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l27 - Law 0&1 u a ¥ air-l In IQ‘B'T Mcm‘kam...

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Unformatted text preview: Law 0&1 u ; a - ¥ air-l In IQ‘B'T Mcm‘kam Poklisaecl Ru‘s work on +39 UH'lUcrsql jam) 0? vaw'k 'm 965 ”MafetmaiL'ch ~P~ri.v.r'ur_3.Flea 0‘? Wvd {\03 Mg “ WW fifxidc 'ufl *Q‘e unwev'ae qu rad) ever 0N“ Farxflc u.) i W a. 'Rnxfie "i“e‘aj‘ {5 J. {Ted-1&6 Fro few" lanai ‘l'o fee :TOJQcJF 09 +22 iv mm 35. e S Q‘Aé inocvatdfls fW‘h or :1)ch +0 ‘l'ee sonar: 0? fee clt'sk-amce he can E “C [Joueé kglkeeu’ <1 wade Lfikfioe u-‘AY‘CMOW‘UJ ostu iovxs ovtv' Re can uvics ox ximtole onicfima alescvlf'LiOw . Ancient CUE. muomexs veto niece! and cm'HemP'l‘eJ 4o ex‘olq'm Re. orJeflinws or; +84: movewerd' 09 +96 sun mu! Plahe‘l's $11M" +9.: MCkkwonJ 0? me SETS. - -m' 2+ '30 1Fviesm'ou 02 seasons ' wioc‘fc F W\ 0? me. Island‘s '40 “wicks 0'9 'I'ft 3L} belfqlke& Josw waltions we‘re (qwicJ 00““ = ‘ qccurcxie CQ‘QMAM‘S - 5h? ““95 ° Meriwbs 0? flame-{’5 «1919‘ l. Rifisgéoms gsm-cm cc) P acts (+21— 341 BC.) 'spaerkaj sita+iomrt3 eqr’l’a " RGQUCVJ 504685 move in CLYXZL’S 'ia'tqfslgt‘xul 0n <1 '50er SWTthCm "ee («MAR * SUV“ moow‘ Inland! «who on s‘ogmreb SKKQ <15 'l-c Mtg teat? fsov‘ioslfi- I Mb‘cmsi 'sovne. r‘mheks requn’ue 4o backamné 0'? stun squttl T‘Ck‘mcti‘ttAQ m0*iow. .35“ cvnk ‘3\QV\C'{‘S OLA “0+ (.1?qu +0 “(We Umevrm‘}. ‘ FLINA'; wade in BW'ER'L ness , Effictcksi Nana‘s move En cu Comte (deEWCVfi') ch amok emit civcotqv mc'rccvxs OJOH} {at oVLitfi 9f1f60 SHEET “x I East ' West Fig. The retrograde motion of Mars through the Gemini constellation during 1960 and early 1961. The position of the planet on the first of each moon is shown. The path has the shape of a loop because the planes in which the Earth and Mars revolve do not exactly coincide. ,1. Max em? ("3091)! 'Guxewli‘ucl a.“ +9( Greek mOYL- 'Eqfla t-euLvetl sas'kcwx - E‘Jtt‘bdts - lh'nt‘f P‘th‘S {ockci 4o mist}? t’A “\{he mi +€x BUM 'E‘Klotq't'ncql 151% Mass (“ELI/«16$. ‘COU‘CL Ft<4fcjtcrlL Q Pmi‘l‘r S 0? fialczhe'l'S. deferent upite Saturn \ epicycle The Ptolemaic system of the motion of planets (not to scale), put forward in about 150 AD. Each planet moves on a circular epi‘cycle and the center of each epioycle moves on a circular deferent. The centers of the epicycles of Mercury and Venus lie on a straight line connecting the Earth and the Sun. 3-Co‘o_evn'\cuf> (1413—1543) fROaACCQl new {rat-ow} O‘E Solar 3'63 cm. "Son is «51“ we NEWLY 'Ecvria owl Planets. revolve chi-00+ +9.9 .50“ m cch(es. "Eric Elf/ks 'lo mq‘tntaih uvu" rm circa) ox mellow rAccoochcl haJKN‘G/Ll} Lev OLSQN64 re£m3rm£e we'l‘iou Apparent path of Mars as seen from Earth. Orbit of Mars Orbit of §%/4; 8 Earth 3 5—: un ”mug The apparent retrograde motion of the planets on the basis of the Copernican heliocentric model. 