在地球附近的月潮汐差異ckw

8.Gravity 重力TowardaLawofGravity 邁向一個(gè)重力定律UniversalGravitation 萬(wàn)有引力OrbitalMotion 軌道運(yùn)行GravitationalEnergy 重力能TheGravitationalField 重力場(chǎng)ThisTVdishpointsatasatelliteinafixedpositioninthesky.這碟型電視天線(xiàn)指向在天空中固定一點(diǎn)的人造衛(wèi)星。Howdoesthesatellitemanagetostayatthatposition?衛(wèi)星怎麼能停在那位置？period週期=24hPtolemaic(Geo-Centric)System托勒密(地心)系統(tǒng)Epicycle本輪Equant等點(diǎn)

Deferent均輪

swf8.1.TowardaLawofGravity 邁向一個(gè)重力定律1543:Copernicus–Helio-centrictheory.

哥白尼–日心理論1593:TychoBrahe–Planetaryobs.

泰戈?布拉赫

–行星觀(guān)察1592-1610:Galileo–Jupiter’smoons, sunspots,phasesofVenus.

伽利略

–木星的月亮，日斑，金星的相。1609-19:Kepler’sLaws克卜勒定律1687:Newton–Universalgravitation.

牛頓–萬(wàn)有引力。PhasesofVenus:Sizewouldbeconstantinageocentricsystem.金星的相：在一個(gè)以地球?yàn)橹行牡南到y(tǒng)裏，它的大小應(yīng)該不變Kepler’sLaws 克卜勒定律Firstlaw:Theorbitiselliptical,withtheSunatonefocus…第一定律：軌道為橢圓，太陽(yáng)在其中一焦點(diǎn)上…Secondlaw:Iftheshadedareasareequal,soisthetimetogofromAtoBandfromCtoD第二定律：如果有色的面積相等，則從A到B的時(shí)間與從C到D的相等。Thirdlaw:Thesquareoftheorbitalperiodisproportionaltothecubeofthesemimajoraxis.第三定律：軌道週期的平方與半長(zhǎng)軸的立方成正比。Explainsretrogrademotion解釋行星逆行Mathematica8.2.UniversalGravitation 萬(wàn)有引力Newton’slawofuniversalgravitation牛頓的萬(wàn)有引力定律:m1&m2are2pointmasses質(zhì)點(diǎn).r12=positionvectorfrom1to2.從1到2的位置向量F12=forceof1on2. 1加於2的力G=Constantofuniversalgravitation 重力常數(shù)=6.671011Nm2/kg2.Lawalsoappliestosphericalmasses.定律亦可用於球形質(zhì)量。m1m2r12F12.AccelerationofGravity 重力加速度Usethelawofgravitationtofindtheaccelerationofgravity 用重力定律來(lái)找以下的重力加速度atEarth’ssurface 在地球表面。atthe380-kmaltitudeoftheInternationalSpaceStation 在高380-km的國(guó)際太空站中。onthesurfaceofMars. 在火星表面。(a)(b)(c).Understanding“InverseSquare〞

策略.了解〞反平方〞GivenMoon’sorbitalperiodT&distanceRfromEarth,知道月球的週期T和它離地球的距離R，Newtoncalculateditsorbitalspeedvandhenceaccelerationa=v2/R.牛頓便能算出它的運(yùn)行速率v和加速度a=v2/R。Hefound他得到a~g/3600. Moon-Earthdistanceisabout60timesEarth’sradius.

月-地球的距離約為地球半徑的60倍。 Inversesquarelaw 反平方定律CavendishExperiment:WeighingtheEarth

卡文迪什實(shí)驗(yàn):稱(chēng)地球MEcanbecalculatedifg,G,&RE

areknown.知道g,G,&RE

就能算ME

。Cavendish卡文迪什:Gdeterminedusingtwo5cm&two30cmdiameterleadspheres.G用兩個(gè)5cm和兩個(gè)30cm直徑的鉛球量得。Gravityisweakest&longranged 重力最弱且長(zhǎng)程alwaysattractive 總是吸引的dominatesatlargerange. 在遠(yuǎn)距離佔(zhàn)優(yōu)勢(shì)EMisstrong&longranged, 電磁力強(qiáng)且長(zhǎng)程canbeattractive&repulsive 能吸引也能排斥cancelledoutinneutralobjects. 中性物體內(nèi)會(huì)抵消掉Weak&strongforces:veryshort-range. 弱和強(qiáng)作用：非常短程小球因重力而被吸向大球8.3.OrbitalMotion 軌道運(yùn)行Orbitalmotion:Motionofobjectduetogravityfromanotherlargerbody.軌道運(yùn)行：物體因另一較大物體的重力而做成的運(yùn)動(dòng)。E.g.Sunorbitsthecenterofourgalaxywithaperiodof~200millionyrs.如：太陽(yáng)繞銀河中心而轉(zhuǎn)，週期~兩億年。Conditionforcircularorbit圓形軌道的條件Speedforcircularorbit圓形軌道的速率Orbitalperiod軌道週期Kepler’s3rdlaw克卜勒定律第三定律g=0orbit軌道projectiles拋物體Newton’s“thoughtexperiment〞牛頓的“假想實(shí)驗(yàn)〞.TheSpaceStation 國(guó)際太空站TheISSisinacircularorbitatanaltitudeof380km.國(guó)際太空站的軌道是圓的，高度為380km。Whatareitsorbitalspeed&period? 它軌道的速率和週期為何？Orbitalspeed:軌道速率Orbitalperiod:軌道週期Near-Earthorbit 近地軌道 T~90min.Moonorbit 月球軌道 T~27d.Geosynchronousorbit 地球同步軌道 T=24h..GeosynchronousOrbit 地球同步軌道Whataltitudeisrequiredforgeosynchronousorbits?地球同步軌道的高度為何？Altitude高度=rREEarthcircumference地球的圓週長(zhǎng)Earthnotperfectsphereorbitalcorrectionrequiredeveryfewweeks.地球不是完美的球

