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151-410: In physics, gravity (from Latin gravitas  'weight') is a fundamental interaction primarily observed as mutual attraction between all things that have mass . Gravity is, by far, the weakest of the four fundamental interactions, approximately 10 times weaker than the strong interaction , 10 times weaker than the electromagnetic force and 10 times weaker than the weak interaction . As

302-433: A false vacuum , quantum vacuum or virtual particle , in a currently unknown manner. Scientists are currently working to develop a theory of gravity consistent with quantum mechanics , a quantum gravity theory, which would allow gravity to be united in a common mathematical framework (a theory of everything ) with the other three fundamental interactions of physics. Gravitation , also known as gravitational attraction,

453-424: A " fictitious force " arising in a rotating reference. Centrifugal force has also played a role in debates in classical mechanics about detection of absolute motion. Newton suggested two arguments to answer the question of whether absolute rotation can be detected: the rotating bucket argument , and the rotating spheres argument. According to Newton, in each scenario the centrifugal force would be observed in

604-456: A centripetal acceleration. When considered in an inertial frame (that is to say, one that is not rotating with the Earth), the non-zero acceleration means that force of gravity will not balance with the force from the spring. In order to have a net centripetal force, the magnitude of the restoring force of the spring must be less than the magnitude of force of gravity. This reduced restoring force in

755-553: A co-rotating frame. However, the Lagrangian use of "centrifugal force" in other, more general cases has only a limited connection to the Newtonian definition. In another instance the term refers to the reaction force to a centripetal force, or reactive centrifugal force . A body undergoing curved motion, such as circular motion , is accelerating toward a center at any particular point in time. This centripetal acceleration

906-627: A falling object is proportional to the square of the time elapsed. This was later confirmed by Italian scientists Jesuits Grimaldi and Riccioli between 1640 and 1650. They also calculated the magnitude of the Earth's gravity by measuring the oscillations of a pendulum. In 1657, Robert Hooke published his Micrographia , in which he hypothesised that the Moon must have its own gravity. In 1666, he added two further principles: that all bodies move in straight lines until deflected by some force and that

1057-526: A faster pace. It is characterised by greater use of prepositions, and word order that is closer to modern Romance languages, for example, while grammatically retaining more or less the same formal rules as Classical Latin. Ultimately, Latin diverged into a distinct written form, where the commonly spoken form was perceived as a separate language, for instance early French or Italian dialects, that could be transcribed differently. It took some time for these to be viewed as wholly different from Latin however. After

1208-743: A few in German , Dutch , Norwegian , Danish and Swedish . Latin is still spoken in Vatican City, a city-state situated in Rome that is the seat of the Catholic Church . The works of several hundred ancient authors who wrote in Latin have survived in whole or in part, in substantial works or in fragments to be analyzed in philology . They are in part the subject matter of the field of classics . Their works were published in manuscript form before

1359-404: A few. Famous and well regarded writers included Petrarch, Erasmus, Salutati , Celtis , George Buchanan and Thomas More . Non fiction works were long produced in many subjects, including the sciences, law, philosophy, historiography and theology. Famous examples include Isaac Newton 's Principia . Latin was also used as a convenient medium for translations of important works first written in

1510-429: A force applied to an object would cause it to deviate from a geodesic. For instance, people standing on the surface of the Earth are prevented from following a geodesic path because the mechanical resistance of the Earth exerts an upward force on them. This explains why moving along the geodesics in spacetime is considered inertial. Einstein's description of gravity was quickly accepted by the majority of physicists, as it

1661-500: A frictional force against the seat) in order to remain in a fixed position inside. Since they push the seat toward the right, Newton's third law says that the seat pushes them towards the left. The centrifugal force must be included in the passenger's reference frame (in which the passenger remains at rest): it counteracts the leftward force applied to the passenger by the seat, and explains why this otherwise unbalanced force does not cause them to accelerate. However, it would be apparent to

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1812-399: A groundbreaking book called Philosophiæ Naturalis Principia Mathematica ( Mathematical Principles of Natural Philosophy ). In this book, Newton described gravitation as a universal force, and claimed that "the forces which keep the planets in their orbs must [be] reciprocally as the squares of their distances from the centers about which they revolve." This statement was later condensed into

1963-560: A native language, Medieval Latin was used across Western and Catholic Europe during the Middle Ages as a working and literary language from the 9th century to the Renaissance , which then developed a classicizing form, called Renaissance Latin . This was the basis for Neo-Latin which evolved during the early modern period . In these periods Latin was used productively and generally taught to be written and spoken, at least until

2114-454: A new approach to quantum mechanics) is required. Testing the predictions of general relativity has historically been difficult, because they are almost identical to the predictions of Newtonian gravity for small energies and masses. Still, since its development, an ongoing series of experimental results have provided support for the theory: In 1919, the British astrophysicist Arthur Eddington

2265-686: A reaction to a centripetal force in some scenarios. From 1659, the Neo-Latin term vi centrifuga ("centrifugal force") is attested in Christiaan Huygens ' notes and letters. Note, that in Latin centrum means "center" and ‑fugus (from fugiō ) means "fleeing, avoiding". Thus, centrifugus means "fleeing from the center" in a literal translation . In 1673, in Horologium Oscillatorium , Huygens writes (as translated by Richard J. Blackwell ): There

2416-478: A result, it has no significant influence at the level of subatomic particles . However, gravity is the most significant interaction between objects at the macroscopic scale , and it determines the motion of planets , stars , galaxies , and even light . On Earth , gravity gives weight to physical objects , and the Moon's gravity is responsible for sublunar tides in the oceans. The corresponding antipodal tide

2567-567: A result, the list has variants, as well as alternative names. In addition to the historical phases, Ecclesiastical Latin refers to the styles used by the writers of the Roman Catholic Church from late antiquity onward, as well as by Protestant scholars. The earliest known form of Latin is Old Latin, also called Archaic or Early Latin, which was spoken from the Roman Kingdom , traditionally founded in 753 BC, through

2718-425: A rotating reference frame because it rotates once every 23 hours and 56 minutes around its axis. Because the rotation is slow, the fictitious forces it produces are often small, and in everyday situations can generally be neglected. Even in calculations requiring high precision, the centrifugal force is generally not explicitly included, but rather lumped in with the gravitational force : the strength and direction of

2869-407: A separate language, existing more or less in parallel with the literary or educated Latin, but this is now widely dismissed. The term 'Vulgar Latin' remains difficult to define, referring both to informal speech at any time within the history of Latin, and the kind of informal Latin that had begun to move away from the written language significantly in the post-Imperial period, that led ultimately to

3020-429: A simple motion, will continue to move in a straight line, unless continually deflected from it by some extraneous force, causing them to describe a circle, an ellipse, or some other curve. 3. That this attraction is so much the greater as the bodies are nearer. As to the proportion in which those forces diminish by an increase of distance, I own I have not discovered it.... Hooke's 1674 Gresham lecture, An Attempt to prove

