¨kyF®k yAkym Classical Mechanics
(Introduction) Tdq 1
Tr Anh .As± Tr :An Xy ¨t Tywy Ty`ybW r¡ w\ y bt ¨l§ Amy ¤AnF . , wk Tr ,r ªwqs ,Ty An¶Ak .Tr AbF rysf dh As³ Ah`R¤ ¨t A§r\nl ¨ §CAt CwWt :As T`C Y Cwm @¡ ysq km§ §dq rO` Trtqm ryFAft LAnnF :(free fall) r ªwqs • §d yCA ¨lyA wlyA Am T§A Y (TyAwy CAS ) . wk Tr TA` d` A Y TyÐAl wy wA ¨ §CAt CwWt A`nF :(Newton’s laws of motion) wyn Tr y w • , Az :¨ Tlmtm ¤ ,y wq £@¡ TAy} Ahyl dmt` ¨t y¡Afml .wq ¤ ,Tr Tym ,TAW` , rf T}A ºASf rJ ¤ }w Artqm lt xCdnF :(Astronomy) wk Tr • .TyÐAl wy wA LAnnF Ð d` . wk Tr y¡Afm {` Yl AnAmt¡ OnyF :(Beyond Newton) wy d` A • ,_Af³ y w : TykyF®k yAkym ¨ CwV ¨t TyFAF± .Tynq TKAn © AyA ¤ AyWF AnRr wkyF . wmk Anf`F - ¤AnF .(electromagnetism) TysVAn¤rhk w¡ rb± ¶A .wRwm @h ®A Cw PO -^ :¨¤rtk³ wm fO thm ¹CAql km§ https://plato.stanford.edu/contents.html .¨l§ Amy hn {`b rÐ tyF .ºAml` ¤ TfF®f {` Am Yl ®V²
(Free Fall) r ªwqs 2
.TWs |C± Aqt³ Yl dmt` r ªwqsl Y¤± rysft A © Y At ¯¤ (natural) Ty`ybV Tr ¨¡ fF Y Yl ªwqsA ¨ w |C± T§¤r C AA} d`§ ÐAs rysft @¡ k .rysf .(1) ®ym b A rq x As rq ¨ w A®W ,Ð b |C± T§¤r TyAk §r³ TfF®f LA dq(1) .hnym z§z`t T ± {` wd ¤ , ®ym b
1 §dqt T`C± r}An` T§r\ Yl (Aristotle 384-322 BC) wWFC dmt dw ¨t As± w¡ @ d¶As Aqt³ A .r ªwqsl rysf ,(Air) º wh ,(Water) ºAm :(3)r}An T`C §z ¨¡ (Earth) (2)|C± Yl TyFAF³ r}An` £@h wWFC YW .(Earth) Trt ¤ |C± ¤ ,(Fire) CAn :Tyr P¶AO Universe) wk zr £A ¨ AWqs§ Amhl` ºAm ¤ Trt T`ybV • .(Earth center) |C± zr ¢sf w¡ ©@ (center
.(Heaven) ºAms w d`O§ Amhl` CAn ¤ º wh T`ybV Aqm ¨ • sA .Ahbyr ¨ TyFAF± r}An` Tbsn As° Ty`ybW Tr l`t Hk` ¤ TbA ¨¡ Trt ¤ ºAm Tbs A |C± zr w Xqs§ AhE¤ FAnt As± ªwqF TrF wWFC dqt , @¡ Y TAR .y} .Tfyf As± rF Xqs Tlyq As± :(weight) AJAqn \`m .r ªwqsl wWFC r\ HF ymlsm AAR Hm r@ .d` Amy Tsl Ah` An wkyF ¨t wk Tr w Cwmt A rq ¨ w ,(Abu al-Fath Khazini) ¨EA tf w Am Aqm @¡ ¨ gravitational potential) TyÐAl TnAk TAW whf CwV y ,rK © A Am .A¡zr TAsm Aysk FAnt |C± TyÐA rt ¤ ,(energy .(weight) q ¤ (mass) Tltk y zyymt ¨ Abs A ¢ ryyt ¢Am ¤ (Galileo Galilei 1564-1642) ¨lyA wylyA CA\t Anyl A Ð y rk ¢yC dt ¨t CwWF± C .r ªwqs Ay An r\ TrF Ab³ (Leaning Tower of Piza) ¶Am zy r yflt yE¤ Yl` .Ð dt ¯ Twtkm ¢Am ¯ , EwA l`t ¯ r ªwqs w¤ Ab³ (thought experiment) Tylq` Trt wylyA m`tF ,Hk` r s r ªwqs xCd An y .¨ µA wWFC T§r\ ¨ {An Atyt An¡ .Tltk mh ySq ytVwr yflt yE¤ Ð y r :r ªwqsl wWFC T§r\ s Trt £@h Atnkm .rb± w¡ ¢E¤ ± ,¯¤ k s Xqs§ ,Th • .± rk ,q± rk Xqs ,«r Th • T}® A .T·VA Ahn AnqlW ¨t T§r\n Yl y R w {Ant @¡ .« As± Ew l`t ¯ r ªwqs TrF » ¨¡ wylyA Tymt Am dtl Trt m`tF d wylyA A Ð A w wC¥m lt A ¢ dqt`§ ¨t (inclined surface) ¶Am ©wtsm Tr Anh .¢y }w r ªwqs TrF ryy ¶Am ©wtsm d tF º C¤ dh A .Ah xAy ¯ r@t § . ªwqs d xAy `§ Am W Ahl` ¤ Yl ®V³ km§ Awl`m d§zm .TyA T Ð k @ z : Atk ¨ ¤± Of dn |C± CwOt Annkmy .T§wA ªAq ¨ Anwhf §r³ dn |C± whf lt §(2) .©w Ah® TyRC± rk Ah Yl §r³ .(Chemisty) ºAymyk Cw ¨ yOft º¨K T§r\n £@h w`nF(3)
