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Gravitation , or gravity, isa natural phenomenon by

whichphysicalbodies attract witha forceproportional totheirmasses. Gravitation ismost familiar as the agent

that gives weightto objectswith mass and causes themto fall to the ground whendropped. Gravitation causesdispersed matter to

coalesce, and coalescedmatter to remain intact, thusaccounting for the existenceof the Earth, the Sun, andmost of the macroscopic

objects in theuniverse.Gravitation is responsible forkeeping the Earth and theother planets in

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theirorbits around the Sun;for keeping the Moon in its

orbit around the Earth; forthe formation oftides; fornatural convection, by whichfluid flow occurs under theinfluence of a density

gradientand gravity; forheating the interiors offorming stars and planets tovery high temperatures; andfor various other phenomena

observed on Earth.Gravitation is one of thefourfundamentalinteractions of nature, alongwith electromagnetism, and

the nuclearstrongforce and weak force.Modernphysics describesgravitation using

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the general theory ofrelativityby Einstein, in

which it is a consequence ofthe curvatureofspacetime governing themotion of inertial objects.The simplerNewton's law of

universalgravitationprovides anaccurate approximation formost physical situations.

Main article: Newton's law ofuniversal gravitation

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Isaac Newton

In 1687, English

mathematician SirIsaacNewtonpublishedPrincipia,which hypothesizesthe inverse-square law ofuniversal gravitation. In his

own words, I deduced thatthe forces which keep the

planets in their orbs must[be] reciprocally as thesquares of their distances

from the centers aboutwhich they revolve: andthereby compared the forcerequisite to keep the Moonin her Orb with the force of

gravity at the surface of theEarth; and found themanswer pretty nearly.[3]

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Newton's theory enjoyed itsgreatest success when it

was used to predict theexistence ofNeptune basedon motions ofUranus thatcould not be accounted forby the actions of the other

planets. Calculations bybothJohn Couch

Adams andUrbain LeVerrierpredicted thegeneral position of the

planet, and Le Verrier'scalculations are whatledJohann Gottfried Galle tothe discovery of Neptune.

A discrepancy in Mercury's

orbit pointed out flaws inNewton's theory. By the endof the 19th century, it wasknown that its orbit showed

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slight perturbations thatcould not be accounted for

entirely under Newton'stheory, but all searches foranother perturbing body(such as a planet orbitingthe Sun even closer than

Mercury) had been fruitless.The issue was resolved in1915 byAlbert Einstein'snew theory ofgeneralrelativity, which accounted

for the small discrepancy inMercury's orbit.

Although Newton's theoryhas been superseded, mostmodern non-relativistic gravi

tational calculations are stillmade using Newton's theorybecause it is a much simplertheory to work with than

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general relativity, and givessufficiently accurate results

for most applicationsinvolving sufficiently smallmasses, speeds andenergies.

Main article: Earth's gravity

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Every planetary body(including the Earth) is

surrounded by its owngravitational field, whichexerts an attractive force onall objects. Assuming aspherically symmetrical

planet, the strength of thisfield at any given point is

proportional to theplanetary body's mass andinversely proportional to the

square of the distance fromthe center of the body.

The strength of thegravitational field isnumerically equal to the

acceleration of objects underits influence, and its value atthe Earth's surface,denoted g, is approximately

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expressed below asthestandard average.

g = 9.81 m/s2 = 32.2 ft/s2This means that, ignoring airresistance, an object fallingfreely near the Earth'ssurface increases its velocity

by 9.81 m/s (32.2 ft/s or22 mph) for each second ofits descent. Thus, an objectstarting from rest will attaina velocity of 9.81 m/s

(32.2 ft/s) after one second,19.62 m/s (64.4 ft/s) aftertwo seconds, and so on,adding 9.81 m/s (32.2 ft/s) toeach resulting velocity. Also,

again ignoring airresistance, any and allobjects, when dropped from

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the same height, will hit theground at the same time.

If an object with comparablemass to that of the Earthwere to fall towards it, then

the correspondingacceleration of the Earthreally would be observable.

According to Newton's 3rdLaw, the Earth itself

experiences a force equal inmagnitude and opposite indirection to that which itexerts on a falling object.This means that the Earth

also accelerates towards theobject until they collide.Because the mass of the

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Earth is huge, however, theacceleration imparted to the

Earth by this opposite forceis negligible in comparisonto the object's. If the objectdoesn't bounce after it hascollided with the Earth, each

of them then exerts arepulsive contact force onthe other which effectivelybalances the attractive forceof gravity and prevents

further acceleration.

Mass andWeight

Mass is a measure of how

much material is in anobject, but weight is ameasure of the gravitationalforce exerted on that

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material in a gravitationalfield; thus, mass and weight

are proportional to eachother, with the accelerationdue to gravity as the

proportionality constant. Itfollows that mass is

constant for an object(actually this is not quitetrue, but we will save thatsurprise for our laterdiscussion of the Relativity

Theory), but weight dependson the location of the object.For example, if wetransported the precedingobject of mass m to the

surface of the Moon, thegravitational accelerationwould change because theradius and mass of the Moon

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both differ from those of theEarth. Thus, our object has

mass m both on the surfaceof the Earth and on thesurface of the Moon, but itwillweigh much less on thesurface of the Moon because

the gravitationalacceleration there is a factorof 6 less than at the surfaceof the Earth.

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