Gravity (from Latin gravitas 'weight'[1]), or gravitation, is a natural phenomenon by which all things with mass or energy—including planets, stars, galaxies, and even light[2]—are attracted to (or gravitate toward) one another. On Earth, gravity gives weight to physical objects, and the Moon's gravity causes the tides of the oceans. The gravitational attraction of the original gaseous matter present in the Universe caused it to begin coalescing and forming stars and caused the stars to group together into galaxies, so gravity is responsible for many of the large-scale structures in the Universe. Gravity has an infinite range, although its effects become weaker as objects get further away.
https://en.wikipedia.org/wiki/Gravity
Newton's law of universal gravitation is usually stated as that every particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.[note 1] The publication of the theory has become known as the "first great unification", as it marked the unification of the previously described phenomena of gravity on Earth with known astronomical behaviors.[1][2][3]
This is a general physical law derived from empirical observations by what Isaac Newton called inductive reasoning.[4] It is a part of classical mechanics and was formulated in Newton's work Philosophiæ Naturalis Principia Mathematica ("the Principia"), first published on 5 July 1687. When Newton presented Book 1 of the unpublished text in April 1686 to the Royal Society, Robert Hooke made a claim that Newton had obtained the inverse square law from him.
In today's language, the law states that every point mass attracts every other point mass by a force acting along the lineintersecting the two points. The force is proportional to the product of the two masses, and inversely proportional to the square of the distance between them.[5]
The equation for universal gravitation thus takes the form:
where F is the gravitational force acting between two objects, m1 and m2 are the masses of the objects, r is the distance between the centers of their masses, and G is the gravitational constant.
The first test of Newton's theory of gravitation between masses in the laboratory was the Cavendish experimentconducted by the British scientist Henry Cavendish in 1798.[6] It took place 111 years after the publication of Newton's Principia and approximately 71 years after his death.
Newton's law of gravitation resembles Coulomb's 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 inversely proportional to the square of the distance between the bodies. Coulomb's law has the product of two charges in place of the product of the masses, and the Coulomb constant in place of the gravitational constant.
Newton's law has since been superseded by Albert Einstein's theory of general relativity, but it continues to be used as an excellent approximation of the effects of gravity in most applications. Relativity is required only when there is a need for extreme accuracy, or when dealing with very strong gravitational fields, such as those found near extremely massive and dense objects, or at small distances (such as Mercury's orbit around the Sun).
https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation
In science, an inverse-square law is any scientific law stating that a specified physical quantity is inversely proportional to the square of the distance from the source of that physical quantity. The fundamental cause for this can be understood as geometric dilution corresponding to point-source radiation into three-dimensional space.
Radar energy expands during both the signal transmission and the reflected return, so the inverse square for both paths means that the radar will receive energy according to the inverse fourth power of the range.
To prevent dilution of energy while propagating a signal, certain methods can be used such as a waveguide, which acts like a canal does for water, or how a gun barrel restricts hot gas expansion to one dimension in order to prevent loss of energy transfer to a bullet.
https://en.wikipedia.org/wiki/Inverse-square_law
In quantum mechanics, the inverse square potential is a form of a central force potential which has the unusual property of the eigenstates of the corresponding Hamiltonian operator remaining eigenstates in a scaling of all cartesian coordinates by the same constant.[1] Apart from this curious feature, it's by far less important central force problem than that of the Keplerian inverse square force system.
Description[edit]
The potential energy function of an inverse square potential is
,
where is some constant and is the Euclidean distance from some central point. If is positive, the potential is attractive and if is negative, the potential is repulsive. The corresponding Hamiltonian operator is
,
where is the mass of the particle moving in the potential.
Properties[edit]
The canonical commutation relation of quantum mechanics, , has the property of being invariant in a scaling
![{\displaystyle [{\hat {x}}_{i},{\hat {p}}_{i}]=i\hbar }](https://wikimedia.org/api/rest_v1/media/math/render/svg/29332d10932741647cfa29dc4a06bd5594f2a0f8)
, and ,
where is some scaling factor. The momentum and the position are vectors, while the components , and the radius are scalars. In an inverse square potential system, if a wavefunction is an eigenfunction of the Hamiltonian operator , it is also an eigenfunction of the operator , where the scaled operators and are defined as above.
This also means that if a radially symmetric wave function is an eigenfunction of with eigenvalue , then also is an eigenfunction, with eigenvalue . Therefore, the energy spectrum of the system is a continuum of values.
The system with a particle in an inverse square potential with positive (attractive potential) is an example of so-called falling-to-center problem, where there is no lowest energy wavefunction and there are eigenfunctions where the particle is arbitrarily localized in the vicinity of the central point .[2]
See also[edit]
https://en.wikipedia.org/wiki/Inverse_square_potential
In physics, mathematics and statistics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor, and thus represent a universality.
The technical term for this transformation is a dilatation (also known as dilation), and the dilatations can also form part of a larger conformal symmetry.
- In mathematics, scale invariance usually refers to an invariance of individual functions or curves. A closely related concept is self-similarity, where a function or curve is invariant under a discrete subset of the dilations. It is also possible for the probability distributions of random processes to display this kind of scale invariance or self-similarity.
- In classical field theory, scale invariance most commonly applies to the invariance of a whole theory under dilatations. Such theories typically describe classical physical processes with no characteristic length scale.
