Mercury (planet)
First planet from the Sun
Mercury is the first planet from the Sun and the smallest in the Solar System. In English, it is named after the ancient Roman god (Mercury), god of commerce and communication, and the messenger of the gods. Mercury is classified as a terrestrial planet, with roughly the same surface gravity as Mars. The surface of Mercury is heavily cratered, as a result of countless impact events that have accumulated over billions of years. Its largest crater, Caloris Planitia, has a diameter of , which is about one-third the diameter of the planet (). Similarly to the Earth's Moon, Mercury's surface displays an expansive rupes system generated from thrust faults and bright ray systems formed by impact event remnants.
Mercury's sidereal year (88.0 Earth days) and sidereal day (58.65 Earth days) are in a 3:2 ratio. This relationship is called spin–orbit resonance, and "sidereal" here means "relative to the stars". Consequently, one solar day (sunrise to sunrise) on Mercury lasts for around 176 Earth days: twice the planet's sidereal year. This means that one side of Mercury will remain in sunlight for one Mercurian year of 88 Earth days; while during the next orbit, that side will be in darkness all the time until the next sunrise after another 88 Earth days.
Combined with its high orbital eccentricity, the planet's surface has widely varying sunlight intensity and temperature, with the equatorial regions ranging from at night to during sunlight. Due to the very small axial tilt, the planet's poles are permanently shadowed. This strongly suggests that water ice could be present in the craters. Above the planet's surface is an extremely tenuous exosphere and a faint magnetic field that is strong enough to deflect solar winds. Mercury has no natural satellites.
As of the early 2020s, many broad details of Mercury's geological history are still under investigation or pending data from space probes. Like other planets in the Solar System, Mercury was formed approximately 4.5 billion years ago. Its mantle is highly homogeneous, which suggests that Mercury had a magma ocean early in its history, like the Moon. According to current models, Mercury may have a solid silicate crust and mantle overlying a solid outer core, a deeper liquid core layer, and a solid inner core. There are many competing hypotheses about Mercury's origins and development, some of which incorporate collision with planetesimals and rock vaporization.
Nomenclature.
Historically, humans knew Mercury by different names depending on whether it was an evening star or a morning star. By about 350 BC, the ancient Greeks had realized the two stars were one. They knew the planet as , meaning "twinkling", and , for its fleeting motion, a name that is retained in modern [[Greek language|Greek]] ( ). The Romans named the planet after the swift-footed Roman messenger god, [[Mercury (mythology)|Mercury]] (Latin ), whom they equated with the Greek Hermes, because it moves across the sky faster than any other planet, though some associated the planet with [[Apollo]] instead, as detailed by [[Pliny the Elder]]. The [[astronomical symbol]] for Mercury is a stylized version of Hermes' [[caduceus]]; a [[Christian cross]] was added in the 16th century:[[File:Mercury symbol (fixed width).svg|16px|☿]].
Physical characteristics.
[[File:Terrestrial planet size comparisons-2.jpg|thumb|upright=1.4|Mercury to scale among the [[Inner Solar System]] [[planetary-mass object]]s beside the Sun, arranged by the order of their orbits outward from the Sun (from left: Mercury, [[Venus]],
[[Earth]], the [[Moon]], [[Mars]] and [[Ceres (dwarf planet)|Ceres]])]]
Mercury is one of four [[terrestrial planet]]s in the [[Solar System]], which means it is a rocky body like Earth. It is the smallest planet in the Solar System, with an [[equator]]ial [[radius]] of . Mercury is also [[list of Solar System objects by radius|smaller]]—albeit more massive—than the largest [[natural satellite]]s in the Solar System, [[Ganymede (moon)|Ganymede]] and [[Titan (moon)|Titan]]. Mercury consists of approximately 70% metallic and 30% [[silicate]] material.
Internal structure.
[[File:Mercury with magnetic field.svg|left|thumb|upright=1.6|Mercury's internal structure and magnetic field]]
Mercury appears to have a solid silicate [[Crust (geology)|crust]] and mantle overlying a solid, metallic outer core layer, a deeper liquid core layer, and a solid inner core. The composition of the iron-rich core remains uncertain, but it likely contains nickel, silicon and perhaps sulfur and carbon, plus trace amounts of other elements. The planet's density is the second highest in the Solar System at 5.427 g/cm3, only slightly less than Earth's density of 5.515 g/cm3. If the effect of [[gravitational compression]] were to be factored out from both planets, the materials of which Mercury is made would be denser than those of Earth, with an uncompressed density of 5.3 g/cm3 versus Earth's 4.4 g/cm3. Mercury's density can be used to infer details of its inner structure. Although Earth's high density results appreciably from gravitational compression, particularly at the [[planetary core|core]], Mercury is much smaller and its inner regions are not as compressed. Therefore, for it to have such a high density, its core must be large and rich in iron.
The radius of Mercury's core is estimated to be , based on interior models constrained to be consistent with a [[moment of inertia factor]] of . Hence, Mercury's core occupies about 57% of its volume; for Earth this proportion is 17%. Research published in 2007 suggests that Mercury has a molten core. The mantle-crust layer is in total thick. Projections differ as to the size of the crust specifically; data from the "Mariner 10" and "MESSENGER" probes suggests a thickness of , whereas an [[Airy isostacy]] model suggests a thickness of . One distinctive feature of Mercury's surface is the presence of numerous narrow ridges, extending up to several hundred kilometers in length. It is thought that these were formed as Mercury's core and mantle cooled and contracted at a time when the crust had already solidified.
Mercury's core has a higher iron content than that of any other planet in the Solar System, and several theories have been proposed to explain this. The most widely accepted theory is that Mercury originally had a metal–silicate ratio similar to common [[chondrite]] meteorites, thought to be typical of the Solar System's rocky matter, and a mass approximately 2.25 times its current mass. Early in the Solar System's history, Mercury may have been struck by a [[planetesimal]] of approximately <templatestyles src="Fraction/styles.css" />1⁄6 Mercury's mass and several thousand kilometers across. The impact would have stripped away much of the original crust and mantle, leaving the core behind as a relatively major component. A similar process, known as the [[giant impact hypothesis]], has been proposed to explain the formation of Earth's Moon.
Alternatively, Mercury may have formed from the [[solar nebula]] before the Sun's energy output had stabilized. It would initially have had twice its present mass, but as the [[protostar|protosun]] contracted, temperatures near Mercury could have been between 2,500 and 3,500 K and possibly even as high as 10,000 K. Much of Mercury's surface rock could have been vaporized at such temperatures, forming an atmosphere of "rock vapor" that could have been carried away by the [[solar wind]]. A third hypothesis proposes that the solar nebula caused [[drag (physics)|drag]] on the particles from which Mercury was [[Accretion (astrophysics)|accreting]], which meant that lighter particles were lost from the accreting material and not gathered by Mercury.
Each hypothesis predicts a different surface composition, and two space missions have been tasked with making observations of this composition. The first "[[MESSENGER]]", which ended in 2015, found higher-than-expected potassium and sulfur levels on the surface, suggesting that the giant impact hypothesis and vaporization of the crust and mantle did not occur because said potassium and sulfur would have been driven off by the extreme heat of these events. "[[BepiColombo]]", which will arrive at Mercury in 2025, will make observations to test these hypotheses. The findings so far would seem to favor the third hypothesis; however, further analysis of the data is needed.
Surface geology.
Mercury's surface is similar in appearance to that of the Moon, showing extensive [[Lunar mare|mare]]-like plains and heavy cratering, indicating that it has been geologically inactive for billions of years. It is more [[heterogeneous]] than the surface of [[Mars]] or the Moon, both of which contain significant stretches of similar geology, such as [[Lunar mare|maria]] and plateaus. [[Albedo]] features are areas of markedly different reflectivity, which include impact craters, the resulting ejecta, and [[ray system]]s. Larger albedo features correspond to higher reflectivity plains. Mercury has "[[wrinkle-ridge]]s" (dorsa), Moon-like [[highland]]s, mountains (montes), plains (planitiae), escarpments (rupes), and valleys ([[Vallis (planetary geology)|valles]]).
[[File:Unmasking the Secrets of Mercury.jpg|thumb|left|[[MESSENGER#Scientific instruments|MASCS]] spectrum scan of Mercury's surface by "MESSENGER"]]
The planet's mantle is chemically heterogeneous, suggesting the planet went through a [[magma ocean]] phase early in its history. Crystallization of minerals and convective overturn resulted in a layered, chemically heterogeneous crust with large-scale variations in chemical composition observed on the surface. The crust is low in iron but high in sulfur, resulting from the stronger early [[Chemical reduction|chemically reducing]] conditions than is found on other terrestrial planets. The surface is dominated by iron-poor [[pyroxene]] and [[olivine]], as represented by [[enstatite]] and [[forsterite]], respectively, along with sodium-rich [[plagioclase]] and minerals of mixed magnesium, calcium, and iron-sulfide. The less reflective regions of the crust are high in carbon, most likely in the form of graphite.
Names for features on Mercury come from a variety of sources and are set according to the [[IAU]] [[planetary nomenclature]] system. Names coming from people are limited to the deceased. Craters are named for artists, musicians, painters, and authors who have made outstanding or fundamental contributions to their field. Ridges, or dorsa, are named for scientists who have contributed to the study of Mercury. Depressions or [[fossa (geology)|fossae]] are named for works of architecture. Montes are named for the word "hot" in a variety of languages. [[Plain]]s or planitiae are named for [[Mercury (god)|Mercury]] in various languages. [[Escarpment]]s or [[rupēs]] are named for ships of scientific expeditions. Valleys or valles are named for abandoned cities, towns, or settlements of antiquity.
Impact basins and craters.
[[File:PIA19421-Mercury-Craters-MunchSanderPoe-20150416.jpg|thumb|left|Enhanced-color image of craters [[Munch (crater)|Munch]] (left), [[Sander (crater)|Sander]] (center), and [[Poe (crater)|Poe]] (right) amid volcanic plains (orange) near [[Caloris Basin]]]]
Mercury was heavily bombarded by comets and [[asteroid]]s during and shortly following its formation 4.6 billion years ago, as well as during a possibly separate subsequent episode called the [[Late Heavy Bombardment]] that ended 3.8 billion years ago. Mercury received impacts over its entire surface during this period of intense crater formation, facilitated by the lack of any [[atmosphere]] to slow impactors down. During this time Mercury was [[volcano|volcanically]] active; basins were filled by [[magma]], producing smooth plains similar to the maria found on the Moon. One of the most unusual craters is [[Apollodorus (crater)|Apollodorus]], or "the Spider", which hosts a series of radiating troughs extending outwards from its impact site.
[[Craters on Mercury]] range in diameter from small bowl-shaped cavities to [[multi-ringed impact basin]]s hundreds of kilometers across. They appear in all states of degradation, from relatively fresh rayed craters to highly degraded crater remnants. Mercurian craters differ subtly from lunar craters in that the area blanketed by their ejecta is much smaller, a consequence of Mercury's stronger surface gravity. According to [[International Astronomical Union]] rules, each new crater must be named after an artist who was famous for more than fifty years, and dead for more than three years, before the date the crater is named.
The largest known crater is [[Caloris Planitia]], or Caloris Basin, with a diameter of . The impact that created the Caloris Basin was so powerful that it caused [[lava]] eruptions and left a concentric mountainous ring ~ tall surrounding the [[impact crater]]. The floor of the Caloris Basin is filled by a geologically distinct flat plain, broken up by ridges and fractures in a roughly polygonal pattern. It is not clear whether they were volcanic lava flows induced by the impact or a large sheet of impact melt.
At the [[antipodes|antipode]] of the Caloris Basin is a large region of unusual, hilly terrain known as the "Weird Terrain". One hypothesis for its origin is that shock waves generated during the Caloris impact traveled around Mercury, converging at the basin's antipode (180 degrees away). The resulting high stresses fractured the surface. Alternatively, it has been suggested that this terrain formed as a result of the convergence of ejecta at this basin's antipode.
[[File:EW1027346412Gnomap.png|thumb|Tolstoj basin is along the bottom of this image of Mercury's limb]]
Overall, 46 impact basins have been identified. A notable basin is the -wide, multi-ring [[Tolstoj Basin]] that has an ejecta blanket extending up to from its rim and a floor that has been filled by smooth plains materials. [[Beethoven Basin]] has a similar-sized ejecta blanket and a -diameter rim. Like the Moon, the surface of Mercury has likely incurred the effects of [[space weathering]] processes, including solar wind and [[micrometeorite]] impacts.
Plains.
There are two geologically distinct plains regions on Mercury. Gently rolling, hilly [[Inter-crater plains on Mercury|plains in the regions between craters]] are Mercury's oldest visible surfaces, predating the heavily cratered terrain. These inter-crater plains appear to have obliterated many earlier craters, and show a general paucity of smaller craters below about in diameter.
Smooth plains are widespread flat areas that fill depressions of various sizes and bear a strong resemblance to lunar maria. Unlike lunar maria, the smooth plains of Mercury have the same albedo as the older inter-crater plains. Despite a lack of unequivocally volcanic characteristics, the localization and rounded, lobate shape of these plains strongly support volcanic origins. All the smooth plains of Mercury formed significantly later than the Caloris basin, as evidenced by appreciably smaller crater densities than on the Caloris ejecta blanket.
Compressional features.
An unusual feature of Mercury's surface is the numerous compression folds, or [[rupes]], that crisscross the plains. These exist on the Moon, but are much more prominent on Mercury. As Mercury's interior cooled, it contracted and its surface began to deform, creating [[wrinkle ridge]]s and [[lobate scarp]]s associated with [[thrust fault]]s. The scarps can reach lengths of and heights of . These compressional features can be seen on top of other features, such as craters and smooth plains, indicating they are more recent. Mapping of the features has suggested a total shrinkage of Mercury's radius in the range of ~. Most activity along the major thrust systems probably ended about 3.6–3.7 billion years ago. Small-scale thrust fault scarps have been found, tens of meters in height and with lengths in the range of a few kilometers, that appear to be less than 50 million years old, indicating that compression of the interior and consequent surface geological activity continue to the present.
Volcanism.
[[File:Picasso crater.png|thumb|[[Picasso (crater)|Picasso crater]]—the large arc-shaped pit located on the eastern side of its floor is postulated to have formed when subsurface magma subsided or drained, causing the surface to collapse into the resulting void.]]
There is evidence for [[pyroclastic flow]]s on Mercury from low-profile [[shield volcano]]es. Fifty-one pyroclastic deposits have been identified, where 90% of them are found within impact craters. A study of the degradation state of the impact craters that host pyroclastic deposits suggests that pyroclastic activity occurred on Mercury over a prolonged interval.
A "rimless depression" inside the southwest rim of the Caloris Basin consists of at least nine overlapping volcanic vents, each individually up to in diameter. It is thus a "[[compound volcano]]". The vent floors are at least below their brinks and they bear a closer resemblance to volcanic craters sculpted by explosive eruptions or modified by collapse into void spaces created by magma withdrawal back down into a conduit. Scientists could not quantify the age of the volcanic complex system but reported that it could be on the order of a billion years.
Surface conditions and exosphere.
[[File:North pole of Mercury -- NASA.jpg|thumb|Composite of the north pole of Mercury, where NASA confirmed the discovery of a large volume of water ice, in permanently dark craters that are found there.]]
The surface temperature of Mercury ranges from . It never rises above 180 K at the poles, due to the absence of an atmosphere and a steep temperature gradient between the equator and the poles. At [[perihelion]], the equatorial [[subsolar point]] is located at latitude 0°W or 180°W, and it climbs to a temperature of about . During [[aphelion]], this occurs at 90° or 270°W and reaches only . On the dark side of the planet, temperatures average . The intensity of [[sunlight]] on Mercury's surface ranges between 4.59 and 10.61 times the [[solar constant]] (1,370 W·m−2).
Although daylight temperatures at the surface of Mercury are generally extremely high, observations strongly suggest that ice (frozen water) exists on Mercury. The floors of deep craters at the poles are never exposed to direct sunlight, and temperatures there remain below 102 K, far lower than the global average. This creates a [[Cold trap (astronomy)|cold trap]] where ice can accumulate. Water ice strongly reflects [[radar]], and observations by the 70-meter [[Goldstone Solar System Radar]] and the [[Very Large Array|VLA]] in the early 1990s revealed that there are patches of high radar [[Reflection (physics)|reflection]] near the poles. Although ice was not the only possible cause of these reflective regions, astronomers thought it to be the most likely explanation. The presence of [[ice|water ice]] was confirmed using "MESSENGER" images of craters at the north pole.
The icy crater regions are estimated to contain about 1014–1015 kg of ice, and may be covered by a layer of [[regolith]] that inhibits [[Sublimation (phase transition)|sublimation]]. By comparison, the [[Antarctica|Antarctic]] ice sheet on Earth has a mass of about 4×1018 kg, and Mars's south polar cap contains about 1016 kg of water. The origin of the ice on Mercury is not yet known, but the two most likely sources are from [[outgassing]] of water from the planet's interior and deposition by impacts of comets.