3171-709: A small number of Latin services held in the Anglican church. These include an annual service in Oxford, delivered with a Latin sermon; a relic from the period when Latin was the normal spoken language of the university. In the Western world, many organizations, governments and schools use Latin for their mottos due to its association with formality, tradition, and the roots of Western culture . Canada's motto A mari usque ad mare ("from sea to sea") and most provincial mottos are also in Latin. The Canadian Victoria Cross

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3322-429: A sort of informal language academy dedicated to maintaining and perpetuating educated speech. Philological analysis of Archaic Latin works, such as those of Plautus , which contain fragments of everyday speech, gives evidence of an informal register of the language, Vulgar Latin (termed sermo vulgi , "the speech of the masses", by Cicero ). Some linguists, particularly in the nineteenth century, believed this to be

3473-572: A spoken and written language by the scholarship by the Renaissance humanists . Petrarch and others began to change their usage of Latin as they explored the texts of the Classical Latin world. Skills of textual criticism evolved to create much more accurate versions of extant texts through the fifteenth and sixteenth centuries, and some important texts were rediscovered. Comprehensive versions of authors' works were published by Isaac Casaubon , Joseph Scaliger and others. Nevertheless, despite

3624-403: A stationary observer watching from an overpass above that the frictional force exerted on the passenger by the seat is not being balanced; it constitutes a net force to the left, causing the passenger to accelerate toward the inside of the curve, as they must in order to keep moving with the car rather than proceeding in a straight line as they otherwise would. Thus the "centrifugal force" they feel

3775-432: A strictly left-to-right script. During the late republic and into the first years of the empire, from about 75 BC to AD 200, a new Classical Latin arose, a conscious creation of the orators, poets, historians and other literate men, who wrote the great works of classical literature , which were taught in grammar and rhetoric schools. Today's instructional grammars trace their roots to such schools , which served as

3926-509: A subject about which I have more to say than I am able to do at present. But, in order that those interested in these things can sooner enjoy these new and not useless speculations, and in order that their publication not be prevented by some accident, I have decided, contrary to my plan, to add this fifth part [...]. The same year, Isaac Newton received Huygens work via Henry Oldenburg and replied "I pray you return [Mr. Huygens] my humble thanks [...] I am glad we can expect another discourse of

4077-492: A sufficiently large and compact object. General relativity states that gravity acts on light and matter equally, meaning that a sufficiently massive object could warp light around it and create a gravitational lens . This phenomenon was first confirmed by observation in 1979 using the 2.1 meter telescope at Kitt Peak National Observatory in Arizona, which saw two mirror images of the same quasar whose light had been bent around

4228-524: A theory of general relativity which was able to accurately model Mercury's orbit. In general relativity, the effects of gravitation are ascribed to spacetime curvature instead of a force. Einstein began to toy with this idea in the form of the equivalence principle , a discovery which he later described as "the happiest thought of my life." In this theory, free fall is considered to be equivalent to inertial motion, meaning that free-falling inertial objects are accelerated relative to non-inertial observers on

4379-410: A tower. In the late 16th century, Galileo Galilei 's careful measurements of balls rolling down inclines allowed him to firmly establish that gravitational acceleration is the same for all objects. Galileo postulated that air resistance is the reason that objects with a low density and high surface area fall more slowly in an atmosphere. In 1604, Galileo correctly hypothesized that the distance of

4530-693: A vernacular, such as those of Descartes . Latin education underwent a process of reform to classicise written and spoken Latin. Schooling remained largely Latin medium until approximately 1700. Until the end of the 17th century, the majority of books and almost all diplomatic documents were written in Latin. Afterwards, most diplomatic documents were written in French (a Romance language ) and later native or other languages. Education methods gradually shifted towards written Latin, and eventually concentrating solely on reading skills. The decline of Latin education took several centuries and proceeded much more slowly than

4681-411: Is Veritas ("truth"). Veritas was the goddess of truth, a daughter of Saturn, and the mother of Virtue. Switzerland has adopted the country's Latin short name Helvetia on coins and stamps, since there is no room to use all of the nation's four official languages . For a similar reason, it adopted the international vehicle and internet code CH , which stands for Confoederatio Helvetica ,

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4832-400: Is a black hole , from which nothing—not even light—can escape once past the black hole's event horizon . However, for most applications, gravity is well approximated by Newton's law of universal gravitation , which describes gravity as a force causing any two bodies to be attracted toward each other, with magnitude proportional to the product of their masses and inversely proportional to

4983-897: Is a classical language belonging to the Italic branch of the Indo-European languages . Latin was originally spoken by the Latins in Latium (now known as Lazio ), the lower Tiber area around Rome , Italy. Through the expansion of the Roman Republic it became the dominant language in the Italian Peninsula and subsequently throughout the Roman Empire . By the late Roman Republic , Old Latin had evolved into standardized Classical Latin . Vulgar Latin refers to

5134-640: Is a reversal of the original phrase Non terrae plus ultra ("No land further beyond", "No further!"). According to legend , this phrase was inscribed as a warning on the Pillars of Hercules , the rocks on both sides of the Strait of Gibraltar and the western end of the known, Mediterranean world. Charles adopted the motto following the discovery of the New World by Columbus, and it also has metaphorical suggestions of taking risks and striving for excellence. In

5285-401: Is a stationary frame in which no fictitious forces need to be invoked. Within this view of physics, any other phenomenon that is usually attributed to centrifugal force can be used to identify absolute rotation. For example, the oblateness of a sphere of freely flowing material is often explained in terms of centrifugal force. The oblate spheroid shape reflects, following Clairaut's theorem ,

5436-478: Is another kind of oscillation in addition to the one we have examined up to this point; namely, a motion in which a suspended weight is moved around through the circumference of a circle. From this we were led to the construction of another clock at about the same time we invented the first one. [...] I originally intended to publish here a lengthy description of these clocks, along with matters pertaining to circular motion and centrifugal force , as it might be called,

5587-406: Is based upon the idea of an inertial frame of reference, which privileges observers for which the laws of physics take on their simplest form, and in particular, frames that do not use centrifugal forces in their equations of motion in order to describe motions correctly. Around 1914, the analogy between centrifugal force (sometimes used to create artificial gravity ) and gravitational forces led to

5738-451: Is caused by the inertia of the Earth and Moon orbiting one another. Gravity also has many important biological functions, helping to guide the growth of plants through the process of gravitropism and influencing the circulation of fluids in multicellular organisms . The gravitational attraction between the original gaseous matter in the universe caused it to coalesce and form stars which eventually condensed into galaxies, so gravity

5889-456: Is especially vexing to physicists because the other three fundamental forces (strong force, weak force and electromagnetism) were reconciled with a quantum framework decades ago. As a result, modern researchers have begun to search for a theory that could unite both gravity and quantum mechanics under a more general framework. One path is to describe gravity in the framework of quantum field theory , which has been successful to accurately describe

