphere and the existence of a belt of high-energy radiation centered on Ios orbit, Io receives about 3,600 rem of ionizing radiation per day. Further observations have made by Cassini–Huygens in 2000 and New Horizons in 2007, as well as from Earth-based telescopes. From the surface of Io, Jupiter would subtend an arc of 19. 5°, although Simon Marius is not credited with the sole discovery of the Galilean satellites, his names for the moons were adopted. Based on a suggestion from Johannes Kepler in October 1613, he devised a naming scheme whereby each moon was named for a lover of the Greek mythological Zeus or his Roman equivalent. He named the innermost large moon of Jupiter after the Greek mythological figure Io, since the surface was first seen up close by Voyager 1, the International Astronomical Union has approved 225 names for Ios volcanoes, mountains, plateaus, and large albedo features. The approved feature categories used for Io for different types of volcanic features include patera, fluctus, vallis, named mountains, plateaus, layered terrain, and shield volcanoes include the terms mons, mensa, planum, and tholus, respectively. Named, bright albedo regions use the term regio, examples of named features are Prometheus, Pan Mensa, Tvashtar Paterae, and Tsũi Goab Fluctus
22.
Stress (mechanics)
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For example, when a solid vertical bar is supporting a weight, each particle in the bar pushes on the particles immediately below it. When a liquid is in a container under pressure, each particle gets pushed against by all the surrounding particles. The container walls and the pressure-inducing surface push against them in reaction and these macroscopic forces are actually the net result of a very large number of intermolecular forces and collisions between the particles in those molecules. Strain inside a material may arise by various mechanisms, such as stress as applied by external forces to the material or to its surface. Any strain of a material generates an internal elastic stress, analogous to the reaction force of a spring. In liquids and gases, only deformations that change the volume generate persistent elastic stress, however, if the deformation is gradually changing with time, even in fluids there will usually be some viscous stress, opposing that change. Elastic and viscous stresses are usually combined under the mechanical stress. Significant stress may exist even when deformation is negligible or non-existent, stress may exist in the absence of external forces, such built-in stress is important, for example, in prestressed concrete and tempered glass. Stress may also be imposed on a material without the application of net forces, for example by changes in temperature or chemical composition, stress that exceeds certain strength limits of the material will result in permanent deformation or even change its crystal structure and chemical composition. In some branches of engineering, the stress is occasionally used in a looser sense as a synonym of internal force. For example, in the analysis of trusses, it may refer to the total traction or compression force acting on a beam, since ancient times humans have been consciously aware of stress inside materials. Until the 17th century the understanding of stress was largely intuitive and empirical, with those tools, Augustin-Louis Cauchy was able to give the first rigorous and general mathematical model for stress in a homogeneous medium. Cauchy observed that the force across a surface was a linear function of its normal vector, and, moreover. The understanding of stress in liquids started with Newton, who provided a formula for friction forces in parallel laminar flow. Stress is defined as the force across a small boundary per unit area of that boundary, following the basic premises of continuum mechanics, stress is a macroscopic concept. In a fluid at rest the force is perpendicular to the surface, in a solid, or in a flow of viscous liquid, the force F may not be perpendicular to S, hence the stress across a surface must be regarded a vector quantity, not a scalar. Moreover, the direction and magnitude depend on the orientation of S. Thus the stress state of the material must be described by a tensor, called the stress tensor, with respect to any chosen coordinate system, the Cauchy stress tensor can be represented as a symmetric matrix of 3×3 real numbers
23.
Beat (acoustics)
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In acoustics, a beat is an interference pattern between two sounds of slightly different frequencies, perceived as a periodic variation in volume whose rate is the difference of the two frequencies. When tuning instruments that can produce sustained tones, beats can readily be recognized, tuning two tones to a unison will present a peculiar effect, when the two tones are close in pitch but not identical, the difference in frequency generates the beating. The volume varies like in a tremolo as the sounds alternately interfere constructively and destructively, as the two tones gradually approach unison, the beating slows down and may become so slow as to be imperceptible. It can be proven that the envelope of the maxima and minima form a wave frequency is half the difference between the frequencies of the two original waves. Instead, it is perceived as a variation in the amplitude of the first term in the expression above. It can be said that the lower frequency cosine term is an envelope for the higher frequency one, the frequency of the modulation is f1 + f2/2, that is, the average of the two frequencies. It can be noted that every second burst in the pattern is inverted. Each peak is replaced by a trough and vice versa, however, because the human ear is not sensitive to the phase of a sound, only its amplitude or intensity, only the magnitude of the envelope is heard. A physical interpretation is that when cos =1 the two waves are in phase and they interfere constructively, when it is zero, they are out of phase and interfere destructively. Beats occur also in more complex sounds, or in sounds of different volumes, beating can also be heard between notes that are near to, but not exactly, a harmonic interval, due to some harmonic of the first note beating with a harmonic of the second note. For example, in the case of perfect fifth, the harmonic of the bass note beats with the second harmonic of the other note. Musicians commonly use interference beats to objectively check tuning at the unison, perfect fifth, piano and organ tuners even use a method involving counting beats, aiming at a particular number for a specific interval. The composer Alvin Lucier has written many pieces that feature interference beats as their main focus, composer Phill Niblocks music is entirely based on beating caused by microtonal differences. Binaural beats are heard when the right ear listens to a different tone than the left ear. Here, the tones do not interfere physically, but are summed by the brain in the olivary nucleus and this effect is related to the brains ability to locate sounds in three dimensions. Combination tone Gamelan tuning Heterodyne Consonance and dissonance Moiré pattern, a form of interference that generates new frequencies
24.