Mercury is too small and hot for its [[gravity]] to retain any significant [[atmosphere]] over long periods of time; it does have a tenuous surface-bounded [[exosphere]] at a surface pressure of less than approximately 0.5 nPa (0.005 picobars). It includes [[hydrogen]], [[helium]], [[oxygen]], [[sodium]], [[calcium]], [[potassium]], [[magnesium]], [[silicon]], and [[hydroxide]], among others. This exosphere is not stable—atoms are continuously lost and replenished from a variety of sources. [[Hydrogen atom]]s and [[helium atom]]s probably come from the solar wind, [[diffusion|diffusing]] into Mercury's [[magnetosphere]] before later escaping back into space. The [[radioactive decay]] of elements within Mercury's crust is another source of helium, as well as sodium and potassium. Water vapor is present, released by a combination of processes such as comets striking its surface, [[sputtering]] creating water out of hydrogen from the solar wind and oxygen from rock, and sublimation from reservoirs of water ice in the permanently shadowed polar craters. The detection of high amounts of water-related ions like O+, OH−, and [[hydronium|H3O+]] was a surprise. Because of the quantities of these ions that were detected in Mercury's space environment, scientists surmise that these molecules were blasted from the surface or exosphere by the solar wind.
Sodium, potassium, and calcium were discovered in the atmosphere during the 1980s–1990s, and are thought to result primarily from the vaporization of surface rock struck by micrometeorite impacts including presently from [[Comet Encke]]. In 2008, magnesium was discovered by "MESSENGER". Studies indicate that, at times, sodium emissions are localized at points that correspond to the planet's magnetic poles. This would indicate an interaction between the magnetosphere and the planet's surface.
According to NASA, Mercury is not a suitable planet for Earth-like life. It has a [[exosphere|surface boundary exosphere]] instead of a layered atmosphere, extreme temperatures, and high solar radiation. It is unlikely that any living beings can withstand those conditions. Some parts of the subsurface of Mercury may have been [[Planetary habitability|habitable]], and perhaps [[life form]]s, albeit likely primitive [[microorganism]]s, may have existed on the planet.
Magnetic field and magnetosphere.
[[File:Mercury Magnetic Field NASA.jpg|thumb|Graph showing relative strength of Mercury's magnetic field]]
Despite its small size and slow 59-day-long rotation, Mercury has a significant, and apparently global, [[magnetic field]]. According to measurements taken by "Mariner 10", it is about 1.1% the strength of [[Earth's magnetic field|Earth's]]. The magnetic-field strength at Mercury's equator is about 300 [[Tesla (unit)|nT]]. Like that of Earth, Mercury's magnetic field is [[dipolar]] and nearly aligned with the planet's spin axis (10° dipolar tilt, compared to 11° for Earth). Measurements from both the "Mariner 10" and "MESSENGER" space probes have indicated that the strength and shape of the magnetic field are stable.
It is likely that this magnetic field is generated by a [[Dynamo theory|dynamo]] effect, in a manner similar to the magnetic field of Earth. This dynamo effect would result from the circulation of the planet's iron-rich liquid core. Particularly strong [[tidal heating]] effects caused by the planet's high orbital eccentricity would serve to keep part of the core in the liquid state necessary for this dynamo effect.
Mercury's magnetic field is strong enough to deflect the solar wind around the planet, creating a magnetosphere. The planet's magnetosphere, though small enough to fit within Earth, is strong enough to trap solar wind [[plasma (physics)|plasma]]. This contributes to the space weathering of the planet's surface. Observations taken by the "Mariner 10" spacecraft detected this low energy plasma in the magnetosphere of the planet's nightside. Bursts of energetic particles in the planet's magnetotail indicate a dynamic quality to the planet's magnetosphere.
During its second flyby of the planet on October 6, 2008, "MESSENGER" discovered that Mercury's magnetic field can be extremely "leaky". The spacecraft encountered magnetic "tornadoes"—twisted bundles of magnetic fields connecting the planetary magnetic field to interplanetary space—that were up to 800 km wide or a third of the radius of the planet. These twisted magnetic flux tubes, technically known as [[flux transfer event]]s, form open windows in the planet's magnetic shield through which the solar wind may enter and directly impact Mercury's surface via [[magnetic reconnection]]. This also occurs in Earth's magnetic field. The "MESSENGER" observations showed the reconnection rate was ten times higher at Mercury, but its proximity to the Sun only accounts for about a third of the reconnection rate observed by "MESSENGER".
Orbit, rotation, and longitude.
Mercury has the most [[Orbital eccentricity|eccentric]] orbit of all the planets in the Solar System; its eccentricity is 0.21 with its distance from the Sun ranging from . It takes 87.969 Earth days to complete an orbit. The diagram illustrates the effects of the eccentricity, showing Mercury's orbit overlaid with a circular orbit having the same [[semi-major axis]]. Mercury's higher velocity when it is near perihelion is clear from the greater distance it covers in each 5-day interval. In the diagram, the varying distance of Mercury to the Sun is represented by the size of the planet, which is inversely proportional to Mercury's distance from the Sun.
This varying distance to the Sun leads to Mercury's surface being flexed by [[tidal bulge]]s raised by the [[Sun]] that are about 17 times stronger than the Moon's on Earth. Combined with a 3:2 [[#Spin-orbit resonance|spin–orbit resonance]] of the planet's rotation around its axis, it also results in complex variations of the surface temperature. The resonance makes a single [[solar day]] (the length between two [[meridian (astronomy)|meridian]] transits of the Sun) on Mercury last exactly two Mercury years, or about 176 Earth days.
Mercury's orbit is inclined by 7 degrees to the plane of Earth's orbit (the [[ecliptic]]), the largest of all eight known solar planets. As a result, [[transits of Mercury]] across the face of the Sun can only occur when the planet is crossing the plane of the ecliptic at the time it lies between Earth and the Sun, which is in May or November. This occurs about every seven years on average.
Mercury's [[axial tilt]] is almost zero, with the best measured value as low as 0.027 degrees. This is significantly smaller than that of [[Jupiter]], which has the second smallest axial tilt of all planets at 3.1 degrees. This means that to an observer at Mercury's poles, the center of the Sun never rises more than 2.1 [[arcminutes]] above the horizon. By comparison, the [[angular size]] of the Sun as seen from Mercury ranges from <templatestyles src="Fraction/styles.css" />1+1⁄4 to 2 degrees across.
At certain points on Mercury's surface, an observer would be able to see the Sun peek up a little more than two-thirds of the way over the horizon, then reverse and set before rising again, all within the same [[Extraterrestrial skies#Mercury|Mercurian day]]. This is because approximately four Earth days before perihelion, Mercury's angular [[orbital speed|orbital velocity]] equals its angular [[rotational velocity]] so that the Sun's [[improper motion|apparent motion]] ceases; closer to perihelion, Mercury's angular orbital velocity then exceeds the angular rotational velocity. Thus, to a hypothetical observer on Mercury, the Sun appears to move in a [[apparent retrograde motion|retrograde]] direction. Four Earth days after perihelion, the Sun's normal apparent motion resumes. A similar effect would have occurred if Mercury had been in synchronous rotation: the alternating gain and loss of rotation over a revolution would have caused a libration of 23.65° in longitude.
For the same reason, there are two points on Mercury's equator, 180 degrees apart in [[longitude]], at either of which, around perihelion in alternate Mercurian years (once a Mercurian day), the Sun passes overhead, then reverses its apparent motion and passes overhead again, then reverses a second time and passes overhead a third time, taking a total of about 16 Earth-days for this entire process. In the other alternate Mercurian years, the same thing happens at the other of these two points. The amplitude of the retrograde motion is small, so the overall effect is that, for two or three weeks, the Sun is almost stationary overhead, and is at its most brilliant because Mercury is at perihelion, its closest to the Sun. This prolonged exposure to the Sun at its brightest makes these two points the hottest places on Mercury. Maximum temperature occurs when the Sun is at an angle of about 25 degrees past noon due to [[Diurnal temperature variation#Temperature lag|diurnal temperature lag]], at 0.4 Mercury days and 0.8 Mercury years past sunrise. Conversely, there are two other points on the equator, 90 degrees of longitude apart from the first ones, where the Sun passes overhead only when the planet is at aphelion in alternate years, when the apparent motion of the Sun in Mercury's sky is relatively rapid. These points, which are the ones on the equator where the apparent retrograde motion of the Sun happens when it is crossing the horizon as described in the preceding paragraph, receive much less solar heat than the first ones described above.
Mercury attains an inferior conjunction (nearest approach to Earth) every 116 Earth days on average, but this interval can range from 105 days to 129 days due to the planet's eccentric orbit. Mercury can come as near as to Earth, and that is slowly declining: The next approach to within is in 2679, and to within in 4487, but it will not be closer to Earth than until 28,622. Its period of retrograde motion as seen from Earth can vary from 8 to 15 days on either side of an inferior conjunction. This large range arises from the planet's high orbital eccentricity. Essentially, because Mercury is closest to the Sun, when taking an average over time, Mercury is most often the closest planet to the Earth, and—in that measure—it is the closest planet to each of the other planets in the Solar System.
Longitude convention.
The longitude convention for Mercury puts the zero of longitude at one of the two hottest points on the surface, as described above. However, when this area was first visited, by "Mariner 10", this zero meridian was in darkness, so it was impossible to select a feature on the surface to define the exact position of the meridian. Therefore, a small crater further west was chosen, called [[Hun Kal]], which provides the exact reference point for measuring longitude. The center of Hun Kal defines the 20° west meridian. A 1970 International Astronomical Union resolution suggests that longitudes be measured positively in the westerly direction on Mercury. The two hottest places on the equator are therefore at longitudes 0° W and 180° W, and the coolest points on the equator are at longitudes 90° W and 270° W. However, the "MESSENGER" project uses an east-positive convention.
Spin-orbit resonance.
[[File:Mercury's orbital resonance.svg|thumb|After one orbit, Mercury has rotated 1.5 times, so after two complete orbits the same hemisphere is again illuminated.]]
For many years it was thought that Mercury was synchronously [[tidally locked]] with the Sun, [[rotating]] once for each orbit and always keeping the same face directed towards the Sun, in the same way that the same side of the Moon always faces Earth. Radar observations in 1965 proved that the planet has a 3:2 spin-orbit resonance, rotating three times for every two revolutions around the Sun. The eccentricity of Mercury's orbit makes this resonance stable—at perihelion, when the solar tide is strongest, the Sun is nearly stationary in Mercury's sky.
The 3:2 resonant tidal locking is stabilized by the variance of the tidal force along Mercury's eccentric orbit, acting on a permanent dipole component of Mercury's mass distribution. In a circular orbit there is no such variance, so the only resonance stabilized in such an orbit is at 1:1 (e.g., Earth–Moon), when the tidal force, stretching a body along the "center-body" line, exerts a torque that aligns the body's axis of least inertia (the "longest" axis, and the axis of the aforementioned dipole) to always point at the center. However, with noticeable eccentricity, like that of Mercury's orbit, the tidal force has a maximum at perihelion and therefore stabilizes resonances, like 3:2, ensuring that the planet points its axis of least inertia roughly at the Sun when passing through perihelion.
The original reason astronomers thought it was synchronously locked was that, whenever Mercury was best placed for observation, it was always nearly at the same point in its 3:2 resonance, hence showing the same face. This is because, coincidentally, Mercury's rotation period is almost exactly half of its synodic period with respect to Earth. Due to Mercury's 3:2 spin-orbit resonance, a solar day lasts about 176 Earth days. A [[sidereal day]] (the period of rotation) lasts about 58.7 Earth days.
Simulations indicate that the orbital eccentricity of Mercury varies [[chaos theory|chaotically]] from nearly zero (circular) to more than 0.45 over millions of years due to [[Perturbation (astronomy)|perturbations]] from the other planets. This was thought to explain Mercury's 3:2 spin-orbit resonance (rather than the more usual 1:1), because this state is more likely to arise during a period of high eccentricity. However, accurate modeling based on a realistic model of tidal response has demonstrated that Mercury was captured into the 3:2 spin-orbit state at a very early stage of its history, within 20 (more likely, 10) million years after its formation.
Numerical simulations show that a future [[Secular resonance|secular]] [[Orbital resonance|orbital resonant]] interaction with the perihelion of Jupiter may cause the eccentricity of Mercury's orbit to increase to the point where there is a 1% chance that the orbit will be destabilized in the next five billion years. If this happens, Mercury may fall into the Sun, collide with Venus, be ejected from the Solar System, or even disrupt the rest of the inner Solar System.
Advance of perihelion.
[[File:Drehung der Apsidenlinie light.svg|right|thumb|[[Apsidal precession]] of Mercury's orbit]]
In 1859, the French mathematician and astronomer [[Urbain Le Verrier]] reported that the slow [[precession]] of Mercury's orbit around the Sun could not be completely explained by [[Newtonian mechanics]] and perturbations by the known planets. He suggested, among possible explanations, that another planet (or perhaps instead a series of smaller "corpuscules") might exist in an orbit even closer to the Sun than that of Mercury, to account for this perturbation. Other explanations considered included a slight oblateness of the Sun. The success of the search for [[Neptune]] based on its perturbations of the orbit of [[Uranus]] led astronomers to place faith in this possible explanation, and the hypothetical planet was named [[Vulcan (hypothetical planet)|Vulcan]], but no such planet was ever found.
The observed [[perihelion precession]] of Mercury is 5,600 [[arcseconds]] (1.5556°) per century relative to Earth, or per century relative to the inertial [[International Celestial Reference Frame|ICRF]]. Newtonian mechanics, taking into account all the effects from the other planets and including 0.0254 arcseconds per century due to the oblateness of the Sun, predicts a precession of 5,557 arcseconds (1.5436°) per century relative to Earth, or per century relative to ICRF. In the early 20th century, [[Albert Einstein]]'s [[general theory of relativity]] provided the explanation for the observed precession, by formalizing gravitation as being mediated by the curvature of spacetime. The effect is small: just per century (or 0.43 arcsecond per year, or 0.1035 arcsecond per orbital period) for Mercury; it therefore requires a little over 12.5 million orbits, or 3 million years, for a full excess turn. Similar, but much smaller, effects exist for other Solar System bodies: 8.6247 arcseconds per century for Venus, 3.8387 for Earth, 1.351 for Mars, and 10.05 for [[1566 Icarus]].
Observation.
[[File:Mercury.jpg|thumb|Image mosaic by "Mariner 10", 1974]]
Mercury's [[apparent magnitude]] is calculated to vary between −2.48 (brighter than [[Sirius]]) around [[superior conjunction]] and +7.25 (below the limit of naked-eye visibility) around [[inferior conjunction]]. The mean apparent magnitude is 0.23 while the standard deviation of 1.78 is the largest of any planet. The mean apparent magnitude at superior conjunction is −1.89 while that at inferior conjunction is +5.93. Observation of Mercury is complicated by its proximity to the Sun, as it is lost in the Sun's glare for much of the time. Mercury can be observed for only a brief period during either morning or evening twilight.
Ground-based telescope observations of Mercury reveal only an illuminated partial disk with limited detail. The [[Hubble Space Telescope]] cannot observe Mercury at all, due to safety procedures that prevent its pointing too close to the Sun. Because the shift of 0.15 revolutions of Earth in a Mercurian year makes up a seven-Mercurian-year cycle (0.15 × 7 ≈ 1.0), in the seventh Mercurian year, Mercury follows almost exactly (earlier by 7 days) the sequence of phenomena it showed seven Mercurian years before.
Like the Moon and Venus, Mercury exhibits [[Lunar phase|phases]] as seen from Earth. It is "new" at [[inferior conjunction]] and "full" at superior conjunction. The planet is rendered invisible from Earth on both of these occasions because of its being obscured by the Sun, except at its new phase during a transit. Mercury is technically brightest as seen from Earth when it is at a full phase. Although Mercury is farthest from Earth when it is full, the greater illuminated area that is visible and the [[opposition effect|opposition brightness surge]] more than compensates for the distance. The opposite is true for Venus, which appears brightest when it is a [[crescent]], because it is much closer to Earth than when [[gibbous]].
[[File:PIA19247-Mercury-NPolarRegion-Messenger20150316.jpg|thumb|left|False-color map showing the maximum temperatures of the north polar region]]
[[File:Mercury Venus Moon over San Jose 08 Jan 2024.png|thumb|right|Mercury (lower left) as seen from [[San Jose, California]] with Venus and the Moon.]]
Mercury is best observed at the first and last quarter, although they are phases of lesser brightness. The first and last quarter phases occur at greatest [[elongation (astronomy)|elongation]] east and west of the Sun, respectively. At both of these times, Mercury's separation from the Sun ranges anywhere from 17.9° at perihelion to 27.8° at aphelion. At greatest "western" elongation, Mercury rises at its earliest before sunrise, and at greatest "eastern" elongation, it sets at its latest after sunset.
[[File:PIA19422-Mercury-CarnegieRupes-MDIS-MLA-20150416.jpg|thumb|right|False-color image of [[Carnegie Rupes]], a tectonic landform—high terrain (red); low (blue).]]
Mercury is more often and easily visible from the [[Southern Hemisphere]] than from the [[Northern Hemisphere|Northern]]. This is because Mercury's maximum western elongation occurs only during early autumn in the Southern Hemisphere, whereas its greatest eastern elongation happens only during late winter in the Southern Hemisphere. In both of these cases, the angle at which the planet's orbit intersects the horizon is maximized, allowing it to rise several hours before sunrise in the former instance and not set until several hours after sundown in the latter from southern mid-latitudes, such as Argentina and South Africa.