2 http://www.arvindguptatoys.com/arvindgupta/ten-beautiful-experiments.pdf .r ªwqsl rysf Yl On wy Am r\tn Anyl y` k
(Newton’s Laws of Motion) Trl wy y w 3 rb TfF® ¤ yy¶A§zy d wh rA\ At ¨¡ Trl wy y w ¨ AFAbt³ lt ¤ TqyK TOq £@¡ w {` ¨ Qw b . §CAt Ansf r@ Aw ,A¡E¤A yy¶A§zyf Yl A ¨t Aw`O ¤ y¡Afm . §CAtl ArbF ¢yw dh Tr ¹ Abm
(The Principles) ¹ Abm 1.3
¤ ,¢tfyR¤ wA k .Trl y w T® (Newton 1642-1726) wy R¤ yqr y wq £@¡ QwO -¨l§ Amy- |r`nF .TlAkt Twm kK§ k .¢yn`§ A ¤ Ahn Tym¡ w Xys MAqn Ð
(Principle of Inertia) TAW` wA 1.1.3 :T}A (frames) A` An r`§ ¢± TAW` wAq wyn ¤± wAq Yms§ .(Inertial frames) TyAW` A`m (Tm\tn Tyqts Tr ¤ wkF) ¢A Yl s © Yqb§ ,¨AW l` ¨» «.¨CA r¥ ¢yl r¥§
“In an inertial frame, an object either remains at rest or continues to move at a constant velocity −→v , unless acted upon by a force.” ¤A Adn Annk .TyAW` A`m £@¡ ¨ kK Hf @ ºA§zyf y wq (time) zl A}A Awhf lWt Ah ^® TyAW` A`m £@¡ Ty¡A h r¡AZ © Xb r ¯ ¤ Ahsfn ww TyAW` A`mA .(space) ºASf ¤ yqlW yAy Akm ¤ Az wy rbt ,A`m £@h CAV ºAW³ .Ty¶A§zy ¤ z whf CwW LAn Adn TWqn £@¡ Y w`nF .(absolute entities) .¨l§ Amy -(vacuum) rf T}A- ºASf perpetual) Tb¶ d Tr w¡ ¤ ¯ r h whf Yl wAq @¡ ©wt§ Tr wn @¡ .Tm\tnm Tmyqtsm Tr ¨ Tlmtm ¤ (motion -d` Amy Ð «rnF Am- CwO` r Yl xAbt ¤ Amt¡ Rw A
(The Second Law) ¨A wAq 2.1.3 .yAkyml ¨FAF± wAq ¨A dbm ¨W`§
3 −→ Tlt s Yl r¥m F TyCA «wq wm ©¤As§ ,¨AW l` ¨» «.−→a CAst rR m s @¡ −→ “In an inertial frame, the vector sum of external forces “F ” on an object is equal to the mass “m” of that object multiplied by its acceleration “−→a ””.
X −→ d F = m · −→a = −→p . dt :¨¡ }± TAyO ¯ ¯¤ d r± ¨¡ wAql TAyO £@¡ C −→ C dq s Yl r¥m F TyCA «wq wm ©¤As§ ,¨AW l` ¨» «.zl TbsnA s @¡ (momentum) Tr Tym ry k ,−→v ¢trF rR m s Tlt Ah Yl A Tr Tym r` .yAkyml (Hamiltonian formulation) ¨wtlyAh }w m`ts§ ± §r`t ¤ wq :¨¡ wAq @¡ ¨ TyFAF± y¡Afm St§ TAyO £@¡ ® .Tr Tym wAq CAbt ,(mathematical formulas) TyRA§r TyO Y r\nA ,Annkm§ ¨FAF± bs A r\n £@¡ k .¨A wAq T}A TA ¤± ,r@ AnflF Am .(¤± wAq ) }w @¡ ¢¶AW ¤ ¤± wAq TAyO .TyAW` A`ml §r` ºAW w¡ ¤± wAq dh
(The Third Law) A wAq 3.1.3 .(equilibrium) E w wA A wAq CAbt km§ « .£A ³ ¨ ¢sA`§ ¤ dK ¨ ¢§¤As§ ` C ` k »