- In quantum field theory, scale invariance has an interpretation in terms of particle physics. In a scale-invariant theory, the strength of particle interactions does not depend on the energy of the particles involved.
- In statistical mechanics, scale invariance is a feature of phase transitions. The key observation is that near a phase transition or critical point, fluctuations occur at all length scales, and thus one should look for an explicitly scale-invariant theory to describe the phenomena. Such theories are scale-invariant statistical field theories, and are formally very similar to scale-invariant quantum field theories.
- Universality is the observation that widely different microscopic systems can display the same behaviour at a phase transition. Thus phase transitions in many different systems may be described by the same underlying scale-invariant theory.
- In general, dimensionless quantities are scale invariant. The analogous concept in statistics are standardized moments, which are scale invariant statistics of a variable, while the unstandardized moments are not.
An electrical grid is an interconnected network for electricity delivery from producers to consumers. Electrical grids vary in size and can cover whole countries or continents. It consists of:[1]
- power stations: often located near energy and away from heavily populated areas
- electrical substations to step voltage up or down
- electric power transmission to carry power long distances
- electric power distribution to individual customers, where voltage is stepped down again to the required service voltage(s).
Although electrical grids are widespread, as of 2016, 1.4 billion people worldwide were not connected to an electricity grid.[2] As electrification increases, the number of people with access to grid electricity is growing. About 840 million people (mostly in Africa) had no access to grid electricity in 2017, down from 1.2 billion in 2010.[3]
Electrical grids can be prone to malicious intrusion or attack; thus, there is a need for electric grid security. Also as electric grids modernize and introduce computer technology, cyber threats start to become a security risk.[4] Particular concerns relate to the more complex computer systems needed to manage grids.[5]
Grids are nearly always synchronous, meaning all distribution areas operate with three phase alternating current (AC) frequencies synchronized (so that voltage swings occur at almost the same time). This allows transmission of AC power throughout the area, connecting a large number of electricity generators and consumers and potentially enabling more efficient electricity markets and redundant generation.
The combined transmission and distribution network is part of electricity delivery, known as the "power grid" in North America, or just "the grid". In the United Kingdom, India, Tanzania, Myanmar, Malaysia and New Zealand, the network is known as the National Grid.
https://en.wikipedia.org/wiki/Electrical_grid
A waveguide is a structure that guides waves, such as electromagnetic waves or sound, with minimal loss of energy by restricting the transmission of energy to one direction. Without the physical constraint of a waveguide, wave intensities decrease according to the inverse square law as they expand into three dimensional space.
There are different types of waveguides for different types of waves. The original and most common[1] meaning is a hollow conductive metal pipe used to carry high frequency radio waves, particularly microwaves. Dielectric waveguides are used at higher radio frequencies, and transparent dielectric waveguides and optical fibers serve as waveguides for light. In acoustics, air ducts and horns are used as waveguides for sound in musical instruments and loudspeakers, and specially-shaped metal rods conduct ultrasonic waves in ultrasonic machining.
The geometry of a waveguide reflects its function; in addition to more common types that channel the wave in one dimension, there are two-dimensional slab waveguides which confine waves to two dimensions. The frequency of the transmitted wave also dictates the size of a waveguide: each waveguide has a cutoff wavelength determined by its size and will not conduct waves of greater wavelength; an optical fiber that guides light will not transmit microwaves which have a much larger wavelength. Some naturally occurring structures can also act as waveguides. The SOFAR channel layer in the ocean can guide the sound of whale song across enormous distances.[2] Any shape of crossection of waveguide can support EM waves. Irregular shapes are difficult to analyse. Commonly used waveguides are rectangular and circular in shape.
https://en.wikipedia.org/wiki/Waveguide
A tether is a cord, fixture, or flexible attachment that characteristically anchors something movable to something fixed; it also maybe used to connect two movable objects, such as an item being towed by its tow.
Applications for tethers include: fall arrest systems, lanyards, balloons, kites, airborne wind-power systems, anchors, floating water power systems, towing, animal constraint, space walks, power kiteing, and anti-theft devices.[1]
https://en.wikipedia.org/wiki/Tether
Electrodynamic tethers (EDTs) are long conducting wires, such as one deployed from a tether satellite, which can operate on electromagnetic principles as generators, by converting their kinetic energy to electrical energy, or as motors, converting electrical energy to kinetic energy.[1] Electric potential is generated across a conductive tether by its motion through a planet's magnetic field.
A number of missions have demonstrated electrodynamic tethers in space, most notably the TSS-1, TSS-1R, and Plasma Motor Generator (PMG) experiments.
https://en.wikipedia.org/wiki/Electrodynamic_tether
Plastic pipe is a tubular section, or hollow cylinder, made of plastic. It is usually, but not necessarily, of circular cross-section, used mainly to convey substances which can flow—liquids and gases (fluids), slurries, powders and masses of small solids. It can also be used for structural applications; hollow pipesare far stiffer per unit weight than solid members.