軌道每隔幾個(gè)星期就要調(diào)整。EllipticalOrbits 橢圓形軌道Orbitsofmostknowncomets,arehighlyelliptical.的彗星軌道，大部份都是非常橢圓的。Perihelion:closestpointtosun.近日點(diǎn)：靠太陽(yáng)最近那點(diǎn)。Aphelion:furthestpointfromsun.遠(yuǎn)日點(diǎn)：離太陽(yáng)最遠(yuǎn)那點(diǎn)。ProjectiletrajectoryisparaboliconlyifcurvatureofEarthisneglected.拋體的軌跡祇有在地球的曲度可以忽略時(shí)才是一條拋物線(xiàn)。ellipse橢圓這一段差不多是條拋物線(xiàn)焦點(diǎn)是地球的中心OpenOrbits 開(kāi)放型軌道Closed密閉型(circle圓)Closed密閉型(ellipse橢圓)Open 開(kāi)放型(hyperbola雙曲線(xiàn))Borderline兩者之間(parabola拋物線(xiàn))Mathematica8.4.GravitationalEnergy 重力能Howmuchenergyisrequiredtoboostasatellitetogeosynchronousorbit?把衛(wèi)星送上地球的同步軌道要多少能量？U12dependsonlyonradialpositions.U12祇與徑向位置有關(guān)。onthispathU=0在此路徑上U=0…soU12isthesameasifwestarthere.…所以U12跟在這裡開(kāi)始算一樣.StepstotheMoon 到月球的步驟Materialstoconstructan11,000-kglunarobservatoryareboostedfromEarthtogeosynorbit.用來(lái)建做一個(gè)11,000-kg月球天文臺(tái)的材料已從地球送上同步軌道。Theretheyareassembled&launchedtotheMoon,385,000kmfromEarth.材料先在那裡裝組，再送到離地球385,000km的月球。ComparetheworkdoneagainstEarth’sgravityonthe2legsofthetrip.比較這兩段路程上，對(duì)地球重力所作的功。1stleg:第一段2ndleg:第二段ZeroofPotentialEnergy 位能的零(原)點(diǎn)Gravitationalpotentialenergy重力位能E>0,openorbitOpen開(kāi)放的Closed密閉的E<0,closedorbitBoundedmotion有限運(yùn)動(dòng)Turningpoint轉(zhuǎn)折點(diǎn).BlastOff! 發(fā)射Arocketlaunchedverticallyat3.1km/s.一枚火箭以3.1km/s垂直發(fā)射。Howhighdoesitgo? 它能達(dá)多高？Initialstate:初態(tài)：Finalstate:終態(tài)：Energyconservation:能量守恆：Altitude=rRE高度EscapeVelocity 逸速BodywithE

0canescapetoE

0的物體可以逃到Escapevelocity逸速M(fèi)oontripshavev<vesc.到月球的v<vesc.OpenClosedEnergyinCircularOrbits 圓形運(yùn)動(dòng)的能量Circularorbits:圓形軌道:HigherKorvLower

E&orbit

(r).較大

較低

軌道0EUKKConceptualExample8.1. SpaceManeuvers 太空操作AstronautsheadingfortheInternationalSpaceStationfindthemselvesintherightcircularorbit,butwellbehindthestation.去國(guó)際太空站的太空人發(fā)現(xiàn)他們?cè)谡_的軌道上，卻遠(yuǎn)遠(yuǎn)落在站的後面。Howshouldtheymaneuvertocatchup?他們應(yīng)該怎樣操作來(lái)追上？Firerocketbackwardtodecreaseenergy&droptolower,&fasterorbit.往後發(fā)動(dòng)火箭以減低能量，並降到低和快一點(diǎn)的軌道。Firetocircularizeorbit.發(fā)動(dòng)火箭以達(dá)成圓周軌道。Aftercatchingupwiththestation,firetoboosttouptoitslevel.追上太空站後，發(fā)動(dòng)火箭以升至它的高度。Firetocircularizeorbit.發(fā)動(dòng)火箭以達(dá)成圓周軌道。Mathematicaenergy0UGAltitude0E=K+U=U/2UE=K+U<E

(K<K)hE=K+U=U/2U<UKK>Kh<hGOTIT懂嗎.SpacecraftsA&BareincircularorbitsaboutEarth,withBathigheraltitude.太空船A&B都在繞地球的圓形軌道上，但B的比較高。Whichofthestatementsaretrue? 下面的表述中，那些是對(duì)的？Bhasgreaterenergy. B的能量較大。Bismovingfaster. B跑的比較快。Btakeslongertocompleteanorbit. B要較長(zhǎng)的時(shí)間來(lái)繞一圈。Bhasgreaterpotentialenergy. B的位能較大。alargerproportionofB’senergyispotentialenergy. B的能量裏位能占的成份較高8.5.TheGravitationalField 重力場(chǎng)Twodescriptionsofgravity: 重力的兩種看法bodyattractsanotherbody(action-at-a-distance)物體吸引另一物體(遠(yuǎn)距作用)Bodycreatesgravitationalfield. 物體產(chǎn)生重力場(chǎng)Fieldactsonano