6040-552: Is found in any widespread language, the languages of Spain, France, Portugal, and Italy have retained a remarkable unity in phonological forms and developments, bolstered by the stabilising influence of their common Christian (Roman Catholic) culture. It was not until the Muslim conquest of Spain in 711, cutting off communications between the major Romance regions, that the languages began to diverge seriously. The spoken Latin that would later become Romanian diverged somewhat more from

6191-411: Is made, fictitious forces, including the centrifugal force, arise. In a reference frame rotating about an axis through its origin, all objects, regardless of their state of motion, appear to be under the influence of a radially (from the axis of rotation) outward force that is proportional to their mass, to the distance from the axis of rotation of the frame, and to the square of the angular velocity of

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6342-689: Is modelled after the British Victoria Cross which has the inscription "For Valour". Because Canada is officially bilingual, the Canadian medal has replaced the English inscription with the Latin Pro Valore . Spain's motto Plus ultra , meaning "even further", or figuratively "Further!", is also Latin in origin. It is taken from the personal motto of Charles V , Holy Roman Emperor and King of Spain (as Charles I), and

6493-403: Is no net force acting on the object and the force from the spring is equal in magnitude to the force of gravity on the object. In this case, the balance shows the value of the force of gravity on the object. When the same object is weighed on the equator , the same two real forces act upon the object. However, the object is moving in a circular path as the Earth rotates and therefore experiencing

6644-541: Is not dependent on a substance's weight but rather on its "nature". In the 6th century CE, the Byzantine Alexandrian scholar John Philoponus proposed the theory of impetus, which modifies Aristotle's theory that "continuation of motion depends on continued action of a force" by incorporating a causative force that diminishes over time. In 628 CE, the Indian mathematician and astronomer Brahmagupta proposed

6795-438: Is often applied to rotating devices, such as centrifuges , centrifugal pumps , centrifugal governors , and centrifugal clutches , and in centrifugal railways , planetary orbits and banked curves , when they are analyzed in a non–inertial reference frame such as a rotating coordinate system. The term has sometimes also been used for the reactive centrifugal force , a real frame-independent Newtonian force that exists as

6946-456: Is often expressed in the form G μ ν + Λ g μ ν = κ T μ ν , {\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }=\kappa T_{\mu \nu },} where G μν is the Einstein tensor , g μν is the metric tensor , T μν is the stress–energy tensor , Λ

7097-401: Is provided by a centripetal force, which is exerted on the body in curved motion by some other body. In accordance with Newton's third law of motion , the body in curved motion exerts an equal and opposite force on the other body. This reactive force is exerted by the body in curved motion on the other body that provides the centripetal force and its direction is from that other body toward

7248-408: Is removed (for example if the string breaks) the stone moves in a straight line, as viewed from above. In this inertial frame, the concept of centrifugal force is not required as all motion can be properly described using only real forces and Newton's laws of motion. In a frame of reference rotating with the stone around the same axis as the stone, the stone is stationary. However, the force applied by

7399-505: Is required. These fictitious forces are necessary for the formulation of correct equations of motion in a rotating reference frame and allow Newton's laws to be used in their normal form in such a frame (with one exception: the fictitious forces do not obey Newton's third law: they have no equal and opposite counterparts). Newton's third law requires the counterparts to exist within the same frame of reference, hence centrifugal and centripetal force, which do not, are not action and reaction (as

7550-511: 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 farther away. Gravity is most accurately described by the general theory of relativity , proposed by Albert Einstein in 1915, which describes gravity not as a force, but as the curvature of spacetime , caused by the uneven distribution of mass, and causing masses to move along geodesic lines. The most extreme example of this curvature of spacetime

7701-463: Is sometimes erroneously contended). A common experience that gives rise to the idea of a centrifugal force is encountered by passengers riding in a vehicle, such as a car, that is changing direction. If a car is traveling at a constant speed along a straight road, then a passenger inside is not accelerating and, according to Newton's second law of motion , the net force acting on them is therefore zero (all forces acting on them cancel each other out). If

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7852-956: Is taught at many high schools, especially in Europe and the Americas. It is most common in British public schools and grammar schools, the Italian liceo classico and liceo scientifico , the German Humanistisches Gymnasium and the Dutch gymnasium . Occasionally, some media outlets, targeting enthusiasts, broadcast in Latin. Notable examples include Radio Bremen in Germany, YLE radio in Finland (the Nuntii Latini broadcast from 1989 until it

8003-486: Is the cosmological constant , G {\displaystyle G} is the Newtonian constant of gravitation and c {\displaystyle c} is the speed of light . The constant κ = 8 π G c 4 {\displaystyle \kappa ={\frac {8\pi G}{c^{4}}}} is referred to as the Einstein gravitational constant. A major area of research

8154-444: Is the discovery of exact solutions to the Einstein field equations. Solving these equations amounts to calculating a precise value for the metric tensor (which defines the curvature and geometry of spacetime) under certain physical conditions. There is no formal definition for what constitutes such solutions, but most scientists agree that they should be expressable using elementary functions or linear differential equations . Some of

8305-453: Is the mutual attraction between all masses in the universe. Gravity is the gravitational attraction at the surface of a planet or other celestial body; gravity may also include, in addition to gravitation, the centrifugal force resulting from the planet's rotation (see § Earth's gravity ) . The nature and mechanism of gravity were explored by a wide range of ancient scholars. In Greece , Aristotle believed that objects fell towards

8456-407: Is the result of a "centrifugal tendency" caused by inertia. Similar effects are encountered in aeroplanes and roller coasters where the magnitude of the apparent force is often reported in " G's ". If a stone is whirled round on a string, in a horizontal plane, the only real force acting on the stone in the horizontal plane is applied by the string (gravity acts vertically). There is a net force on

8607-543: The Corpus Inscriptionum Latinarum (CIL). Authors and publishers vary, but the format is about the same: volumes detailing inscriptions with a critical apparatus stating the provenance and relevant information. The reading and interpretation of these inscriptions is the subject matter of the field of epigraphy . About 270,000 inscriptions are known. The Latin influence in English has been significant at all stages of its insular development. In

8758-584: The Coriolis force − 2 m ω × [ d r / d t ] {\displaystyle -2m{\boldsymbol {\omega }}\times \left[\mathrm {d} {\boldsymbol {r}}/\mathrm {d} t\right]} , and the centrifugal force − m ω × ( ω × r ) {\displaystyle -m{\boldsymbol {\omega }}\times ({\boldsymbol {\omega }}\times {\boldsymbol {r}})} , respectively. Unlike

8909-583: The Holy See , the primary language of its public journal , the Acta Apostolicae Sedis , and the working language of the Roman Rota . Vatican City is also home to the world's only automatic teller machine that gives instructions in Latin. In the pontifical universities postgraduate courses of Canon law are taught in Latin, and papers are written in the same language. There are

9060-569: The Hulse–Taylor binary in 1973. This system consists of a pulsar and neutron star in orbit around one another. Its orbital period has decreased since its initial discovery due to a loss of energy, which is consistent for the amount of energy loss due to gravitational radiation. This research was awarded the Nobel Prize in Physics in 1993. The first direct evidence for gravitational radiation