An alternate method for viewing Mercury involves observing the planet with a [[telescope]] during daylight hours when conditions are clear, ideally when it is at its greatest elongation. This allows the planet to be found easily, even when using telescopes with apertures. However, great care must be taken to obstruct the Sun from sight because of the extreme risk for eye damage. This method bypasses the limitation of twilight observing when the ecliptic is located at a low elevation (e.g. on autumn evenings). The planet is higher in the sky and less atmospheric effects affect the view of the planet. Mercury can be viewed as close as 4° to the Sun near superior conjunction when it is almost at its brightest.
Mercury can, like several other planets and the brightest stars, be seen during a total [[solar eclipse]].
Observation history.
Ancient astronomers.
[[File:Mercury-bonatti.png|thumb|Mercury, from "Liber astronomiae", 1550]]
The earliest known recorded observations of Mercury are from the [[MUL.APIN]] tablets. These observations were most likely made by an [[Assyria]]n astronomer around the 14th century BC. The [[cuneiform]] name used to designate Mercury on the MUL.APIN tablets is transcribed as UDU.IDIM.GU\U4.UD ("the jumping planet"). [[Babylonian astronomy|Babylonian records]] of Mercury date back to the 1st millennium BC. The [[Babylonia]]ns called the planet [[Nabu]] after the messenger to the gods in [[Babylonian mythology|their mythology]].
The [[Greeks in Egypt|Greco]]-[[Ancient Egypt|Egyptian]] astronomer [[Ptolemy]] wrote about the possibility of planetary transits across the face of the Sun in his work "Planetary Hypotheses". He suggested that no transits had been observed either because planets such as Mercury were too small to see, or because transits were too infrequent.
[[File:Shatir500.jpg|thumb|left|[[Ibn al-Shatir]]'s model for the appearances of Mercury, showing the multiplication of [[epicycles]] using the [[Tusi couple]], thus eliminating the Ptolemaic eccentrics and [[equant]].]]
In [[ancient China]], Mercury was known as "the Hour Star" ("Chen-xing" ). It was associated with the direction north and the phase of water in the [[Five Phases]] system of metaphysics. Modern [[Chinese culture|Chinese]], [[Korean culture|Korean]], [[Japanese culture|Japanese]] and [[Vietnamese culture|Vietnamese]] cultures refer to the planet literally as the "water star" (), based on the [[Five elements (Chinese philosophy)|Five elements]]. [[Hindu mythology]] used the name [[Budha]] for Mercury, and this god was thought to preside over Wednesday. The god [[Odin]] (or Woden) of [[Germanic paganism]] was associated with the planet Mercury and Wednesday. The [[Maya civilization|Maya]] may have represented Mercury as an owl (or possibly four owls; two for the morning aspect and two for the evening) that served as a messenger to the [[underworld]]. Mercury was sometimes known as [[Stilbon (mythology)|Stilbon]] ([[Greek language|Greek]]: Στίλβων) meaning 'the shining, glittering'.
In [[medieval Islamic astronomy]], the [[Al-Andalus|Andalusian]] astronomer [[Abū Ishāq Ibrāhīm al-Zarqālī]] in the 11th century described the [[deferent]] of Mercury's [[geocentric orbit]] as being oval, like an egg or a [[Pine nut|pignon]], although this insight did not influence his astronomical theory or his astronomical calculations. In the 12th century, [[Ibn Bajjah]] observed "two planets as black spots on the face of the Sun", which was later suggested as the transit of Mercury and/or Venus by the [[Maragheh observatory|Maragha]] astronomer [[Qotb al-Din Shirazi]] in the 13th century. Most such medieval reports of transits were later taken as observations of [[sunspot]]s.
In India, the [[Kerala school of astronomy and mathematics|Kerala school]] astronomer [[Nilakantha Somayaji]] in the 15th century developed a partially heliocentric planetary model in which Mercury orbits the Sun, which in turn orbits Earth, similar to the [[Tychonic system]] later proposed by [[Tycho Brahe]] in the late 16th century.
Ground-based telescopic research.
The first telescopic observations of Mercury were made by [[Thomas Harriot]] and [[Galileo]] from 1610. In 1612, [[Simon Marius]] observed the brightness of Mercury varied with the planet's orbital position and concluded it had phases "in the same way as Venus and the Moon". In 1631, [[Pierre Gassendi]] made the first telescopic observations of the transit of a planet across the Sun when he saw a transit of Mercury predicted by [[Johannes Kepler]]. In 1639, [[Giovanni Zupi]] used a telescope to discover that the planet had orbital phases similar to Venus and the Moon. The observation demonstrated conclusively that Mercury orbited the Sun.
A rare event in astronomy is the passage of one planet in front of another ([[occultation]]), as seen from Earth. Mercury and Venus occult each other every few centuries, and the event of May 28, 1737, is the only one historically observed, having been seen by [[John Bevis]] at the [[Royal Greenwich Observatory]]. The next occultation of Mercury by Venus will be on December 3, 2133.
The difficulties inherent in observing Mercury meant that it was far less studied than the other planets. In 1800, [[Johann Schröter]] made observations of surface features, claiming to have observed mountains. [[Friedrich Bessel]] used Schröter's drawings to erroneously estimate the rotation period as 24 hours and an axial tilt of 70°. In the 1880s, [[Giovanni Schiaparelli]] mapped the planet more accurately, and suggested that Mercury's rotational period was 88 days, the same as its orbital period due to tidal locking. This phenomenon is known as [[synchronous rotation]]. The effort to map the surface of Mercury was continued by [[Eugenios Antoniadi]], who published a book in 1934 that included both maps and his own observations. Many of the planet's surface features, particularly the [[List of albedo features on Mercury|albedo features]], take their names from Antoniadi's map.
In June 1962, Soviet scientists at the [[Institute of Radio-engineering and Electronics]] of the [[USSR Academy of Sciences]], led by [[Vladimir Kotelnikov]], became the first to bounce a radar signal off Mercury and receive it, starting radar observations of the planet. Three years later, radar observations by Americans [[Gordon H. Pettengill]] and Rolf B. Dyce, using the [[Arecibo radio telescope]] in [[Puerto Rico]], showed conclusively that the planet's rotational period was about 59 days. The theory that Mercury's rotation was synchronous had become widely held, and it was a surprise to astronomers when these radio observations were announced. If Mercury were tidally locked, its dark face would be extremely cold, but measurements of radio emission revealed that it was much hotter than expected. Astronomers were reluctant to drop the synchronous rotation theory and proposed alternative mechanisms such as powerful heat-distributing winds to explain the observations.
In 1965, Italian astronomer [[Giuseppe Colombo]] noted that the rotation value was about two-thirds of Mercury's orbital period, and proposed that the planet's orbital and rotational periods were locked into a 3:2 rather than a 1:1 resonance. Data from "Mariner 10" subsequently confirmed this view. This means that Schiaparelli's and Antoniadi's maps were not "wrong". Instead, the astronomers saw the same features during every "second" orbit and recorded them, but disregarded those seen in the meantime, when Mercury's other face was toward the Sun, because the orbital geometry meant that these observations were made under poor viewing conditions.
Ground-based optical observations did not shed much further light on Mercury, but radio astronomers using interferometry at microwave wavelengths, a technique that enables removal of the solar radiation, were able to discern physical and chemical characteristics of the subsurface layers to a depth of several meters. Not until the first space probe flew past Mercury did many of its most fundamental morphological properties become known. Moreover, technological advances have led to improved ground-based observations. In 2000, high-resolution [[lucky imaging]] observations were conducted by the [[Mount Wilson Observatory]] Hale telescope. They provided the first views that resolved surface features on the parts of Mercury that were not imaged in the "Mariner 10" mission. Most of the planet has been mapped by the Arecibo radar telescope, with resolution, including polar deposits in shadowed craters of what may be water ice.
Research with space probes.
[[File:MESSENGER Assembly.jpg|thumb|left|"MESSENGER" being prepared for launch]]
[[File:PIA18389-MarsCuriosityRover-MercuryTransitsSun-20140603.gif|thumb|Mercury transiting the [[Sun]] as viewed by the Mars rover [[Curiosity (rover)|"Curiosity"]] (June 3, 2014).]]
Reaching Mercury from Earth poses significant technical challenges, because it orbits so much closer to the Sun than Earth. A Mercury-bound spacecraft launched from Earth must travel over into the Sun's gravitational [[potential well]]. Mercury has an [[orbital speed]] of , whereas Earth's orbital speed is . Therefore, the spacecraft must make a larger change in [[velocity]] ([[delta-v]]) to get to Mercury and then enter orbit, as compared to the delta-v required for, say, [[Exploration of Mars|Mars planetary missions]].
The [[potential energy]] liberated by moving down the Sun's potential well becomes [[kinetic energy]], requiring a delta-v change to do anything other than pass by Mercury. Some portion of this [[delta-v budget]] can be provided from a [[gravity assist]] during one or more fly-bys of Venus. To land safely or enter a stable orbit the spacecraft would rely entirely on rocket motors. [[Aerobraking]] is ruled out because Mercury has a negligible atmosphere. A trip to Mercury requires more rocket fuel than that required to [[escape velocity|escape]] the Solar System completely. As a result, only three space probes have visited it so far. A proposed alternative approach would use a [[solar sail]] to attain a Mercury-synchronous orbit around the Sun.
"Mariner 10".
[[File:Mariner 10.jpg|thumb|"Mariner 10", the first probe to visit Mercury]]
The first spacecraft to visit Mercury was NASA's "Mariner 10" (1974–1975). The spacecraft used the gravity of Venus to adjust its orbital velocity so that it could approach Mercury, making it both the first spacecraft to use this gravitational "slingshot" effect and the first NASA mission to visit multiple planets. "Mariner 10" provided the first close-up images of Mercury's surface, which immediately showed its heavily cratered nature, and revealed many other types of geological features, such as the giant scarps that were later ascribed to the effect of the planet shrinking slightly as its iron core cools. Unfortunately, the same face of the planet was lit at each of "Mariner 10"'s close approaches. This made close observation of both sides of the planet impossible, and resulted in the mapping of less than 45% of the planet's surface.
The spacecraft made three close approaches to Mercury, the closest of which took it to within of the surface. At the first close approach, instruments detected a magnetic field, to the great surprise of planetary geologists—Mercury's rotation was expected to be much too slow to generate a significant [[dynamo]] effect. The second close approach was primarily used for imaging, but at the third approach, extensive magnetic data were obtained. The data revealed that the planet's magnetic field is much like Earth's, which deflects the solar wind around the planet. For many years after the "Mariner 10" encounters, the origin of Mercury's magnetic field remained the subject of several competing theories.
On March 24, 1975, just eight days after its final close approach, "Mariner 10" ran out of fuel. Because its orbit could no longer be accurately controlled, mission controllers instructed the probe to shut down. "Mariner 10" is thought to be still orbiting the Sun, passing close to Mercury every few months.
"MESSENGER".
[[File:Details of MESSENGER's Impact Location.jpg|thumb|Estimated details of the impact of "MESSENGER" on April 30, 2015]]
A second NASA mission to Mercury, named "MESSENGER" (MErcury Surface, Space ENvironment, GEochemistry, and Ranging), was launched on August 3, 2004. It made a fly-by of Earth in August 2005, and of Venus in October 2006 and June 2007 to place it onto the correct trajectory to reach an orbit around Mercury. A first fly-by of Mercury occurred on January 14, 2008, a second on October 6, 2008, and a third on September 29, 2009. Most of the hemisphere not imaged by "Mariner 10" was mapped during these fly-bys. The probe successfully entered an elliptical orbit around the planet on March 18, 2011. The first orbital image of Mercury was obtained on March 29, 2011. The probe finished a one-year mapping mission, and then entered a one-year extended mission into 2013. In addition to continued observations and mapping of Mercury, "MESSENGER" observed the 2012 [[solar maximum]].
[[File:MercuryTopo.png|thumb|right|Topography of Mercury based on MDIS (Mercury Dual Imaging System) data]] The mission was designed to clear up six key issues: Mercury's high density, its geological history, the nature of its magnetic field, the structure of its core, whether it has ice at its poles, and where its tenuous atmosphere comes from. To this end, the probe carried imaging devices that gathered much-higher-resolution images of much more of Mercury than "Mariner 10", assorted [[spectrometer]]s to determine the abundances of elements in the crust, and [[magnetometer]]s and devices to measure velocities of charged particles. Measurements of changes in the probe's orbital velocity were expected to be used to infer details of the planet's interior structure. "MESSENGER"'s final maneuver was on April 24, 2015, and it crashed into Mercury's surface on April 30, 2015. The spacecraft's impact with Mercury occurred at 3:26:01 p.m. [[Eastern Time Zone|EDT]] on April 30, 2015, leaving a crater estimated to be in diameter.
"BepiColombo".
The [[European Space Agency]] and the [[Japanese Space Agency]] developed and launched a joint mission called "BepiColombo", which will orbit Mercury with two probes: one to map the planet and the other to study its magnetosphere. Launched on October 20, 2018, "BepiColombo" is expected to reach Mercury in 2025. It will release a magnetometer probe into an elliptical orbit, then chemical rockets will fire to deposit the mapper probe into a circular orbit. Both probes will operate for one terrestrial year. The mapper probe carries an array of spectrometers similar to those on "MESSENGER", and will study the planet at many different wavelengths including [[infrared]], [[ultraviolet]], [[X-ray]] and [[gamma ray]]. "BepiColombo" conducted the first of its six planned Mercury flybys on October 1, 2021, and the sixth was completed on January 9, 2025. The spacecraft will enter the planet's orbit in 2026.
"Perseverance" rover.
On March 5, 2024, NASA released images of transits of the moon [[Deimos (moon)|Deimos]], the moon [[Phobos (moon)|Phobos]] and the planet Mercury as viewed by the "Perseverance" rover on the planet Mars.
See also.
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Notes.
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References.
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External links.
[[Category:Mercury (planet)| ]]
[[Category:Planets of the Solar System]]
[[Category:Terrestrial planets]]
[[Category:Astronomical objects known since antiquity]]
[[Category:Solar System]]

Isaac Newton
English polymath (1642–1726)
Sir Isaac Newton (; 4 January [O.S. 25 December] 1643 – 31 March [O.S. 20 March] 1727) was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author. Newton was a key figure in the Scientific Revolution and the Enlightenment that followed. His book ("Mathematical Principles of Natural Philosophy"), first published in 1687, achieved the first great unification in physics and established classical mechanics. Newton also made seminal contributions to optics, and shares credit with German mathematician Gottfried Wilhelm Leibniz for formulating infinitesimal calculus, though he developed calculus years before Leibniz. He contributed to and refined the scientific method, and his work is considered the most influential in bringing forth modern science.
In the , Newton formulated the laws of motion and universal gravitation that formed the dominant scientific viewpoint for centuries until it was superseded by the theory of relativity. He used his mathematical description of gravity to derive Kepler's laws of planetary motion, account for tides, the trajectories of comets, the precession of the equinoxes and other phenomena, eradicating doubt about the Solar System's heliocentricity. Newton solved the two-body problem, and introduced the three-body problem. He demonstrated that the motion of objects on Earth and celestial bodies could be accounted for by the same principles. Newton's inference that the Earth is an oblate spheroid was later confirmed by the geodetic measurements of Maupertuis, La Condamine, and others, thereby convincing most European scientists of the superiority of Newtonian mechanics over earlier systems. Newton was also the first to calculate the age of Earth by experiment, and described a precursor to the modern wind tunnel.
Newton built the first reflecting telescope and developed a sophisticated theory of colour based on the observation that a prism separates white light into the colours of the visible spectrum. His work on light was collected in his book "Opticks", published in 1704. He originated prisms as beam expanders and multiple-prism arrays, which would later become integral to the development of tunable lasers. He also anticipated wave-particle duality. Newton further formulated an empirical law of cooling, which was the first heat transfer formulation and serves as the formal basis of convective heat transfer, made the first theoretical calculation of the speed of sound, and introduced the notions of a Newtonian fluid and a black body. Furthermore, he made early studies into electricity. In addition to his creation of calculus, Newton's work on mathematics was extensive. He generalized the binomial theorem to any real number, introduced the Puiseux series, was the first to state Bézout's theorem, classified most of the cubic plane curves, contributed to the study of Cremona transformations, developed a method for approximating the roots of a function, and also originated the Newton-Cotes formulas for numerical integration. He further initiated the field of calculus of variations, devised an early form of regression analysis, and was a pioneer of vector analysis.
Newton was a fellow of Trinity College and the second Lucasian Professor of Mathematics at the University of Cambridge; he was appointed at the age of 26. He was a devout but unorthodox Christian who privately rejected the doctrine of the Trinity. He refused to take holy orders in the Church of England, unlike most members of the Cambridge faculty of the day. Beyond his work on the mathematical sciences, Newton dedicated much of his time to the study of alchemy and biblical chronology, but most of his work in those areas remained unpublished until long after his death. Politically and personally tied to the Whig party, Newton served two brief terms as Member of Parliament for the University of Cambridge, in 1689–1690 and 1701–1702. He was knighted by Queen Anne in 1705 and spent the last three decades of his life in London, serving as Warden (1696–1699) and Master (1699–1727) of the Royal Mint, in which he increased the accuracy and security of British coinage, as well as president of the Royal Society (1703–1727).