Neutron star
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A neutron star is the collapsed core of a large star. Neutron stars are the smallest and densest stars known to exist, though neutron stars typically have a radius on the order of 10 km, they can have masses of about twice that of the Sun. They result from the explosion of a massive star, combined with gravitational collapse. They are supported against further collapse by neutron degeneracy pressure, a described by the Pauli exclusion principle. If the remnant has too great a density, something which occurs in excess of a limit of the size of neutron stars at 2–3 solar masses. Neutron stars that can be observed are very hot and typically have a temperature around 6×105 K. They are so dense that a normal-sized matchbox containing neutron-star material would have a mass of approximately 3 billion tonnes and their magnetic fields are between 108 and 1015 times as strong as that of the Earth. The gravitational field at the stars surface is about 2×1011 times that of the Earth. As the stars core collapses, its rotation rate increases as a result of conservation of angular momentum, some neutron stars emit beams of electromagnetic radiation that make them detectable as pulsars. Indeed, the discovery of pulsars in 1967 was the first observational suggestion that stars exist. The radiation from pulsars is thought to be emitted from regions near their magnetic poles. The fastest-spinning neutron star known is PSR J1748-2446ad, rotating at a rate of 716 times a second or 43,000 revolutions per minute, giving a linear speed at the surface on the order of 0.24 c. There are thought to be around 100 million neutron stars in the Milky Way, however, most are old and cold, and neutron stars can only be easily detected in certain instances, such as if they are a pulsar or part of a binary system. Soft gamma repeaters are conjectured to be a type of neutron star with strong magnetic fields, known as magnetars, or alternatively. Additionally, such accretion can recycle old pulsars and potentially cause them to mass and spin-up to very fast rotation rates. The merger of binary stars may be the source of short-duration gamma-ray bursts and are likely strong sources of gravitational waves. Any main-sequence star with a mass of above 8 times the mass of the sun has the potential to produce a neutron star. As the star evolves away from the sequence, subsequent nuclear burning produces an iron-rich core
25.
Black hole
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A black hole is a region of spacetime exhibiting such strong gravitational effects that nothing—not even particles and electromagnetic radiation such as light—can escape from inside it. The theory of relativity predicts that a sufficiently compact mass can deform spacetime to form a black hole. The boundary of the region from which no escape is possible is called the event horizon, although the event horizon has an enormous effect on the fate and circumstances of an object crossing it, no locally detectable features appear to be observed. In many ways a black hole acts like a black body. Moreover, quantum theory in curved spacetime predicts that event horizons emit Hawking radiation. This temperature is on the order of billionths of a kelvin for black holes of stellar mass, objects whose gravitational fields are too strong for light to escape were first considered in the 18th century by John Michell and Pierre-Simon Laplace. Black holes were considered a mathematical curiosity, it was during the 1960s that theoretical work showed they were a generic prediction of general relativity. The discovery of neutron stars sparked interest in gravitationally collapsed compact objects as a possible astrophysical reality, black holes of stellar mass are expected to form when very massive stars collapse at the end of their life cycle. After a black hole has formed, it can continue to grow by absorbing mass from its surroundings, by absorbing other stars and merging with other black holes, supermassive black holes of millions of solar masses may form. There is general consensus that supermassive black holes exist in the centers of most galaxies, despite its invisible interior, the presence of a black hole can be inferred through its interaction with other matter and with electromagnetic radiation such as visible light. Matter that falls onto a black hole can form an accretion disk heated by friction. If there are other stars orbiting a black hole, their orbits can be used to determine the black holes mass, such observations can be used to exclude possible alternatives such as neutron stars.3 million solar masses. On 15 June 2016, a detection of a gravitational wave event from colliding black holes was announced. The idea of a body so massive that light could not escape was briefly proposed by astronomical pioneer John Michell in a letter published in 1783-4. Michell correctly noted that such supermassive but non-radiating bodies might be detectable through their effects on nearby visible bodies. In 1915, Albert Einstein developed his theory of general relativity, only a few months later, Karl Schwarzschild found a solution to the Einstein field equations, which describes the gravitational field of a point mass and a spherical mass. A few months after Schwarzschild, Johannes Droste, a student of Hendrik Lorentz, independently gave the solution for the point mass. This solution had a peculiar behaviour at what is now called the Schwarzschild radius, the nature of this surface was not quite understood at the time
26.