9211-480: The International System of Units (SI). The force of gravity on Earth is the resultant (vector sum) of two forces: (a) The gravitational attraction in accordance with Newton's universal law of gravitation, and (b) the centrifugal force, which results from the choice of an earthbound, rotating frame of reference. The force of gravity is weakest at the equator because of the centrifugal force caused by

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9362-574: The Middle Ages , borrowing from Latin occurred from ecclesiastical usage established by Saint Augustine of Canterbury in the 6th century or indirectly after the Norman Conquest , through the Anglo-Norman language . From the 16th to the 18th centuries, English writers cobbled together huge numbers of new words from Latin and Greek words, dubbed " inkhorn terms ", as if they had spilled from a pot of ink. Many of these words were used once by

9513-576: The Roman Rite of the Catholic Church at the Vatican City . The church continues to adapt concepts from modern languages to Ecclesiastical Latin of the Latin language. Contemporary Latin is more often studied to be read rather than spoken or actively used. Latin has greatly influenced the English language , along with a large number of others, and historically contributed many words to

9664-569: The Romance languages . During the Classical period, informal language was rarely written, so philologists have been left with only individual words and phrases cited by classical authors, inscriptions such as Curse tablets and those found as graffiti . In the Late Latin period, language changes reflecting spoken (non-classical) norms tend to be found in greater quantities in texts. As it

9815-636: The Western Roman Empire fell in 476 and Germanic kingdoms took its place, the Germanic people adopted Latin as a language more suitable for legal and other, more formal uses. While the written form of Latin was increasingly standardized into a fixed form, the spoken forms began to diverge more greatly. Currently, the five most widely spoken Romance languages by number of native speakers are Spanish , Portuguese , French , Italian , and Romanian . Despite dialectal variation, which

9966-428: The equivalence principle of general relativity . Centrifugal force is an outward force apparent in a rotating reference frame . It does not exist when a system is described relative to an inertial frame of reference . All measurements of position and velocity must be made relative to some frame of reference. For example, an analysis of the motion of an object in an airliner in flight could be made relative to

10117-458: The square of the distance between them. Current models of particle physics imply that the earliest instance of gravity in the universe, possibly in the form of quantum gravity , supergravity or a gravitational singularity , along with ordinary space and time , developed during the Planck epoch (up to 10 seconds after the birth of the universe), possibly from a primeval state, such as

10268-402: The vector cross product . In other words, the rate of change of P in the stationary frame is the sum of its apparent rate of change in the rotating frame and a rate of rotation ω × P {\displaystyle {\boldsymbol {\omega }}\times {\boldsymbol {P}}} attributable to the motion of the rotating frame. The vector ω has magnitude ω equal to

10419-477: The vis centrifuga , which speculation may prove of good use in natural philosophy and astronomy , as well as mechanics ". In 1687, in Principia , Newton further develops vis centrifuga ("centrifugal force"). Around this time, the concept is also further evolved by Newton, Gottfried Wilhelm Leibniz , and Robert Hooke . In the late 18th century, the modern conception of the centrifugal force evolved as

10570-483: The Annual Motion of the Earth , explained that gravitation applied to "all celestial bodies" In 1684, Newton sent a manuscript to Edmond Halley titled De motu corporum in gyrum ('On the motion of bodies in an orbit') , which provided a physical justification for Kepler's laws of planetary motion . Halley was impressed by the manuscript and urged Newton to expand on it, and a few years later Newton published

10721-590: The Big Bang. Neutron star and black hole formation also create detectable amounts of gravitational radiation. This research was awarded the Nobel Prize in Physics in 2017. In December 2012, a research team in China announced that it had produced measurements of the phase lag of Earth tides during full and new moons which seem to prove that the speed of gravity is equal to the speed of light. This means that if

10872-637: The British Crown. The motto is featured on all presently minted coinage and has been featured in most coinage throughout the nation's history. Several states of the United States have Latin mottos , such as: Many military organizations today have Latin mottos, such as: Some law governing bodies in the Philippines have Latin mottos, such as: Some colleges and universities have adopted Latin mottos, for example Harvard University 's motto

11023-473: The Coriolis force in particular, it is independent of the motion of the particle in the rotating frame. As expected, for a non-rotating inertial frame of reference ( ω = 0 ) {\displaystyle ({\boldsymbol {\omega }}=0)} the centrifugal force and all other fictitious forces disappear. Similarly, as the centrifugal force is proportional to the distance from object to

11174-473: The Earth because the Earth was the center of the Universe and attracted all of the mass in the Universe towards it. He also thought that the speed of a falling object should increase with its weight, a conclusion that was later shown to be false. While Aristotle's view was widely accepted throughout Ancient Greece, there were other thinkers such as Plutarch who correctly predicted that the attraction of gravity

11325-481: The Earth's rotation and because points on the equator are furthest from the center of the Earth. The force of gravity varies with latitude and increases from about 9.780 m/s at the Equator to about 9.832 m/s at the poles. General relativity predicts that energy can be transported out of a system through gravitational radiation. The first indirect evidence for gravitational radiation was through measurements of

11476-411: The Earth) is surrounded by its own gravitational field, which can be conceptualized with Newtonian physics as exerting an attractive force on all objects. Assuming a spherically symmetrical planet, the strength of this field at any given point above the surface is proportional to the planetary body's mass and inversely proportional to the square of the distance from the center of the body. The strength of

11627-458: The Earth. This is due to the large mass and velocity of the Sun (relative to the Earth). If an object is weighed with a simple spring balance at one of the Earth's poles, there are two forces acting on the object: the Earth's gravity, which acts in a downward direction, and the equal and opposite restoring force in the spring, acting upward. Since the object is stationary and not accelerating, there

11778-613: The English lexicon , particularly after the Christianization of the Anglo-Saxons and the Norman Conquest . Latin and Ancient Greek roots are heavily used in English vocabulary in theology , the sciences , medicine , and law . A number of phases of the language have been recognized, each distinguished by subtle differences in vocabulary, usage, spelling, and syntax. There are no hard and fast rules of classification; different scholars emphasize different features. As

11929-599: The Grinch Stole Christmas! , The Cat in the Hat , and a book of fairy tales, " fabulae mirabiles ", are intended to garner popular interest in the language. Additional resources include phrasebooks and resources for rendering everyday phrases and concepts into Latin, such as Meissner's Latin Phrasebook . Some inscriptions have been published in an internationally agreed, monumental, multivolume series,

12080-572: The Sun suddenly disappeared, the Earth would keep orbiting the vacant point normally for 8 minutes, which is the time light takes to travel that distance. The team's findings were released in Science Bulletin in February 2013. In October 2017, the LIGO and Virgo detectors received gravitational wave signals within 2 seconds of gamma ray satellites and optical telescopes seeing signals from

12231-467: The United States the unofficial national motto until 1956 was E pluribus unum meaning "Out of many, one". The motto continues to be featured on the Great Seal . It also appears on the flags and seals of both houses of congress and the flags of the states of Michigan, North Dakota, New York, and Wisconsin. The motto's 13 letters symbolically represent the original Thirteen Colonies which revolted from