Early life.
Isaac Newton was born (according to the Julian calendar in use in England at the time) on Christmas Day, 25 December 1642 (NS 4 January 1643) at Woolsthorpe Manor in Woolsthorpe-by-Colsterworth, a hamlet in the county of Lincolnshire. His father, also named Isaac Newton, had died three months before. Born prematurely, Newton was a small child; his mother Hannah Ayscough reportedly said that he could have fit inside a quart mug. When Newton was three, his mother remarried and went to live with her new husband, the Reverend Barnabas Smith, leaving her son in the care of his maternal grandmother, Margery Ayscough (née Blythe). Newton disliked his stepfather and maintained some enmity towards his mother for marrying him, as revealed by this entry in a list of sins committed up to the age of 19: "Threatening my father and mother Smith to burn them and the house over them." Newton's mother had three children (Mary, Benjamin, and Hannah) from her second marriage.
The King's School.
From the age of about twelve until he was seventeen, Newton was educated at The King's School in Grantham, which taught Latin and Ancient Greek and probably imparted a significant foundation of mathematics. He was removed from school by his mother and returned to Woolsthorpe-by-Colsterworth by October 1659. His mother, widowed for the second time, attempted to make him a farmer, an occupation he hated. Henry Stokes, master at The King's School, persuaded his mother to send him back to school. Motivated partly by a desire for revenge against a schoolyard bully, he became the top-ranked student, distinguishing himself mainly by building sundials and models of windmills.
University of Cambridge.
In June 1661, Newton was admitted to Trinity College at the University of Cambridge. His uncle the Reverend William Ayscough, who had studied at Cambridge, recommended him to the university. At Cambridge, Newton started as a subsizar, paying his way by performing valet duties until he was awarded a scholarship in 1664, which covered his university costs for four more years until the completion of his MA. At the time, Cambridge's teachings were based on those of Aristotle, whom Newton read along with then more modern philosophers, including René Descartes and astronomers such as Galileo Galilei and Thomas Street. He set down in his notebook a series of ""Quaestiones"" about mechanical philosophy as he found it. In 1665, he discovered the generalised binomial theorem and began to develop a mathematical theory that later became calculus. Soon after Newton obtained his BA degree at Cambridge in August 1665, the university temporarily closed as a precaution against the Great Plague.
Although he had been undistinguished as a Cambridge student, his private studies and the years following his bachelor's degree have been described as "the richest and most productive ever experienced by a scientist". The next two years alone saw the development of theories on calculus, optics, and the law of gravitation, at his home in Woolsthorpe. The physicist Louis T. More stated that "There are no other examples of achievement in the history of science to compare with that of Newton during those two golden years."
Newton has been described as an "exceptionally organized" person when it came to note-taking, further dog-earing pages he saw as important. Furthermore, Newton's "indexes look like present-day indexes: They are alphabetical, by topic." His books showed his interests to be wide-ranging, with Newton himself described as a "Janusian thinker, someone who could mix and combine seemingly disparate fields to stimulate creative breakthroughs."
In April 1667, Newton returned to the University of Cambridge, and in October he was elected as a fellow of Trinity. Fellows were required to take holy orders and be ordained as Anglican priests, although this was not enforced in the Restoration years, and an assertion of conformity to the Church of England was sufficient. He made the commitment that "I will either set Theology as the object of my studies and will take holy orders when the time prescribed by these statutes [7 years] arrives, or I will resign from the college." Up until this point he had not thought much about religion and had twice signed his agreement to the Thirty-nine Articles, the basis of Church of England doctrine. By 1675 the issue could not be avoided, and his unconventional views stood in the way.
His academic work impressed the Lucasian Professor Isaac Barrow, who was anxious to develop his own religious and administrative potential (he became master of Trinity College two years later); in 1669, Newton succeeded him, only one year after receiving his MA. Newton argued that this should exempt him from the ordination requirement, and King Charles II, whose permission was needed, accepted this argument; thus, a conflict between Newton's religious views and Anglican orthodoxy was averted. He was appointed at the age of 26.
The Lucasian Professor of Mathematics at Cambridge position included the responsibility of instructing geography. In 1672, and again in 1681, Newton published a revised, corrected, and amended edition of the "Geographia Generalis", a geography textbook first published in 1650 by the then-deceased Bernhardus Varenius. In the "Geographia Generalis," Varenius attempted to create a theoretical foundation linking scientific principles to classical concepts in geography, and considered geography to be a mix between science and pure mathematics applied to quantifying features of the Earth. While it is unclear if Newton ever lectured in geography, the 1733 Dugdale and Shaw English translation of the book stated Newton published the book to be read by students while he lectured on the subject. The "Geographia Generalis" is viewed by some as the dividing line between ancient and modern traditions in the history of geography, and Newton's involvement in the subsequent editions is thought to be a large part of the reason for this enduring legacy.
Newton was elected a Fellow of the Royal Society (FRS) in 1672.
Mid-life.
Calculus.
Newton's work has been said "to distinctly advance every branch of mathematics then studied". His work on calculus, usually referred to as fluxions, began in 1664, and by 20 May 1665 as seen in a manuscript, Newton "had already developed the calculus to the point where he could compute the tangent and the curvature at any point of a continuous curve". Another manuscript of October 1666, is now published among Newton's mathematical papers. His work "De analysi per aequationes numero terminorum infinitas", sent by Isaac Barrow to John Collins in June 1669, was identified by Barrow in a letter sent to Collins that August as the work "of an extraordinary genius and proficiency in these things". Newton later became involved in a dispute with Gottfried Wilhelm Leibniz over priority in the development of calculus. Both are now credited with independently developing calculus, though with very different mathematical notations. However, it is established that Newton came to develop calculus much earlier than Leibniz. Leibniz's notation is recognized as the more convenient notation, being adopted by continental European mathematicians, and after 1820, by British mathematicians.
Historian of science A. Rupert Hall notes that while Leibniz deserves credit for his independent formulation of calculus, Newton was undoubtedly the first to develop it, stating:<templatestyles src="Template:Blockquote/styles.css" />But all these matters are of little weight in comparison with the central truth, which has indeed long been universally recognized, that Newton was master of the essential techniques of the calculus by the end of 1666, almost exactly nine years before Leibniz . . . Newton’s claim to have mastered the new infinitesimal calculus long before Leibniz, and even to have written — or at least made a good start upon — a publishable exposition of it as early as 1671, is certainly borne out by copious evidence, and though Leibniz and some of his friends sought to belittle Newton’s case, the truth has not been seriously in doubt for the last 250 years.Hall further notes that in "Principia", Newton was able to "formulate and resolve problems by the integration of differential equations" and "in fact, he anticipated in his book many results that later exponents of the calculus regarded as their own novel achievements." Hall notes Newton's rapid development of calculus in comparison to his contemporaries, stating that Newton "well before 1690 . . . had reached roughly the point in the development of the calculus that Leibniz, the two Bernoullis, L’Hospital, Hermann and others had by joint efforts reached in print by the early 1700s".
It has been noted that despite the convenience of Leibniz's notation, Newton's notation could still have been used to develop multivariate techniques, with his dot notation still widely used in physics. Some academics have noted the richness and depth of Newton's work, such as physicist Roger Penrose, stating "in most cases Newton’s geometrical methods are not only more concise and elegant, they reveal deeper principles than would become evident by the use of those formal methods of calculus that nowadays would seem more direct." Mathematician Vladimir Arnold states "Comparing the texts of Newton with the comments of his successors, it is striking how Newton’s original presentation is more modern, more understandable and richer in ideas than the translation due to commentators of his geometrical ideas into the formal language of the calculus of Leibniz."
His work extensively uses calculus in geometric form based on limiting values of the ratios of vanishingly small quantities: in the "Principia" itself, Newton gave demonstration of this under the name of "the method of first and last ratios" and explained why he put his expositions in this form, remarking also that "hereby the same thing is performed as by the method of indivisibles." Because of this, the "Principia" has been called "a book dense with the theory and application of the infinitesimal calculus" in modern times and in Newton's time "nearly all of it is of this calculus." His use of methods involving "one or more orders of the infinitesimally small" is present in his "De motu corporum in gyrum" of 1684 and in his papers on motion "during the two decades preceding 1684".
Newton had been reluctant to publish his calculus because he feared controversy and criticism. He was close to the Swiss mathematician Nicolas Fatio de Duillier. In 1691, Duillier started to write a new version of Newton's "Principia", and corresponded with Leibniz. In 1693, the relationship between Duillier and Newton deteriorated and the book was never completed. Starting in 1699, Duillier accused Leibniz of plagiarism. Mathematician John Keill accused Leibniz of plagiarism in 1708 in the Royal Society journal, thereby deteriorating the situation even more. The dispute then broke out in full force in 1711 when the Royal Society proclaimed in a study that it was Newton who was the true discoverer and labelled Leibniz a fraud; it was later found that Newton wrote the study's concluding remarks on Leibniz. Thus began the bitter controversy which marred the lives of both men until Leibniz's death in 1716.
Newton is credited with the generalised binomial theorem, valid for any exponent. He discovered Newton's identities, Newton's method, classified cubic plane curves (polynomials of degree three in two variables), is a founder of the theory of Cremona transformations, made substantial contributions to the theory of finite differences, with Newton regarded as "the single most significant contributor to finite difference interpolation", with many formulas created by Newton. He was the first to state Bézout's theorem, and was also the first to use fractional indices and to employ coordinate geometry to derive solutions to Diophantine equations. He approximated partial sums of the harmonic series by logarithms (a precursor to Euler's summation formula) and was the first to use power series with confidence and to revert power series. He introduced the Puisseux series. He originated the Newton-Cotes formulas for numerical integration. His work on infinite series was inspired by Simon Stevin's decimals. He also initiated the field of calculus of variations, being the first to clearly formulate and correctly solve a problem in the field, that being Newton's minimal resistance problem, which he posed and solved in 1685, and then later published in "Principia" in 1687. It is regarded as one of the most difficult problems tackled by variational methods prior to the twentieth century. He then used calculus of variations in his solving of the brachistochrone curve problem in 1697, which was posed by Johann Bernoulli in 1696, thus he pioneered the field with his work on the two problems. He was also a pioneer of vector analysis, as he demonstrated how to apply the parallelogram law for adding various physical quantities and realized that these quantities could be broken down into components in any direction.
Optics.
In 1666, Newton observed that the spectrum of colours exiting a prism in the position of minimum deviation is oblong, even when the light ray entering the prism is circular, which is to say, the prism refracts different colours by different angles. This led him to conclude that colour is a property intrinsic to light – a point which had, until then, been a matter of debate.
From 1670 to 1672, Newton lectured on optics. During this period he investigated the refraction of light, demonstrating that the multicoloured image produced by a prism, which he named a spectrum, could be recomposed into white light by a lens and a second prism. Modern scholarship has revealed that Newton's analysis and resynthesis of white light owes a debt to corpuscular alchemy.
In his work on Newton's rings in 1671, he used a method that was unprecedented in the 17th century, as "he "averaged" all of the differences, and he then calculated the difference between the average and the value for the first ring", in effect introducing a now standard method for reducing noise in measurements, and which does not appear elsewhere at the time. He extended his "error-slaying method" to studies of equinoxes in 1700, which was described as an "altogether unprecedented method" but differed in that here "Newton required good values for each of the original equinoctial times, and so he devised a method that allowed them to, as it were, self-correct." Newton wrote down the first of the two 'normal equations' known from ordinary least squares and introduced "an embryonic linear regression analysis", as he averaged a set of data, 50 years before Tobias Mayer and also "summing the residuals to zero he "forced" the regression line to pass through the average point". He also "distinguished between two inhomogeneous sets of data and might have thought of an "optimal" solution in terms of bias, though not in terms of effectiveness".
He showed that coloured light does not change its properties by separating out a coloured beam and shining it on various objects, and that regardless of whether reflected, scattered, or transmitted, the light remains the same colour. Thus, he observed that colour is the result of objects interacting with already-coloured light rather than objects generating the colour themselves. This is known as Newton's theory of colour. His 1672 paper on the nature of white light and colours forms the basis for all work that followed on colour and colour vision.
From this work, he concluded that the lens of any refracting telescope would suffer from the dispersion of light into colours (chromatic aberration). As a proof of the concept, he constructed a telescope using reflective mirrors instead of lenses as the objective to bypass that problem. Building the design, the first known functional reflecting telescope, today known as a Newtonian telescope, involved solving the problem of a suitable mirror material and shaping technique. He grounded his own mirrors out of a custom composition of highly reflective speculum metal, using Newton's rings to judge the quality of the optics for his telescopes. In late 1668, he was able to produce this first reflecting telescope. It was about eight inches long and it gave a clearer and larger image. In 1671, he was asked for a demonstration of his reflecting telescope by the Royal Society. Their interest encouraged him to publish his notes, "Of Colours", which he later expanded into the work "Opticks". When Robert Hooke criticised some of Newton's ideas, Newton was so offended that he withdrew from public debate. However, the two had brief exchanges in 1679–80, when Hooke, who had been appointed Secretary of the Royal Society, opened a correspondence intended to elicit contributions from Newton to Royal Society transactions, which had the effect of stimulating Newton to work out a proof that the elliptical form of planetary orbits would result from a centripetal force inversely proportional to the square of the radius vector.
Newton argued that light is composed of particles or corpuscles, which were refracted by accelerating into a denser medium. He verged on soundlike waves to explain the repeated pattern of reflection and transmission by thin films ("Opticks" Bk. II, Props. 12), but still retained his theory of 'fits' that disposed corpuscles to be reflected or transmitted (Props.13). Physicists later favoured a purely wavelike explanation of light to account for the interference patterns and the general phenomenon of diffraction. Despite his known preference of a particle theory, Newton in fact noted that light had both particle-like and wave-like properties in "Opticks", and was the first to attempt to reconcile the two theories, thereby anticipating later developments of wave-particle duality, which is the modern understanding of light. Physicist David Finkelstein called him "the first quantum physicist" as a result.
In his "Hypothesis of Light" of 1675, Newton posited the existence of the ether to transmit forces between particles. The contact with the Cambridge Platonist philosopher Henry More revived his interest in alchemy. He replaced the ether with occult forces based on Hermetic ideas of attraction and repulsion between particles. His contributions to science cannot be isolated from his interest in alchemy. This was at a time when there was no clear distinction between alchemy and science.
In 1704, Newton published "Opticks", in which he expounded his corpuscular theory of light, and included a set of queries at the end, which were posed as unanswered questions and positive assertions. In line with his corpuscle theory, he thought that normal matter was made of grosser corpuscles and speculated that through a kind of alchemical transmutation, with query 30 stating "Are not gross Bodies and Light convertible into one another, and may not Bodies receive much of their Activity from the Particles of Light which enter their Composition?" Query 6 introduced the concept of a black body.
Newton investigated electricity by constructing a primitive form of a frictional electrostatic generator using a glass globe, and detailed an experiment in 1675 that showed when one side of a glass sheet is rubbed to create an electric charge, it attracts "light bodies" to the opposite side. He interpreted this as evidence that electric forces could pass through glass. His idea in "Opticks" that optical reflection and refraction arise from interactions across the entire surface is regarded as the beginning of the field theory of electric force. He recognized the crucial role of electricity in nature, believing it to be responsible for various phenomena, including the emission, reflection, refraction, inflection, and heating effects of light. He also proposed that electricity was involved in the sensations experienced by the human body, affecting everything from muscle movement to brain function. His mass-dispersion model, ancestral to the successful use of the least action principle, provided a credible framework for understanding refraction, particularly in its approach to refraction in terms of momentum.
In "Opticks", he was the first to show a diagram using a prism as a beam expander, and also the use of multiple-prism arrays. Some 278 years after Newton's discussion, multiple-prism beam expanders became central to the development of narrow-linewidth tunable lasers. The use of these prismatic beam expanders led to the multiple-prism dispersion theory.
Newton was also the first to propose the Goos–Hänchen effect, an optical phenomenon in which linearly polarized light undergoes a small lateral shift when totally internally reflected. He provided both experimental and theoretical explanations for the effect using a mechanical model.
Science came to realise the difference between perception of colour and mathematisable optics. The German poet and scientist, Johann Wolfgang von Goethe, could not shake the Newtonian foundation but "one hole Goethe did find in Newton's armour, ... Newton had committed himself to the doctrine that refraction without colour was impossible. He, therefore, thought that the object-glasses of telescopes must forever remain imperfect, achromatism and refraction being incompatible. This inference was proved by Dollond to be wrong."
Gravity.
Newton had been developing his theory of gravitation as far back as 1665. In 1679, he returned to his work on celestial mechanics by considering gravitation and its effect on the orbits of planets with reference to Kepler's laws of planetary motion. Newton's reawakening interest in astronomical matters received further stimulus by the appearance of a comet in the winter of 1680–1681, on which he corresponded with John Flamsteed. After the exchanges with Hooke, Newton worked out a proof that the elliptical form of planetary orbits would result from a centripetal force inversely proportional to the square of the radius vector. He shared his results with Edmond Halley and the Royal Society in , a tract written on about nine sheets which was copied into the Royal Society's Register Book in December 1684. This tract contained the nucleus that Newton developed and expanded to form the "Principia".