Plastic pipework is used for the conveyance of drinking water, waste water, chemicals, heating fluid and cooling fluids, foodstuffs, ultra-pure liquids, slurries, gases, compressed air, irrigation, plastic pressure pipe systems, and vacuum system applications.
https://en.wikipedia.org/wiki/Plastic_pipework
- clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a lake. Dynamical systems theory began in the late nineteenth century
Hydronics (hydro- meaning "water") is the use of liquid water or gaseous water (steam) or a water solution (usually glycol with water) as heat-transfer medium in heating and cooling systems. The name differentiates such systems from oil and steam systems.[clarification needed] Historically, in large-scale commercial buildings such as high-rise and campus facilities, a hydronic system may include both a chilled and a heated water loop, to provide for both heating and air conditioning. Chillers and cooling towers are used either separately or together as means to provide water cooling, while boilers heat water. A recent innovation is the chiller boiler system, which provides an efficient form of HVAC for homes and smaller commercial spaces.
https://en.wikipedia.org/wiki/Hydronics
Sewerage (or sewage system) is the infrastructure that conveys sewage or surface runoff (stormwater, meltwater, rainwater) using sewers. It encompasses components such as receiving drains, manholes, pumping stations, storm overflows, and screening chambers of the combined sewer or sanitary sewer. Sewerage ends at the entry to a sewage treatment plant or at the point of discharge into the environment. It is the system of pipes, chambers, manholes, etc. that conveys the sewage or storm water.
In many cities, sewage (or municipal wastewater) is carried together with stormwater, in a combined sewer system, to a sewage treatment plant. In some urban areas, sewage is carried separately in sanitary sewers and runoff from streets is carried in storm drains. Access to these systems, for maintenance purposes, is typically through a manhole. During high precipitation periods a sewer system may experience a combined sewer overflow event or a sanitary sewer overflow event, which forces untreated sewage to flow directly to receiving waters. This can pose a serious threat to public health and the surrounding environment.
The system of sewers is called sewerage or sewerage system in British English and sewage system in American English.[1]
https://en.wikipedia.org/wiki/Sewerage
A water distribution system is a part of water supply network with components that carry potable water from a centralized treatment plant or wells to consumers to satisfy residential, commercial, industrial and fire fighting requirements.[3][4]
https://en.wikipedia.org/wiki/Water_distribution_system
A nuclear reactor, formerly known as an atomic pile, is a device used to initiate and control a fission nuclear chain reaction or nuclear fusion reactions. Nuclear reactors are used at nuclear power plants for electricity generation and in nuclear marine propulsion. Heat from nuclear fission is passed to a working fluid (water or gas), which in turn runs through steam turbines. These either drive a ship's propellers or turn electrical generators' shafts. Nuclear generated steam in principle can be used for industrial process heat or for district heating. Some reactors are used to produce isotopes for medical and industrial use, or for production of weapons-gradeplutonium. As of early 2019, the IAEA reports there are 454 nuclear power reactors and 226 nuclear research reactors in operation around the world.[1][2][3]
https://en.wikipedia.org/wiki/Nuclear_reactor
The Electromagnetic Aircraft Launch System (EMALS) is a type of aircraft launching system developed by General Atomics for the United States Navy. The system launches carrier-based aircraft by means of a catapultemploying a linear induction motor rather than the conventional steam piston. EMALS was first installed on the United States Navy's Gerald R. Ford-class aircraft carrier, USS Gerald R. Ford.
Its main advantage is that it accelerates aircraft more smoothly, putting less stress on their airframes. Compared to steam catapults, the EMALS also weighs less, is expected to cost less and require less maintenance, and can launch both heavier and lighter aircraft than a steam piston-driven system. It also reduces the carrier's requirement of fresh water, thus reducing the demand for energy-intensive desalination.
China is reportedly developing a similar system which is expected to be used on China's Type 003 aircraft carriers.[1][2]
https://en.wikipedia.org/wiki/Electromagnetic_Aircraft_Launch_System
A linear induction motor (LIM) is an alternating current (AC), asynchronous linear motor that works by the same general principles as other induction motors but is typically designed to directly produce motion in a straight line. Characteristically, linear induction motors have a finite primary or secondary length, which generates end-effects, whereas a conventional induction motor is arranged in an endless loop.[1]
Despite their name, not all linear induction motors produce linear motion; some linear induction motors are employed for generating rotations of large diameters where the use of a continuous primary would be very expensive.
As with rotary motors, linear motors frequently run on a three-phase power supply and can support very high speeds. However, there are end-effects that reduce the motor's force, and it is often not possible to fit a gearbox to trade off force and speed. Linear induction motors are thus frequently less energy efficient than normal rotary motors for any given required force output.
LIMs, unlike their rotary counterparts, can give a levitation effect. They are therefore often used where contactless force is required, where low maintenance is desirable, or where the duty cycle is low. Their practical uses include magnetic levitation, linear propulsion, and linear actuators. They have also been used for pumping liquid metals.[2]
https://en.wikipedia.org/wiki/Linear_induction_motor
Electromagnetic or magnetic induction is the production of an electromotive force across an electrical conductor in a changing magnetic field.
Michael Faraday is generally credited with the discovery of induction in 1831, and James Clerk Maxwell mathematically described it as Faraday's law of induction. Lenz's law describes the direction of the induced field. Faraday's law was later generalized to become the Maxwell–Faraday equation, one of the four Maxwell equations in his theory of electromagnetism.