218-5- 4. keelev gram—nae) -El1{P\-CC otkijrs -Moa.v\c10uecl C(V‘CUIQT OVLiI'S 'Ma‘bov qéuqmce in "fag ‘1Eeor oe lee'Favi mo'1‘t'on. “Qumvd’iececl fexe Precise daul‘cn o; TqacQo 312.9...» ("546 160!) 11A“ P1qvxc‘1‘5 mow ivx euif'hcai 01-10(1-5 wWQx +9“: mm 0:1 owz be 1%. Coca1 Pom 2.. 4'3) 7% V‘aJius Vcd'mr (Wotan 9mm '19“: ~50“ ‘1-0 mama Plane—1' smears on ech «was: in 9.341 “L'me irv'xwvaja. .979. -m :2 +2.. (”L-4.1 ...4 .e .. P/WJL .3 1'0“»! 10 1&9 ('01:? cc 1&9 scrub—made»! it's 03 169 511.11;ch OTBE'L- TABLE 14.2 Useful Planetary Data Distance Mean from E [10-" (i)] Body Mass (kg) Radius (:11) Period (s) Sun (m) r‘ 11:3 Mercury 3.13 X10” 2.43 X10° 7.60 X 10' 5.79 X 10” 2.97 Venus 4.38 X 10" 6.06 X 10‘ 1.94 X 10'r 1.03 X 10” 2.99 Earth 5.93 X 10“ 6.37 X10‘ 3.156 X H}-r 1.493 X10” 2.97 Mus 6.42 X10“ 3.37 X 10' 5.94 X 10" 2.23 X 10" 2.93 Jupiter 1.90 X 10rlr 6.99 X107 3.74 X10“ 7.73 X10" 2.97 Saturn 5.53 X 10“ 5.35 X10.r 9.35 X10n 1.43 X10" 2.99 Uranus 3.53 X 10" 2.33 X 10" 2.64 X 10' 2.37 X 10" 2.95 Neptune 1.03 X 10“ 2.21 x107 5.22 X 10" 4.50 X10" 2.99 Pluto ‘1 X 10” “'3 X10“ 7.32 X 10' 5.91X10" 2.96 Moon 7.36 X 10'1 1.74 X 10‘ — — _ Wzé Neujxovxtfs L353 02 fiflhliLM‘, . 2.84 wu—w '1’? I; 'Ws; PmAic‘tS Q‘qve masses m! and ma our? ‘59PCLVQJ‘CJ it)“ +9“ éis‘Lance Y‘ +9“; mdzn3k3tle 0P 19v: so“: is G = 6°57J~K 'O—IIN 'ml/htgl GTaVi‘laJ‘th ConS‘Lani‘. q “quan (3% E KPcfiMen“ - lnucvse :5 gave law 430ch ' Alma? «£TA<JT;VC ' Applas +0 au 0 '90“; chihg Wis ‘ HQ&$€EMQ‘R NEME. Nvaxdwfi W‘a £13ch in Vedov 30w“ f ._=~, _ GI A fit. _- My: LR TM --'-‘a F”. = {:O‘NQ on “N A“ *0 "‘3- The gravitational force on m1 due to m2 is F12 4: -7 Haw—Ex (flck‘on — Reac‘Lion (Pair) Grawi‘rccl'ioud 2&ciiql E33351?! in: 443m“! PTEV;OU'>\IB tea} «leg QQ ,{ {in PonemLM-J QVRV‘E associdrekl mm at diSPlacemeW‘ is. i?“ he Jim 0?- ‘l'ke «smith do“? Little TwiémeJ _ 'QNCQ (4‘3“‘1’3, +9“ “list- teme ' :Sniozaersfltgrljnfimetgsg above the earth's surface, the potential en- 1 AM : full-hit". '-'- ”S ‘Ekflié? TI Fmr Q quxt‘de m above, lee easel-{‘9'} sovfiqte C 'c Gr ' ' aph of the graVItational ut‘. _ui : 6 memg 4“ 7' G mem I" ‘L potential energy, U. versus rfor T ‘f a particle above the earth's 4‘ f , surface. The potential energy "‘ goes to zero as rapproaches ‘ug: -Gm¢m _L...i. U; ‘Qi' ‘9' QQM'U: 0Q ‘cteevu‘we Po'tiid‘ is QTBE¥TQV%. kc‘r 11X =0 (1+ CA- ‘—' 0-0 F(¢D\=O utfl: —GQO v>Re ‘C For most he Tufsh‘cks. mk anvil m1 ’ HUN ='- "' emit“; Prinqlmle 0C SS¥IF$EL(% 318-3 WC RDA +24!" +92 nek' (ea-d" on an 0193190!“ 09 amumiocv a? tomes F. [:2 Fit-- I I I is simfaisa Elven bid —->—=> _., —‘2 Flt": FIFFk+IF3+'- h "-Fi‘inci‘p‘e OB soferfOS’iItt'Qh. ”MM chU’C Re (act: («LQM UM ? Cons-Act +211? qukC£\€$_ anCQ 1 . Foul? cow'kn‘o-Jtcs CL “Levy“ “(VA 3 -— Gt Wk "11 Diagram of three interacting particles. Y 'Tae ‘L‘O'Ld ‘oé‘cwi‘kfl (xx-QT ovvf (Lu [acu'v‘s 09 Fax Yl‘td:a 31V!“ ['33 00 sum ukkq‘l 11 u‘a“\- (KB-L 1113 ’po{ew\.-d EVAN 0c ¢ '01! 39v?“ (:1 la; 'c‘ 894 ~‘aow1rcc\e 05?