The was published on 5 July 1687 with encouragement and financial help from Halley. In this work, Newton stated the three universal laws of motion. Together, these laws describe the relationship between any object, the forces acting upon it and the resulting motion, laying the foundation for classical mechanics. They contributed to many advances during the Industrial Revolution which soon followed and were not improved upon for more than 200 years. Many of these advances continue to be the underpinnings of non-relativistic technologies in the modern world. He used the Latin word "gravitas" (weight) for the effect that would become known as gravity, and defined the law of universal gravitation. His work achieved the first great unification in physics. He further solved the two-body problem, and introduced the three-body problem.
In the same work, Newton presented a calculus-like method of geometrical analysis using 'first and last ratios', gave the first analytical determination (based on Boyle's law) of the speed of sound in air, inferred the oblateness of Earth's spheroidal figure, accounted for the precession of the equinoxes as a result of the Moon's gravitational attraction on the Earth's oblateness, initiated the gravitational study of the irregularities in the motion of the Moon, provided a theory for the determination of the orbits of comets, and much more. Newton's biographer David Brewster reported that the complexity of applying his theory of gravity to the motion of the moon was so great it affected Newton's health: "[H]e was deprived of his appetite and sleep" during his work on the problem in 1692–93, and told the astronomer John Machin that "his head never ached but when he was studying the subject". According to Brewster, Halley also told John Conduitt that when pressed to complete his analysis Newton "always replied that it made his head ache, and "kept him awake so often, that he would think of it no more"". [Emphasis in original] He provided the first calculation of the age of Earth by experiment, and described a precursor to the modern wind tunnel.
Newton made clear his heliocentric view of the Solar System—developed in a somewhat modern way because already in the mid-1680s he recognised the "deviation of the Sun" from the centre of gravity of the Solar System. For Newton, it was not precisely the centre of the Sun or any other body that could be considered at rest, but rather "the common centre of gravity of the Earth, the Sun and all the Planets is to be esteem'd the Centre of the World", and this centre of gravity "either is at rest or moves uniformly forward in a right line". (Newton adopted the "at rest" alternative in view of common consent that the centre, wherever it was, was at rest.)
Newton was criticised for introducing "occult agencies" into science because of his postulate of an invisible force able to act over vast distances. Later, in the second edition of the "Principia" (1713), Newton firmly rejected such criticisms in a concluding General Scholium, writing that it was enough that the phenomena implied a gravitational attraction, as they did; but they did not so far indicate its cause, and it was both unnecessary and improper to frame hypotheses of things that were not implied by the phenomena. (Here he used what became his famous expression .)
With the , Newton became internationally recognised. He acquired a circle of admirers, including the Swiss-born mathematician Nicolas Fatio de Duillier.
In the 1660s and 1670s, Newton found 72 of the 78 "species" of cubic curves and categorised them into four types, systemizing his results in later publications. However, a 1690s manuscript later analyzed showed that Newton had identified all 78 cubic curves, but chose not to publish the remaining six for unknown reasons. In 1717, and probably with Newton's help, James Stirling proved that every cubic was one of these four types. He claimed that the four types could be obtained by plane projection from one of them, and this was proved in 1731, four years after his death.
Other significant work.
Newton studied heat and energy flow, formulating an empirical law of cooling which states that the rate at which an object cools is proportional to the temperature difference between the object and its surrounding environment. It was first formulated in 1701, and is the first heat transfer formulation and serves as the formal basis of convective heat transfer.
Newton introduced the notion of a Newtonian fluid with his formulation of his law of viscosity in "Principia" in 1687. It states that the shear stress between two fluid layers is directly proportional to the velocity gradient between them. He also discussed the circular motion of fluids and was the first to discuss Couette flow.
Philosophy of Science.
Starting with the second edition of his "Principia", Newton included a final section on science philosophy or method. It was here that he wrote his famous line, in Latin, "hypotheses non fingo", which can be translated as "I don't make hypotheses," (the direct translation of "fingo" is "frame", but in context he was advocating against the use of hypotheses in science). He went on to posit that if there is no data to explain a finding, one should simply wait for that data, rather than guessing at an explanation. The quote in part as translated is, "Hitherto I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses, for whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction".
Newton contributed to and refined the scientific method. In his work on the properties of light in the 1670s, he showed his rigorous method, which was conducting experiments, taking detailed notes, making measurements, conducting more experiments that grew out of the initial ones, he formulated a theory, created more experiments to test it, and finally described the entire process so other scientists could replicate every step.
In his 1687 "Principia", he outlined four rules: the first is, 'Admit no more causes of natural things than are both true and sufficient to explain their appearances'; the second is, 'To the same natural effect, assign the same causes'; the third is, 'Qualities of bodies, which are found to belong to all bodies within experiments, are to be esteemed universal'; and lastly, 'Propositions collected from observation of phenomena should be viewed as accurate or very nearly true until contradicted by other phenomena'. These rules have become the basis of the modern approaches to science.
Later life.
Royal Mint.
In the 1690s, Newton wrote a number of religious tracts dealing with the literal and symbolic interpretation of the Bible. A manuscript Newton sent to John Locke in which he disputed the fidelity of —the Johannine Comma—and its fidelity to the original manuscripts of the New Testament, remained unpublished until 1785.
Newton was also a member of the Parliament of England for Cambridge University in 1689 and 1701, but according to some accounts his only comments were to complain about a cold draught in the chamber and request that the window be closed. He was, however, noted by Cambridge diarist Abraham de la Pryme to have rebuked students who were frightening locals by claiming that a house was haunted.
Newton moved to London to take up the post of warden of the Royal Mint during the reign of King William III in 1696, a position that he had obtained through the patronage of Charles Montagu, 1st Earl of Halifax, then Chancellor of the Exchequer. He took charge of England's great recoining, trod on the toes of Lord Lucas, Governor of the Tower, and secured the job of deputy comptroller of the temporary Chester branch for Edmond Halley. Newton became perhaps the best-known Master of the Mint upon the death of Thomas Neale in 1699, a position he held for the last 30 years of his life. These appointments were intended as sinecures, but Newton took them seriously. He retired from his Cambridge duties in 1701, and exercised his authority to reform the currency and punish clippers and counterfeiters.
As Warden, and afterwards as Master, of the Royal Mint, Newton estimated that 20 percent of the coins taken in during the Great Recoinage of 1696 were counterfeit. Counterfeiting was high treason, punishable by the felon being hanged, drawn and quartered. Despite this, convicting even the most flagrant criminals could be extremely difficult, but Newton proved equal to the task.
Disguised as a habitué of bars and taverns, he gathered much of that evidence himself. For all the barriers placed to prosecution, and separating the branches of government, English law still had ancient and formidable customs of authority. Newton had himself made a justice of the peace in all the home counties. A draft letter regarding the matter is included in Newton's personal first edition of "Philosophiæ Naturalis Principia Mathematica", which he must have been amending at the time. Then he conducted more than 100 cross-examinations of witnesses, informers, and suspects between June 1698 and Christmas 1699. He successfully prosecuted 28 coiners, including serial counterfeiter William Chaloner, who was subsequently hanged.
Beyond prosecuting counterfeiters, he improved minting technology and reduced the standard deviation of the weight of guineas from 1.3 grams to 0.75 grams. Starting in 1707, Newton introduced the practice of testing a small sample of coins, a pound in weight, in the trial of the pyx, which helped to reduce the size of admissible error. He ultimately saved the Treasury a then £41,510, roughly £3 million in 2012, with his improvements lasting until the 1770s, thereby increasing the accuracy of British coinage.
Newton was made president of the Royal Society in 1703 and an associate of the French Académie des Sciences. In his position at the Royal Society, Newton made an enemy of John Flamsteed, the Astronomer Royal, by prematurely publishing Flamsteed's "Historia Coelestis Britannica", which Newton had used in his studies.
Knighthood.
In April 1705, Queen Anne knighted Newton during a royal visit to Trinity College, Cambridge. The knighthood is likely to have been motivated by political considerations connected with the parliamentary election in May 1705, rather than any recognition of Newton's scientific work or services as Master of the Mint. Newton was the second scientist to be knighted, after Francis Bacon.
As a result of a report written by Newton on 21 September 1717 to the Lords Commissioners of His Majesty's Treasury, the bimetallic relationship between gold coins and silver coins was changed by royal proclamation on 22 December 1717, forbidding the exchange of gold guineas for more than 21 silver shillings. This inadvertently resulted in a silver shortage as silver coins were used to pay for imports, while exports were paid for in gold, effectively moving Britain from the silver standard to its first gold standard. It is a matter of debate as to whether he intended to do this or not. It has been argued that Newton conceived of his work at the Mint as a continuation of his alchemical work.
Newton was invested in the South Sea Company and lost at least £10,000, and plausibly more than £20,000 (£4.4 million in 2020) when it collapsed in around 1720. Since he was already rich before the bubble, he still died rich, at estate value around £30,000.
Toward the end of his life, Newton took up residence at Cranbury Park, near Winchester, with his niece and her husband, until his death. His half-niece, Catherine Barton, served as his hostess in social affairs at his house on Jermyn Street in London; he was her "very loving Uncle", according to his letter to her when she was recovering from smallpox.
Death.
Newton died in his sleep in London on 20 March 1727 (NS 31 March 1727). He was given a ceremonial funeral, attended by nobles, scientists, and philosophers, and was buried in Westminster Abbey among kings and queens. He was the first scientist to be buried in the abbey. Voltaire may have been present at his funeral. A bachelor, he had divested much of his estate to relatives during his last years, and died intestate. His papers went to John Conduitt and Catherine Barton.
Shortly after his death, a plaster death mask was moulded of Newton. It was used by Flemish sculptor John Michael Rysbrack in making a sculpture of Newton. It is now held by the Royal Society.
Newton's hair was posthumously examined and found to contain mercury, probably resulting from his alchemical pursuits. Mercury poisoning could explain Newton's eccentricity in late life.
Personality.
Although it was claimed that he was once engaged, Newton never married. The French writer and philosopher Voltaire, who was in London at the time of Newton's funeral, said that he "was never sensible to any passion, was not subject to the common frailties of mankind, nor had any commerce with women—a circumstance which was assured me by the physician and surgeon who attended him in his last moments.”
Newton had a close friendship with the Swiss mathematician Nicolas Fatio de Duillier, whom he met in London around 1689; some of their correspondence has survived. Their relationship came to an abrupt and unexplained end in 1693, and at the same time Newton suffered a nervous breakdown, which included sending wild accusatory letters to his friends Samuel Pepys and John Locke. His note to the latter included the charge that Locke had endeavoured to "embroil" him with "woemen & by other means".
Newton appeared to be relatively modest about his achievements, writing in a later memoir, "I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me." Nonetheless, he could be fiercely competitive and did on occasion hold grudges against his intellectual rivals, not abstaining from personal attacks when it suited him—a common trait found in many of his contemporaries. In a letter to Robert Hooke in February 1675, for instance, he confessed "If I have seen further it is by standing on the shoulders of giants." Some historians argued that this, written at a time when Newton and Hooke were disputing over optical discoveries, was an oblique attack on Hooke who was presumably short and hunchbacked, rather than (or in addition to) a statement of modesty. On the other hand, the widely known proverb about standing on the shoulders of giants, found in 17th century poet George Herbert's (1651) among others, had as its main point that "a dwarf on a giant's shoulders sees farther of the two", and so in effect place Newton himself rather than Hooke as the 'dwarf' who saw farther.
Theology.
Religious views.
Although born into an Anglican family, by his thirties Newton held a Christian faith that, had it been made public, would not have been considered orthodox by mainstream Christianity, with historian Stephen Snobelen labelling him a heretic.
By 1672, he had started to record his theological researches in notebooks which he showed to no one and which have only been available for public examination since 1972. Over half of what Newton wrote concerned theology and alchemy, and most has never been printed. His writings demonstrate an extensive knowledge of early Church writings and show that in the conflict between Athanasius and Arius which defined the Creed, he took the side of Arius, the loser, who rejected the conventional view of the Trinity. Newton "recognized Christ as a divine mediator between God and man, who was subordinate to the Father who created him." He was especially interested in prophecy, but for him, "the great apostasy was trinitarianism."
Newton tried unsuccessfully to obtain one of the two fellowships that exempted the holder from the ordination requirement. At the last moment in 1675 he received a dispensation from the government that excused him and all future holders of the Lucasian chair.
Worshipping Jesus Christ as God was, in Newton's eyes, idolatry, an act he believed to be the fundamental sin. In 1999, Snobelen wrote, that "Isaac Newton was a heretic. But ... he never made a public declaration of his private faith—which the orthodox would have deemed extremely radical. He hid his faith so well that scholars are still unraveling his personal beliefs." Snobelen concludes that Newton was at least a Socinian sympathiser (he owned and had thoroughly read at least eight Socinian books), possibly an Arian and almost certainly an anti-trinitarian.
Although the laws of motion and universal gravitation became Newton's best-known discoveries, he warned against using them to view the Universe as a mere machine, as if akin to a great clock. He said, "So then gravity may put the planets into motion, but without the Divine Power it could never put them into such a circulating motion, as they have about the sun".
Along with his scientific fame, Newton's studies of the Bible and of the early Church Fathers were also noteworthy. Newton wrote works on textual criticism, most notably "An Historical Account of Two Notable Corruptions of Scripture" and '. He placed the crucifixion of Jesus Christ at 3 April, AD 33, which agrees with one traditionally accepted date.
He believed in a rationally immanent world, but he rejected the hylozoism implicit in Gottfried Wilhelm Leibniz and Baruch Spinoza. The ordered and dynamically informed Universe could be understood, and must be understood, by an active reason. In his correspondence, he claimed that in writing the "Principia" "I had an eye upon such Principles as might work with considering men for the belief of a Deity". He saw evidence of design in the system of the world: "Such a wonderful uniformity in the planetary system must be allowed the effect of choice". But Newton insisted that divine intervention would eventually be required to reform the system, due to the slow growth of instabilities. For this, Leibniz lampooned him: "God Almighty wants to wind up his watch from time to time: otherwise it would cease to move. He had not, it seems, sufficient foresight to make it a perpetual motion."
Newton's position was defended by his follower Samuel Clarke in a famous correspondence. A century later, Pierre-Simon Laplace's work "Celestial Mechanics" had a natural explanation for why the planet orbits do not require periodic divine intervention. The contrast between Laplace's mechanistic worldview and Newton's one is the most strident considering the famous answer which the French scientist gave Napoleon, who had criticised him for the absence of the Creator in the "Mécanique céleste": "Sire, j'ai pu me passer de cette hypothèse" ("Sir, I didn't need this hypothesis").
Scholars long debated whether Newton disputed the doctrine of the Trinity. His first biographer, David Brewster, who compiled his manuscripts, interpreted Newton as questioning the veracity of some passages used to support the Trinity, but never denying the doctrine of the Trinity as such. In the twentieth century, encrypted manuscripts written by Newton and bought by John Maynard Keynes (among others) were deciphered and it became known that Newton did indeed reject Trinitarianism.
Religious thought.
Newton and Robert Boyle's approach to the mechanical philosophy was promoted by rationalist pamphleteers as a viable alternative to the pantheists and enthusiasts, and was accepted hesitantly by orthodox preachers as well as dissident preachers like the latitudinarians. The clarity and simplicity of science was seen as a way to combat the emotional and metaphysical superlatives of both superstitious enthusiasm and the threat of atheism, and at the same time, the second wave of English deists used Newton's discoveries to demonstrate the possibility of a "Natural Religion".
The attacks made against pre-Enlightenment "magical thinking", and the mystical elements of Christianity, were given their foundation with Boyle's mechanical conception of the universe. Newton gave Boyle's ideas their completion through mathematical proofs and, perhaps more importantly, was very successful in popularising them.
Alchemy.
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Newton was not the first of the age of reason. He was the last of the magicians, the last of the Babylonians and Sumerians, the last great mind which looked out on the visible and intellectual world with the same eyes as those who began to build our intellectual inheritance rather less than 10,000 years ago. Isaac Newton, a posthumous child born with no father on Christmas Day, 1642, was the last wonderchild to whom the Magi could do sincere and appropriate homage.
 –John Maynard Keynes, "Newton, the Man"
Of an estimated ten million words of writing in Newton's papers, about one million deal with alchemy. Many of Newton's writings on alchemy are copies of other manuscripts, with his own annotations. Alchemical texts mix artisanal knowledge with philosophical speculation, often hidden behind layers of wordplay, allegory, and imagery to protect craft secrets. Some of the content contained in Newton's papers could have been considered heretical by the church.
In 1888, after spending sixteen years cataloguing Newton's papers, Cambridge University kept a small number and returned the rest to the Earl of Portsmouth. In 1936, a descendant offered the papers for sale at Sotheby's. The collection was broken up and sold for a total of about £9,000. John Maynard Keynes was one of about three dozen bidders who obtained part of the collection at auction. Keynes went on to reassemble an estimated half of Newton's collection of papers on alchemy before donating his collection to Cambridge University in 1946.
All of Newton's known writings on alchemy are currently being put online in a project undertaken by Indiana University: "The Chymistry of Isaac Newton" and has been summarised in a book.
