《大學(xué)物理》英文課件13 Gravitation

?大學(xué)物理?英文課件13GravitationTheWorldandtheGravitationalForceGravitationalforce

-holdsbodiestogether,-keepeverythingonthesurfaceofEarth,-holdstheMooninorbitaroundtheEarth-holdstheEarthinorbitaroundtheSun420m)fromthegalacticcenter15mGravitationandthePrincipleofSuperpositionForparticlesystem:Forrealobject:SampleProblemProblem:

particle1ofmassm1=6.0kg,particle2and3ofmassm2=m3=4.0kg,anddistancea=2.0cm.Whatisthenetgravitationalforceonparticle1duetotheotherparticles?Solution:GravitationNearEarth’sSurface

Altitude(km)ag(m/s2)Altitudeexample09.83MeanEarthsurface8.89.80Mt.Everest(珠穆朗瑪峰）36.69.71Highestcrewedballoon4008.70Spaceshuttleorbit357000.225CommunicationsatelliteGravitationNearEarth’sSurface–Earth’smassisnotuniformlydistributedgvariesfromregiontoregionoverthesurface.GravitationNearEarth’sSurface–EarthisnotasphereEarth-isnotaperfectsphere-butanellipsoid,flattenedatthepolesandbulgingattheequator.-equatorialradiusis21kmgreaterthanitspolarradius-gatthepolarisgreaterthanthatattheequatorNorthpoleSouthpoleEquatorGravitationNearEarth’sSurface–EarthisrotatingSampleProblemProblem:(a)anastronautwhoseheightis1.70mfloats“feetdown〞inanorbitingspaceshuttleatdistancer6mawayfromthecenterofEarth.Whatisthedifferencebetweenthegravitationalforceatherfeetandatherhead?(b)iftheastronautisnow“feetdown〞atthesameorbitalradiusr6maboutablackholeofmassMh=1.99x1031kg(10timesourSun’smass).Whatisthedifferencebetweenthegravitationalaccelerationatherfeetandatherhead?TheblackholehasamathematicalsurfaceofradiusRh4m.Nothing,notevenlight,canescapefromthatsurfaceoranywhereinsideit.Solution:(a)(b)AsaparticlemovestowardthecenterofEarth,thegravitationalforcedecreasesfromMaxto0.GravitationInsideEarthNewton’sshelltheorem:Auniformshellofmatterexertsnonetgravitationalforceonaparticlelocatedinsideit.SampleProblemProblem:anearlysciencefictionstorybyGeorgeGriffith:threeexplorersattempttotravelbycapsulethroughanaturallyformedtunneldirectlyfromthesouthpoletothenorthpole.AsthecapsuleapproachesEarth’scenter,thegravitationalforceontheexplorersbecomesalarminglylargeandthen,exactlyatthecenter,itsuddenlybutonlymomentarilydisappears.Thenthecapsuletravelsthroughthesecondhalfofthetunneltothenorthpole.CheckGriffith’sdescriptionbyfindingthegravitationalforceonthecapsuleofmassmwhenitreachesadistancerfromEarth’scenter.AssumethatEarthisasphereofuniformdensityρSolution:Discussion:Whenrdecreases,Falsodecreases.ThisisoppositeofGriffith’sdescription.Whenr=0atthecenteroftheEarth,Fisalso0.Griffithwascorrectatthispoint.GravitationalPotentialEnergy–two-particlesystem

GravitationalpotentialenergyonthesurfaceofEarthGravitationalpotentialenergyoftwoparticlesGravitationalPotentialEnergy–more-particlesystem

Potentialenergybelongstothesystem.GravitationalPotentialEnergy–pathindependenceGravitationalforceisaconservativeforce-->PathIndependence.EscapeSpeedSampleProblemProblem:anasteroid,headeddirectlytowardEarth,hassspeedof12km/srelativetotheplanetwhentheasteroidis10EarthradiifromEarth’scenter.NeglectingtheeffectofEarth’satmosphereontheasteroid,findtheasteroid’sspeedvfwhenitreachesEarth’ssurface.Solution:PlanetsandSatellites:Kepler’sLawsThepathseenfromEarthfortheplanetMars〔火星〕asitmovedagainstabackgroundoftheconstellationCapricorn(魔蝎座〕during1971.TheLawofOrbits:Allplanetsmoveinellipticalorbits,withtheSunatfocus.a:semimajoraxis(半長(zhǎng)軸〕e:eccentricity〔離心率〕Example:theeccentricityofEarth’sorbitisonly0.0167.PlanetsandSatellites:Kepler’sLawsTheLawofAreas:AlinethatconnectsaplanettotheSunsweepsoutequalareasintheplaneoftheplanet’sorbitinequaltimeintervals,thatis,theratedA/dtatwhichitsweepsoutareaAisconstant.PlanetsandSatellites:Kepler’sLawsTheLawofPeriods:Thesquareoftheperiodofanyplanetisproportionaltothecubeofthesemimajoraxisofitsorbit.PlanetSemimajorAxisa(1010m)PeriodT(y)T2/a3(10-34y2/m3)Earth15.01.002.96Satellites:OrbitsandEnergyEarth-satellitesystem:FourorbitswithdifferenteccentricitieseaboutanobjectofmassM.SampleProblemProblem:aplayfulastronautreleasesabowlingball,ofmassm=7.20kg,intocircularorbitaboutEarthatanaltitudehof350km.(a)WhatisthemechanicalenergyEoftheballinitsorbit?(b)WhatisthemechanicalenergyE0oftheballonthelaunchpadatCapeCanaveral(beforeit,theastronaut,andthespacecraftarelaunched)?Fromtheretotheorbit,whatisthechangeintheball’smechanicalenergy?Solution:(a)(b)EinsteinandGravitation–