Electromagnetic induction has found many applications, including electrical components such as inductors and transformers, and devices such as electric motors and generators.
https://en.wikipedia.org/wiki/Electromagnetic_induction
A launch loop, or Lofstrom loop, is a proposed system for launching objects into orbit using a moving cable-like system situated inside a sheath attached to the Earth at two ends and suspended above the atmosphere in the middle. The design concept was published by Keith Lofstrom and describes an active structure maglev cable transport system that would be around 2,000 km (1,240 mi) long and maintained at an altitude of up to 80 km (50 mi). A launch loop would be held up at this altitude by the momentum of a belt that circulates around the structure. This circulation, in effect, transfers the weight of the structure onto a pair of magnetic bearings, one at each end, which support it.
Launch loops are intended to achieve non-rocket spacelaunch of vehicles weighing 5 metric tons by electromagnetically accelerating them so that they are projected into Earth orbit or even beyond. This would be achieved by the flat part of the cable which forms an acceleration track above the atmosphere.[1]
The system is designed to be suitable for launching humans for space tourism, space exploration and space colonization, and provides a relatively low 3g acceleration.[2]
https://en.wikipedia.org/wiki/Launch_loop
A linear stage or translation stage is a component of a precise motion system used to restrict an object to a single axis of motion. The term linear slide is often used interchangeably with "linear stage", though technically "linear slide" refers to a linear motion bearing, which is only a component of a linear stage. All linear stages consist of a platform and a base, joined by some form of guide or linear bearing in such a way that the platform is restricted to linear motion with respect to the base. In common usage, the term linear stage may or may not also include the mechanism by which the position of the platform is controlled relative to the base.
https://en.wikipedia.org/wiki/Linear_stage
Motion system is a component of a test and measurement system that provides motion to a load or loads in a one or many directions. Generally a motion system is made up of a set (or stack) of linear and rotational stages. A linear stage moves in a straight line, while a rotation stage moves in a partial or full circle. A stage can either be manually controlled with a knob control, or automated with a motion controller.
A motion system generally is computer controlled and can perform fast, reliable, repeatable, and accurate positioning of loads. Most systems will support motion in X and Y directions, which is referred to as an XY stack. Often either a Z axis (up/down motion) or R axis (rotational motion) is placed on top of the XY stack.
For automated stages, a scale can be attached to the internals of the stage and an encoder used to measure the position on the scale and report this to the controller, thereby determining the precise position of the stage. This allows for a motion controller to reliably and repeatably move to set positions with the linear stage.
https://en.wikipedia.org/wiki/Motion_system
A system of measurement is a collection of units of measurement and rules relating them to each other. Systems of measurement have historically been important, regulated and defined for the purposes of science and commerce. Systems of measurement in use include the International System of Units (SI), the modern form of the metric system, the British imperial system, and the United States customary system.
https://en.wikipedia.org/wiki/System_of_measurement
Magnetic levitation (maglev) or magnetic suspension is a method by which an object is suspended with no support other than magnetic fields. Magnetic force is used to counteract the effects of the gravitational force and any other forces.
The two primary issues involved in magnetic levitation are lifting forces: providing an upward force sufficient to counteract gravity, and stability: ensuring that the system does not spontaneously slide or flip into a configuration where the lift is neutralized.
Magnetic levitation is used for maglev trains, contactless melting, magnetic bearings and for product display purposes.
https://en.wikipedia.org/wiki/Magnetic_levitation
Magnetic resonance imaging (MRI) is a medical imaging technique used in radiology to form pictures of the anatomyand the physiological processes of the body. MRI scanners use strong magnetic fields, magnetic field gradients, and radio waves to generate images of the organs in the body. MRI does not involve X-rays or the use of ionizing radiation, which distinguishes it from CT and PET scans. MRI is a medical application of nuclear magnetic resonance (NMR) which can also be used for imaging in other NMR applications, such as NMR spectroscopy.
MRI is widely used in hospitals and clinics for medical diagnosis, staging and follow-up of disease. Compared to CT, MRI provides better contrast in images of soft-tissues, e.g. in the brain or abdomen. However, it may be perceived as less comfortable by patients, due to the usually longer and louder measurements with the subject in a long, confining tube. Additionally, implants and other non-removable metal in the body can pose a risk and may exclude some patients from undergoing an MRI examination safely.
MRI was originally called NMRI (nuclear magnetic resonance imaging), but "nuclear" was dropped to avoid negative associations.[1] Certain atomic nuclei are able to absorb radio frequency energy when placed in an external magnetic field; the resultant evolving spin polarization can induce a RF signal in a radio frequency coil and thereby be detected.[2]In clinical and research MRI, hydrogen atoms are most often used to generate a macroscopic polarization that is detected by antennae close to the subject being examined.[2] Hydrogen atoms are naturally abundant in humans and other biological organisms, particularly in water and fat. For this reason, most MRI scans essentially map the location of water and fat in the body. Pulses of radio waves excite the nuclear spin energy transition, and magnetic field gradients localize the polarization in space. By varying the parameters of the pulse sequence, different contrasts may be generated between tissues based on the relaxation properties of the hydrogen atoms therein.
Since its development in the 1970s and 1980s, MRI has proven to be a versatile imaging technique. While MRI is most prominently used in diagnostic medicine and biomedical research, it also may be used to form images of non-living objects. Diffusion MRI and Functional MRI extends the utility of MRI to capture neuronal tracts and blood flow respectively in the nervous system, in addition to detailed spatial images. The sustained increase in demand for MRI within health systems has led to concerns about cost effectiveness and overdiagnosis.[3][4]
https://en.wikipedia.org/wiki/Magnetic_resonance_imaging
Earth is the third planet from the Sun and the only astronomical object known to harbour and support life. About 29.2% of Earth's surface is land consisting of continents and islands. The remaining 70.8% is covered with water, mostly by oceans, seas, gulfs, and other salt-water bodies, but also by lakes, rivers, and other freshwater, which together constitute the hydrosphere. Much of Earth's polar regions are covered in ice. Earth's outer layer is divided into several rigid tectonic plates that migrate across the surface over many millions of years, while its interior remains active with a solid iron inner core, a liquid outer core that generates Earth's magnetic field, and a convective mantle that drives plate tectonics.