“When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in the direction on the first body.” isolated) T¤z`m TykyAkym m TF C dn AyFAF C¤ wAq @¡ `l§ Yl r¥ ¯ ¨t m ¨¡ T¤z`m TykyAkym mA .(mechanical systems .{`b AhS` Yl r ¥ Ah Awk lt k ,¨CA XFw Ahyl r¥§ ¯ ¤ m ºAntF m £@¡ A§ km§ ¯ £® A wAq w¤ ¤db .(trivial systems) Tym¡± Tm§d` A` ¤ wslyf d§ Yl wAq @¡ TAyO ¯¤Am ¤ «d A « AS w r¥ w k » :A y .(Avempace 1095-1138) TA lsm d§ ¢nk .(“there is always a reaction force for every force exerted”) .`fl A§¤As `f C A
4 (Force) wq 2.3 (Aristotle 384-322 BC) wWFC Y (external force) TyCA wq lWO w`§ :An} T® Y «wq s ©@ As± T`ybW l`t ¨t «wq ¨¡ ¤ :(Natural Forces) Ty`ybW «wq • T§¤Ams r± Tr ¤ (r ªwqs rq AV) r ªwqsA .(TysmK Twmm rq AV) (Heavenly Bodies) An¶Ak T`An «wq ¨¡ ¤ :(Spontaneous Forces) Ty¶Aqlt «wq • .(Living Orgamisms) Ty .«r± «wq ym ¨¡¤ :(External Forces) TyCA «wq • Ty¶Aqlt ¤ Ty`ybW «wq CAbt kmy .Tymst bF ysqt @¡ Ayl rh\§ .TyCA «wq Hk ,A º¨J T`A Ah± Tyl «w :(4)TyCA wq ryt ¨At }w wWFC YW −→ Aysk ¤F TyCA wq dJ A§ rV TbFAtn −→v s TrF wk » .«ρ XFw TA ¤ m s E¤
“The speed “−→v ” at which an object moves is proportional to the amount of −→ force exerted on it “F ” and inversly proportional to its weight “m” and the density of medium “ρ” through which it moves.” :¨At kK Yl wWFC± Tr wA TAy} km§ −→ m F = · −→v ρ :§r wAq TAy} ¨ Tbk rm ºAW± XC An`Fw ¤ ¨ Aqy z xAy k§ :(Time Measurement) z xAy • AV ,rytA ¢WC ©@ zl wWFC §r` Tl yW E A ¤ .wWFC .Awl`m d§zm zA T}A rqf As± Tr wWFC ^¯ :(Friction or Resistance) Akt³ • XC .s kJ @ ¤ ¢y rt ©@ (ºAm ¤ º wh ) XFwA l`t rysf d§ ¢nk ,(5)XFw TA ryt Y¤± T\®m wWFC CAq§ wWFC Cr ,ry± TyAkJ³ Yl ltl .TyA T\®ml Yl rOt @¡ h km§ .¢sf kK Ð As Yl wq ry w w¤ ¨¡ T§d r\n .¢t`ybV ºz s kJ rbt wWFC .¢y rt§ ©@ XFw ¤ s y Akt
.TyA`K r§ Aqm ¤d wAq @h wWFC TAy} wk km§(4) {` dqt`§ .Aqy Af§r` AhW`§ ¢ ¯ ¢ny w ¨ XFw TA m`tF wWFC C(5) .XFw (viscosity) T¤z dO ¢ yC¥m
5 ºAyJ±A A¡A§ yCAq ¢wA ¶At LAn ¤ wWFC P J Pmqt Aw : wAq dqn TlyFw Tl·F rV Annkm§ . @ T¤r`m ?Tny` TynE dm wq r¥ Adn d§ ÐA - ?(vacuum) rf ¨ d§ ÐA - y AAm wt§ s -AnwA A®W- tnts hs ¶ @q Tr TyAkJ dW} ¢nk wWFC w @¡ A .wq ry wt§ |rt ,TyAkJ³ £@¡ .wq ry ºAht C rmts ¨t (projectiles) xAmt³A r¥ wqA .ryt yWts ¨k XFw At wq wWFC (ºAm ¤) º wh §rV Ahlq t§ ¤ ,A Ams s ¤ d Adn (contact) .Tf§@q TA ¨ £@¡ ¨ lO§ ¯ AnwA ± (dilemma) TlS` A ¨A ¥s An`S§ XF¤ w¤ Ty z As rt³ TyAkJ³ Hf AO .(ρ = 0) TA §@¡ rf Pl t§ wWFC Cr .r¥ wq yWts ¨k £@h w`nF .(horror vacui) ®} ww ry ¢y TbsnA rfA .yAkJ³ . rf An§d dn TWqn Archimedes) xdymC A` Y TyCA wq TyRA§C TAy} ¤ w` @¡ wq§ .(Archimedes law of buoyancy) xdymC T` ¨¡¤ (287-212 BC .« zm ºAm q FAnt wq H§ ºAm ¨ Cwm s » wAq s ¤ z xAy ¯ TAn} dq wWFC wA wy rh\ d ¤ wm TA §r`t (yy¶Aymyk T}A) ºAml` Amt¡ Ð Yl E .Aht ry A l` Yf ©@ (Avempace 1095-1138) TA A` Anh .AhAs wA {qn (1080-1164) © db ¢l Tb¡ £r}A` A .XFw TAk wq Trs |w (acceleration) CAst FAnt wq A y wWFC dJC A .z Trs ry C dq ¢ Yl CAst r ¤ .