l29 - WGenexmj flawe‘awgf Wo‘holm Cot/A. LACxlc...

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Unformatted text preview: WGenexmj flawe‘awgf Wo‘holm Cot/A. LACxlc Eww‘g: 5. Q‘kA Momewx‘uwx We kmkc (mewgkgcj'm Ww Newlfid IRIOJNVQ ‘0, Can he clfw‘tx 'm ‘hYMs 0? “v: “Zr Ve‘OCL'Ld 0: 7R8 CM aAJ ;\3 HZ? V‘QLCJLKUP MINA? 08: H30 1 K: {im‘v} + jimlvl V11 313 El}: 451‘ Q5: . A J: QPC 4%: Ulswix E3; 69 @MA @ Cor QWCL E: '9 w- .— \<= LM(§&> E) + L ii 4 c; :1ch 1 4% t KE ~(V\ “fmavmt ‘O/ (‘5 4&9 30M 0C Q oJ‘RJchafl Umhcb 0&1 mass M=m\+m1(m0vinj mg: Mod: \/ 013 CM rIU$ Hie KEHOP q} Ff . {C(e a? MQS‘S mom wh‘a +61, neg {Up Voou VS? / % K Lihecur MvachUM Eh Era/me O 7;: Fri—F: : MV (RQLA‘NG’ ({V\{O.\( movnerLq Of- +e~< [aqu 0'? qu‘l‘w/es i5 )1: 4a: 5 Am Die {Macks gs 50 um! cm mamaan rm) ——=> p : Con$+¢m¥ 734-! F) in CM {:«cmc =0. Ana u‘qv Nomtvfllom 30-5 _; —<evx£w~1 ches " 01 +\i\Q€ a "W'CLe r) V\ [37' S - no +o~r oes .. __3 “:0 “w —§ -§ "-3 0‘ + I; -. m‘ V‘"x1?+ mgqxxr; - COhSlQIAA', _ —-> 9 ' Y x \T’ a /u 1 _ x myav (,0 ’ covxs aw . value 0'? ‘Wm Wulaw momasl‘om o? \(Rf [oqu 010 urhY'kC/‘t q‘ood’ Weir Cm is eiuivoxlfinf 4o all) a 'siNA/‘e Fqsr-L'C‘e a? mass/u. " Eht :flfium'fl Wu tow»: a? \AJYCchc-Shon L3 LeWLwecm 16w ’oanL'c‘eJ ,(s 4 C(2er \Qnrct JeYiUoJole “(cm on. lad/er}qu 71M, +fx€V\ th (Wu/63 0‘9 fa: 533mm is CL coms+mdl 0‘9 _+C-e mojriowi E3 Lfin/\Vi-F _L/4mrl+l((\’\ : consul/0‘. 1 Nol-c? Fov m‘vwml /x~m1 qwcl €/U«j7bfl5 reJuce I “'0 +etbf SHAWL qu‘L'clp fiulUm/‘C S~ CM ~ ‘3‘“?on Momevc‘um "T4 9 —9 ml.” M1 R, N\+W\3‘ ~=> 4» [11' ~ ~‘N\\ rt ~32 ‘ ~3 A; A *5, Lcw\ " “\W’L '1 ’k’v.‘ . WMMl rk XV} plqywi‘cpfg MO‘EOM " Q Pav¥tdf Sglhitlmé -$uvx+ quvxe‘l’ - Planet 4— Moon ' Earle + 3&4ch -C9‘oose QM fich‘zm 0% cooYACVWJ‘CPS,' A _ a R Z 0 ani V E o . M 1 W‘\+m1 fl is Yh \ V“; M —1 a “T Y : V3. _ “X a - -:> I _ _ Ail a \r ‘— 3 9‘ The polar components of Wax velocity. 7% “All enevzstx oli ‘WK sxztem l3 e=l<+u = i/nra‘ar ’bU‘A 1 (a) Two particles orbit aroundtheir common center of mass at O. (b) The situation in (a) is described in terms of the equivalent single particle with mass u=m1m2/(m1+m2). The vector r is the relative coordinate of the particles, so, in magnitude, r= r1 + r2, YVEO CM Sadiem] (’Re veloct‘lté) X}: 1);?* VS; 3 I 243 racli'a( cmc‘ oia'mul‘ed COW‘FOl/lffl/fS - ® 4%» ~— wo: elf Lyric =/¢,w2(3i: 50-7 E= _I («rjurll + um g 9’ / 1 V 5L J plow“ r - L LGWVE‘LJCOMJ PE KE Que +0 cw}. Y‘o‘l- 4000+ CM. KE 40: ‘Lo watched mo'l’ions Luv“: 'CM. in" W“ 2 .L: “ Gmlml [Eggecl‘ive PE FQnC{fl'OV\.) , VT]; .__Y Let it: GmflYla = (yum ~. ymfimfi mm: i3 _ _;k_ V“ V l 1 @ The effective potential energy function V(r) for the case of planetary motion. The ordinary potential energy function is U(r)= -GnM/r =—K/r. ‘(‘= NH ,5: W , ‘ Y = 94¢) 7—3 erxed‘wck 0? oYLiJr. W : Ex: 2 ____ :’V(V5 ‘nom ® ~( QR (L 3 f Z (9 1. Eli : i— qum E . @ 4+ /W1 X 5415— - .5. ‘ 556. Y 1 *“L 2% z ‘ fi/Q‘ (CDMVQN‘MM) l - G cos ¢ :1 : \— E cosys : g [Ezuwkon o? afom'c 321*”; Y Y V0 : 5i RQA‘W 0Q (\‘lcokav o~c\oi+ cowes. flk +0 ‘v/A, «w! k. e: e: \+ £9" flh" iO‘rL 1+ (“Pqua’efls'kC3 = O C(VCUqu Odoi‘s E = Em“A Q > 1 Hxflowbo‘ it ~/ 5 > o age :1 Pauladoolic \/ E = O i; Vo<e<l e\\;\e,l;cq\ v E< o '5 (a) Parabola e = 1 I35 =e(QP) (b) Ellipse O < 9 <1 r/e Q P r Parabola F D (c) Hyperbola e > 1 The conic sections. (a) The parabola has 9 =1 . (b) The elipse has 0< 6 <1. (0) The hyperbola has 9 >1 . There is another branch of the hyperbole (not shown), which lies to the left of the branch illustrated and has the opposite curvature. The circle (not shown) has 9 =0 and corresponds to an ellipse for which F and F ' coincide. 