- W$S m ’ POINHAQQ wastes M omega M ‘ RCCknesS ‘t - Helms R " sepo‘wA-ton 45% Cew‘Ltr o? 50w“ 'tc recitals-1? Geometry for the calculation of the potential energy of a thin spherical shell and a particle. The thickness of the shell is t. Pnfx'ic‘c <11" point (P. COWfittltT ox. winch 0P- maitn'wl uoin éswslsta g We‘l‘sk {Jmf'k— 0% wax'ci 1‘3 '5.me s. Jis‘t-QMQQ 3 0m Nté "\Q o?- Tih [S R <18 J *P‘Cgkness {-5. "t" qua! A3 unlit/is is Rs‘m 9. Mass elm 0Q winch is Am: Lacie) - smegma .t, % mtttfi ' QNCMEWcNe (knit‘r‘t‘. W4 Volumfl cg Rama. Am 2 lWRl‘LgsinG cle SEE-lo flQ‘Po'Lele-{u( enevguk 0g +Qg win} our“! +91 Pav'k‘x'df m 1.5 cm: —GW\Q‘M : *- ”item R34: gin/1949 S S 7:) 010*“in +01%! PE {for 5Q£\l' neat-J “Lo in‘l‘einj't 5‘2st ovev tnjclvt 39.41“. 5‘5“!" *0 "\d‘t‘vd" 006?” ‘5 t‘hS‘I‘CCLJ cg 9. (‘quth UQT§QL§‘93_ 3L . $1 = rLD‘i-R ‘ JY‘R (039- (Lad) O'e Cosihcs) 25 é: 1..- 31“ R 'Sin 9 .du= — :LTc GmRJCS <18 \r Cast—L: ‘(5 R Ennis cushiée 0e SQW.“] 6:0 s=\r— R E3=fi s: Y+R rdR mum = §4u= —1fiGmRchS 35 \r V'R 1“- - 111* (41160ch (wR) 33-11 M -.: VS ..": (41TR2‘t\g '. 1k: —GmM (Y>R) Y‘ r; v——-——~1 M m 'Po'ltzwjrial Cine ‘LO Q 59¢“ 0‘1 ‘maSS m mikex Tacliué. R {s exaouuk 49¢ same as 4% 0? cu ivd'li‘tu mass M [occiaeé GEL We gemLc‘f. Foxr [acids Cd‘siée Jrae 39‘1“]. “Em: -cfl( 1: = —e_n_\1n 1: cm) cN (‘1 A’ 496d£ 51-2“ of" Ox so‘ic‘. SFQVQV‘Q [3 cu Smmdkiovx 0‘?- CK IQVYQQ \nOML-QY' o-fi ‘l'ew‘ Sa-ells. " 7er WLUCJVACOMJ 999:6} e? (1 ("rated lrk Cl£$¥f§k>d+§0h o-E mCOHcV' if m La w-Hc‘e is +2.4: same as Raf 09- a.) qu‘C/{e Fifi'khfi) £19in mass m [ocqfieé at +E: «er 0?— ‘l-gdz SIAM.” 5mm 9.943. C4152 III T<R YEnSLAe Sac“ be (“(45.51 'qulric‘e is {“3149 We Eva-e“ G = O '5: R—Y‘ e = i s. = Rw R-W‘ utr < M: ' ___S__"G“‘t RS- 3‘5 = *1.“GMRES[(RW\-LR—rfl V RY Y‘ - —C-l___w_\ (Mt Rktg) = - 613"] (MR) - R R po‘kn‘kial is Q cow‘s-{CLV‘i‘ eVQY‘Ywa-W‘C insrclf +63 Ska“ Foxme entail pav’t‘icke m. "Pt?“ 2 ~41 Ta“ = 0 (MR) Separation r (a) U9 as a function of r Separation r (b) F as a function of r Potential energy and gravitational attraction of a particle m by a spherical shell of mass M and radius R, where r is the distance from the center of the shell l: —‘ GmM 'r {1. 370/1? (LA ‘lo COUFIQ M +R€ sugrawxiou .0va i' Rah-kg. us'xY‘f wesisAs fiwiue 1“)ch *‘Qmi i “it: "K516 Hookers 9:01“) ROY q ‘LMS‘QJ !- inQ. IS «1%? of: +u3i$+ - K 1'5 'w 121“ka 0P- maxwid 3i a“; M 4m. éi ! T?- QTP PONOJ 'COT cu 4oniona.’ :' K Pm‘lu‘om. ii I: “£1 Mmtnk a? inertial 0-? ‘ T wages on 49.4; v04- G‘-' 2" Rog'tcfiu'Oh o? mas-0r $rom {Jam mi wow - " —' Wm («kn *orues. F5, 3 11 GM“ To+al (lcc‘cA‘cOh Cw reversal JJrrchom 06 4mg”. m : .OIS h I = lo 0m . ‘- m Y‘bt‘thquce mirrov —=; wan] K = 8.5m“I Urn/{43 .. AS = L. 9 G = 5.67.1 no" ”Ma/k2" l w lo'mih, As = 4£L GmM Kv" u —_ 4 x O-IOL x 6671 no- x .0th 1.50 ‘3 -5 x :o‘qx gows)“ L: ”7 M L-STM >4.6Z m5) -- m cm “'— ...
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