Earth
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Earth, otherwise known as the World, or the Globe, is the third planet from the Sun and the only object in the Universe known to harbor life. It is the densest planet in the Solar System and the largest of the four terrestrial planets, according to radiometric dating and other sources of evidence, Earth formed about 4.54 billion years ago. Earths gravity interacts with objects in space, especially the Sun. During one orbit around the Sun, Earth rotates about its axis over 365 times, thus, Earths axis of rotation is tilted, producing seasonal variations on the planets surface. The gravitational interaction between the Earth and Moon causes ocean tides, stabilizes the Earths orientation on its axis, Earths lithosphere is divided into several rigid tectonic plates that migrate across the surface over periods of many millions of years. About 71% of Earths surface is covered with water, mostly by its oceans, the remaining 29% is land consisting of continents and islands that together have many lakes, rivers and other sources of water that contribute to the hydrosphere. The majority of Earths polar regions are covered in ice, including the Antarctic ice sheet, Earths interior remains active with a solid iron inner core, a liquid outer core that generates the Earths magnetic field, and a convecting mantle that drives plate tectonics. Within the first billion years of Earths history, life appeared in the oceans and began to affect the Earths atmosphere and surface, some geological evidence indicates that life may have arisen as much as 4.1 billion years ago. Since then, the combination of Earths distance from the Sun, physical properties, in the history of the Earth, biodiversity has gone through long periods of expansion, occasionally punctuated by mass extinction events. Over 99% of all species that lived on Earth are extinct. Estimates of the number of species on Earth today vary widely, over 7.4 billion humans live on Earth and depend on its biosphere and minerals for their survival. Humans have developed diverse societies and cultures, politically, the world has about 200 sovereign states, the modern English word Earth developed from a wide variety of Middle English forms, which derived from an Old English noun most often spelled eorðe. It has cognates in every Germanic language, and their proto-Germanic root has been reconstructed as *erþō, originally, earth was written in lowercase, and from early Middle English, its definite sense as the globe was expressed as the earth. By early Modern English, many nouns were capitalized, and the became the Earth. More recently, the name is simply given as Earth. House styles now vary, Oxford spelling recognizes the lowercase form as the most common, another convention capitalizes Earth when appearing as a name but writes it in lowercase when preceded by the. It almost always appears in lowercase in colloquial expressions such as what on earth are you doing, the oldest material found in the Solar System is dated to 4. 5672±0.0006 billion years ago. By 4. 54±0.04 Gya the primordial Earth had formed, the formation and evolution of Solar System bodies occurred along with the Sun
27.
Moon
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The Moon is an astronomical body that orbits planet Earth, being Earths only permanent natural satellite. It is the fifth-largest natural satellite in the Solar System, following Jupiters satellite Io, the Moon is second-densest satellite among those whose densities are known. The average distance of the Moon from the Earth is 384,400 km, the Moon is thought to have formed about 4.51 billion years ago, not long after Earth. It is the second-brightest regularly visible celestial object in Earths sky, after the Sun and its surface is actually dark, although compared to the night sky it appears very bright, with a reflectance just slightly higher than that of worn asphalt. Its prominence in the sky and its cycle of phases have made the Moon an important cultural influence since ancient times on language, calendars, art. The Moons gravitational influence produces the ocean tides, body tides, and this matching of apparent visual size will not continue in the far future. The Moons linear distance from Earth is currently increasing at a rate of 3.82 ±0.07 centimetres per year, since the Apollo 17 mission in 1972, the Moon has been visited only by uncrewed spacecraft. The usual English proper name for Earths natural satellite is the Moon, the noun moon is derived from moone, which developed from mone, which is derived from Old English mōna, which ultimately stems from Proto-Germanic *mǣnōn, like all Germanic language cognates. Occasionally, the name Luna is used, in literature, especially science fiction, Luna is used to distinguish it from other moons, while in poetry, the name has been used to denote personification of our moon. The principal modern English adjective pertaining to the Moon is lunar, a less common adjective is selenic, derived from the Ancient Greek Selene, from which is derived the prefix seleno-. Both the Greek Selene and the Roman goddess Diana were alternatively called Cynthia, the names Luna, Cynthia, and Selene are reflected in terminology for lunar orbits in words such as apolune, pericynthion, and selenocentric. The name Diana is connected to dies meaning day, several mechanisms have been proposed for the Moons formation 4.51 billion years ago, and some 60 million years after the origin of the Solar System. These hypotheses also cannot account for the angular momentum of the Earth–Moon system. This hypothesis, although not perfect, perhaps best explains the evidence, eighteen months prior to an October 1984 conference on lunar origins, Bill Hartmann, Roger Phillips, and Jeff Taylor challenged fellow lunar scientists, You have eighteen months. Go back to your Apollo data, go back to computer, do whatever you have to. Dont come to our conference unless you have something to say about the Moons birth, at the 1984 conference at Kona, Hawaii, the giant impact hypothesis emerged as the most popular. Afterward there were only two groups, the giant impact camp and the agnostics. Giant impacts are thought to have been common in the early Solar System, computer simulations of a giant impact have produced results that are consistent with the mass of the lunar core and the present angular momentum of the Earth–Moon system
28.