12382-563: The University of Kentucky, the University of Oxford and also Princeton University. There are many websites and forums maintained in Latin by enthusiasts. The Latin Misplaced Pages has more than 130,000 articles. Italian , French , Portuguese , Spanish , Romanian , Catalan , Romansh , Sardinian and other Romance languages are direct descendants of Latin. There are also many Latin borrowings in English and Albanian , as well as

12533-652: The absolute angular velocity of the rotating frame is ω then the derivative d P /d t of P with respect to the stationary frame is related to [d P /d t ] by the equation: d P d t = [ d P d t ] + ω × P   , {\displaystyle {\frac {\mathrm {d} {\boldsymbol {P}}}{\mathrm {d} t}}=\left[{\frac {\mathrm {d} {\boldsymbol {P}}}{\mathrm {d} t}}\right]+{\boldsymbol {\omega }}\times {\boldsymbol {P}}\ ,} where × {\displaystyle \times } denotes

12684-502: The absolute acceleration d 2 r d t 2 {\displaystyle {\frac {\mathrm {d} ^{2}{\boldsymbol {r}}}{\mathrm {d} t^{2}}}} . Therefore, the observer perceives the extra terms as contributions due to fictitious forces. These terms in the apparent acceleration are independent of mass; so it appears that each of these fictitious forces, like gravity, pulls on an object in proportion to its mass. When these forces are added,

12835-3224: The absolute acceleration of the particle can be written as: a = d 2 r d t 2 = d d t d r d t = d d t ( [ d r d t ] + ω × r   ) = [ d 2 r d t 2 ] + ω × [ d r d t ] + d ω d t × r + ω × d r d t = [ d 2 r d t 2 ] + ω × [ d r d t ] + d ω d t × r + ω × ( [ d r d t ] + ω × r   ) = [ d 2 r d t 2 ] + d ω d t × r + 2 ω × [ d r d t ] + ω × ( ω × r )   . {\displaystyle {\begin{aligned}{\boldsymbol {a}}&={\frac {\mathrm {d} ^{2}{\boldsymbol {r}}}{\mathrm {d} t^{2}}}={\frac {\mathrm {d} }{\mathrm {d} t}}{\frac {\mathrm {d} {\boldsymbol {r}}}{\mathrm {d} t}}={\frac {\mathrm {d} }{\mathrm {d} t}}\left(\left[{\frac {\mathrm {d} {\boldsymbol {r}}}{\mathrm {d} t}}\right]+{\boldsymbol {\omega }}\times {\boldsymbol {r}}\ \right)\\&=\left[{\frac {\mathrm {d} ^{2}{\boldsymbol {r}}}{\mathrm {d} t^{2}}}\right]+{\boldsymbol {\omega }}\times \left[{\frac {\mathrm {d} {\boldsymbol {r}}}{\mathrm {d} t}}\right]+{\frac {\mathrm {d} {\boldsymbol {\omega }}}{\mathrm {d} t}}\times {\boldsymbol {r}}+{\boldsymbol {\omega }}\times {\frac {\mathrm {d} {\boldsymbol {r}}}{\mathrm {d} t}}\\&=\left[{\frac {\mathrm {d} ^{2}{\boldsymbol {r}}}{\mathrm {d} t^{2}}}\right]+{\boldsymbol {\omega }}\times \left[{\frac {\mathrm {d} {\boldsymbol {r}}}{\mathrm {d} t}}\right]+{\frac {\mathrm {d} {\boldsymbol {\omega }}}{\mathrm {d} t}}\times {\boldsymbol {r}}+{\boldsymbol {\omega }}\times \left(\left[{\frac {\mathrm {d} {\boldsymbol {r}}}{\mathrm {d} t}}\right]+{\boldsymbol {\omega }}\times {\boldsymbol {r}}\ \right)\\&=\left[{\frac {\mathrm {d} ^{2}{\boldsymbol {r}}}{\mathrm {d} t^{2}}}\right]+{\frac {\mathrm {d} {\boldsymbol {\omega }}}{\mathrm {d} t}}\times {\boldsymbol {r}}+2{\boldsymbol {\omega }}\times \left[{\frac {\mathrm {d} {\boldsymbol {r}}}{\mathrm {d} t}}\right]+{\boldsymbol {\omega }}\times ({\boldsymbol {\omega }}\times {\boldsymbol {r}})\ .\end{aligned}}} The apparent acceleration in

12986-494: The airliner, to the surface of the Earth, or even to the Sun. A reference frame that is at rest (or one that moves with no rotation and at constant velocity) relative to the " fixed stars " is generally taken to be an inertial frame. Any system can be analyzed in an inertial frame (and so with no centrifugal force). However, it is often more convenient to describe a rotating system by using a rotating frame—the calculations are simpler, and descriptions more intuitive. When this choice

13137-502: The attractive force is stronger for closer bodies. In a communication to the Royal Society in 1666, Hooke wrote I will explain a system of the world very different from any yet received. It is founded on the following positions. 1. That all the heavenly bodies have not only a gravitation of their parts to their own proper centre, but that they also mutually attract each other within their spheres of action. 2. That all bodies having

13288-447: The author and then forgotten, but some useful ones survived, such as 'imbibe' and 'extrapolate'. Many of the most common polysyllabic English words are of Latin origin through the medium of Old French . Romance words make respectively 59%, 20% and 14% of English, German and Dutch vocabularies. Those figures can rise dramatically when only non-compound and non-derived words are included. Centrifugal force This fictitious force

13439-429: The axis of rotation of the frame, the centrifugal force vanishes for objects that lie upon the axis. Three scenarios were suggested by Newton to answer the question of whether the absolute rotation of a local frame can be detected; that is, if an observer can decide whether an observed object is rotating or if the observer is rotating. In these scenarios, the effects attributed to centrifugal force are only observed in

13590-509: The balance between containment by gravitational attraction and dispersal by centrifugal force. That the Earth is itself an oblate spheroid, bulging at the equator where the radial distance and hence the centrifugal force is larger, is taken as one of the evidences for its absolute rotation. The operations of numerous common rotating mechanical systems are most easily conceptualized in terms of centrifugal force. For example: Nevertheless, all of these systems can also be described without requiring

13741-425: The benefit of those who do not understand Latin. There are also songs written with Latin lyrics . The libretto for the opera-oratorio Oedipus rex by Igor Stravinsky is in Latin. Parts of Carl Orff 's Carmina Burana are written in Latin. Enya has recorded several tracks with Latin lyrics. The continued instruction of Latin is seen by some as a highly valuable component of a liberal arts education. Latin

13892-488: The body in curved motion. This reaction force is sometimes described as a centrifugal inertial reaction , that is, a force that is centrifugally directed, which is a reactive force equal and opposite to the centripetal force that is curving the path of the mass. The concept of the reactive centrifugal force is sometimes used in mechanics and engineering. It is sometimes referred to as just centrifugal force rather than as reactive centrifugal force although this usage