Earth's atmosphere consists mostly of nitrogen and oxygen. More solar energy is received by tropical regions than polar regions and is redistributed by atmospheric and ocean circulation. Greenhouse gases also play an important role in regulating the surface temperature. A region's climate is not only determined by latitude, but also by elevation and proximity to moderating oceans, among other factors. Severe weather, such as tropical cyclones, thunderstorms, and heatwaves, occurs in most areas and greatly impacts life.
Earth's gravity interacts with other objects in space, especially the Moon, which is Earth's only natural satellite. Earth orbits around the Sun in about 365.25 days. Earth's axis of rotation is tilted with respect to its orbital plane, producing seasons on Earth. The gravitational interaction between Earth and the Moon causes tides, stabilizes Earth's orientation on its axis, and gradually slows its rotation. Earth is the densest planet in the Solar System and the largest and most massive of the four rocky planets.
According to radiometric dating estimation and other evidence, Earth formed over 4.5 billion years ago. Within the first billion years of Earth's history, life appeared in the oceans and began to affect Earth's atmosphere and surface, leading to the proliferation of anaerobic and, later, aerobic organisms. Some geological evidence indicates that life may have arisen as early as 4.1 billion years ago. Since then, the combination of Earth's distance from the Sun, physical properties, and geological history have allowed life to evolve and thrive. In the history of life on Earth, biodiversity has gone through long periods of expansion, occasionally punctuated by mass extinctions. More than 99% of all species that ever lived on Earth are extinct. Almost 8 billion humans live on Earth and depend on its biosphere and natural resources for their survival. Humans increasingly impact Earth's surface, hydrology, atmospheric processes, and other life.
 The Blue Marble, the most widely used photograph of Earth,[1][2] taken by the Apollo 17 mission in 1972 | |||||||||||||
| Designations | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Gaia, Terra, Tellus, the world, the globe | |||||||||||||
| Adjectives | Earthly, terrestrial, terran, tellurian | ||||||||||||
| Orbital characteristics | |||||||||||||
| Epoch J2000[n 1] | |||||||||||||
| Aphelion | 152100000 km (94500000 mi)[n 2] | ||||||||||||
| Perihelion | 147095000 km (91401000 mi)[n 2] | ||||||||||||
| 149598023 km (92955902 mi)[3] | |||||||||||||
| Eccentricity | 0.0167086[3] | ||||||||||||
| 365.256363004 d[4] (31558.1497635 ks) | |||||||||||||
Average orbital speed | 29.78 km/s[5] (107200 km/h; 66600 mph) | ||||||||||||
| 358.617° | |||||||||||||
| Inclination |
| ||||||||||||
| −11.26064°[5] to J2000 ecliptic | |||||||||||||
| 2022-Jan-04[7] | |||||||||||||
| 114.20783°[5] | |||||||||||||
| Satellites |
| ||||||||||||
| Physical characteristics | |||||||||||||
Mean radius | 6371.0 km (3958.8 mi)[9] | ||||||||||||
Equatorialradius | 6378.137 km (3963.191 mi)[10][11] | ||||||||||||
Polar radius | 6356.752 km (3949.903 mi)[12] | ||||||||||||
| Flattening | 1/298.257222101 (ETRS89)[13] | ||||||||||||
| Circumference |
| ||||||||||||
| Volume | 1.08321×1012 km3 (2.59876×1011 cu mi)[5] | ||||||||||||
| Mass | 5.97237×1024 kg (1.31668×1025 lb)[16] (3.0×10−6 M☉) | ||||||||||||
Mean density | 5.514 g/cm3 (0.1992 lb/cu in)[5] | ||||||||||||
| 9.80665 m/s2 (1 g; 32.1740 ft/s2)[17] | |||||||||||||
| 0.3307[18] | |||||||||||||
| 11.186 km/s[5] (40270 km/h; 25020 mph) | |||||||||||||
Sidereal rotation period | |||||||||||||
Equatorial rotation velocity | 0.4651 km/s[20] (1674.4 km/h; 1040.4 mph) | ||||||||||||
| 23.4392811°[4] | |||||||||||||
| Albedo | |||||||||||||
| |||||||||||||
| Atmosphere | |||||||||||||
Surface pressure | 101.325 kPa (at MSL) | ||||||||||||
| Composition by volume | |||||||||||||
https://en.wikipedia.org/wiki/Earth
The ΛCDM (Lambda cold dark matter) or Lambda-CDM model is a parameterization of the Big Bang cosmologicalmodel in which the universe contains three major components: first, a cosmological constant denoted by Lambda (GreekΛ) associated with dark energy; second, the postulated cold dark matter (abbreviated CDM); and third, ordinary matter. It is frequently referred to as the standard model of Big Bang cosmology because it is the simplest model that provides a reasonably good account of the following properties of the cosmos:
- the existence and structure of the cosmic microwave background
- the large-scale structure in the distribution of galaxies
- the observed abundances of hydrogen (including deuterium), helium, and lithium
- the accelerating expansion of the universe observed in the light from distant galaxies and supernovae
The model assumes that general relativity is the correct theory of gravity on cosmological scales. It emerged in the late 1990s as a concordance cosmology, after a period of time when disparate observed properties of the universe appeared mutually inconsistent, and there was no consensus on the makeup of the energy density of the universe.
