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ch 1 - ChJ-Thc Capemican Revolution The Bird nl'Modnrn...

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Unformatted text preview: ChJ -Thc Capemican Revolution The Bird: nl'Modnrn Sciatic: l in 2003, tachmcims are prepping a 2004. (19L; spacecrnfl called Spin! it arrived a: Mars in LEARNth 60115 Swdying this chapter will enable you to: {Discuss how {he observed motions offiic plant's led to an! modem View of): Slur centered will: system 2.5}:ctch Lhc major cuntriburions ul' Galileo, Braille, and Kepler {a the. developmcnl of astronomy, 3.5mm Kepler's laws of planetary modem. 4. Expiain how astronomers haw: measured the true size oflhe sular system . Siam Newton‘s lhrec laws urination and his law of universal gravitafion A. masses of uslmnumicul bodie; 31.] Thefiotlons of the Planets‘ ICwar the course Ufa gigh; the stars and lhe Mann slide smumhly across the Sky from ..................... Why? During the (Lay, me Sun mow: frum like any Stu. Why? O’VEI’ the course 0r 3 mpg, Ehc Mann mmv$ [smoothly and swadii}, from r. ‘_ along ils ipaui on (h: sky rclam‘c In Lhc smrs‘ passing Edmugl‘z its familiar cycle of phases. Why? iner the cuursc bf a fig lhc Sun progresses {along the ecliptic from V , , a! an aEmOSi oonsmnarm, varying liule in brightness from day E0 day. Why? in sham the behavior of me Sun, the Moon, and the stars seems fairly simple and orderly i Ancient astronomers were also awnre offivn lomer botfies in Hue sky - lhe planets m iThcy vary in brighlness and don't. maintain a Efixed pusiu'on. Unlike the Sun and the Mum, gthey seem to wander amumi Lhc celestial Esphch—windccd, the word planet derives from gthc Grcck warci planelcs, mennirg “wanderer" El’lancls never stray far {mm the ecliptic and Egenemfig traverse the celestial sphere {mm Ewesl to arm, as the Sun does. ;Mfll‘§ Engine: an; ngm stem Io speed up and :Sti down during theirjounmys, and at limes 33m); even uppcar 10 100p hack and forth ireiative to the suns Motion in the castwani snusc progracie muLion. The backward (weshvard)mclion ‘ retrograde motion. (Mars 1994) EN“: apparent brightness of a plane: in the night ssky is reiaaed to ils distance from Ezra] i (planets appear brightest when closest lo us. lars: Jupiter, imii Saturn are always bfiginast during 1h: relmgrade portions uffimir orbits. ST‘he challenge facing nslmzmmcrs Em explain the observed motions and variations gin pianeiary brightness. 5/23/2011 The Geocenmc Universe iTheearliest models of the Sula! system ‘ allowed the teachings of the Greek hilasopiler firi_stc_tt_i§ (384322 BC.) and ware coccntzric , meaning that Earth lay 31th:: icenwr of the universe and nit ether budies imovai mound it This model provided a fairiy good approximation so the orbiis ut' the Sun and the Mann, but it 001 id not new mfivfij’m ; m u' it in lane!“ 'bri tsiesser i i l:geir retrograde mofigi. i i : iTiu: first steiiiuward a new model is shown in i the figure. iETyt'mken‘ig with dis relative sues ofcpieycie ifind duh-rent, with the pianei’s speed an die icplcycic‘ amf with the c'pioyoie‘s speeri aicng i the deferent, early astronomers were able to bring this "cpicyclb" motion inm fairiy good agreement with the observes} paths of the piancls in the sky, As the number and lhc quality of Dbserval‘ians increased, smali corrections had to be introducei into the simple epicyclic modei to bring, it into line with new observations The center of the defereni had so be shifted slightly from the center of Earth. and tile mulion of the epicycles had to be imagined unit'uun with respeclnui to Earth but in yet another paint in space in-uund AD, 140, using a series afno fewer 3 ithxn BU circles‘ a Greek astronomer named i ; Ptolemy constructed perhaps the best g {geometric model Dfflii time. This model iaxplamed remarkably well the observed paths iofflie pinnets, the Sun and the Moon, ‘ Ptulemy’s Mode! iAnsinrclx-Js of Smos (MOVED BC.) preposeci itha! all the pimiefis, imiudizig Earth, revolve awund lite Sun and that Earth rotates on its axis mice each day Because Aristotle's influenza was too strong, ristarchus mode! was not accepted. Win: i’telcmzic picture of file universe survived 1 almost 53 centuries untii the Polish eicrie, Nichoias Copeniicus(14?3-1543), rediscovered jArislarchus‘s hciiucmiric model. :Tlus model explains the ubsm'ed daily and easenai changes in the