<templatestyles src="Template:Blockquote/styles.css" />Newton's fundamental contributions to science include the quantification of gravitational attraction, the discovery that white light is actually a mixture of immutable spectral colors, and the formulation of the calculus. Yet there is another, more mysterious side to Newton that is imperfectly known, a realm of activity that spanned some thirty years of his life, although he kept it largely hidden from his contemporaries and colleagues. We refer to Newton's involvement in the discipline of alchemy, or as it was often called in seventeenth-century England, "chymistry."
In June 2020, two unpublished pages of Newton's notes on Jan Baptist van Helmont's book on plague, "De Peste", were being auctioned online by Bonhams. Newton's analysis of this book, which he made in Cambridge while protecting himself from London's 1665–1666 infection, is the most substantial written statement he is known to have made about the plague, according to Bonhams. As far as the therapy is concerned, Newton writes that "the best is a toad suspended by the legs in a chimney for three days, which at last vomited up earth with various insects in it, on to a dish of yellow wax, and shortly after died. Combining powdered toad with the excretions and serum made into lozenges and worn about the affected area drove away the contagion and drew out the poison".
Legacy.
Recognition.
The mathematician and astronomer Joseph-Louis Lagrange frequently asserted that Newton was the greatest genius who ever lived, and once added that Newton was also "the most fortunate, for we cannot find more than once a system of the world to establish." English poet Alexander Pope wrote the famous epitaph:
<templatestyles src="Template:Blockquote/styles.css" />Nature, and Nature's laws lay hid in night.
God said, "Let Newton be!" and all was light.
But this was not allowed to be inscribed in Newton's monument at Westminster. The epitaph added is as follows:
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which can be translated as follows:
<templatestyles src="Template:Blockquote/styles.css" />Here is buried Isaac Newton, Knight, who by a strength of mind almost divine, and mathematical principles peculiarly his own, explored the course and figures of the planets, the paths of comets, the tides of the sea, the dissimilarities in rays of light, and, what no other scholar has previously imagined, the properties of the colours thus produced. Diligent, sagacious and faithful, in his expositions of nature, antiquity and the holy Scriptures, he vindicated by his philosophy the majesty of God mighty and good, and expressed the simplicity of the Gospel in his manners. Mortals rejoice that there has existed such and so great an ornament of the human race! He was born on 25th December 1642, and died on 20th March 1726.
Newton has been called "the most influential figure in the history of Western science", and has been regarded as "the central figure in the history of science", who "more than anyone else is the source of our great confidence in the power of science." "New Scientist" called Newton "the supreme genius and most enigmatic character in the history of science". The philosopher and historian David Hume also declared that Newton was "the greatest and rarest genius that ever arose for the ornament and instruction of the species". In his home of Monticello, Thomas Jefferson, a Founding Father and President of the United States, kept portraits of John Locke, Sir Francis Bacon, and Newton, whom he described as "the three greatest men that have ever lived, without any exception", and who he credited with laying "the foundation of those superstructures which have been raised in the Physical and Moral sciences".
Newton has further been called "the towering figure of the Scientific Revolution" and that "In a period rich with outstanding thinkers, Newton was simply the most outstanding." The polymath Johann Wolfgang von Goethe labeled Newton's birth as the "Christmas of the modern age". In the Italian polymath Vilfredo Pareto's estimation, Newton was the greatest human being who ever lived. On the bicentennial of Newton's death in 1927, astronomer James Jeans stated that he "was certainly the greatest man of science, and perhaps the greatest intellect, the human race has seen". Newton ultimately conceived four revolutions—in optics, mathematics, mechanics, and gravity—but also foresaw a fifth in electricity, though he lacked the time and energy in old age to fully accomplish it.
The physicist Ludwig Boltzmann called Newton's "Principia" "the first and greatest work ever written about theoretical physics". Physicist Stephen Hawking similarly called "Principia" "probably the most important single work ever published in the physical sciences". Lagrange called "Principia" "the greatest production of the human mind", and noted that "he felt dazed at such an illustration of what man's intellect might be capable".
Physicist Edward Andrade stated that Newton "was capable of greater sustained mental effort than any man, before or since", and noted earlier the place of Isaac Newton in history, stating:<templatestyles src="Template:Blockquote/styles.css" />From time to time in the history of mankind a man arises who is of universal significance, whose work changes the current of human thought or of human experience, so that all that comes after him bears evidence of his spirit. Such a man was Shakespeare, such a man was Beethoven, such a man was Newton, and, of the three, his kingdom is the most widespread.The French physicist and mathematician Jean-Baptiste Biot praised Newton's genius, stating that:
<templatestyles src="Template:Blockquote/styles.css" />Never was the supremacy of intellect so justly established and so fully confessed . . . In mathematical and in experimental science without an equal and without an example; combining the genius for both in its highest degree.Despite his rivalry with Gottfried Wilhem Leibniz, Leibniz still praised the work of Newton, with him responding to a question at a dinner in 1701 from Sophia Charlotte, the Queen of Prussia, about his view of Newton with:<templatestyles src="Template:Blockquote/styles.css" />Taking mathematics from the beginning of the world to the time of when Newton lived, what he had done was much the better half.
Mathematician E.T. Bell ranked Newton alongside Carl Friedrich Gauss and Archimedes as the three greatest mathematicians of all time, with the mathematician Donald M. Davis also noting that Newton is generally ranked with the other two as the greatest mathematicians ever. In "The Cambridge Companion to Isaac Newton" (2016), he is described as being "from a very young age, an extraordinary problem-solver, as good, it would appear, as humanity has ever produced". He is ultimately ranked among the top two or three greatest theoretical scientists ever, alongside James Clerk Maxwell and Albert Einstein, the greatest mathematician ever alongside Carl F. Gauss, and among the best experimentalists ever, thereby "putting Newton in a class by himself among empirical scientists, for one has trouble in thinking of any other candidate who was in the first rank of even two of these categories." Also noted is "At least in comparison to subsequent scientists, Newton was also exceptional in his ability to put his scientific effort in much wider perspective". Gauss himself had Archimedes and Newton as his heroes, and used terms such as "clarissimus" or "magnus" to describe other intellectuals such as great mathematicians and philosophers, but reserved "summus" for Newton only, and once remarked that "Newton remains forever the master of all masters!"
Albert Einstein kept a picture of Newton on his study wall alongside ones of Michael Faraday and of James Clerk Maxwell. Einstein stated that Newton's creation of calculus in relation to his laws of motion was "perhaps the greatest advance in thought that a single individual was ever privileged to make." He also noted the influence of Newton, stating that:<templatestyles src="Template:Blockquote/styles.css" />The whole evolution of our ideas about the processes of nature, with which we have been concerned so far, might be regarded as an organic development of Newton's ideas.In 1999, an opinion poll of 100 of the day's leading physicists voted Einstein the "greatest physicist ever," with Newton the runner-up, while a parallel survey of rank-and-file physicists ranked Newton as the greatest. In 2005, a dual survey of both the public and of members of Britain's Royal Society (formerly headed by Newton) asking who had the greater effect on both the history of science and on the history of mankind, Newton or Einstein, both the public and the Royal Society deemed Newton to have made the greater overall contributions for both.
In 1999, "Time" named Newton the Person of the Century for the 17th century. Newton placed sixth in the "100 Greatest Britons" poll conducted by BBC in 2002. However, in 2003, he was voted as the greatest Briton in a poll conducted by BBC World, with Winston Churchill second. He was voted as the greatest Cantabrigian by University of Cambridge students in 2009.
Physicist Lev Landau ranked physicists on a logarithmic scale of productivity and genius ranging from 0 to 5. The highest ranking, 0, was assigned to Newton. Einstein was ranked 0.5. A rank of 1 was awarded to the fathers of quantum mechanics, such as Werner Heisenberg and Paul Dirac. Landau, a Nobel prize winner and the discoverer of superfluidity, ranked himself as 2.
The SI derived unit of force is named the Newton in his honour.
Apple incident.
Newton himself often told the story that he was inspired to formulate his theory of gravitation by watching the fall of an apple from a tree. The story is believed to have passed into popular knowledge after being related by Catherine Barton, Newton's niece, to Voltaire. Voltaire then wrote in his "Essay on Epic Poetry" (1727), "Sir Isaac Newton walking in his gardens, had the first thought of his system of gravitation, upon seeing an apple falling from a tree."
Although it has been said that the apple story is a myth and that he did not arrive at his theory of gravity at any single moment, acquaintances of Newton (such as William Stukeley, whose manuscript account of 1752 has been made available by the Royal Society) do in fact confirm the incident, though not the apocryphal version that the apple actually hit Newton's head. Stukeley recorded in his "Memoirs of Sir Isaac Newton's Life" a conversation with Newton in Kensington on 15 April 1726:
<templatestyles src="Template:Blockquote/styles.css" />we went into the garden, & drank thea under the shade of some appletrees, only he, & myself. amidst other discourse, he told me, he was just in the same situation, as when formerly, the notion of gravitation came into his mind. "why should that apple always descend perpendicularly to the ground," thought he to him self: occasion'd by the fall of an apple, as he sat in a comtemplative mood: "why should it not go sideways, or upwards? but constantly to the earths centre? assuredly, the reason is, that the earth draws it. there must be a drawing power in matter. & the sum of the drawing power in the matter of the earth must be in the earths center, not in any side of the earth. therefore dos this apple fall perpendicularly, or toward the center. if matter thus draws matter; it must be in proportion of its quantity. therefore the apple draws the earth, as well as the earth draws the apple."
John Conduitt, Newton's assistant at the Royal Mint and husband of Newton's niece, also described the event when he wrote about Newton's life:
<templatestyles src="Template:Blockquote/styles.css" />In the year 1666 he retired again from Cambridge to his mother in Lincolnshire. Whilst he was pensively meandering in a garden it came into his thought that the power of gravity (which brought an apple from a tree to the ground) was not limited to a certain distance from earth, but that this power must extend much further than was usually thought. Why not as high as the Moon said he to himself & if so, that must influence her motion & perhaps retain her in her orbit, whereupon he fell a calculating what would be the effect of that supposition.
It is known from his notebooks that Newton was grappling in the late 1660s with the idea that terrestrial gravity extends, in an inverse-square proportion, to the Moon; however, it took him two decades to develop the full-fledged theory. The question was not whether gravity existed, but whether it extended so far from Earth that it could also be the force holding the Moon to its orbit. Newton showed that if the force decreased as the inverse square of the distance, one could indeed calculate the Moon's orbital period, and get good agreement. He guessed the same force was responsible for other orbital motions, and hence named it "universal gravitation".
Various trees are claimed to be "the" apple tree which Newton describes. The King's School, Grantham claims that the tree was purchased by the school, uprooted and transported to the headmaster's garden some years later. The staff of the (now) National Trust-owned Woolsthorpe Manor dispute this, and claim that a tree present in their gardens is the one described by Newton. A descendant of the original tree can be seen growing outside the main gate of Trinity College, Cambridge, below the room Newton lived in when he studied there. The National Fruit Collection at Brogdale in Kent can supply grafts from their tree, which appears identical to Flower of Kent, a coarse-fleshed cooking variety.
Commemorations.
Newton's monument (1731) can be seen in Westminster Abbey, at the north of the entrance to the choir against the choir screen, near his tomb. It was executed by the sculptor Michael Rysbrack (1694–1770) in white and grey marble with design by the architect William Kent. The monument features a figure of Newton reclining on top of a sarcophagus, his right elbow resting on several of his great books and his left hand pointing to a scroll with a mathematical design. Above him is a pyramid and a celestial globe showing the signs of the Zodiac and the path of the comet of 1680. A relief panel depicts putti using instruments such as a telescope and prism.
From 1978 until 1988, an image of Newton designed by Harry Ecclestone appeared on Series D £1 banknotes issued by the Bank of England (the last £1 notes to be issued by the Bank of England). Newton was shown on the reverse of the notes holding a book and accompanied by a telescope, a prism and a map of the Solar System.
A statue of Isaac Newton, looking at an apple at his feet, can be seen at the Oxford University Museum of Natural History. A large bronze statue, "Newton, after William Blake", by Eduardo Paolozzi, dated 1995 and inspired by Blake's etching, dominates the piazza of the British Library in London. A bronze statue of Newton was erected in 1858 in the centre of Grantham where he went to school, prominently standing in front of Grantham Guildhall.
The still-surviving farmhouse at Woolsthorpe By Colsterworth is a Grade I listed building by Historic England through being his birthplace and "where he discovered gravity and developed his theories regarding the refraction of light".
The Enlightenment.
Enlightenment philosophers chose a short history of scientific predecessors—Galileo Galilei, Robert Boyle, and Newton, principally—as the guides and guarantors of their applications of the singular concept of nature and natural law to every physical and social field of the day. In this respect, the lessons of history and the social structures built upon it could be discarded.
It is held by European philosophers of the Enlightenment and by historians of the Enlightenment that Newton's publication of the "Principia" was a turning point in the Scientific Revolution and started the Enlightenment. It was Newton's conception of the universe based upon natural and rationally understandable laws that became one of the seeds for Enlightenment ideology. John Locke and Voltaire applied concepts of natural law to political systems advocating intrinsic rights; the physiocrats and Adam Smith applied natural conceptions of psychology and self-interest to economic systems; and sociologists criticised the current social order for trying to fit history into natural models of progress. Monboddo and Samuel Clarke resisted elements of Newton's work, but eventually rationalised it to conform with their strong religious views of nature.
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Force
Influence that can change motion of an object
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A force is an influence that can cause an object to change its velocity unless counterbalanced by other forces. The concept of force makes the everyday notion of pushing or pulling mathematically precise. Because the magnitude and direction of a force are both important, force is a vector quantity. The SI unit of force is the newton (N), and force is often represented by the symbol F.
Force plays an important role in classical mechanics. The concept of force is central to all three of Newton's laws of motion. Types of forces often encountered in classical mechanics include elastic, frictional, contact or "normal" forces, and gravitational. The rotational version of force is torque, which produces changes in the rotational speed of an object. In an extended body, each part applies forces on the adjacent parts; the distribution of such forces through the body is the internal mechanical stress. In the case of multiple forces, if the net force on an extended body is zero the body is in equilibrium.
In modern physics, which includes relativity and quantum mechanics, the laws governing motion are revised to rely on fundamental interactions as the ultimate origin of force. However, the understanding of force provided by classical mechanics is useful for practical purposes.
Development of the concept.
Philosophers in antiquity used the concept of force in the study of stationary and moving objects and simple machines, but thinkers such as Aristotle and Archimedes retained fundamental errors in understanding force. In part, this was due to an incomplete understanding of the sometimes non-obvious force of friction and a consequently inadequate view of the nature of natural motion. A fundamental error was the belief that a force is required to maintain motion, even at a constant velocity. Most of the previous misunderstandings about motion and force were eventually corrected by Galileo Galilei and Sir Isaac Newton. With his mathematical insight, Newton formulated laws of motion that were not improved for over two hundred years.
By the early 20th century, Einstein developed a theory of relativity that correctly predicted the action of forces on objects with increasing momenta near the speed of light and also provided insight into the forces produced by gravitation and inertia. With modern insights into quantum mechanics and technology that can accelerate particles close to the speed of light, particle physics has devised a Standard Model to describe forces between particles smaller than atoms. The Standard Model predicts that exchanged particles called gauge bosons are the fundamental means by which forces are emitted and absorbed. Only four main interactions are known: in order of decreasing strength, they are: strong, electromagnetic, weak, and gravitational. High-energy particle physics observations made during the 1970s and 1980s confirmed that the weak and electromagnetic forces are expressions of a more fundamental electroweak interaction.
Pre-Newtonian concepts.
Since antiquity the concept of force has been recognized as integral to the functioning of each of the simple machines. The mechanical advantage given by a simple machine allowed for less force to be used in exchange for that force acting over a greater distance for the same amount of work. Analysis of the characteristics of forces ultimately culminated in the work of Archimedes who was especially famous for formulating a treatment of buoyant forces inherent in fluids.
Aristotle provided a philosophical discussion of the concept of a force as an integral part of Aristotelian cosmology. In Aristotle's view, the terrestrial sphere contained four elements that come to rest at different "natural places" therein. Aristotle believed that motionless objects on Earth, those composed mostly of the elements earth and water, were in their natural place when on the ground, and that they stay that way if left alone. He distinguished between the innate tendency of objects to find their "natural place" (e.g., for heavy bodies to fall), which led to "natural motion", and unnatural or forced motion, which required continued application of a force. This theory, based on the everyday experience of how objects move, such as the constant application of a force needed to keep a cart moving, had conceptual trouble accounting for the behavior of projectiles, such as the flight of arrows. An archer causes the arrow to move at the start of the flight, and it then sails through the air even though no discernible efficient cause acts upon it. Aristotle was aware of this problem and proposed that the air displaced through the projectile's path carries the projectile to its target. This explanation requires a continuous medium such as air to sustain the motion.
Though Aristotelian physics was criticized as early as the 6th century, its shortcomings would not be corrected until the 17th century work of Galileo Galilei, who was influenced by the late medieval idea that objects in forced motion carried an innate force of impetus. Galileo constructed an experiment in which stones and cannonballs were both rolled down an incline to disprove the Aristotelian theory of motion. He showed that the bodies were accelerated by gravity to an extent that was independent of their mass and argued that objects retain their velocity unless acted on by a force, for example friction. Galileo's idea that force is needed to change motion rather than to sustain it, further improved upon by Isaac Beeckman, René Descartes, and Pierre Gassendi, became a key principle of Newtonian physics.