The ΛCDM model can be extended by adding cosmological inflation, quintessence and other elements that are current areas of speculation and research in cosmology.
Some alternative models challenge the assumptions of the ΛCDM model. Examples of these are modified Newtonian dynamics, entropic gravity, modified gravity, theories of large-scale variations in the matter density of the universe, bimetric gravity, scale invariance of empty space, and decaying dark matter (DDM).[1][2][3][4][5]
https://en.wikipedia.org/wiki/Lambda-CDM_model
https://en.wikipedia.org/wiki/Cosmic_neutrino_background
https://en.wikipedia.org/wiki/Atmosphere
https://en.wikipedia.org/wiki/Atmosphere_of_Earth
https://en.wikipedia.org/wiki/Vacuum
https://en.wikipedia.org/wiki/Spinor
https://en.wikipedia.org/wiki/Spring
https://en.wikipedia.org/wiki/Spiral
https://en.wikipedia.org/wiki/Pendulum
https://en.wikipedia.org/wiki/String
https://en.wikipedia.org/wiki/Beam
https://en.wikipedia.org/wiki/angular_momentum
A vacuum is a space devoid of matter. The word is derived from the Latin adjective vacuus for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure.[1] Physicists often discuss ideal test results that would occur in a perfect vacuum, which they sometimes simply call "vacuum" or free space, and use the term partial vacuum to refer to an actual imperfect vacuum as one might have in a laboratory or in space. In engineering and applied physics on the other hand, vacuum refers to any space in which the pressure is considerably lower than atmospheric pressure.[2] The Latin term in vacuo is used to describe an object that is surrounded by a vacuum.
The quality of a partial vacuum refers to how closely it approaches a perfect vacuum. Other things equal, lower gas pressuremeans higher-quality vacuum. For example, a typical vacuum cleaner produces enough suction to reduce air pressure by around 20%.[3] But higher-quality vacuums are possible. Ultra-high vacuum chambers, common in chemistry, physics, and engineering, operate below one trillionth (10−12) of atmospheric pressure (100 nPa), and can reach around 100 particles/cm3.[4] Outer space is an even higher-quality vacuum, with the equivalent of just a few hydrogen atoms per cubic meter on average in intergalactic space.[5]
Vacuum has been a frequent topic of philosophical debate since ancient Greek times, but was not studied empirically until the 17th century. Evangelista Torricelliproduced the first laboratory vacuum in 1643, and other experimental techniques were developed as a result of his theories of atmospheric pressure. A Torricellian vacuum is created by filling a tall glass container closed at one end with mercury, and then inverting it in a bowl to contain the mercury (see below).[6]
Vacuum became a valuable industrial tool in the 20th century with the introduction of incandescent light bulbs and vacuum tubes, and a wide array of vacuum technologies has since become available. The development of human spaceflight has raised interest in the impact of vacuum on human health, and on life forms in general.
https://en.wikipedia.org/wiki/Vacuum
The atmosphere of Earth, commonly known as air, is the layer of gases retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing for liquid water to exist on the Earth's surface, absorbing ultraviolet solar radiation, warming the surface through heat retention (greenhouse effect), and reducing temperature extremes between day and night (the diurnal temperature variation).
By mole fraction (i.e., by number of molecules), dry air contains 78.08% nitrogen, 20.95% oxygen, 0.93% argon, 0.04% carbon dioxide, and small amounts of other gases.[8] Air also contains a variable amount of water vapor, on average around 1% at sea level, and 0.4% over the entire atmosphere. Air composition, temperature, and atmospheric pressure vary with altitude. Within the atmosphere, air suitable for use in photosynthesis by terrestrial plants and breathing of terrestrial animalsis found only in Earth's troposphere.[citation needed]
Earth's early atmosphere consisted of gases in the solar nebula, primarily hydrogen. The atmosphere changed significantly over time, affected by many factors such as volcanism, life, and weathering. Recently, human activity has also contributed to atmospheric changes, such as global warming, ozone depletion and acid deposition.
The atmosphere has a mass of about 5.15×1018 kg,[9] three quarters of which is within about 11 km (6.8 mi; 36,000 ft) of the surface. The atmosphere becomes thinner with increasing altitude, with no definite boundary between the atmosphere and outer space. The Kármán line, at 100 km (62 mi) or 1.57% of Earth's radius, is often used as the border between the atmosphere and outer space. Atmospheric effects become noticeable during atmospheric reentry of spacecraft at an altitude of around 120 km (75 mi). Several layers can be distinguished in the atmosphere, based on characteristics such as temperature and composition.