30-7 1 13:; v +\/(Y) 1/ V L1 be " \oojre ilorms a minimum. \l(\“\ #5 0 VW‘) :- ~ Gmtm-‘L N. Y‘ Sum Contrlioolfir? +0 V”) FroJOCes ‘18 Y—§C>'D. 1‘; L740 WW V£ URN? (‘E’c'ni‘rifu <1 ofnlf‘icu‘ l ———Q°—~—-—-—~. domkhcales quU v, 729 ill» {Jo‘iemkiol Gm‘ma/v dominajfi‘e5 c5!“ {qY‘J-e Y‘. W KE {Em 3&ng Wallet! mention i3 K 2 E —-\/(v) molrlovx 1'5 regjtricjtecl +0 (Ne (MAB meere K2 0‘ MAO“, a: m0“fiovx (iathmkheCL E (Elliptic orbit) __M_k2 min 2L2 (Circular orbit) The effective potential energy function for the case of planetary motion, showing radius values for two energies, corresponding to elliptic and circular orbits. 3040 :W TQM/«4* i'owJ 30 -l\ Ll. E>O '- [Hxxfevko‘orl f is onloowulaé ‘Slw [qvae values BOWL mus‘lL Lio- parjra'c‘es QYC kepT éeeceecl CL.) Qévfilm minimom {(3 tara‘rk’ \oa Icevétrigaqfl Lavriev‘. 550 ‘ [Pcw‘qkooiql _ Exacuxk ow +Qw ‘oDQwAaV‘X Iodine?“ [OOUAJfJ WC) .'UV\\000V\A€4 mo'\‘(om_ 3.E<O : [El‘i‘ase] A H mo‘fi'ow '13 L300 nelch “(20V large QAJ :mq Y‘- l—wo faY‘rQC/(PS £04m cx 50g)an em. :4' E : EM: [Civc‘e] I ‘C ROMS Con exqcIr 15'er VQAHQ. PwA-m‘és oV‘Ll'fll 1 «UR O‘Wxtv “V covxsfim“ ult's‘l‘cunfe QIOQ r'l’. Different orbitals paths corresponding to the same vaiue of anguiar momentum. C {\r CL)qu 0Y‘oi‘\’5 ERAS 0; minimum voJUQ a;an r\]~ ‘0 , r1_ ~ Ely :0 . ch vm: J: __k_ M). 13 +12 =0 QlY /M\(% \(‘3‘ 1 Y0“ J; (Raina) /uk Emzvx‘ VUO): #2 3L4 k ‘ _ 2 u fo) (GV‘QVA‘QL'OIAGJ PE) 76+“! {mtv is he an‘w ccwa ' {2416 o? fi4dionqfl3 IS 6X46”; OWL {Defininle encrata , 30 ’19s 3043 09:0) +0‘H\\n% Poihjfs in mojrl'ow (‘6:7T> (Lehxla OPP m15ov Cntls) Pigtails ‘ Ectth Pet‘th \ ion Pewx'tkee qu Q9 \u‘ou qro e6 Geometry for obtaining ck the general equation for a conic. (a) Elliptic motion of m and m2 around their at The pOint The corresponding 0 is the right-hand focus of the elliptic motion of M smaller ellipse and the left-hand around 01 focus of the larger ellipse. Lg“ e o“3 qu‘ov ch'S O~£\oi5 samt ma\o‘r cmu'S Rave +6? same ew-Q‘Fm. Wfifiw fifwxxa may: Mam fiumwr mm“? imam Wmm % % i Mum? __ mast-mm. am“ imam w: a ; mm»; {Rim-3% ’& fifléfifi‘fi ‘5 i ‘2 M $5” $1 «3» :18 {Mi- H— AELJ‘ m M" . mfim 3'5 incjepinil {NI‘ 0? Rfififi $333 “3% “‘3 é $33? $3638 $fi$$8 1%; 3:31 at 3&3fi‘3 ‘4‘ MWWVuAHfl-iflmhvfiwH/WM/wfifié’vk gm; u 3.: Pp F p 3044' l y eeiev '5 Laws “WOXR‘MCJV. ~0‘o8e0‘1 Rowe Coquv‘axco‘e masses (bian‘Lfi-s'tqu). —- C(V‘dfl cormsva common ~T€xtd E Conserch ‘ Totai J- T‘req‘} qs q V‘cAUCeA mass " ?e<'\o‘<\o£\iom clue 40 0424‘ flame 5. L4 to = 23: rad/ month at) To moon —> Ocean Earth 18. 