heavens, the planetary errograde motion, and their variations in nghtncss 5/23/20” The Retrograde Mutiafirrol' Mars? The ethical real auon lhat Earth is not at 93m center a! the universe is now known as the Copsmicanmvulmim , Copemicusb major mnfivafinn was mjfifl. He was mi} influcmcd by Greek thinking and clung to the idea ofcimlcs lo mndcl fin: Epiazaets‘ motions. I To hdng his theory inm agrmmmt with obs aliens, hr: was fumeé L9 :M p, '12:: idea ofgmcfliig motion. with the deferent annexed 5 on the Emil. : 1.2 The Birth a New Astronomy Gfiifleo Gaifiei (1564-1642) was an 'Eiaiian .mafiacmalbian and phiiasnphar By his I mingness i0 perform cxmn‘mmts to test his dcas, he revalnt‘zmimd the wny science was gaione. He is now regarded as the father of 'expcs-imertal suimus {aggggi‘l'amggmgbgg}. 5%; m was mvcnmd in Holland in 1h: geariy swmlfimih canary Gaiiico buiil a gmicscopc forhimself in 1609 and aimed it at :the sky, He ohmrvsd: :a) Mountains, vniicys. am} craters an m: Mann i i i b) lmpmficdnns on the Sun (sunxpats) Ha inferred that the Sun rotates. about once par met-1h, amund an ms roughly perpendicuiar m the ecliptic plane. a) Fuur moms ufJupihar (Galilean mamas)w slmngcsl support for the Copernican modei. Galileo’s skclchcs mit- 15 January, 161 U‘ 5/23/2011 )Venus‘ complete cycle of phases (an idea 0f Bcncffcm Clsmlli) irénhieo publishui his Sailings and his mmmversial conclusions supporting the Copcmicm Lheory in 16H). In 16%. bolls his and Copernums‘s works wemjudgai hemticfli and banned by {he Roman Catimljc Church. | Em I63 2, Galileo’s great book Dialogue of the ETwo ChiefWoricl Systems was published :Thc inqmsisim sentenccd him In prison 5(1633), n scmcncc commuted by the pope to Shousc my, untii he died in 1642‘ l a £992, Galileo was publicly forgiven by the :anm Catholic Church, (Eiurdann Bruno —- 1548-1600 “"3 képler’s Lalws of Planetarglm Motion At about the lime Galileo was becoming famuns fer his mlcscapic abscrvafions, Johanngs Eculgr “HE-1630}, a German mathematician and astronomer, announced hxs disccvcry of a so: of simpic omnidcal (le31 is, based on uhservalion) "la. ,5“ that accurately l describad she moLions of Aha planeLs. Keplur was a purc theorist. He based his work an the observations of ychu Bruha (1546-1601), one ofthe greatest bscrvalicna! astronomers (Witlluul ntclcscope) whoever livcd. ycbo Ernim in hus obscn-alory in Dmmm’k. 5/23/2011 1“ Law: The urbilli paths bf the planets an: ciiipu'cai (nclcimuiar),_wid1the Sun at am: 53; “Mum—RE";- - w The ccccnfliciw offllc chips: is the raiio of the rdistm'lce between. the {uni In due lcngfll of 1}": imajur axisl (A circle is a specia} kind of ellipse in which the two l'oci happen to cainciéc, Sn 1'15 geccentricity is mm). WWEMLEEWHE This helper} Ptolcmuic amt Copernican models to describe reality :2“ Law: An imaginary line connecting the ISIm in any plane! sweeps am cquai areas of fix: ellipse in equal inmals of tum: : - - . . . . . . y i'l'hwe two law: 3550 apply to orbiting abject Bike manila; ichlcr Pubiishnd his first two laws in 1609, stafiing thatlae had proved {hem uniy for the orbit nfMaux. a K semi-major axis a areccmnlxicity = (foal dis}. Imajur axis) thclion : 1(1-c) Aphslion = 30%) jun yam am, he attended m w and the 2nd E ilaws In all the known plmcls (Mercury, Venus, E flank Mars. Jupiter, and Emma) and added a 13” an, ‘i 13*‘Law: The square ofn planet's orbital isiéemal period is proportional In :11: cube ems Emmi-major axis. i Kepler’s third law becomes panicularly simph‘: ‘when we choose Lhc (Earth) yca: as our unit of ilime and the Mancunian! unit as m unit of l {engdx 10:1: mm (Ali) is [kc semi-major iaxis of Earth's ("hit around the Sun— icssentiaiiy 33w avemgc distance human-n Earth 1 and the Sun. 1 i P‘{iz| yenrs}= a‘ (in astronomical \mils). l iwhcrcFislhc lane? is I ri i x33 and a igfiwjmglh fissflm,,,i WW - Nulmflsad . pizza WWW , sunkmajur axis P = sidcrcal period I . i ecceummzy iBocle’s Rule “a curious xciazionship Ediswvered by Johann Tilius popularized by his culleagm Johann Bod: in 1772 E M..