Sun
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The Sun is the star at the center of the Solar System. It is a perfect sphere of hot plasma, with internal convective motion that generates a magnetic field via a dynamo process. It is by far the most important source of energy for life on Earth. Its diameter is about 109 times that of Earth, and its mass is about 330,000 times that of Earth, accounting for about 99. 86% of the total mass of the Solar System. About three quarters of the Suns mass consists of hydrogen, the rest is mostly helium, with smaller quantities of heavier elements, including oxygen, carbon, neon. The Sun is a G-type main-sequence star based on its spectral class and it formed approximately 4.6 billion years ago from the gravitational collapse of matter within a region of a large molecular cloud. Most of this matter gathered in the center, whereas the rest flattened into a disk that became the Solar System. The central mass became so hot and dense that it eventually initiated nuclear fusion in its core and it is thought that almost all stars form by this process. The Sun is roughly middle-aged, it has not changed dramatically for more than four billion years and it is calculated that the Sun will become sufficiently large enough to engulf the current orbits of Mercury, Venus, and probably Earth. The enormous effect of the Sun on Earth has been recognized since prehistoric times, the synodic rotation of Earth and its orbit around the Sun are the basis of the solar calendar, which is the predominant calendar in use today. The English proper name Sun developed from Old English sunne and may be related to south, all Germanic terms for the Sun stem from Proto-Germanic *sunnōn. The English weekday name Sunday stems from Old English and is ultimately a result of a Germanic interpretation of Latin dies solis, the Latin name for the Sun, Sol, is not common in general English language use, the adjectival form is the related word solar. The term sol is used by planetary astronomers to refer to the duration of a solar day on another planet. A mean Earth solar day is approximately 24 hours, whereas a mean Martian sol is 24 hours,39 minutes, and 35.244 seconds. From at least the 4th Dynasty of Ancient Egypt, the Sun was worshipped as the god Ra, portrayed as a falcon-headed divinity surmounted by the solar disk, and surrounded by a serpent. In the New Empire period, the Sun became identified with the dung beetle, in the form of the Sun disc Aten, the Sun had a brief resurgence during the Amarna Period when it again became the preeminent, if not only, divinity for the Pharaoh Akhenaton. The Sun is viewed as a goddess in Germanic paganism, Sól/Sunna, in ancient Roman culture, Sunday was the day of the Sun god. It was adopted as the Sabbath day by Christians who did not have a Jewish background, the symbol of light was a pagan device adopted by Christians, and perhaps the most important one that did not come from Jewish traditions
29.
Tidal acceleration
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Tidal acceleration is an effect of the tidal forces between an orbiting natural satellite, and the primary planet that it orbits. The acceleration causes a gradual recession of a satellite in a prograde orbit away from the primary, the process eventually leads to tidal locking, usually of the smaller first, and later the larger body. The Earth–Moon system is the best studied case, the similar process of tidal deceleration occurs for satellites that have an orbital period that is shorter than the primarys rotational period, or that orbit in a retrograde direction. The naming is somewhat confusing, because the speed of the relative to the body it orbits is decreased as a result of tidal acceleration. Laplaces initial computation accounted for the effect, thus seeming to tie up the theory neatly with both modern and ancient observations. It took some time for the community to accept the reality. But eventually it became clear that three effects are involved, when measured in terms of solar time. Beside the effects of changes in Earths orbital eccentricity, as found by Laplace and corrected by Adams. First there is a real retardation of the Moons angular rate of orbital motion and this increases the Moons angular momentum around Earth. Secondly there is an apparent increase in the Moons angular rate of orbital motion and this arises from Earths loss of angular momentum and the consequent increase in length of day. Because the Moons mass is a fraction of that of Earth. The mass of the Moon is sufficiently large, and it is sufficiently close, in particular, the water of the oceans bulges out towards and away from the Moon. The average tidal bulge is synchronized with the Moons orbit, however, Earths rotation drags the position of the tidal bulge ahead of the position directly under the Moon. As a consequence, there exists a substantial amount of mass in the bulge that is offset from the line through the centers of Earth and the Moon. Because of this offset, a portion of the pull between Earths tidal bulges and the Moon is not perpendicular to the Earth–Moon line, i. e. there exists a torque between Earth and the Moon. This boosts the Moon in its orbit, and slows the rotation of Earth, as a result of this process, the mean solar day, which is nominally 86,400 seconds long, is actually getting longer when measured in SI seconds with stable atomic clocks. The small difference accumulates over time, which leads to a difference between our clock time on the one hand, and Atomic Time and Ephemeris Time on the other hand. This led to the introduction of the second in 1972 to compensate for differences in the bases for time standardization
30.