In the early 17th century, before Newton's "Principia", the term "force" () was applied to many physical and non-physical phenomena, e.g., for an acceleration of a point. The product of a point mass and the square of its velocity was named (live force) by Leibniz. The modern concept of force corresponds to Newton's (accelerating force).
Newtonian mechanics.
Sir Isaac Newton described the motion of all objects using the concepts of inertia and force. In 1687, Newton published his magnum opus, "Philosophiæ Naturalis Principia Mathematica". In this work Newton set out three laws of motion that have dominated the way forces are described in physics to this day. The precise ways in which Newton's laws are expressed have evolved in step with new mathematical approaches.
First law.
Newton's first law of motion states that the natural behavior of an object at rest is to continue being at rest, and the natural behavior of an object moving at constant speed in a straight line is to continue moving at that constant speed along that straight line. The latter follows from the former because of the principle that the laws of physics are the same for all inertial observers, i.e., all observers who do not feel themselves to be in motion. An observer moving in tandem with an object will see it as being at rest. So, its natural behavior will be to remain at rest with respect to that observer, which means that an observer who sees it moving at constant speed in a straight line will see it continuing to do so.
Second law.
According to the first law, motion at constant speed in a straight line does not need a cause. It is "change" in motion that requires a cause, and Newton's second law gives the quantitative relationship between force and change of motion.
Newton's second law states that the net force acting upon an object is equal to the rate at which its momentum changes with time. If the mass of the object is constant, this law implies that the acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional to the mass of the object.
A modern statement of Newton's second law is a vector equation:
formula_1
where formula_2 is the momentum of the system, and formula_3 is the net (vector sum) force.399 If a body is in equilibrium, there is zero "net" force by definition (balanced forces may be present nevertheless). In contrast, the second law states that if there is an "unbalanced" force acting on an object it will result in the object's momentum changing over time.
In common engineering applications the mass in a system remains constant allowing as simple algebraic form for the second law. By the definition of momentum,
formula_4
where "m" is the mass and formula_5 is the velocity. If Newton's second law is applied to a system of constant mass, "m" may be moved outside the derivative operator. The equation then becomes
formula_6
By substituting the definition of acceleration, the algebraic version of Newton's second law is derived:
formula_7
Third law.
Whenever one body exerts a force on another, the latter simultaneously exerts an equal and opposite force on the first. In vector form, if formula_8 is the force of body 1 on body 2 and formula_9 that of body 2 on body 1, then
formula_10
This law is sometimes referred to as the "action-reaction law", with formula_11 called the "action" and formula_12 the "reaction".
Newton's Third Law is a result of applying symmetry to situations where forces can be attributed to the presence of different objects. The third law means that all forces are "interactions" between different bodies. and thus that there is no such thing as a unidirectional force or a force that acts on only one body.
In a system composed of object 1 and object 2, the net force on the system due to their mutual interactions is zero:
formula_13
More generally, in a closed system of particles, all internal forces are balanced. The particles may accelerate with respect to each other but the center of mass of the system will not accelerate. If an external force acts on the system, it will make the center of mass accelerate in proportion to the magnitude of the external force divided by the mass of the system.
Combining Newton's Second and Third Laws, it is possible to show that the linear momentum of a system is conserved in any closed system. In a system of two particles, if formula_14 is the momentum of object 1 and formula_15 the momentum of object 2, then
formula_16
Using similar arguments, this can be generalized to a system with an arbitrary number of particles. In general, as long as all forces are due to the interaction of objects with mass, it is possible to define a system such that net momentum is never lost nor gained.ch.12
Defining "force".
Some textbooks use Newton's second law as a "definition" of force. However, for the equation formula_17 for a constant mass formula_18 to then have any predictive content, it must be combined with further information. Moreover, inferring that a force is present because a body is accelerating is only valid in an inertial frame of reference. The question of which aspects of Newton's laws to take as definitions and which to regard as holding physical content has been answered in various ways, which ultimately do not affect how the theory is used in practice. Notable physicists, philosophers and mathematicians who have sought a more explicit definition of the concept of force include Ernst Mach and Walter Noll.
Combining forces.
Forces act in a particular direction and have sizes dependent upon how strong the push or pull is. Because of these characteristics, forces are classified as "vector quantities". This means that forces follow a different set of mathematical rules than physical quantities that do not have direction (denoted scalar quantities). For example, when determining what happens when two forces act on the same object, it is necessary to know both the magnitude and the direction of both forces to calculate the result. If both of these pieces of information are not known for each force, the situation is ambiguous.
Historically, forces were first quantitatively investigated in conditions of static equilibrium where several forces canceled each other out. Such experiments demonstrate the crucial properties that forces are additive vector quantities: they have magnitude and direction. When two forces act on a point particle, the resulting force, the "resultant" (also called the "net force"), can be determined by following the parallelogram rule of vector addition: the addition of two vectors represented by sides of a parallelogram, gives an equivalent resultant vector that is equal in magnitude and direction to the transversal of the parallelogram. The magnitude of the resultant varies from the difference of the magnitudes of the two forces to their sum, depending on the angle between their lines of action.ch.12
Free-body diagrams can be used as a convenient way to keep track of forces acting on a system. Ideally, these diagrams are drawn with the angles and relative magnitudes of the force vectors preserved so that graphical vector addition can be done to determine the net force.
As well as being added, forces can also be resolved into independent components at right angles to each other. A horizontal force pointing northeast can therefore be split into two forces, one pointing north, and one pointing east. Summing these component forces using vector addition yields the original force. Resolving force vectors into components of a set of basis vectors is often a more mathematically clean way to describe forces than using magnitudes and directions. This is because, for orthogonal components, the components of the vector sum are uniquely determined by the scalar addition of the components of the individual vectors. Orthogonal components are independent of each other because forces acting at ninety degrees to each other have no effect on the magnitude or direction of the other. Choosing a set of orthogonal basis vectors is often done by considering what set of basis vectors will make the mathematics most convenient. Choosing a basis vector that is in the same direction as one of the forces is desirable, since that force would then have only one non-zero component. Orthogonal force vectors can be three-dimensional with the third component being at right angles to the other two.ch.12
Equilibrium.
When all the forces that act upon an object are balanced, then the object is said to be in a state of equilibrium. Hence, equilibrium occurs when the resultant force acting on a point particle is zero (that is, the vector sum of all forces is zero). When dealing with an extended body, it is also necessary that the net torque be zero. A body is in "static equilibrium" with respect to a frame of reference if it at rest and not accelerating, whereas a body in "dynamic equilibrium" is moving at a constant speed in a straight line, i.e., moving but not accelerating. What one observer sees as static equilibrium, another can see as dynamic equilibrium and vice versa.
Static.
Static equilibrium was understood well before the invention of classical mechanics. Objects that are not accelerating have zero net force acting on them.
The simplest case of static equilibrium occurs when two forces are equal in magnitude but opposite in direction. For example, an object on a level surface is pulled (attracted) downward toward the center of the Earth by the force of gravity. At the same time, a force is applied by the surface that resists the downward force with equal upward force (called a normal force). The situation produces zero net force and hence no acceleration.
Pushing against an object that rests on a frictional surface can result in a situation where the object does not move because the applied force is opposed by static friction, generated between the object and the table surface. For a situation with no movement, the static friction force "exactly" balances the applied force resulting in no acceleration. The static friction increases or decreases in response to the applied force up to an upper limit determined by the characteristics of the contact between the surface and the object.
A static equilibrium between two forces is the most usual way of measuring forces, using simple devices such as weighing scales and spring balances. For example, an object suspended on a vertical spring scale experiences the force of gravity acting on the object balanced by a force applied by the "spring reaction force", which equals the object's weight. Using such tools, some quantitative force laws were discovered: that the force of gravity is proportional to volume for objects of constant density (widely exploited for millennia to define standard weights); Archimedes' principle for buoyancy; Archimedes' analysis of the lever; Boyle's law for gas pressure; and Hooke's law for springs. These were all formulated and experimentally verified before Isaac Newton expounded his three laws of motion.ch.12
Dynamic.
Dynamic equilibrium was first described by Galileo who noticed that certain assumptions of Aristotelian physics were contradicted by observations and logic. Galileo realized that simple velocity addition demands that the concept of an "absolute rest frame" did not exist. Galileo concluded that motion in a constant velocity was completely equivalent to rest. This was contrary to Aristotle's notion of a "natural state" of rest that objects with mass naturally approached. Simple experiments showed that Galileo's understanding of the equivalence of constant velocity and rest were correct. For example, if a mariner dropped a cannonball from the crow's nest of a ship moving at a constant velocity, Aristotelian physics would have the cannonball fall straight down while the ship moved beneath it. Thus, in an Aristotelian universe, the falling cannonball would land behind the foot of the mast of a moving ship. When this experiment is actually conducted, the cannonball always falls at the foot of the mast, as if the cannonball knows to travel with the ship despite being separated from it. Since there is no forward horizontal force being applied on the cannonball as it falls, the only conclusion left is that the cannonball continues to move with the same velocity as the boat as it falls. Thus, no force is required to keep the cannonball moving at the constant forward velocity.
Moreover, any object traveling at a constant velocity must be subject to zero net force (resultant force). This is the definition of dynamic equilibrium: when all the forces on an object balance but it still moves at a constant velocity. A simple case of dynamic equilibrium occurs in constant velocity motion across a surface with kinetic friction. In such a situation, a force is applied in the direction of motion while the kinetic friction force exactly opposes the applied force. This results in zero net force, but since the object started with a non-zero velocity, it continues to move with a non-zero velocity. Aristotle misinterpreted this motion as being caused by the applied force. When kinetic friction is taken into consideration it is clear that there is no net force causing constant velocity motion.ch.12
Examples of forces in classical mechanics.
Some forces are consequences of the fundamental ones. In such situations, idealized models can be used to gain physical insight. For example, each solid object is considered a rigid body.
Gravitational force or Gravity.
What we now call gravity was not identified as a universal force until the work of Isaac Newton. Before Newton, the tendency for objects to fall towards the Earth was not understood to be related to the motions of celestial objects. Galileo was instrumental in describing the characteristics of falling objects by determining that the acceleration of every object in free-fall was constant and independent of the mass of the object. Today, this acceleration due to gravity towards the surface of the Earth is usually designated as formula_19 and has a magnitude of about 9.81 meters per second squared (this measurement is taken from sea level and may vary depending on location), and points toward the center of the Earth. This observation means that the force of gravity on an object at the Earth's surface is directly proportional to the object's mass. Thus an object that has a mass of formula_18 will experience a force:
formula_21
For an object in free-fall, this force is unopposed and the net force on the object is its weight. For objects not in free-fall, the force of gravity is opposed by the reaction forces applied by their supports. For example, a person standing on the ground experiences zero net force, since a normal force (a reaction force) is exerted by the ground upward on the person that counterbalances his weight that is directed downward.ch.12
Newton's contribution to gravitational theory was to unify the motions of heavenly bodies, which Aristotle had assumed were in a natural state of constant motion, with falling motion observed on the Earth. He proposed a law of gravity that could account for the celestial motions that had been described earlier using Kepler's laws of planetary motion.
Newton came to realize that the effects of gravity might be observed in different ways at larger distances. In particular, Newton determined that the acceleration of the Moon around the Earth could be ascribed to the same force of gravity if the acceleration due to gravity decreased as an inverse square law. Further, Newton realized that the acceleration of a body due to gravity is proportional to the mass of the other attracting body. Combining these ideas gives a formula that relates the mass (formula_22) and the radius (formula_23) of the Earth to the gravitational acceleration:
formula_24
where formula_25 is the distance between the two objects' centers of mass and formula_26 is the unit vector pointed in the direction away from the center of the first object toward the center of the second object.
This formula was powerful enough to stand as the basis for all subsequent descriptions of motion within the Solar System until the 20th century. During that time, sophisticated methods of perturbation analysis were invented to calculate the deviations of orbits due to the influence of multiple bodies on a planet, moon, comet, or asteroid. The formalism was exact enough to allow mathematicians to predict the existence of the planet Neptune before it was observed.
Electromagnetic.
The electrostatic force was first described in 1784 by Coulomb as a force that existed intrinsically between two charges. The properties of the electrostatic force were that it varied as an inverse square law directed in the radial direction, was both attractive and repulsive (there was intrinsic polarity), was independent of the mass of the charged objects, and followed the superposition principle. Coulomb's law unifies all these observations into one succinct statement.
Subsequent mathematicians and physicists found the construct of the "electric field" to be useful for determining the electrostatic force on an electric charge at any point in space. The electric field was based on using a hypothetical "test charge" anywhere in space and then using Coulomb's Law to determine the electrostatic force. Thus the electric field anywhere in space is defined as
formula_27
where formula_28 is the magnitude of the hypothetical test charge. Similarly, the idea of the "magnetic field" was introduced to express how magnets can influence one another at a distance. The Lorentz force law gives the force upon a body with charge formula_28 due to electric and magnetic fields:
formula_30
where formula_3 is the electromagnetic force, formula_32 is the electric field at the body's location, formula_33 is the magnetic field, and formula_5 is the velocity of the particle. The magnetic contribution to the Lorentz force is the cross product of the velocity vector with the magnetic field.
The origin of electric and magnetic fields would not be fully explained until 1864 when James Clerk Maxwell unified a number of earlier theories into a set of 20 scalar equations, which were later reformulated into 4 vector equations by Oliver Heaviside and Josiah Willard Gibbs. These "Maxwell's equations" fully described the sources of the fields as being stationary and moving charges, and the interactions of the fields themselves. This led Maxwell to discover that electric and magnetic fields could be "self-generating" through a wave that traveled at a speed that he calculated to be the speed of light. This insight united the nascent fields of electromagnetic theory with optics and led directly to a complete description of the electromagnetic spectrum.
Normal.
When objects are in contact, the force directly between them is called the normal force, the component of the total force in the system exerted normal to the interface between the objects. The normal force is closely related to Newton's third law. The normal force, for example, is responsible for the structural integrity of tables and floors as well as being the force that responds whenever an external force pushes on a solid object. An example of the normal force in action is the impact force on an object crashing into an immobile surface.ch.12
Friction.
Friction is a force that opposes relative motion of two bodies. At the macroscopic scale, the frictional force is directly related to the normal force at the point of contact. There are two broad classifications of frictional forces: static friction and kinetic friction.
The static friction force (formula_35) will exactly oppose forces applied to an object parallel to a surface up to the limit specified by the coefficient of static friction (formula_36) multiplied by the normal force (formula_37). In other words, the magnitude of the static friction force satisfies the inequality:
formula_38
The kinetic friction force (formula_39) is typically independent of both the forces applied and the movement of the object. Thus, the magnitude of the force equals:
formula_40
where formula_41 is the coefficient of kinetic friction. The coefficient of kinetic friction is normally less than the coefficient of static friction.
Tension.
Tension forces can be modeled using ideal strings that are massless, frictionless, unbreakable, and do not stretch. They can be combined with ideal pulleys, which allow ideal strings to switch physical direction. Ideal strings transmit tension forces instantaneously in action–reaction pairs so that if two objects are connected by an ideal string, any force directed along the string by the first object is accompanied by a force directed along the string in the opposite direction by the second object. By connecting the same string multiple times to the same object through the use of a configuration that uses movable pulleys, the tension force on a load can be multiplied. For every string that acts on a load, another factor of the tension force in the string acts on the load. Such machines allow a mechanical advantage for a corresponding increase in the length of displaced string needed to move the load. These tandem effects result ultimately in the conservation of mechanical energy since the work done on the load is the same no matter how complicated the machine.ch.12
Spring.
A simple elastic force acts to return a spring to its natural length. An ideal spring is taken to be massless, frictionless, unbreakable, and infinitely stretchable. Such springs exert forces that push when contracted, or pull when extended, in proportion to the displacement of the spring from its equilibrium position. This linear relationship was described by Robert Hooke in 1676, for whom Hooke's law is named. If formula_42 is the displacement, the force exerted by an ideal spring equals:
formula_43
where formula_44 is the spring constant (or force constant), which is particular to the spring. The minus sign accounts for the tendency of the force to act in opposition to the applied load.ch.12
Centripetal.
For an object in uniform circular motion, the net force acting on the object equals:
formula_45
where formula_18 is the mass of the object, formula_47 is the velocity of the object and formula_25 is the distance to the center of the circular path and formula_49 is the unit vector pointing in the radial direction outwards from the center. This means that the net force felt by the object is always directed toward the center of the curving path. Such forces act perpendicular to the velocity vector associated with the motion of an object, and therefore do not change the speed of the object (magnitude of the velocity), but only the direction of the velocity vector. More generally, the net force that accelerates an object can be resolved into a component that is perpendicular to the path, and one that is tangential to the path. This yields both the tangential force, which accelerates the object by either slowing it down or speeding it up, and the radial (centripetal) force, which changes its direction.ch.12
Continuum mechanics.