14043-420: The car enters a curve that bends to the left, the passenger experiences an apparent force that seems to be pulling them towards the right. This is the fictitious centrifugal force. It is needed within the passengers' local frame of reference to explain their sudden tendency to start accelerating to the right relative to the car—a tendency which they must resist by applying a rightward force to the car (for instance,

14194-409: The careful work of Petrarch, Politian and others, first the demand for manuscripts, and then the rush to bring works into print, led to the circulation of inaccurate copies for several centuries following. Neo-Latin literature was extensive and prolific, but less well known or understood today. Works covered poetry, prose stories and early novels, occasional pieces and collections of letters, to name

14345-415: The classicised Latin that followed through to the present are often grouped together as Neo-Latin , or New Latin, which have in recent decades become a focus of renewed study , given their importance for the development of European culture, religion and science. The vast majority of written Latin belongs to this period, but its full extent is unknown. The Renaissance reinforced the position of Latin as

14496-405: The concept of centrifugal force, in terms of motions and forces in a stationary frame, at the cost of taking somewhat more care in the consideration of forces and motions within the system. While the majority of the scientific literature uses the term centrifugal force to refer to the particular fictitious force that arises in rotating frames, there are a few limited instances in the literature of

14647-465: The country's full Latin name. Some film and television in ancient settings, such as Sebastiane , The Passion of the Christ and Barbarians (2020 TV series) , have been made with dialogue in Latin. Occasionally, Latin dialogue is used because of its association with religion or philosophy, in such film/television series as The Exorcist and Lost (" Jughead "). Subtitles are usually shown for

14798-503: The decline in written Latin output. Despite having no native speakers, Latin is still used for a variety of purposes in the contemporary world. The largest organisation that retains Latin in official and quasi-official contexts is the Catholic Church . The Catholic Church required that Mass be carried out in Latin until the Second Vatican Council of 1962–1965 , which permitted the use of the vernacular . Latin remains

14949-589: The educated and official world, Latin continued without its natural spoken base. Moreover, this Latin spread into lands that had never spoken Latin, such as the Germanic and Slavic nations. It became useful for international communication between the member states of the Holy Roman Empire and its allies. Without the institutions of the Roman Empire that had supported its uniformity, Medieval Latin

15100-1212: The equation of motion has the form: F + ( − m d ω d t × r ) ⏟ Euler + ( − 2 m ω × [ d r d t ] ) ⏟ Coriolis + ( − m ω × ( ω × r ) ) ⏟ centrifugal = m [ d 2 r d t 2 ]   . {\displaystyle {\boldsymbol {F}}+\underbrace {\left(-m{\frac {\mathrm {d} {\boldsymbol {\omega }}}{\mathrm {d} t}}\times {\boldsymbol {r}}\right)} _{\text{Euler}}+\underbrace {\left(-2m{\boldsymbol {\omega }}\times \left[{\frac {\mathrm {d} {\boldsymbol {r}}}{\mathrm {d} t}}\right]\right)} _{\text{Coriolis}}+\underbrace {\left(-m{\boldsymbol {\omega }}\times ({\boldsymbol {\omega }}\times {\boldsymbol {r}})\right)} _{\text{centrifugal}}=m\left[{\frac {\mathrm {d} ^{2}{\boldsymbol {r}}}{\mathrm {d} t^{2}}}\right]\ .} From

15251-469: The fall of bodies. The mid-16th century Italian physicist Giambattista Benedetti published papers claiming that, due to specific gravity , objects made of the same material but with different masses would fall at the same speed. With the 1586 Delft tower experiment , the Flemish physicist Simon Stevin observed that two cannonballs of differing sizes and weights fell at the same rate when dropped from

15402-428: The following inverse-square law: F = G m 1 m 2 r 2 , {\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}},} where F is the force, m 1 and m 2 are the masses of the objects interacting, r is the distance between the centers of the masses and G is the gravitational constant 6.674 × 10 m⋅kg⋅s . Newton's Principia

15553-408: The forces be zero to match the apparent lack of acceleration. Note: In fact, the observed weight difference is more — about 0.53%. Earth's gravity is a bit stronger at the poles than at the equator, because the Earth is not a perfect sphere , so an object at the poles is slightly closer to the center of the Earth than one at the equator; this effect combines with the centrifugal force to produce

15704-461: The frame. This is the centrifugal force. As humans usually experience centrifugal force from within the rotating reference frame, e.g. on a merry-go-round or vehicle, this is much more well-known than centripetal force. Motion relative to a rotating frame results in another fictitious force: the Coriolis force . If the rate of rotation of the frame changes, a third fictitious force (the Euler force )

15855-404: The framework for the understanding of gravity. Physicists continue to work to find solutions to the Einstein field equations that form the basis of general relativity and continue to test the theory, finding excellent agreement in all cases. The Einstein field equations are a system of 10 partial differential equations which describe how matter affects the curvature of spacetime. The system

16006-453: The galaxy YGKOW G1 . Frame dragging , the idea that a rotating massive object should twist spacetime around it, was confirmed by Gravity Probe B results in 2011. In 2015, the LIGO observatory detected faint gravitational waves , the existence of which had been predicted by general relativity. Scientists believe that the waves emanated from a black hole merger that occurred 1.5 billion light-years away. Every planetary body (including

16157-521: The gravitational field is numerically equal to the acceleration of objects under its influence. The rate of acceleration of falling objects near the Earth's surface varies very slightly depending on latitude, surface features such as mountains and ridges, and perhaps unusually high or low sub-surface densities. For purposes of weights and measures, a standard gravity value is defined by the International Bureau of Weights and Measures , under

16308-470: The ground. In contrast to Newtonian physics , Einstein believed that it was possible for this acceleration to occur without any force being applied to the object. Einstein proposed that spacetime is curved by matter, and that free-falling objects are moving along locally straight paths in curved spacetime. These straight paths are called geodesics . As in Newton's first law of motion, Einstein believed that

16459-435: The idea that gravity is an attractive force that draws objects to the Earth and used the term gurutvākarṣaṇ to describe it. In the ancient Middle East , gravity was a topic of fierce debate. The Persian intellectual Al-Biruni believed that the force of gravity was not unique to the Earth, and he correctly assumed that other heavenly bodies should exert a gravitational attraction as well. In contrast, Al-Khazini held

16610-593: The idea that time runs more slowly in the presence of a gravitational field. The time delay of light passing close to a massive object was first identified by Irwin I. Shapiro in 1964 in interplanetary spacecraft signals. In 1971, scientists discovered the first-ever black hole in the galaxy Cygnus . The black hole was detected because it was emitting bursts of x-rays as it consumed a smaller star, and it came to be known as Cygnus X-1 . This discovery confirmed yet another prediction of general relativity, because Einstein's equations implied that light could not escape from

16761-455: The interactions of three or more massive bodies (the " n -body problem"), and some scientists suspect that the Einstein field equations will never be solved in this context. However, it is still possible to construct an approximate solution to the field equations in the n -body problem by using the technique of post-Newtonian expansion . In general, the extreme nonlinearity of the Einstein field equations makes it difficult to solve them in all but