Earth's magnetic field
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Its magnitude at the Earths surface ranges from 25 to 65 microteslas. The North geomagnetic pole, located near Greenland in the hemisphere, is actually the south pole of the Earths magnetic field. Unlike a bar magnet, Earths magnetic field changes over time because it is generated by a geodynamo, however, at irregular intervals averaging several hundred thousand years, the Earths field reverses and the North and South Magnetic Poles relatively abruptly switch places. These reversals of the geomagnetic poles leave a record in rocks that are of value to paleomagnetists in calculating geomagnetic fields in the past, such information in turn is helpful in studying the motions of continents and ocean floors in the process of plate tectonics. The magnetosphere is the region above the ionosphere that is defined by the extent of the Earths magnetic field in space. The Earths magnetic field serves to deflect most of the solar wind, one stripping mechanism is for gas to be caught in bubbles of magnetic field, which are ripped off by solar winds. The study of past magnetic field of the Earth is known as paleomagnetism, reversals also provide the basis for magnetostratigraphy, a way of dating rocks and sediments. The field also magnetizes the crust, and magnetic anomalies can be used to search for deposits of metal ores, humans have used compasses for direction finding since the 11th century A. D. and for navigation since the 12th century. Although the magnetic declination does shift with time, this wandering is slow enough that a simple compass remains useful for navigation, using magnetoception various other organisms, ranging from some types of bacteria to pigeons, use the Earths magnetic field for orientation and navigation. At any location, the Earths magnetic field can be represented by a three-dimensional vector, a typical procedure for measuring its direction is to use a compass to determine the direction of magnetic North. Its angle relative to true North is the declination or variation, facing magnetic North, the angle the field makes with the horizontal is the inclination or magnetic dip. The intensity of the field is proportional to the force it exerts on a magnet, another common representation is in X, Y and Z coordinates. The intensity of the field is measured in gauss, but is generally reported in nanoteslas. A nanotesla is also referred to as a gamma, the tesla is the SI unit of the Magnetic field, B. The Earths field ranges between approximately 25,000 and 65,000 nT, by comparison, a strong refrigerator magnet has a field of about 10,000,000 nanoteslas. A map of intensity contours is called an isodynamic chart, as the World Magnetic Model shows, the intensity tends to decrease from the poles to the equator. A minimum intensity occurs in the South Atlantic Anomaly over South America while there are maxima over northern Canada, Siberia, the inclination is given by an angle that can assume values between -90° to 90°. In the northern hemisphere, the field points downwards and it is straight down at the North Magnetic Pole and rotates upwards as the latitude decreases until it is horizontal at the magnetic equator
31.
Euclidean vector
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In mathematics, physics, and engineering, a Euclidean vector is a geometric object that has magnitude and direction. Vectors can be added to other vectors according to vector algebra, a Euclidean vector is frequently represented by a line segment with a definite direction, or graphically as an arrow, connecting an initial point A with a terminal point B, and denoted by A B →. A vector is what is needed to carry the point A to the point B and it was first used by 18th century astronomers investigating planet rotation around the Sun. The magnitude of the vector is the distance between the two points and the direction refers to the direction of displacement from A to B. These operations and associated laws qualify Euclidean vectors as an example of the more generalized concept of vectors defined simply as elements of a vector space. Vectors play an important role in physics, the velocity and acceleration of a moving object, many other physical quantities can be usefully thought of as vectors. Although most of them do not represent distances, their magnitude and direction can still be represented by the length, the mathematical representation of a physical vector depends on the coordinate system used to describe it. Other vector-like objects that describe physical quantities and transform in a similar way under changes of the system include pseudovectors and tensors. The concept of vector, as we know it today, evolved gradually over a period of more than 200 years, about a dozen people made significant contributions. Giusto Bellavitis abstracted the basic idea in 1835 when he established the concept of equipollence, working in a Euclidean plane, he made equipollent any pair of line segments of the same length and orientation. Essentially he realized an equivalence relation on the pairs of points in the plane, the term vector was introduced by William Rowan Hamilton as part of a quaternion, which is a sum q = s + v of a Real number s and a 3-dimensional vector. Like Bellavitis, Hamilton viewed vectors as representative of classes of equipollent directed segments, grassmanns work was largely neglected until the 1870s. Peter Guthrie Tait carried the standard after Hamilton. His 1867 Elementary Treatise of Quaternions included extensive treatment of the nabla or del operator ∇, in 1878 Elements of Dynamic was published by William Kingdon Clifford. Clifford simplified the quaternion study by isolating the dot product and cross product of two vectors from the complete quaternion product and this approach made vector calculations available to engineers and others working in three dimensions and skeptical of the fourth. Josiah Willard Gibbs, who was exposed to quaternions through James Clerk Maxwells Treatise on Electricity and Magnetism, the first half of Gibbss Elements of Vector Analysis, published in 1881, presents what is essentially the modern system of vector analysis. In 1901 Edwin Bidwell Wilson published Vector Analysis, adapted from Gibbs lectures, in physics and engineering, a vector is typically regarded as a geometric entity characterized by a magnitude and a direction. It is formally defined as a line segment, or arrow
32.
Free fall
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In Newtonian physics, free fall is any motion of a body where gravity is the only force acting upon it. In the context of relativity, where gravitation is reduced to a space-time curvature. The present article only concerns itself with free fall in the Newtonian domain, an object in the technical sense of free fall may not necessarily be falling down in the usual sense of the term. An object moving upwards would not normally be considered to be falling, the moon is thus in free fall. The term free fall is used more loosely than in the strict sense defined above. Thus, falling through an atmosphere without a parachute, or lifting device, is also often referred to as free fall. The ancient Greek philosopher Aristotle discussed falling objects in Physics which was perhaps the first book on mechanics, the Italian scientist Galileo Galilei subjected the Aristotelian theories to experimentation and careful observation. He then combined the results of experiments with mathematical analysis in an unprecedented way. According to a tale that may be apocryphal, in 1589–92 Galileo dropped two objects of mass from the Leaning Tower of Pisa. Given the speed at such a fall would occur, it is doubtful that Galileo could have extracted much information from this experiment. Most of his observations of falling bodies were really of bodies rolling down ramps and this slowed things down enough to the point where he was able to measure the time intervals with water clocks and his own pulse. This he repeated a full hundred times until he had achieved an accuracy such that the deviation between two observations never exceeded one-tenth of a pulse beat, in 1589–92, Galileo wrote De Motu Antiquiora, an unpublished manuscript on the motion of falling bodies. Examples of objects in free fall include, A spacecraft with propulsion off, an object dropped at the top of a drop tube. An object thrown upward or a jumping off the ground at low speed. Technically, an object is in free fall even when moving upwards or instantaneously at rest at the top of its motion, if gravity is the only influence acting, then the acceleration is always downward and has the same magnitude for all bodies, commonly denoted g. Since all objects fall at the rate in the absence of other forces, objects. Examples of objects not in free fall, Flying in an aircraft, standing on the ground, the gravitational force is counteracted by the normal force from the ground. Descending to the Earth using a parachute, which balances the force of gravity with a drag force
33.