(speed) y HA`m £A ³ ¨ Tr wA Y r\nA (Averroes 1126-1198) TA ryyt E® m` C dq Ah Yl Ahr y, wq x Ayq ¢lm`tF Anyl A ¢ ¯ wmlsm ºAml` ¢y ¡Ð A T} C ¤ .A s Tyr .¨A ¢wAq Tqyd TyRA§r TyO Tr`m wy CA\t Amh Awhf LAn Aw ,TAW`A Xb rm ¨At wRwm Y C¤rm b :¨At ¥sA ºd wyn ¨A wAq ¨ «?yAkym ¨ (£d ©@ ) (mass) Tltk y¡Af d » Tylq Tltk ¤ (inertial mass) TyAW` Tltk : Awhf w¡ ¢yl CA`tm w , wyn ¨A wAq ¨ rh\ ¨t ¨¡ TyAW` TltkA .(gravitational mass) wd §@ ¶ ¤± ºAml` ¤ .TyÐA wq rt ¨t ¨h Tylq Tltk A ªwqs TrF Am ¢nk .(Averroes 1126-1198) dJC TyAW` Tltk -Trl ¨A wAq Yl Amt- Q® tF Ankmy ,TltkA l`t ¯ r CAyt At§¤Ast Amhl` An`Fw ¤ . AtbFAnt Tylq Tltk ¤ TyAW` Tltk :A¤rW Yqb§ ©@ ¦Ast k . dwl FAn «?T`ybW Hf Tylq Tltk ¤ TyAW` Tltkl ¡» .(general relativity) TA` Tybsn A§d dn ¥s @¡ Yl TA³ LAnnF
6 (Momentum) Tr Tym 3.3 Yl ©wt§ ¢ ^® wyn Trl ¤± wAq Y `mt r\n Adn .Tb¶ d Tm\tnm Tmyqtsm Tr ¤ ,¨AW` l`m ,TAW` :y¡Af T® Tr T}A TA m ¨t Tm\tnm Tmyqtsm Tr ¨ ¯¤ r\nnF .Tr Tym TKAnm AntlC A wqtF .Tb¶ d
(Inclination) ym 1.3.3
.(rest) wks ¤ (movement) Tr y A§r¡w Ar An¡ §r³ dqt ¢fA Amny As° (natural state) Ty`ybW TA w¡ wks wWFC rbt As° Ty`ybW TA dqt y (Lucritius 99-55 BC) (6)xwyt§rw ©r Y rJAb ¥ r\n £@¡ C .(7)TtA TrF Ð Tr CAb ¨¡ ¨ Y¤ wW rbt`§ Tb¶ Tr w¤ TyAk wb ¯ ,CAk± ¨ Cw ?Tb¶ d Tr T§C rmtF mS ¨t Ty}A ¨¡ A k .yO £A ³ Tr A A·yJ ¢bK Tr xCd -Ty}A £@¡ rk §wkt- Annkm§ .¶ @q Tr :rmtst T§r¡AZ w Yl dmt` ¯ Tr .Tb¶ d ,Tyl A`nq ¶ @q Tr wWFC rysf k§ ,AqAF AnflF Am £@¡ rJ w` C §@ TfF®f y . rf ¨l t Y A ¢ T}A xwwwly rt .(John Philoponus 490-570) xwwwly w Tr ± XFw rV w ry q bs Hy Tf§@q Tr C rmtF ¢nk .Ah C A dn (inclination/motive power) y A¡AmF Ty}A stk Tf§@q .Ahfw Y © ¥§ Am Ty}A £@¡ Ay§Cd dqf Tf§@q dqt . CAt Yl §dmt` A¡r§wW ¤ xwwwly rk @ wmlsm A ¢ybJ db Y Pl ©@ (avicenna 980-1037) AnyF Am ybF Yl r@ . wyn TAW` dbm w ¢yl r¥ A £A ³ Hf ¨ ¢tr rtm s } w§» .«TyCA
“A body moves perpetually unless an external force stops it or changes its direction of motion”. perpetual) Tb¶ d Tr TyAk w\¯ §@ ¶ ¤± @h AnyF A Am .Ak TAW` db Yl wOl ¨AW` l`m «wF ¢Oqn§ .(motion rR }A Ah Yl (momentum) (8)Tr Tym §r` ¨ bs ¢ A Tr Tym -xwwwly Hk- AnyF dqt .¢trF ¨ s Tlt ,£® dbm R ¤ w¡ Amk .Ahsf ºAql ¨ft ¯ ¤ TZwf Tym ¨¡ .TyCA w ryt Tr Tym db AnyF XC
.(Epicurus 341-270 BC) Cwqy Am r d wk§ km§(6) .Tm\tn Tr © ¤ Tmyqtsm Tr w¡ wOqm A d§dtA r`§ ¯(7) .Tr Tym d xwwwlyf ym lWO AnyF m`tF(8)