16912-703: The invention of printing and are now published in carefully annotated printed editions, such as the Loeb Classical Library , published by Harvard University Press , or the Oxford Classical Texts , published by Oxford University Press . Latin translations of modern literature such as: The Hobbit , Treasure Island , Robinson Crusoe , Paddington Bear , Winnie the Pooh , The Adventures of Tintin , Asterix , Harry Potter , Le Petit Prince , Max and Moritz , How

17063-704: The language of the Roman Rite . The Tridentine Mass (also known as the Extraordinary Form or Traditional Latin Mass) is celebrated in Latin. Although the Mass of Paul VI (also known as the Ordinary Form or the Novus Ordo) is usually celebrated in the local vernacular language, it can be and often is said in Latin, in part or in whole, especially at multilingual gatherings. It is the official language of

17214-440: The large areas where it had come to be natively spoken. However, even after the fall of Western Rome , Latin remained the common language of international communication , science, scholarship and academia in Europe until well into the early 19th century, by which time modern languages had supplanted it in common academic and political usage. Late Latin is the literary language from the 3rd century AD onward. No longer spoken as

17365-467: The late seventeenth century, when spoken skills began to erode. It then became increasingly taught only to be read. Latin grammar is highly fusional , with classes of inflections for case , number , person , gender , tense , mood , voice , and aspect . The Latin alphabet is directly derived from the Etruscan and Greek alphabets . Latin remains the official language of the Holy See and

17516-431: The later part of the Roman Republic , up to 75 BC, i.e. before the age of Classical Latin . It is attested both in inscriptions and in some of the earliest extant Latin literary works, such as the comedies of Plautus and Terence . The Latin alphabet was devised from the Etruscan alphabet . The writing later changed from what was initially either a right-to-left or a boustrophedon script to what ultimately became

17667-421: The less prestigious colloquial registers , attested in inscriptions and some literary works such as those of the comic playwrights Plautus and Terence and the author Petronius . While often called a "dead language", Latin did not undergo language death . By the 6th to 9th centuries, natural language change eventually resulted in Latin as a vernacular language evolving into distinct Romance languages in

17818-452: The local " gravity " at any point on the Earth's surface is actually a combination of gravitational and centrifugal forces. However, the fictitious forces can be of arbitrary size. For example, in an Earth-bound reference system (where the earth is represented as stationary), the fictitious force (the net of Coriolis and centrifugal forces) is enormous and is responsible for the Sun orbiting around

17969-405: The local frame (the frame in which the object is stationary) if the object is undergoing absolute rotation relative to an inertial frame. By contrast, in an inertial frame, the observed effects arise as a consequence of the inertia and the known forces without the need to introduce a centrifugal force. Based on this argument, the privileged frame, wherein the laws of physics take on the simplest form,

18120-429: The most notable solutions of the equations include: Today, there remain many important situations in which the Einstein field equations have not been solved. Chief among these is the two-body problem , which concerns the geometry of spacetime around two mutually interacting massive objects, such as the Sun and the Earth, or the two stars in a binary star system . The situation gets even more complicated when considering

18271-404: The most specific cases. Despite its success in predicting the effects of gravity at large scales, general relativity is ultimately incompatible with quantum mechanics . This is because general relativity describes gravity as a smooth, continuous distortion of spacetime, while quantum mechanics holds that all forces arise from the exchange of discrete particles known as quanta . This contradiction

18422-483: The motion is described in terms of generalized forces , using in place of Newton's laws the Euler–;Lagrange equations . Among the generalized forces, those involving the square of the time derivatives {(d q k   ⁄ d t  ) } are sometimes called centrifugal forces. In the case of motion in a central potential the Lagrangian centrifugal force has the same form as the fictitious centrifugal force derived in

18573-401: The object's local frame (the frame where the object is stationary) only if the frame were rotating with respect to absolute space. Around 1883, Mach's principle was proposed where, instead of absolute rotation, the motion of the distant stars relative to the local inertial frame gives rise through some (hypothetical) physical law to the centrifugal force and other inertia effects. Today's view

18724-449: The observed weight difference. For the following formalism, the rotating frame of reference is regarded as a special case of a non-inertial reference frame that is rotating relative to an inertial reference frame denoted the stationary frame. In a rotating frame of reference, the time derivatives of any vector function P of time—such as the velocity and acceleration vectors of an object—will differ from its time derivatives in

18875-422: The orbit of the planet Mercury which could not be explained by Newton's theory: the perihelion of the orbit was increasing by about 42.98 arcseconds per century. The most obvious explanation for this discrepancy was an as-yet-undiscovered celestial body, such as a planet orbiting the Sun even closer than Mercury, but all efforts to find such a body turned out to be fruitless. In 1915, Albert Einstein developed

19026-462: The other fundamental interactions . The electromagnetic force arises from an exchange of virtual photons , where the QFT description of gravity is that there is an exchange of virtual gravitons . This description reproduces general relativity in the classical limit . However, this approach fails at short distances of the order of the Planck length , where a more complete theory of quantum gravity (or

19177-500: The other two fictitious forces, the centrifugal force always points radially outward from the axis of rotation of the rotating frame, with magnitude m ω 2 r ⊥ {\displaystyle m\omega ^{2}r_{\perp }} , where r ⊥ {\displaystyle r_{\perp }} is the component of the position vector perpendicular to ω {\displaystyle {\boldsymbol {\omega }}} , and unlike

19328-466: The other varieties, as it was largely separated from the unifying influences in the western part of the Empire. Spoken Latin began to diverge into distinct languages by the 9th century at the latest, when the earliest extant Romance writings begin to appear. They were, throughout the period, confined to everyday speech, as Medieval Latin was used for writing. For many Italians using Latin, though, there

19479-410: The particle, given by: a = d 2 r d t 2   , {\displaystyle {\boldsymbol {a}}={\frac {\mathrm {d} ^{2}{\boldsymbol {r}}}{\mathrm {d} t^{2}}}\ ,} where r is the position vector of the particle (not to be confused with radius, as used above.) By applying the transformation above from the stationary to

19630-491: The perspective of the rotating frame, the additional force terms are experienced just like the real external forces and contribute to the apparent acceleration. The additional terms on the force side of the equation can be recognized as, reading from left to right, the Euler force − m d ω / d t × r {\displaystyle -m\mathrm {d} {\boldsymbol {\omega }}/\mathrm {d} t\times {\boldsymbol {r}}} ,

19781-501: The planet's actual trajectory. In order to explain this discrepancy, many astronomers speculated that there might be a large object beyond the orbit of Uranus which was disrupting its orbit. In 1846, the astronomers John Couch Adams and Urbain Le Verrier independently used Newton's law to predict Neptune's location in the night sky, and the planet was discovered there within a day. Eventually, astronomers noticed an eccentricity in