2 days later QM . C ween/:4 . Sasha/n. St Q no+cs. (a) The ocean bulges on opposite sides of the earth because of the interaction with the moon. (b) The earth orbits about the center of mass 0 of the earth—moon system. We show the earth at three times during this motion. Note that the earth's rotation is not included in this analysis: point A on the earth has not rotated. lKeFlev's Laws - RQV\'S(‘\E:1, 30-5 1- A rolcma’ moves in co elll'ro'l-‘Caj Palfi “mil? +36 ,‘FOCUS a‘t me Position 0? +69 cm 01C {’Kf P/qmnl'SOw saujfem- (EQVK'SUM stasl‘tm gas his cm can/1 4-So‘em Prom Jrexe (emlcr 09 +6. sow). L—L—L- Tem Basilio" uedl‘oV ‘For OJ P'wne'l' (measuvci Rom r‘lexe CM 043 +e€ [QM€+"$UM sixlwm) 3002!: S 00+ 70a] comes in eioov! ime iN+CYV 5" Ma} 15/ ClA/d£:COV\S+QM)L.— Velocity v2 Velocity v1 Distance V1At Time interval / At Time interval At \ Distance VZAt ' Illustrating Kepler's Geometric representation of Kepler's second law. second law Avxckulatv momth‘uwx {5 consevveJ QM V'hO'Lt'OW J02 +0 .w CQNJTFJ RNCC —-& . ‘KV‘CLVI'LJIIOIAJ tone. Cvasicle‘f K Pp" 330nm} 44m! At) roshlfom 10463 TH.) EwQe {)5 00+ +69 our: cu 30% III. 7R4 \rog‘io 0: +9“, 570mm 09 +Ee Pev‘kotl (Tl) +0 +88 cube a“: 4R6 semwmq oY cow's (q?) )3 q rum-mate] +64 &~me fin" a” A f} (H: cm L [Ah/afijéfi Fov ou comraIA’P VEVO‘U‘L'OW we QCMK’ szzng :jg‘rmb L. FW oorx tHQYo‘kCofl or\o{‘L b: cx 31—9" Wk _. 2 3‘: 4&3 v a‘k = 45 "‘21 030—5) 1.2 L" 2 3 2 3 : 41/572631; : 4 Tj‘a - 4fic1 mM 7“; k A” ' L / 6mm GMm gwrm) 3 T1“ 473a 60mm) WW Comloiflkj WWLSS (50h+p{ane+> W ‘FanIOVx a? Examfle ~ with“? Odth 30-13 ‘E\\{P+{C ovBE-L qvoovd We «MK. E? ‘2 G400 km wx: 3000 L3 Penman : HOOkM ' 1,10pkm.) 4Qoo perigee m : 4.100 km . perigee Grove m<< Me Mafia! {HUS o“? ~e\\\' 56' 23 Y’ A: [€P+Qq+ 2E5] =' ):Hoo+ 4|oo+ 2%4063 km ’7 = L'fimo m. .1 A : i : _; GWME : Re (£3 (-E) (-E) (—E3 ._ 2 3 6 2 (O f: 3-mj Re : ~2xlO x7-3’x(g-4x10) : ~4.5‘x)0 J A [.8 we" (Energy 0? sJeui'L' M Nth}; lulkriki on—e‘! o4: 5JL‘ti4‘f '0‘)!“ Y‘l'O‘f +0 laUhC‘Q. a.“ Q E ~ 10...... A : -G\h{Y‘v Z flange : Iii-5x10 J Ew‘ewm T<2uiif£JK 1L1» {OIQC‘Q SqftHhée in ovLfib nofix‘dl/o; \5 "“ b. -. 8x10103’ A. L. Am ulcuf momcd‘om _%_____________ \(m‘n : Yo l+€ 50-1? Celebrating Newton T lze legacy and legend of Isaac Newton live on 300 years afler the pee/2mm of as masterpiece, Then ye who now on heavenly nectar fare, Come celebrate with me in song the name 0f Newton, to the Muses dear; for he Unlocked the hidden treasures of Truth: in Principal By STEFl WEISBURD ter stage during the Age of Reason and they inspired the French and American authors of new governments. “The New- tonian revolution . . . remains one of the So richly through his mind had Phoebus cast most profound revolutions in the history The radiance of his own divinity. Nearer the gods no mortal may approach — Edmund Halley‘s preface to Newton's Principia cience is a search for the essence of Severything, for the fundamental laws that govern the universe. If there is one person whose work embod» ies the spirit and remarkable products of this pursuit, it is lsaac Newton. His Phi- losophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Phi- losophy), commonly known as the Prin- cipia, may well be the most important document in the history of science. in many ways. the Principia is a blue- print for modern physical science. With it, Newton created a mathematical frame- work for physics and conceived basic laws of motion and of universal gravita- tion that unify a diverse array of