7 Impetus z 2.3.3 Yl Tynb Tb¶ d Tr ¤ Tr Tym yyC¤± A` A§ d A (Jean Buridan 1295-1363) d§Cw w YmF .AnyF ¤ xwwwly Am ¤ .(Impetus) z :wq ¢yl ryt d` s Ahbstk§ ¨t Ty}A rbt`§ .¢sf ºAql dbt§ ¯ z rbt y ©r AnyF d§Cw d ¨ ArtK§ ywhfm ®k (momentum) Tr Tym whf lF z TA ºAntF _wf Am¡® ¤ ,Trs ¤ Tltk Yl dmt`§ y P¶AO CAb zA :ywhfm y ©r¡w r dw§ ¢nk .TyCA w ry vectorial) ¨A`J C dq ¨¡ ¨t Tr Tym Hk (scalar quantity) ¨mlF C dq ¨t Tr Tym Hk (speed) Trs A`J Tl§wW l`t§ zA .(quantity .Trs A`K l`t z §r` A®W .(9) wk Tr rysft z d§Cw m`tF Tmyqtsm ytr rysf km§ ¨r r¥ Ay ¨ ¢ZAf ¤ Giambattista) ¨t§dyny Atsy AbAy Y Sf w`§ .ytm\tnm T§r¶ d ¤ km§ ¨t Ar rO ¤ r\n £@¡ yOt (Benedetti 1530-1590 :Tm\tnm Tmyqtsm Tr Y zA A¡rysf w ry §rV ¢bst E ry © A ys ©± Ty @ Tr » «.Tynn ry Tmyqts Tr ¨¡ TyCA “. . . [Any] portion of corporeal matter which moves by itself when an impetus has been impressed on it by any external motive force has a natural tendency to move on a rectilinear, not a curved, path.”. Ab³ Am (sling) ®qm ¤ T@ m ¨ r Tr ¨t§dyny m`tF Y¤± ¯¤Am Yl z T§r\ r .T§rO Tr ¨¡ T§r¶ d Tr .¨l§ Amy Ð AS` «rnF .yAkym y w TAyO
(Impetus Dynamics) ¨mz yAn§d 3.3.3 yy¶A§zyf ¯ yAn§dl wWFC T§r\ ¨ P¶Aq d CwhZ C º r CAb Y¤± ¯¤Am A .Ayl Ahn ¨l tl §d`ts wwk§ ¢ r\ C- d§Cw A ,Am ybF Yl .T§r\n £@h Tylym Aylm Tr ¤ wks CAbt ¨ ©r wWFC rVAK§ -Tf§@q Tr Tflt m AbF± ¡ A AhA} ¨t z T§r\ k .A§r¡w yflt y·yJ d ¤ Y z T§r\ dq .yAn§dl wWFC T§r\ ¤ Y ¨t Tr ¨¡ ¤ ¯ ºA§zyf §CA ¨ (thought experiment) T§rkf CAt ¡ pendulum) x wn Tr T w Trt £@¡ A .(The tunnel experiment) fn .yAkym A Y wwl (oscillatory motion) T§E zt¡³ Tr ¤ (motion r rysf ºAW³ T¤Am z T§r\ A§ d A ,AqAF AnflF Am :§dbm ¨ P lt T§r\n £@¡ CwW .¶ @q Tr
sy wk Tr A @ d¶As Aqt³ r@ .Tm\tnm T§r¶ d Tr ©(9) .w © At
8 .ry± @¡ E A§E Y © ¥ wkF TA ¨ s Yl w ry • .TyCA w ry ¯ ryt§ ¯ z Tym • :¤rWm ¦Ast k «? @ yAkym d¶A Y d§d z T§r\ AR ÐA» Y Trt rk sn Annkm§ .¦Ast @h TA fn Tr A ¤ .Trt A Tlr ¨ A¡ry £A ry T`ybW ¨ w A§ T¤A @ Aqt³ A .Ty}A £@¡ q Ah± |C± TyÐA Yl CAyt³ ¤ |C± zr w ªwqsl Ah`d ¨t As± T`ybV w¡ TyÐA bF @h TbsnA y rZAnt ytWq ¨ An .As± ¢y @§ |C± zr ¨k .ysA`t y¡A ¨ TyÐA w ry wkyF ,(antipodal) zrm (10)|C± zrm rm§ f rf Anyl wt§ Trt £@h Ayq kmt .Tymst bF ©@ y` Af C Yl wkF TA ¨ s ` ¨ fn Tr mt £@¡ Ah`wt Annkm§ ¨t ¶Atn ¨¡A .fn @¡ ¨ Xqs§ |C± WF ?Trt dn Ay¶Ah Tr wt§ s ,wWFC T§r\ Yl Admt • T§r\ rtK T§r\ © Anlm`tF ¤ .|C± zr Y ¢w}¤ .Ahsf Tytn Y }wt ¹ Abm ¨ wWFC ¤ s ªwqF dn .AAm Tflt Tyt z T§r\ ¨W` Aqm ¨ • lb Yt w C¤r ¢mE Tym z ,|C± zr ¢wl b ¢sf ºAql dbt§ ¯ z ± .|C± zr dn «wOq Ahtmy k .|C± zr Y w}w d` rmts wt ¯ s Tr Y © ¥§ Am Tr £A Hk w¡ rm £@¡ TyÐA ry £A ± ¤ TyÐA w¡ z Tym } ± ¤ .A·yK A·yJ z Tym db Yt Tr wt§ ¯ s ,z db bF ¨¡ Ahsf TyÐA ,|C± «r± Th ¨ k ,¢n d ©@ Af C³ Hf Yl wk§ CAk± Hf Am`tF .T§ db Ty`Rw ThAK Ty`R¤ Y Ady`§ Am Yl ytWq y AA§ ¤ AA¡Ð T§E zt¡ wk s Tr Y Pl .A¡zrm TbsnA y rZAnt k |C± WF Af C³ Hf :wylyA TyAt Twqm ¨ Tytn £@¡ Py l km§ Y ¢ A³ TyA z Tym A Af C ¢VwqF ºAn s stk§ » « .Af C³ Hf