Newton's law of universal gravitation
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This is a general physical law derived from empirical observations by what Isaac Newton called inductive reasoning. It is a part of classical mechanics and was formulated in Newtons work Philosophiæ Naturalis Principia Mathematica, in modern language, the law states, Every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them, the first test of Newtons theory of gravitation between masses in the laboratory was the Cavendish experiment conducted by the British scientist Henry Cavendish in 1798. It took place 111 years after the publication of Newtons Principia, Newtons law of gravitation resembles Coulombs law of electrical forces, which is used to calculate the magnitude of the electrical force arising between two charged bodies. Both are inverse-square laws, where force is proportional to the square of the distance between the bodies. Coulombs law has the product of two charges in place of the product of the masses, and the constant in place of the gravitational constant. Newtons law has since been superseded by Albert Einsteins theory of general relativity, at the same time Hooke agreed that the Demonstration of the Curves generated thereby was wholly Newtons. In this way, the question arose as to what, if anything and this is a subject extensively discussed since that time and on which some points, outlined below, continue to excite controversy. And that these powers are so much the more powerful in operating. Thus Hooke clearly postulated mutual attractions between the Sun and planets, in a way that increased with nearness to the attracting body, Hookes statements up to 1674 made no mention, however, that an inverse square law applies or might apply to these attractions. Hookes gravitation was also not yet universal, though it approached universality more closely than previous hypotheses and he also did not provide accompanying evidence or mathematical demonstration. It was later on, in writing on 6 January 1679|80 to Newton, Newton, faced in May 1686 with Hookes claim on the inverse square law, denied that Hooke was to be credited as author of the idea. Among the reasons, Newton recalled that the idea had been discussed with Sir Christopher Wren previous to Hookes 1679 letter, Newton also pointed out and acknowledged prior work of others, including Bullialdus, and Borelli. D T Whiteside has described the contribution to Newtons thinking that came from Borellis book, a copy of which was in Newtons library at his death. Newton further defended his work by saying that had he first heard of the inverse square proportion from Hooke, Hooke, without evidence in favor of the supposition, could only guess that the inverse square law was approximately valid at great distances from the center. Thus Newton gave a justification, otherwise lacking, for applying the inverse square law to large spherical planetary masses as if they were tiny particles, after his 1679-1680 correspondence with Hooke, Newton adopted the language of inward or centripetal force. They also involved the combination of tangential and radial displacements, which Newton was making in the 1660s, the lesson offered by Hooke to Newton here, although significant, was one of perspective and did not change the analysis. This background shows there was basis for Newton to deny deriving the inverse square law from Hooke, on the other hand, Newton did accept and acknowledge, in all editions of the Principia, that Hooke had separately appreciated the inverse square law in the solar system
34.
Unit vector
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In mathematics, a unit vector in a normed vector space is a vector of length 1. A unit vector is denoted by a lowercase letter with a circumflex, or hat. The term direction vector is used to describe a unit vector being used to represent spatial direction, two 2D direction vectors, d1 and d2 are illustrated. 2D spatial directions represented this way are equivalent numerically to points on the unit circle, the same construct is used to specify spatial directions in 3D. As illustrated, each direction is equivalent numerically to a point on the unit sphere. The normalized vector or versor û of a vector u is the unit vector in the direction of u, i. e. u ^ = u ∥ u ∥ where ||u|| is the norm of u. The term normalized vector is used as a synonym for unit vector. Unit vectors are often chosen to form the basis of a vector space, every vector in the space may be written as a linear combination of unit vectors. By definition, in a Euclidean space the dot product of two vectors is a scalar value amounting to the cosine of the smaller subtended angle. In three-dimensional Euclidean space, the product of two arbitrary unit vectors is a 3rd vector orthogonal to both of them having length equal to the sine of the smaller subtended angle. Unit vectors may be used to represent the axes of a Cartesian coordinate system and they are often denoted using normal vector notation rather than standard unit vector notation. In most contexts it can be assumed that i, j, the notations, or, with or without hat, are also used, particularly in contexts where i, j, k might lead to confusion with another quantity. When a unit vector in space is expressed, with Cartesian notation, as a combination of i, j, k. The value of each component is equal to the cosine of the angle formed by the vector with the respective basis vector. This is one of the used to describe the orientation of a straight line, segment of straight line, oriented axis. It is important to note that ρ ^ and φ ^ are functions of φ, when differentiating or integrating in cylindrical coordinates, these unit vectors themselves must also be operated on. For a more complete description, see Jacobian matrix, to minimize degeneracy, the polar angle is usually taken 0 ≤ θ ≤180 ∘. It is especially important to note the context of any ordered triplet written in spherical coordinates, here, the American physics convention is used
35.