phe- nomena both in the heavens and on earth. The revolutionary power of the Principia and other Newtonian works is felt to this day: His celestial mechanics guide the paths of satellites and space- craft, his reflecting telescope is enabling astronomers to study recently dis— covered supernovas, his numerical meth— ods are used in computers and his mathe- matics and approach to solving many physical problems remain as vital today as in his time. ' And the Principia has influenced not only science but Western culture in gen- eral. Newton‘s ideas fostered the develop- ment of social sciences, they played cen- JULY 4, 1987 of human thought," writes 1. Bernard Cohen in Revolution in Science (1985, The Belknap Press of the Harvard University Press). This year marks the 300th anniversary of the Principia’s publication. While Ein- stein‘s relativity theories and quantum mechanics have shown the limits of New- ton's work (applicable only to the mac— roscopic, slowly moving physical world), scientists today are as much in awe of PHILOSOPHI/E NATURALIS P R I N C I P I A M ATHE MATICA- Autore 7 S NEWTO N, Tmr. Coll. ClMalI. S“. Mamet-:0! Frail-(Tore Lunfiafln, 8c Socienris Regains Sodali. [MI’RIMATUR- S. P E P Y S, Rtg.Sar. PRESES. julu 5. [636. LONDINI, )ullu Souqu chm‘ at Typis jofcpbi Slrulrr. Prom: apud plurcs Bibliopulas. Alma MDCLXXXVII. Smithsonian Institution Libraries i The frontispiece of Newtonis Principia. Newton’s accomplishments as Edmund Halley and others were while Newton lived. To celebrate his genius, scientists and historians are gathering at a number of commemorative symposia planned for this year in Washington, D.C., Tel Aviv, Oxford, Holland and elsewhere. in addi- tion, the Smithsonian's National Museum of American History in Washington, DC, is hosting a special exhibit on Newton and the Principia. And in Britain. four commemorative stamps have been is- sued in Newton's honor. These activities, says physicist Frank A. Wilczek at the institute for Theoretical Physics in Santa Barbara. Calif., are “not only a celebration of Newton, but a cele- bration of [his] whole scientific world view and method that has led to such enormous insights" long after his death. istorians are fond of saying that HNewton was the culmination of the 17th—century scientific revolution. Newton‘s predecessors, such as Galileo, Kepler and Hooke. were moving away from the Aristotelian world view, in which the behavior of objects is dictated by the "qualities" they possess; Aristotelians believed, for example, that a stone fails because its “nature” necessitates that it move toward the center of the universe, or that planets travel in circular orbits because the circle is a heavenly form. in contrast. the emerging view during the scientific revolution was more clearly rooted in the underlying forces or laws that can be expressed mathematically Newton acknowledged that he stood “on the shoulders of Giants" who developed this approach. But, writes Paul Theer- man, curator of the Smithsonian exhibit, “Newton was no mere disciple; his genius 11 ...
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l29 - WGenexmj flawe‘awgf Wo‘holm Cot/A. LACxlc...

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