“The heavy falling body acquires sufficient impetus [in falling from a given height] to carry it back to an equal height”. spherically) ©¤r rZAn ¤Ð TyRC± TyÐA q |rtf Trt £@¡ ^¯(10) Ð l` Annk ,TyÐA bF w¡ |C± zr Arbt Tqq Ty}A £@¡ .(symmetric TAsmA l`t§ § Tltk £@¡ §Ew ¨n`§ @¡ .T§ÐA bF ¨¡ |C± Tlt ± y} ry .Xq |C± zr
9 Yl Amt fn Trt T`wtm ¶Atn y AR ¤ Ar An¡ C ,Ay¶Ah Ahn ¨l t d ¤ .Trt º r km§ ¯ ¢ ¯ Tlm`tsm T§r\n rbt .¨At kKA (pendulum) x wn Tr rK Ah¶At lm`tF dw y T§¤Ams Tbq qF Ydt§ §wV b ªwr zthm s ryk r} |C± rW ± .Am R AF w k kKy (fixed stars) TtA wn r\n µ km§ .Tmyqts x wn r Tr CAbt km§ ,b wV b Twkt ¨wk x wn rO Tlm ¢ Yl © A` x wn Y Otn w¡ |C± zr ¤ ,fn ¯ |C± w rt Tlt ¤ ry} Tym z :T§E zt¡ Tr © rysft rkf Hf ybW .(11)Tr r zt Td`n bOt PAnt Ah ¤CÐ Ot wks A®W z .y ¤ @k¡ ¤ «r
(momentum) Tr Tym 4.3.3 ¢t§r\ ºAn ¨ z Am`tF (Ren´eDescartes 1596–1650) CAk§ ¢yn§C ¤A :(assumptions) yR rt³ lWA .yAkyml .Amys wk wk • .r ys dW} Ð ¯ (Tr ¤ wkF) ¢A Yl Yqb§ ys • ¨FAF dbm (conservation of impetus) z _Af db CAk§ R¤ d` A .d AK A Ahy }w ¨t T§r\n k .yAkyml Christopher) C rwts§r ,(John Wallis 1616-1703) Hy ¤ w Ð (Christiaan Huygens 1629-1695) Hnw¡ Ayts§r ¤ ,(Wren 1632-1723 :(13)§dbm w`R¤ y ,(elastic collision) (12)Trm A AOt Ts . AOt d` ¤ b (total momentum) Tylk Tr Tym ryt ¯ • . AOt d` ¤ b (total kinetic energy) Tylk Tyr TAW ryt ¯ • z w ¨ Tr Tym ¤ z y rf mk§ ,AqAF AnflF Am Ty¶A§zyf ¶Atn k .TyA`J Tym ¨¡ ¨t Tr Tym Hk TymlF Tym ¨ ¨¶A§zy C¤ © z `l§ ¯ w ¨f .«wO Tym¡ Ð rf @h Am T§E zt¡³ Tr rysf ¨ z A rsf y ,k .yAkym .(conservation of energy) TAW _Af l`t§ w ?x wn Tr Ahy
(Inertia) TAW` 4.3 :y¡Af d dOq An (inertia) TAW` lkt Adn ,AqAF AnflF Am T§d r\n rbt` .x wn Tr T§d r\n AAm lt r\n £@¡ ^¯(11) T§E zt¡³ Tr rbt` ¨t z T§r\ Hk ,fF Y Yl wk T§E zt¡³ Tr .CAsy Y ymy TybA Tr ¨¡ .(inelastic collision) Tr ry A AOt AS§ Hy ¤ xC w ¨(12) .Tyr TAW §r` (Gottfried Leibniz 1646-1716) ztnb§¯ d§rf w rt(13)
10 ryyt ¨¶A§zy s © T¤Aq Ah Yl T§ db ¨ (inertia) TAW` r • Tr ¤ (inertial mass) TyAW` Tltk Am`tF km§ .Tyr ¢tA .Ð }w (uniform rectilinear motion) Tm\tnm Tmyqtsm (frames) A`m ¥Ak Yl Pn§ ©@ ¤ (Principle of inertia) TAW` db • .{`b AhS`b TbsnA TtA Trs rt ¨t (Galileo) wylyA A .TyA TWqn Yqbt Y¤± TWqn And dq Tm\tnm T§r¶ d Trl TbsnA ¢A} ¢ C ¥Akt @¡ T\® ¨ Abs ¥s @¡ Yl TA² ?Ð º C¤ bs w¡ A k .(uniform circular motion) y}Aft ¨ wd ¤d -|C± T}A- wk Tr dt § .@ TlA rq PO nF An± A wkt T§¤Ams r± wWFC rbt :(Aristotle) wWFC • dqt .(Ether) (14)ry± A¡AmF ryytl TlA ry ¤ Ah E¤ ¯ TyA ,Tm\tn Tr ¨¡ -TyA Ahw- T§¤Ams r± Tr wWFC .Tm\tn T§r¶ Tr ¨¡ Tr dq T§C¤ Ah± ¤ Twmm zr ¨¡ HmK yrw rbt :(Copernicus) yrw • Tr CAbt km§ ¤ .Ahw C¤d |C± Ahy Am wk ¤ TysmK .(15)Tm\tn T§r¶ Tr |C± @¡ ¢fw Yn . wk Tr yrw A\ ©dAs wylyA A .