Taylor series
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In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the functions derivatives at a single point. The concept of a Taylor series was formulated by the Scottish mathematician James Gregory, a function can be approximated by using a finite number of terms of its Taylor series. Taylors theorem gives quantitative estimates on the error introduced by the use of such an approximation, the polynomial formed by taking some initial terms of the Taylor series is called a Taylor polynomial. The Taylor series of a function is the limit of that functions Taylor polynomials as the degree increases, a function may not be equal to its Taylor series, even if its Taylor series converges at every point. A function that is equal to its Taylor series in an interval is known as an analytic function in that interval. The Taylor series of a real or complex-valued function f that is differentiable at a real or complex number a is the power series f + f ′1. Which can be written in the more compact sigma notation as ∑ n =0 ∞ f n, N where n. denotes the factorial of n and f denotes the nth derivative of f evaluated at the point a. The derivative of order zero of f is defined to be f itself and 0 and 0. are both defined to be 1, when a =0, the series is also called a Maclaurin series. The Maclaurin series for any polynomial is the polynomial itself. The Maclaurin series for 1/1 − x is the geometric series 1 + x + x 2 + x 3 + ⋯ so the Taylor series for 1/x at a =1 is 1 − +2 −3 + ⋯. The Taylor series for the exponential function ex at a =0 is x 00, + ⋯ =1 + x + x 22 + x 36 + x 424 + x 5120 + ⋯ = ∑ n =0 ∞ x n n. The above expansion holds because the derivative of ex with respect to x is also ex and this leaves the terms n in the numerator and n. in the denominator for each term in the infinite sum. The Greek philosopher Zeno considered the problem of summing an infinite series to achieve a result, but rejected it as an impossibility. It was through Archimedess method of exhaustion that a number of progressive subdivisions could be performed to achieve a finite result. Liu Hui independently employed a similar method a few centuries later, in the 14th century, the earliest examples of the use of Taylor series and closely related methods were given by Madhava of Sangamagrama. The Kerala school of astronomy and mathematics further expanded his works with various series expansions, in the 17th century, James Gregory also worked in this area and published several Maclaurin series. It was not until 1715 however that a method for constructing these series for all functions for which they exist was finally provided by Brook Taylor. The Maclaurin series was named after Colin Maclaurin, a professor in Edinburgh, if f is given by a convergent power series in an open disc centered at b in the complex plane, it is said to be analytic in this disc
36.
Amphidromic point
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An amphidromic point is a point of zero amplitude of one harmonic constituent of the tide. The tidal range for that harmonic constituent increases with distance from this point and these points are sometimes called tidal nodes. The term amphidromic point derives from the Greek words amphi and dromos, at the amphidromic points of the dominant tidal constituent, there is almost no vertical movement from tidal action. There can be tidal currents since the levels on either side of the amphidromic point are not the same. A separate amphidromic system is created by periodic tidal component. In most locations the principal lunar semi-diurnal, known as M2, is the largest tidal constituent, having cotidal points means they reach high tide at the same time and low tide at the same time. In the accompanying figure, the low tide lags or leads by 1 hr 2 min from its neighboring lines, kelvin wave Tides Theory of tides
37.
Galactic tide
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A galactic tide is tidal force experienced by objects subject to the gravitational field of a galaxy such as the Milky Way. Tidal forces are dependent on the gradient of a field, rather than its strength. Two interacting galaxies will not always collide head-on, and the tidal forces will distort each galaxy along an axis pointing roughly towards, such tails are typically strongly curved. If a tail appears to be straight, it is probably being viewed edge-on, the stars and gas that comprise the tails will have been pulled from the easily distorted galactic discs of one or both bodies, rather than the gravitationally bound galactic centres. Two very prominent examples of collisions producing tidal tails are the Mice Galaxies, just as the Moon raises two water tides on opposite sides of the Earth, so a galactic tide produces two arms in its galactic companion. Secondly, if one of the two galaxies is in the foreground, then the second galaxy — and the bridge between them — may be partially obscured, together, these effects can make it hard to see where one galaxy ends and the next begins. Tidal loops, where a tail joins with its parent galaxy at both ends, are rarer still, because tidal effects are strongest in the immediate vicinity of a galaxy, satellite galaxies are particularly likely to be affected. The stripping mechanism is the same as between two galaxies, although its comparatively weak gravitational field ensures that only the satellite, not the host galaxy, is affected. If the satellite is very small compared to the host, the tidal tails produced are likely to be symmetric. It has been suggested that the discs of gas and stars around some galaxies, such as Andromeda. Tidal effects are present within a galaxy, where their gradients are likely to be steepest. This can have consequences for the formation of stars and planetary systems, typically a stars gravity will dominate within its own system, with only the passage of other stars substantially affecting dynamics. However, at the outer reaches of the system, the gravity is weak. In the Solar System, the hypothetical Oort cloud, believed to be the source of long-period comets, the Oort cloud is believed to be a vast shell surrounding the Solar System, possibly over a light-year in radius. Across such a vast distance, the gradient of the Milky Ways gravitational field plays a far more noticeable role, such a body, being composed of a rock and ice mixture, would become a comet when subjected to the increased solar radiation present in the inner Solar System. It has been suggested that the tide may also contribute to the formation of an Oort cloud. This shows that the effects of the tide are quite complex. Cumulatively the effect can be significant, however, up to 90% of all comets originating from an Oort cloud may be the result of the galactic tide
38.