The study of Earth's atmosphere and its processes is called atmospheric science (aerology), and includes multiple subfields, such as climatology and atmospheric physics. Early pioneers in the field include Léon Teisserenc de Bort and Richard Assmann.[10] The study of historic atmosphere is called paleoclimatology.
https://en.wikipedia.org/wiki/Atmosphere_of_Earth
An atmosphere (from Ancient Greek ἀτμός (atmós) 'vapour, steam', and σφαῖρα (sphaîra) 'sphere') is a layer of gas or layers of gases that envelope a planet, and is held in place by the gravity of the planetary body. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low.[1] A stellar atmosphere is the outer region of a star, which includes the layers above the opaque photosphere; stars of low temperature might have outer atmospheres containing compound molecules.
The atmosphere of Earth is composed of nitrogen (78%), oxygen (21%), argon (0.9%), carbon dioxide (0.04%) and trace gases.[2] Most organisms use oxygen for respiration; lightning and bacteria perform nitrogen fixation to produce ammonia that is used to make nucleotides and amino acids; plants, algae, and cyanobacteria use carbon dioxide for photosynthesis. The layered composition of the atmosphere minimises the harmful effects of sunlight, ultraviolet radiation, the solar wind, and cosmic rays to protect organisms from genetic damage. The current composition of the atmosphere of the Earth is the product of billions of years of biochemical modificationof the paleoatmosphere by living organisms.
https://en.wikipedia.org/wiki/Atmosphere
n astronomy and planetary science, a magnetosphere is a region of space surrounding an astronomical object in which charged particles are affected by that object's magnetic field.[1][2] It is created by a star or planet with an active interior dynamo.
In the space environment close to a planetary body, the magnetic field resembles a magnetic dipole. Farther out, field linescan be significantly distorted by the flow of electrically conducting plasma, as emitted from the Sun (i.e., the solar wind) or a nearby star.[3][4] Planets having active magnetospheres, like the Earth, are capable of mitigating or blocking the effects of solar radiation or cosmic radiation, that also protects all living organisms from potentially detrimental and dangerous consequences. This is studied under the specialized scientific subjects of plasma physics, space physics and aeronomy.
Study of Earth's magnetosphere began in 1600, when William Gilbert discovered that the magnetic field on the surface of Earth resembled that of a terrella, a small, magnetized sphere. In the 1940s, Walter M. Elsasser proposed the model of dynamo theory, which attributes Earth's magnetic field to the motion of Earth's iron outer core. Through the use of magnetometers, scientists were able to study the variations in Earth's magnetic field as functions of both time and latitude and longitude.
Beginning in the late 1940s, rockets were used to study cosmic rays. In 1958, Explorer 1, the first of the Explorer series of space missions, was launched to study the intensity of cosmic rays above the atmosphere and measure the fluctuations in this activity. This mission observed the existence of the Van Allen radiation belt(located in the inner region of Earth's magnetosphere), with the follow up Explorer 3 later that year definitively proving its existence. Also during 1958, Eugene Parkerproposed the idea of the solar wind, with the term 'magnetosphere' being proposed by Thomas Gold in 1959 to explain how the solar wind interacted with the Earth's magnetic field. The later mission of Explorer 12 in 1961 led by the Cahill and Amazeen observation in 1963 of a sudden decrease in magnetic field strength near the noon-time meridian, later was named the magnetopause. By 1983, the International Cometary Explorer observed the magnetotail, or the distant magnetic field.[4]
https://en.wikipedia.org/wiki/Magnetosphere
Induced magnetosphere[edit]
Venus is known not to have a magnetic field.[39][40] The reason for its absence is not at all clear, but it may be related to a reduced intensity of convection in the Venusian mantle. Venus only has an induced magnetosphere formed by the Sun's magnetic field carried by the solar wind.[39] This process can be understood as the field lines wrapping around an obstacle—Venus in this case. The induced magnetosphere of Venus has a bow shock, magnetosheath, magnetopause and magnetotailwith the current sheet.[39][40]
At the subsolar point the bow shock stands 1900 km (0.3 Rv, where Rv is the radius of Venus) above the surface of Venus. This distance was measured in 2007 near the solar activity minimum.[40] Near the solar activity maximum it can be several times further from the planet.[39] The magnetopause is located at the altitude of 300 km.[40] The upper boundary of the ionosphere (ionopause) is near 250 km. Between the magnetopause and ionopause there exists a magnetic barrier—a local enhancement of the magnetic field, which prevents the solar plasma from penetrating deeper into the Venusian atmosphere, at least near solar activity minimum. The magnetic field in the barrier reaches up to 40 nT.[40] The magnetotail continues up to ten radii from the planet. It is the most active part of the Venusian magnetosphere. There are reconnection events and particle acceleration in the tail. The energies of electrons and ions in the magnetotail are around 100 eV and 1000 eV respectively.[42]
Due to the lack of the intrinsic magnetic field on Venus, the solar wind penetrates relatively deep into the planetary exosphere and causes substantial atmosphere loss.[43] The loss happens mainly via the magnetotail. Currently the main ion types being lost are O+, H+ and He+. The ratio of hydrogen to oxygen losses is around 2 (i.e. almost stoichiometric) indicating the ongoing loss of water.[42]
https://en.wikipedia.org/wiki/Atmosphere_of_Venus#Induced_magnetosphere
Shear strength is a term used in soil mechanics to describe the magnitude of the shear stress that a soil can sustain. The shear resistance of soil is a result of friction and interlocking of particles, and possibly cementation or bonding at particle contacts. Due to interlocking, particulate material may expand or contract in volume as it is subject to shear strains. If soil expands its volume, the density of particles will decrease and the strength will decrease; in this case, the peak strength would be followed by a reduction of shear stress. The stress-strain relationship levels off when the material stops expanding or contracting, and when interparticle bonds are broken. The theoretical state at which the shear stress and density remain constant while the shear strain increases may be called the critical state, steady state, or residual strength.