(telescope) CA\nm Am`tF Tyklf ¢ A\® Yl Amt A Am TyA sy wk ¨n`§ Am rmq WF Yl Ab An¡ • .dqt`§ ¨n`§ Am (Jupiter) ©rtKm w w C¤d CAm T`C w¤ • .«r± wk lt ¯ |C± w C¤d§ ¢ ¨n`§ Am rmq r Hfn (Venus) r¡z w rm§ • .HmK t¡ ?AhWF Yl Tr A®W |C± Tr b yWts ¡ k Tr ym` Yl Amt ,wylyA dqt .Ahsf w |C± Tr wylyA : ,rmq Tr ¤ z T§r\ ®m`ts x wn } w§ |C± zr A¡zr Tm\tn T§r¶ Tr ¨ rt§ s ©» .«TyCA w ¢yl r¥ A ¢tr
“all external impediments removed, a heavy body on a spherical surface concentric with the earth will maintain itself in that state in which it has been; if placed in movement towards the west (for example), it will maintain itself in that movement”. . Am £@¡ Y (Plato) wV® £ÐAtF m dq(14) . @ T\®m T ¤d ¨ ± Yl(15)
11 } wtF Ah , ¢tbst E Tyt TnyfF r ,wylyA TbsnAb .w © Ahyl r¥ A w ¤d |C± w Tm\tnm T§r¶ d Ahtr }w ,Tnyfs r T§rk Tr Am`tF ¤ Tytn £@¡ A®W A wkF ¤ Tr ¨ Tnyfs A Ð A Tr` TAtF Tyt Y wylyA .Tm\tnm T§r¶ d Tr lkt§ A ¢nk .TyCA T\® m`ts TAW` db ¨ rk ¤ Aqm @¡ ¨ r@ An Cd§ TlJA ¯¤A d` .(Isaac Beeckman 1588-1637) Amky AF w¡ yy¤C¤± perpetual) Tb¶ d Trl AbbF rbt`§ A ©@ (impetus) z T`ybV hf :¨At ¦Ast rV ,(motion «?¨CA ry k§ A Tr s wt§ ÐAm» ¨¡ -Ahsf Tr ¯- Tr ¨ ryt AtntF³ Y ¥s @¡ £ A .rysf Y At ¨t
(Vacuum) rf 5.3 rbt .dq @n MAq £ w¤ TyAk ¤ (vacuum) rf whf A (Leucippus 5th century BC) xwbywy A ,(atomism) T§C@ T§r\n ¤d§¥ Tr ¨FAF ¢± ww rf (Democritus 460-370 BC) ª rqm§ ¤ Aristotle) wWFC £@yml ¤ (Plato 427-423 BC) wV® ©r hfA . C@ ,J £ w¤ `§ wV®± TbsnA ¢sf rf §r`t .(384-322 BC £¥lmtF rf Ahny , d ®m`ts £ w¤ d` z dq ,wWFC A Tr wktF rf ¨ s © Tr Ð Yl E ,¢ TWy A © AS§ An¡ .T`ybW dR wWFC £rbt ©@ º¨K ,(perputual motion) Tb¶ @¡ .r¥ ¨ XFw ,wWFC s ,At ¨t wq ry TyAkJ Nature abhors a) rf qm T`ybW ¤ horror vacui lWOm wWFC m`tF .(vacuum A hnm .¯ rf w¤ TyAk w wmlsm ºAml` lt ¨ CAf hny ,wWFC ThybJ A ylm`ts £ w¤ rk dR A rf ww An¡ A Aqm ¨ .(Alpharabius 872-950) ¨¤ryb AWF¤ Afw ¤@ §@ TfF®f ¤ .(Alhazen 965-1040) yh :A y (al-Biruni 973-1048) .«¢d rf w¤ b ¨t T\®ml TlA T An¡ dw ¯»
“there is no observable evidence that rules out the possibility of vacuum.” w Ty®F³ CASl ¨b¡@ rO` ºAn r w MAq An¡ A \` A .(discontinuous) Wqt (continuous) rmts w¡ ,ºASf T`ybV Aq .(atomism) T§C@ T§r\n Yl dmt` A Am @¡ ¨ AJAqn .zt ¯ C@ w |CA`t ºASf T§C rmtF Wqtm ºASf ¤dAs Tr ¨FAF ªrJ rmts ºASf w r\n £@h w¶¤Anm A ¤ . C@