—_ ”MAJ Dimensions 0f the Solar System From Kepler‘s — a scale model of the saint system shagc§ und reigtivg aim or all i(hr: pianclaxy orbits), chcausc Kepiefis [finnguiatim measurements iali used a portion of 551-613 orbit as a baseline, ibis distances cuuid be expressed only in terms in! lAU. from radar (radio detection and ranging) m i absolute scaie ufthe 50hr system i i , IWa manual uw radar to measure the distance so Lhc Sun directly because radio signals are nbsorbccf amine snlar surface and do noi refine! back to Em’fix. lnslcad, the planet Venus, is the most common target for this Icchniqucl The distance Earlll lo Vbnus at the pcinl of clascst approach is appmxizuamly 0.3 All. Radar signals take 300 5 for this munétn'p. 5/23/2011 5/23/2011 Newton's second law The acceicration nfan objeclis direcsiy proponionafi 50 L116 stymied fume and invcfsdy proporiicnal In the obiect‘s mass (a = Ffm7 or F n ma» Newton‘s third Enw Iciis as that forces cannot occur in isolation—wif body Aexerts a form ion body B, lhc‘n body B nwcssariiy exens a gforce on body A thi is squad in magnimde but mpposiwly directed {law ufnctian-rennlilm)‘ 1 aw ofCrravily ny abject havmg mass exams an awn/olive, ravilatiunai Earn: an all other massive mm fllis mchniqm ‘‘‘‘‘‘ distanccs ID planets, .4 Newion’s Laws: :The British malhamntician isaac Nev-ton “1642-1727) dcvcluped a deeper understanding Laf the wax 11E! ubjecLi move alxdfiinterncl 'f E r E. E g Threabasic laws ufmelion, the Law of § universal gravitation, and calcufus (which 3 Nchnn invcnmd) are. sulficim: to explain 1hr: - I ‘ (J an ab}: cwmn's first law cl‘motiun Unless omc 3 'Any place of matter having some mass afiocrs \lemal force changes [E slate urination, an Ithe space aruund, pruducmg a gravitalionai Enact an rest remains at res! and a moving ' ficid A11 who: maficr “fads" the field as a bjccl continues to mow: foreve! in a straight gravilalaoiiai farce m: with constant speed Planetary Motion The mumai gravimlinnai fim‘achfln ofrhc Sun 3 and flu: 933nm. as cxprcssed {a} Newton's law i ofgram}; produces {11: ubsencd piancmy i whim i :The tendency ofan object to keep moving at :Lhe same speed and in the same direction : niess acted upon by a force is known as ncm'a (depends on Lhc mass), The ml: ufchangcofthe velociy nfan bjcclispcwng up, slowmg down, or sampfy ‘ ._?g§j?fitdifgcfl9%is gained its agoeieration More Precisely 1.1 i From Newton’s laws urination Ind the luv of ’ gravity it is possflale [n calculate Line masses 0 celestial objecls. MBM ; 5 x 103mg MSW1 t 2 x1030 kg, Keglcr's Laws Rewnsidcnad Ncwum's laws cfmutim and his law of innivcrsal gravitation provided a meorclica} iexplanalion for Kepler‘s empirical laws inlmrlucing, ellipses in place ufcircies, so too ‘1 din} Ncwwn make corrections to Xavier's first land third iaws. i ilust as KepEer modified Cnpemicus's model by l The orbit of a plane! around Lhc Sun is an ellipse havmg Lhc senior of mass othc planeEnSun system at one focus. Pawmloweo by Sun‘s clamor Kelley's second law as stated earlier. conlimms to apply William modification In each orbit separately; but the: roles at which the two (”hits sweep out area are diffemnlj The change lo Kepiefs third law is also small in Ilia case ofa planet orbiiing the Sun but very imponam in other circumstances, such as the orbital motion nfiwu Stars {1131 are graviluh'unally bound to one another. From Newlon‘s {boom we {incl that the {me relationship between Lhe semi-major axis of like planet's orbit (in astronomical units) and its gurhilnl period P {in Earth years) is 3 Pan Earth y.) m s°(in AUWWfin MW) Notice [hm Newton‘s restnlemml ochpler‘s shirt} law preserves the proportionality between P2 lmi a‘, law. includes Mame The proportionality between P2 am} a3 is no! squib: lhe same for all the planets i‘l‘hc Sun's mass is so greaL however, that the 3difl'erenoes in Mm among the various 3combinal‘nns of lhe Sun and. the other plfincis are ofimost unnoticealfle. 'E'ltcrcfme Kepler‘s third law. as originally stated, is a very gooé appreximalim This modified form of Kepier's third law is {me in all circumstances. inside or oulside the solar system, Newton's laws explain the paths of objects moving aim-1y pace nee: ' gravitating body These laws provide a firm physical and mathmialieal foundation for Copcmicusk heliocentri: model ofthe solar system and For Kepler's laws ofplanelnry modem, but may also do mud: more than than. Newtonian gravitation govems not only 5816 pianets, muons, and salellites in their ielliplicui orbits but aisu Elan slurs and galaxies 2 in their motion throughout our univeise, Earth’s escape velocity is V mm :lllkmfs I 5/23/2011 5/23/2011 ...
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