Newton's laws and Newtonian mechanics in general were first developed to describe how forces affect idealized point particles rather than three-dimensional objects. In real life, matter has extended structure and forces that act on one part of an object might affect other parts of an object. For situations where lattice holding together the atoms in an object is able to flow, contract, expand, or otherwise change shape, the theories of continuum mechanics describe the way forces affect the material. For example, in extended fluids, differences in pressure result in forces being directed along the pressure gradients as follows:
formula_50
where formula_51 is the volume of the object in the fluid and formula_52 is the scalar function that describes the pressure at all locations in space. Pressure gradients and differentials result in the buoyant force for fluids suspended in gravitational fields, winds in atmospheric science, and the lift associated with aerodynamics and flight.ch.12
A specific instance of such a force that is associated with dynamic pressure is fluid resistance: a body force that resists the motion of an object through a fluid due to viscosity. For so-called "Stokes' drag" the force is approximately proportional to the velocity, but opposite in direction:
formula_53
where:
More formally, forces in continuum mechanics are fully described by a stress tensor with terms that are roughly defined as
formula_56
where formula_57 is the relevant cross-sectional area for the volume for which the stress tensor is being calculated. This formalism includes pressure terms associated with forces that act normal to the cross-sectional area (the matrix diagonals of the tensor) as well as shear terms associated with forces that act parallel to the cross-sectional area (the off-diagonal elements). The stress tensor accounts for forces that cause all strains (deformations) including also tensile stresses and compressions.
Fictitious.
There are forces that are frame dependent, meaning that they appear due to the adoption of non-Newtonian (that is, non-inertial) reference frames. Such forces include the centrifugal force and the Coriolis force. These forces are considered fictitious because they do not exist in frames of reference that are not accelerating.ch.12 Because these forces are not genuine they are also referred to as "pseudo forces".
In general relativity, gravity becomes a fictitious force that arises in situations where spacetime deviates from a flat geometry.
Concepts derived from force.
Rotation and torque.
Forces that cause extended objects to rotate are associated with torques. Mathematically, the torque of a force formula_3 is defined relative to an arbitrary reference point as the cross product:
formula_59
where formula_60 is the position vector of the force application point relative to the reference point.
Torque is the rotation equivalent of force in the same way that angle is the rotational equivalent for position, angular velocity for velocity, and angular momentum for momentum. As a consequence of Newton's first law of motion, there exists rotational inertia that ensures that all bodies maintain their angular momentum unless acted upon by an unbalanced torque. Likewise, Newton's second law of motion can be used to derive an analogous equation for the instantaneous angular acceleration of the rigid body:
formula_61
where
This provides a definition for the moment of inertia, which is the rotational equivalent for mass. In more advanced treatments of mechanics, where the rotation over a time interval is described, the moment of inertia must be substituted by the tensor that, when properly analyzed, fully determines the characteristics of rotations including precession and nutation.
Equivalently, the differential form of Newton's Second Law provides an alternative definition of torque:
formula_64
where formula_65 is the angular momentum of the particle.
Newton's Third Law of Motion requires that all objects exerting torques themselves experience equal and opposite torques, and therefore also directly implies the conservation of angular momentum for closed systems that experience rotations and revolutions through the action of internal torques.
Yank.
The yank is defined as the rate of change of force
formula_66
The term is used in biomechanical analysis, athletic assessment and robotic control. The second ("tug"), third ("snatch"), fourth ("shake"), and higher derivatives are rarely used.
Kinematic integrals.
Forces can be used to define a number of physical concepts by integrating with respect to kinematic variables. For example, integrating with respect to time gives the definition of impulse:
formula_67
which by Newton's Second Law must be equivalent to the change in momentum (yielding the Impulse momentum theorem).
Similarly, integrating with respect to position gives a definition for the work done by a force:
formula_68
which is equivalent to changes in kinetic energy (yielding the work energy theorem).
Power "P" is the rate of change d"W"/d"t" of the work "W", as the trajectory is extended by a position change formula_69 in a time interval d"t":
formula_70
so
formula_71
with formula_72 the velocity.
Potential energy.
Instead of a force, often the mathematically related concept of a potential energy field is used. For instance, the gravitational force acting upon an object can be seen as the action of the gravitational field that is present at the object's location. Restating mathematically the definition of energy (via the definition of work), a potential scalar field formula_73 is defined as that field whose gradient is equal and opposite to the force produced at every point:
formula_74
Forces can be classified as conservative or nonconservative. Conservative forces are equivalent to the gradient of a potential while nonconservative forces are not.ch.12
Conservation.
A conservative force that acts on a closed system has an associated mechanical work that allows energy to convert only between kinetic or potential forms. This means that for a closed system, the net mechanical energy is conserved whenever a conservative force acts on the system. The force, therefore, is related directly to the difference in potential energy between two different locations in space, and can be considered to be an artifact of the potential field in the same way that the direction and amount of a flow of water can be considered to be an artifact of the contour map of the elevation of an area.ch.12
Conservative forces include gravity, the electromagnetic force, and the spring force. Each of these forces has models that are dependent on a position often given as a radial vector formula_60 emanating from spherically symmetric potentials. Examples of this follow:
For gravity:
formula_76
where formula_77 is the gravitational constant, and formula_78 is the mass of object "n".
For electrostatic forces:
formula_79
where formula_80 is electric permittivity of free space, and formula_81 is the electric charge of object "n".
For spring forces:
formula_82
where formula_44 is the spring constant.ch.12
For certain physical scenarios, it is impossible to model forces as being due to a simple gradient of potentials. This is often due a macroscopic statistical average of microstates. For example, static friction is caused by the gradients of numerous electrostatic potentials between the atoms, but manifests as a force model that is independent of any macroscale position vector. Nonconservative forces other than friction include other contact forces, tension, compression, and drag. For any sufficiently detailed description, all these forces are the results of conservative ones since each of these macroscopic forces are the net results of the gradients of microscopic potentials.ch.12
The connection between macroscopic nonconservative forces and microscopic conservative forces is described by detailed treatment with statistical mechanics. In macroscopic closed systems, nonconservative forces act to change the internal energies of the system, and are often associated with the transfer of heat. According to the Second law of thermodynamics, nonconservative forces necessarily result in energy transformations within closed systems from ordered to more random conditions as entropy increases.ch.12
Units.
The SI unit of force is the newton (symbol N), which is the force required to accelerate a one kilogram mass at a rate of one meter per second squared, or kg·m·s−2.The corresponding CGS unit is the dyne, the force required to accelerate a one gram mass by one centimeter per second squared, or g·cm·s−2. A newton is thus equal to 100,000 dynes.
The gravitational foot-pound-second English unit of force is the pound-force (lbf), defined as the force exerted by gravity on a pound-mass in the standard gravitational field of 9.80665 m·s−2. The pound-force provides an alternative unit of mass: one slug is the mass that will accelerate by one foot per second squared when acted on by one pound-force. An alternative unit of force in a different foot–pound–second system, the absolute fps system, is the poundal, defined as the force required to accelerate a one-pound mass at a rate of one foot per second squared.
The pound-force has a metric counterpart, less commonly used than the newton: the kilogram-force (kgf) (sometimes kilopond), is the force exerted by standard gravity on one kilogram of mass. The kilogram-force leads to an alternate, but rarely used unit of mass: the metric slug (sometimes mug or hyl) is that mass that accelerates at 1 m·s−2 when subjected to a force of 1 kgf. The kilogram-force is not a part of the modern SI system, and is generally deprecated, sometimes used for expressing aircraft weight, jet thrust, bicycle spoke tension, torque wrench settings and engine output torque.
 See also "Ton-force".
Revisions of the force concept.
At the beginning of the 20th century, new physical ideas emerged to explain experimental results in astronomical and submicroscopic realms. As discussed below, relativity alters the definition of momentum and quantum mechanics reuses the concept of "force" in microscopic contexts where Newton's laws do not apply directly.
Special theory of relativity.
In the special theory of relativity, mass and energy are equivalent (as can be seen by calculating the work required to accelerate an object). When an object's velocity increases, so does its energy and hence its mass equivalent (inertia). It thus requires more force to accelerate it the same amount than it did at a lower velocity. Newton's Second Law,
formula_84
remains valid because it is a mathematical definition. But for momentum to be conserved at relativistic relative velocity, formula_47, momentum must be redefined as:
formula_86
where formula_87 is the rest mass and formula_88 the speed of light.
The expression relating force and acceleration for a particle with constant non-zero rest mass formula_18 moving in the formula_90 direction at velocity formula_47 is:
formula_92
where
formula_93
is called the Lorentz factor. The Lorentz factor increases steeply as the relative velocity approaches the speed of light. Consequently, the greater and greater force must be applied to produce the same acceleration at extreme velocity. The relative velocity cannot reach formula_88.§15–8
If formula_47 is very small compared to formula_88, then formula_97 is very close to 1 and
formula_98
is a close approximation. Even for use in relativity, one can restore the form of
formula_99
through the use of four-vectors. This relation is correct in relativity when formula_100 is the four-force, formula_18 is the invariant mass, and formula_102 is the four-acceleration.
The "general" theory of relativity incorporates a more radical departure from the Newtonian way of thinking about force, specifically gravitational force. This reimagining of the nature of gravity is described more fully below.
Quantum mechanics.
Quantum mechanics is a theory of physics originally developed in order to understand microscopic phenomena: behavior at the scale of molecules, atoms or subatomic particles. Generally and loosely speaking, the smaller a system is, the more an adequate mathematical model will require understanding quantum effects. The conceptual underpinning of quantum physics is different from that of classical physics. Instead of thinking about quantities like position, momentum, and energy as properties that an object "has", one considers what result might "appear" when a measurement of a chosen type is performed. Quantum mechanics allows the physicist to calculate the probability that a chosen measurement will elicit a particular result. The expectation value for a measurement is the average of the possible results it might yield, weighted by their probabilities of occurrence.
In quantum mechanics, interactions are typically described in terms of energy rather than force. The Ehrenfest theorem provides a connection between quantum expectation values and the classical concept of force, a connection that is necessarily inexact, as quantum physics is fundamentally different from classical. In quantum physics, the Born rule is used to calculate the expectation values of a position measurement or a momentum measurement. These expectation values will generally change over time; that is, depending on the time at which (for example) a position measurement is performed, the probabilities for its different possible outcomes will vary. The Ehrenfest theorem says, roughly speaking, that the equations describing how these expectation values change over time have a form reminiscent of Newton's second law, with a force defined as the negative derivative of the potential energy. However, the more pronounced quantum effects are in a given situation, the more difficult it is to derive meaningful conclusions from this resemblance.
Quantum mechanics also introduces two new constraints that interact with forces at the submicroscopic scale and which are especially important for atoms. Despite the strong attraction of the nucleus, the uncertainty principle limits the minimum extent of an electron probability distribution and the Pauli exclusion principle prevents electrons from sharing the same probability distribution. This gives rise to an emergent pressure known as degeneracy pressure. The dynamic equilibrium between the degeneracy pressure and the attractive electromagnetic force give atoms, molecules, liquids, and solids stability.
Quantum field theory.
In modern particle physics, forces and the acceleration of particles are explained as a mathematical by-product of exchange of momentum-carrying gauge bosons. With the development of quantum field theory and general relativity, it was realized that force is a redundant concept arising from conservation of momentum (4-momentum in relativity and momentum of virtual particles in quantum electrodynamics). The conservation of momentum can be directly derived from the homogeneity or symmetry of space and so is usually considered more fundamental than the concept of a force. Thus the currently known fundamental forces are considered more accurately to be "fundamental interactions".
While sophisticated mathematical descriptions are needed to predict, in full detail, the result of such interactions, there is a conceptually simple way to describe them through the use of Feynman diagrams. In a Feynman diagram, each matter particle is represented as a straight line (see world line) traveling through time, which normally increases up or to the right in the diagram. Matter and anti-matter particles are identical except for their direction of propagation through the Feynman diagram. World lines of particles intersect at interaction vertices, and the Feynman diagram represents any force arising from an interaction as occurring at the vertex with an associated instantaneous change in the direction of the particle world lines. Gauge bosons are emitted away from the vertex as wavy lines and, in the case of virtual particle exchange, are absorbed at an adjacent vertex. The utility of Feynman diagrams is that other types of physical phenomena that are part of the general picture of fundamental interactions but are conceptually separate from forces can also be described using the same rules. For example, a Feynman diagram can describe in succinct detail how a neutron decays into an electron, proton, and antineutrino, an interaction mediated by the same gauge boson that is responsible for the weak nuclear force.
Fundamental interactions.
All of the known forces of the universe are classified into four fundamental interactions. The strong and the weak forces act only at very short distances, and are responsible for the interactions between subatomic particles, including nucleons and compound nuclei. The electromagnetic force acts between electric charges, and the gravitational force acts between masses. All other forces in nature derive from these four fundamental interactions operating within quantum mechanics, including the constraints introduced by the Schrödinger equation and the Pauli exclusion principle. For example, friction is a manifestation of the electromagnetic force acting between atoms of two surfaces. The forces in springs, modeled by Hooke's law, are also the result of electromagnetic forces. Centrifugal forces are acceleration forces that arise simply from the acceleration of rotating frames of reference.
The fundamental theories for forces developed from the unification of different ideas. For example, Newton's universal theory of gravitation showed that the force responsible for objects falling near the surface of the Earth is also the force responsible for the falling of celestial bodies about the Earth (the Moon) and around the Sun (the planets). Michael Faraday and James Clerk Maxwell demonstrated that electric and magnetic forces were unified through a theory of electromagnetism. In the 20th century, the development of quantum mechanics led to a modern understanding that the first three fundamental forces (all except gravity) are manifestations of matter (fermions) interacting by exchanging virtual particles called gauge bosons. This Standard Model of particle physics assumes a similarity between the forces and led scientists to predict the unification of the weak and electromagnetic forces in electroweak theory, which was subsequently confirmed by observation.
Gravitational.
Newton's law of gravitation is an example of "action at a distance": one body, like the Sun, exerts an influence upon any other body, like the Earth, no matter how far apart they are. Moreover, this action at a distance is "instantaneous." According to Newton's theory, the one body shifting position changes the gravitational pulls felt by all other bodies, all at the same instant of time. Albert Einstein recognized that this was inconsistent with special relativity and its prediction that influences cannot travel faster than the speed of light. So, he sought a new theory of gravitation that would be relativistically consistent. Mercury's orbit did not match that predicted by Newton's law of gravitation. Some astrophysicists predicted the existence of an undiscovered planet (Vulcan) that could explain the discrepancies. When Einstein formulated his theory of general relativity (GR) he focused on Mercury's problematic orbit and found that his theory added a correction, which could account for the discrepancy. This was the first time that Newton's theory of gravity had been shown to be inexact.
Since then, general relativity has been acknowledged as the theory that best explains gravity. In GR, gravitation is not viewed as a force, but rather, objects moving freely in gravitational fields travel under their own inertia in straight lines through curved spacetime – defined as the shortest spacetime path between two spacetime events. From the perspective of the object, all motion occurs as if there were no gravitation whatsoever. It is only when observing the motion in a global sense that the curvature of spacetime can be observed and the force is inferred from the object's curved path. Thus, the straight line path in spacetime is seen as a curved line in space, and it is called the "ballistic trajectory" of the object. For example, a basketball thrown from the ground moves in a parabola, as it is in a uniform gravitational field. Its spacetime trajectory is almost a straight line, slightly curved (with the radius of curvature of the order of few light-years). The time derivative of the changing momentum of the object is what we label as "gravitational force".
Electromagnetic.
Maxwell's equations and the set of techniques built around them adequately describe a wide range of physics involving force in electricity and magnetism. This classical theory already includes relativity effects. Understanding quantized electromagnetic interactions between elementary particles requires quantum electrodynamics (or QED). In QED, photons are fundamental exchange particles, describing all interactions relating to electromagnetism including the electromagnetic force.
Strong nuclear.
There are two "nuclear forces", which today are usually described as interactions that take place in quantum theories of particle physics. The strong nuclear force is the force responsible for the structural integrity of atomic nuclei, and gains its name from its ability to overpower the electromagnetic repulsion between protons.
The strong force is today understood to represent the interactions between quarks and gluons as detailed by the theory of quantum chromodynamics (QCD). The strong force is the fundamental force mediated by gluons, acting upon quarks, antiquarks, and the gluons themselves. The strong force only acts "directly" upon elementary particles. A residual is observed between hadrons (notably, the nucleons in atomic nuclei), known as the nuclear force. Here the strong force acts indirectly, transmitted as gluons that form part of the virtual pi and rho mesons, the classical transmitters of the nuclear force. The failure of many searches for free quarks has shown that the elementary particles affected are not directly observable. This phenomenon is called color confinement.232
Weak nuclear.
Unique among the fundamental interactions, the weak nuclear force creates no bound states. The weak force is due to the exchange of the heavy W and Z bosons. Since the weak force is mediated by two types of bosons, it can be divided into two types of interaction or "vertices" — charged current, involving the electrically charged W+ and W− bosons, and neutral current, involving electrically neutral Z0 bosons. The most familiar effect of weak interaction is beta decay (of neutrons in atomic nuclei) and the associated radioactivity. This is a type of charged-current interaction. The word "weak" derives from the fact that the field strength is some 1013 times less than that of the strong force. Still, it is stronger than gravity over short distances. A consistent electroweak theory has also been developed, which shows that electromagnetic forces and the weak force are indistinguishable at a temperatures in excess of approximately . Such temperatures occurred in the plasma collisions in the early moments of the Big Bang.
References.
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