19932-465: The rate of rotation and is directed along the axis of rotation according to the right-hand rule . Newton's law of motion for a particle of mass m written in vector form is: F = m a   , {\displaystyle {\boldsymbol {F}}=m{\boldsymbol {a}}\ ,} where F is the vector sum of the physical forces applied to the particle and a is the absolute acceleration (that is, acceleration in an inertial frame) of

20083-424: The rotating frame is [ d 2 r d t 2 ] {\displaystyle \left[{\frac {\mathrm {d} ^{2}{\boldsymbol {r}}}{\mathrm {d} t^{2}}}\right]} . An observer unaware of the rotation would expect this to be zero in the absence of outside forces. However, Newton's laws of motion apply only in the inertial frame and describe dynamics in terms of

20234-431: The rotating frame three times (twice to d r d t {\textstyle {\frac {\mathrm {d} {\boldsymbol {r}}}{\mathrm {d} t}}} and once to d d t [ d r d t ] {\textstyle {\frac {\mathrm {d} }{\mathrm {d} t}}\left[{\frac {\mathrm {d} {\boldsymbol {r}}}{\mathrm {d} t}}\right]} ),

20385-418: The same direction. This confirmed that the speed of gravitational waves was the same as the speed of light. There are some observations that are not adequately accounted for, which may point to the need for better theories of gravity or perhaps be explained in other ways. Latin language Latin ( lingua Latina , pronounced [ˈlɪŋɡʷa ɫaˈtiːna] , or Latinum [ɫaˈtiːnʊ̃] )

20536-801: The same position as Aristotle that all matter in the Universe is attracted to the center of the Earth. In the mid-16th century, various European scientists experimentally disproved the Aristotelian notion that heavier objects fall at a faster rate. In particular, the Spanish Dominican priest Domingo de Soto wrote in 1551 that bodies in free fall uniformly accelerate. De Soto may have been influenced by earlier experiments conducted by other Dominican priests in Italy, including those by Benedetto Varchi , Francesco Beato, Luca Ghini , and Giovan Bellaso which contradicted Aristotle's teachings on

20687-422: The scientific community. In 1959, American physicists Robert Pound and Glen Rebka performed an experiment in which they used gamma rays to confirm the prediction of gravitational time dilation . By sending the rays down a 74-foot tower and measuring their frequency at the bottom, the scientists confirmed that light is redshifted as it moves towards a source of gravity. The observed redshift also supported

20838-399: The spring is reflected on the scale as less weight — about 0.3% less at the equator than at the poles. In the Earth reference frame (in which the object being weighed is at rest), the object does not appear to be accelerating; however, the two real forces, gravity and the force from the spring, are the same magnitude and do not balance. The centrifugal force must be included to make the sum of

20989-433: The stationary frame. If P 1 P 2 , P 3 are the components of P with respect to unit vectors i , j , k directed along the axes of the rotating frame (i.e. P = P 1 i + P 2 j + P 3 k ), then the first time derivative [d P /d t ] of P with respect to the rotating frame is, by definition, d P 1 /d t i + d P 2 /d t j + d P 3 /d t k . If

21140-413: The stone in the horizontal plane which acts toward the center. In an inertial frame of reference , were it not for this net force acting on the stone, the stone would travel in a straight line, according to Newton's first law of motion . In order to keep the stone moving in a circular path, a centripetal force , in this case provided by the string, must be continuously applied to the stone. As soon as it

21291-443: The string is still acting on the stone. If one were to apply Newton's laws in their usual (inertial frame) form, one would conclude that the stone should accelerate in the direction of the net applied force—towards the axis of rotation—which it does not do. The centrifugal force and other fictitious forces must be included along with the real forces in order to apply Newton's laws of motion in the rotating frame. The Earth constitutes

21442-483: The term applied to other distinct physical concepts. One of these instances occurs in Lagrangian mechanics . Lagrangian mechanics formulates mechanics in terms of generalized coordinates { q k }, which can be as simple as the usual polar coordinates ( r ,   θ ) {\displaystyle (r,\ \theta )} or a much more extensive list of variables. Within this formulation

21593-419: Was able to confirm the predicted gravitational lensing of light during that year's solar eclipse . Eddington measured starlight deflections twice those predicted by Newtonian corpuscular theory, in accordance with the predictions of general relativity. Although Eddington's analysis was later disputed, this experiment made Einstein famous almost overnight and caused general relativity to become widely accepted in

21744-458: Was able to explain a wide variety of previously baffling experimental results. In the coming years, a wide range of experiments provided additional support for the idea of general relativity. Today, Einstein's theory of relativity is used for all gravitational calculations where absolute precision is desired, although Newton's inverse-square law is accurate enough for virtually all ordinary calculations. In modern physics , general relativity remains

21895-413: Was free to develop on its own, there is no reason to suppose that the speech was uniform either diachronically or geographically. On the contrary, Romanised European populations developed their own dialects of the language, which eventually led to the differentiation of Romance languages . Late Latin is a kind of written Latin used in the 3rd to 6th centuries. This began to diverge from Classical forms at

22046-408: Was measured on 14 September 2015 by the LIGO detectors. The gravitational waves emitted during the collision of two black holes 1.3 billion light years from Earth were measured. This observation confirms the theoretical predictions of Einstein and others that such waves exist. It also opens the way for practical observation and understanding of the nature of gravity and events in the Universe including

22197-496: Was much more liberal in its linguistic cohesion: for example, in classical Latin sum and eram are used as auxiliary verbs in the perfect and pluperfect passive, which are compound tenses. Medieval Latin might use fui and fueram instead. Furthermore, the meanings of many words were changed and new words were introduced, often under influence from the vernacular. Identifiable individual styles of classically incorrect Latin prevail. Renaissance Latin, 1300 to 1500, and

22348-441: Was no complete separation between Italian and Latin, even into the beginning of the Renaissance . Petrarch for example saw Latin as a literary version of the spoken language. Medieval Latin is the written Latin in use during that portion of the post-classical period when no corresponding Latin vernacular existed, that is from around 700 to 1500 AD. The spoken language had developed into the various Romance languages; however, in

22499-541: Was not unique to the Earth. Although he did not understand gravity as a force, the ancient Greek philosopher Archimedes discovered the center of gravity of a triangle. He postulated that if two equal weights did not have the same center of gravity, the center of gravity of the two weights together would be in the middle of the line that joins their centers of gravity. Two centuries later, the Roman engineer and architect Vitruvius contended in his De architectura that gravity

22650-482: Was shut down in June 2019), and Vatican Radio & Television, all of which broadcast news segments and other material in Latin. A variety of organisations, as well as informal Latin 'circuli' ('circles'), have been founded in more recent times to support the use of spoken Latin. Moreover, a number of university classics departments have begun incorporating communicative pedagogies in their Latin courses. These include

22801-486: Was well received by the scientific community, and his law of gravitation quickly spread across the European world. More than a century later, in 1821, his theory of gravitation rose to even greater prominence when it was used to predict the existence of Neptune . In that year, the French astronomer Alexis Bouvard used this theory to create a table modeling the orbit of Uranus , which was shown to differ significantly from

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