The volume change behavior and interparticle friction depend on the density of the particles, the intergranular contact forces, and to a somewhat lesser extent, other factors such as the rate of shearing and the direction of the shear stress. The average normal intergranular contact force per unit area is called the effective stress.
If water is not allowed to flow in or out of the soil, the stress path is called an undrained stress path. During undrained shear, if the particles are surrounded by a nearly incompressible fluid such as water, then the density of the particles cannot change without drainage, but the water pressure and effective stress will change. On the other hand, if the fluids are allowed to freely drain out of the pores, then the pore pressures will remain constant and the test path is called a drained stress path. The soil is free to dilate or contract during shear if the soil is drained. In reality, soil is partially drained, somewhere between the perfectly undrained and drained idealized conditions.
The shear strength of soil depends on the effective stress, the drainage conditions, the density of the particles, the rate of strain, and the direction of the strain.
For undrained, constant volume shearing, the Tresca theory may be used to predict the shear strength, but for drained conditions, the Mohr–Coulomb theory may be used.
Two important theories of soil shear are the critical state theory and the steady state theory. There are key differences between the critical state condition and the steady state condition and the resulting theory corresponding to each of these conditions.
https://en.wikipedia.org/wiki/Shear_strength_(soil)
https://en.wikipedia.org/wiki/Motion_controller
The chain fountain phenomenon, also known as the self-siphoning beads, Newton's beads or the Mould effect, is a counterintuitive physical phenomenon observed with a chain placed inside a jar, when one end of the chain is pulled from the jar and is allowed to fall to the floor beneath under the influence of gravity. This process establishes a self-sustaining flow of the chain which rises over the edge and goes down to the floor or ground beneath it, as if being sucked out of the jar by an invisible siphon. For chains with small adjacent beads, the arch can ascend into the air over and above the edge of the jar with a noticeable gap.[1]
https://en.wikipedia.org/wiki/Chain_fountain
In physics and geometry, a catenary (US: /ˈkætənɛri/, UK: /kəˈtiːnəri/) is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends.
The catenary curve has a U-like shape, superficially similar in appearance to a parabolic arch, but it is not a parabola.
The curve appears in the design of certain types of arches and as a cross section of the catenoid—the shape assumed by a soap film bounded by two parallel circular rings.
The catenary is also called the alysoid, chainette,[1] or, particularly in the materials sciences, funicular.[2] Rope statics describes catenaries in a classic statics problem involving a hanging rope.[3]
Mathematically, the catenary curve is the graph of the hyperbolic cosine function. The surface of revolution of the catenary curve, the catenoid, is a minimal surface, specifically a minimal surface of revolution. A hanging chain will assume a shape of least potential energy which is a catenary.[4] Galileo Galilei in 1638 discussed the catenary in the book Two New Sciences recognizing that it was different from a parabola. The mathematical properties of the catenary curve were studied by Robert Hooke in the 1670s, and its equation was derived by Leibniz, Huygens and Johann Bernoulli in 1691.
Catenaries and related curves are used in architecture and engineering (e.g., in the design of bridges and arches so that forces do not result in bending moments). In the offshore oil and gas industry, "catenary" refers to a steel catenary riser, a pipeline suspended between a production platform and the seabed that adopts an approximate catenary shape. In the rail industry it refers to the overhead wiring that transfers power to trains. (This often supports a lighter contact wire, in which case it does not follow a true catenary curve.)
In optics and electromagnetics, the hyperbolic cosine and sine functions are basic solutions to Maxwell's equations.[5] The symmetric modes consisting of two evanescent waves would form a catenary shape.[6][7][8]
https://en.wikipedia.org/wiki/Catenary
A catenoid is a type of surface, arising by rotating a catenary curve about an axis.[1] It is a minimal surface, meaning that it occupies the least area when bounded by a closed space.[2] It was formally described in 1744 by the mathematician Leonhard Euler.
Soap film attached to twin circular rings will take the shape of a catenoid.[2] Because they are members of the same associate family of surfaces, a catenoid can be bent into a portion of a helicoid, and vice versa.
https://en.wikipedia.org/wiki/Catenoid
In geometry and physics, spinors /spɪnər/ are elements of a complex vector space that can be associated with Euclidean space.[b] Like geometric vectors and more general tensors, spinors transform linearly when the Euclidean space is subjected to a slight (infinitesimal) rotation.[c] However, when a sequence of such small rotations is composed (integrated) to form an overall final rotation, the resulting spinor transformation depends on which sequence of small rotations was used. Unlike vectors and tensors, a spinor transforms to its negative when the space is continuously rotated through a complete turn from 0° to 360° (see picture). This property characterizes spinors: spinors can be viewed as the "square roots" of vectors (although this is inaccurate and may be misleading; they are better viewed as "square roots" of sections of vector bundles – in the case of the exterior algebra bundle of the cotangent bundle, they thus become "square roots" of differential forms).
https://en.wikipedia.org/wiki/Spinor
The helicoid, after the plane and the catenoid, is the third minimal surface to be known.
https://en.wikipedia.org/wiki/Helicoid
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