Tidal resonance
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In oceanography, a tidal resonance occurs when the tide excites one of the resonant modes of the ocean. The effect is most striking when a continental shelf is about a quarter wavelength wide, then an incident tidal wave can be reinforced by reflections between the coast and the shelf edge, the result producing a much higher tidal range at the coast. Famous examples of this effect are found in the Bay of Fundy, where the worlds highest tides are reportedly found, less well known is Leaf Bay, part of Ungava Bay near the entrance of Hudson Strait, which has tides similar to those of the Bay of Fundy. Other resonant regions with large tides include the Patagonian Shelf and on the northwest Australian continental shelf, most of the resonant regions are also responsible for large fractions of the total amount of tidal energy dissipated in the oceans. The speed of waves in the ocean is given, to a good approximation, by g h. For a typical continental shelf with a depth of 100 m, so if the tidal period is 12 hours, a quarter wavelength shelf will have a width of about 300 km. With a narrower shelf, there is still a resonance but it has less effect at tidal frequencies, however the effect is still enough to partly explain why tides along a coast lying behind a continental shelf are often higher than at offshore islands in the deep ocean. Resonances also generate strong currents and it is the turbulence caused by the currents which is responsible for the large amount of tidal energy dissipated in such regions. In the deep ocean, where the depth is typically 4000 m, the difference in speed, when compared to the shelf, is responsible for reflections at the continental shelf edge. Away from resonance this can reduce tidal energy moving onto the shelf, however near a resonant frequency the phase relationship, between the waves on the shelf and in the deep ocean, can have the effect of drawing energy onto the shelf. The increased speed of waves in the deep ocean means that the tidal wavelength there is of order 10,000 km. As the ocean basins have a size, they also have the potential of being resonant. In practice deep ocean resonances are difficult to observe, probably because the ocean loses tidal energy too rapidly to the resonant shelves
39.
Spacetime curvature
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In general relativity, the curvature of spacetime is expressed by the Einstein tensor in the Einstein field equations. These tensor equations determine how spacetime is warped by the presence of mass-energy, the curvature is highly significant in cosmology, as the shape of the universe affects its ultimate fate. Other hypotheses such as Kaluza-Klein theory and string theory involve a curved spacetime, extended into higher dimensions, in attempts to unify forces as a single phenomenon
40.
Oxford University Press
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Oxford University Press is the largest university press in the world, and the second oldest after Cambridge University Press. It is a department of the University of Oxford and is governed by a group of 15 academics appointed by the known as the delegates of the press. They are headed by the secretary to the delegates, who serves as OUPs chief executive, Oxford University has used a similar system to oversee OUP since the 17th century. The university became involved in the print trade around 1480, and grew into a printer of Bibles, prayer books. OUP took on the project became the Oxford English Dictionary in the late 19th century. Moves into international markets led to OUP opening its own offices outside the United Kingdom, by contracting out its printing and binding operations, the modern OUP publishes some 6,000 new titles around the world each year. OUP was first exempted from United States corporation tax in 1972, as a department of a charity, OUP is exempt from income tax and corporate tax in most countries, but may pay sales and other commercial taxes on its products. The OUP today transfers 30% of its surplus to the rest of the university. OUP is the largest university press in the world by the number of publications, publishing more than 6,000 new books every year, the Oxford University Press Museum is located on Great Clarendon Street, Oxford. Visits must be booked in advance and are led by a member of the archive staff, displays include a 19th-century printing press, the OUP buildings, and the printing and history of the Oxford Almanack, Alice in Wonderland and the Oxford English Dictionary. The first printer associated with Oxford University was Theoderic Rood, the first book printed in Oxford, in 1478, an edition of Rufinuss Expositio in symbolum apostolorum, was printed by another, anonymous, printer. Famously, this was mis-dated in Roman numerals as 1468, thus apparently pre-dating Caxton, roods printing included John Ankywylls Compendium totius grammaticae, which set new standards for teaching of Latin grammar. After Rood, printing connected with the university remained sporadic for over half a century, the chancellor, Robert Dudley, 1st Earl of Leicester, pleaded Oxfords case. Some royal assent was obtained, since the printer Joseph Barnes began work, Oxfords chancellor, Archbishop William Laud, consolidated the legal status of the universitys printing in the 1630s. Laud envisaged a unified press of world repute, Oxford would establish it on university property, govern its operations, employ its staff, determine its printed work, and benefit from its proceeds. To that end, he petitioned Charles I for rights that would enable Oxford to compete with the Stationers Company and the Kings Printer and these were brought together in Oxfords Great Charter in 1636, which gave the university the right to print all manner of books. Laud also obtained the privilege from the Crown of printing the King James or Authorized Version of Scripture at Oxford and this privilege created substantial returns in the next 250 years, although initially it was held in abeyance. The Stationers Company was deeply alarmed by the threat to its trade, under this, the Stationers paid an annual rent for the university not to exercise its full printing rights – money Oxford used to purchase new printing equipment for smaller purposes