12 (Partial Vacuum) ¨¶z rf 1.5.3 .Ty¤C¤± TShn T§ d Th w Y rf w¤ TyAk ¦Ast A ¯¤Am {` C .¨¶z r l TyAk w AFAF Cwmt§ MAqn A .ºA§zyf Y Tfslf MAqn q ¦Ast @¡ ¯ ,£A ³ @¡ ¨ TqAs ¨t - (Evangelista Torricelli 1608-1647) ¨lyKt§Cw AtsylAf§ Trt A A .wRwm @¡ ¨ «rb Tym¡ -(Barometer) rt¤CAb rt Y .Ty¶Am A Sm An} Ah\¯ r¡A\ A§ w¡ Trt £@¡ dh ºAm ¢lb§ ©@ YO± Af C³ w¡ CAt 10 ^w , d`t ¯¤A C Am`tF ¨lyKt§Cw Cr TyAkJ³ £@¡ .(suction pump) XfJ T S TWF w ºAm T`ybW Xb r§ YO± Af C³ A Ð A Tr`m ºAm d b¶z ¤ds Th ¤Ð Ab§rq 1 ¢wV wb TAnO ¨lyKt§Cw A ?r º¨J Af C ^® b¶E ¢ ºA ¨ Twtfm Th rm Ð d` .b¶zA £° A@ As ºAm Af C ¸Ak§ Af C³ @¡ .F76 b} wb± ¨ b¶z º wh XR w¡ r¡A\ £@¡ ¨ bs r` .CAbt³ y` b¶z TA .(atmospheric pressure) A ,¨lyKt§Cw Am (Blaise Pascal 1623-1662) AkFA zyl l d` kt ¨t wq h T¤A Yl ¢Amt¡ } ¢nk . r d ¢tr A w ºASf °m§ ©@ º¨K h ¤ (maximum height) YO± Af C³ ¨ A TAfJ A An¡ @ ºAml` TybA Aqt A . wb± b¶z .ºASf Ð rb rKtn§ ºwS Ð ¨ ht A .ºASf Ð °m «wF An¡ º¨K w¤ ¯ ¢ dqt y ,AAm AfA AkFA w A ¤ ºAml` d§d` A z d Y « @¡ £ Aqt C .(vacuum) rf :¢sf AA A .Ð Yl b ¢nk k ,Aht} Ab³ TyRr A®W r¡ w\ ym rJ TyAk ¨fk ¯» .«Ah·W Ab³ TyRrf £@¡ {An Xq d ¤ r¡AZ ¨fk
“In order to show that a hypothesis is evident, it does not suffice that all the phenomena follow from it; instead, if it leads to something contrary to a single one of the phenomena, that suffices to establish its falsity”. b A k . rf Y yy¶A§zyf r\ ¨ y Y CAt £@¡ ¶At .dq` Cw±
(Ether) ry± 2.5.3 (double slit experiment) w§ ¨qJ Tr d` ºwSl Tywm T`ybW Ab TysyVAn¤rhk T`J± AKt ¤ 1801 TnF (Thomas Young 1773-1829) w§ xAwt ,(Heinrich Hertz 1857-1894) z ry¡ L§rn§A¡ rV (electromagnetic waves) :¨At ¥s wh w§ yy¶A§zyf Yl A «?TysyVAn¤rhk Awm qtn y»
13 .(16)¢y qntt XF¤ Y At w± w¡ @ d¶As Aqt³ A .(Ether) ry± Am ºwlm wk wrt Tybsn CwhZ wy¶A§zyf Ahn Yl ¤ ®§wV rm` r\n £@¡ k . rf ¨ qtn TysyVAn¤rhk w± ¨¡ T§d r\n .T}A r rf whf b} (quantum field theory) Tymk wq T§r\ CwhZ . dyq`
(Time) Az 6.3 .ry ¤ xAbt³A Awf ,«?z T`ybV ¨¡ A» ¦Ast TA³ C A (Antiphon the Sophist, 5th century BC) wfyt ywslyf A§ db A k ¨qyq ry z wfyt rbt .(Parmenides 540-480 BC) xdynyCA ¤ AhAK Afw xdynyCA @ .(measure) xAy ¤ (concept) whf CAb ry As³ T\® Yl dmt ¢t .(illusion) Am¡¤ z rbt y ¨RAmA ,(present instant) rRA T\ ¨ ¯ z Yl ryt Yl C A T\ ¨¡ rRA T\ k .d` § (future) bqtsm ¤ Y¤ d (past) ¡r}A` rbt , Aqt³ @h r .AhFAy Annkm§ ¯ ¤ (instantaneous) Ty ,rmts ry ¨ º¨J k ¢A Yl Yqb§ º¨J ¯ (Heraclitus) HWylr¡ .Tqyq z rbt` r . wk l T\ l w (Plato 427-347 BC) wV® dqt £@¡ (period) C¤d AqAW £rbt ¤ T§¤Ams r± Tr z wV® rbt ¤ Tr z r ¨ (Aristotle) wWFC £@yml ¢q ¤ .Tr dq .z dw§ ¯ Amh¤db ,ry ¤ Tr w¤ AWb r z w¤ “numeration of continuous) «rmtsm Trl yr » ¢ Yl z }¤ «d` T\ Y b T\ ryt d» r ryb`t ¤ (movement” wWFC± TbsnA wA .(“number of change in respect of before and after”) T§ d ¯- ¨¶Ah ¯ z wWFC dqt .¢sf ryt Hy ¢nk rytl xAy w¡ .rmts Tyn ¤Ð ¢ dqt Am ,¢tn w¡ ©@ ºASf Hk -¢ T§Ah ¯ ¤ (cyclic) A§C¤ ¢w TyAk ¨¡ Kw ¨t zl «r± P¶AO rt r Aml Crkt§ km§ ,T§Ah ¤\¤ T§ d Ð ¤ ,Ay¶Ah ¯ ¢w db A³ ¤ (creation) l Tlsls rm§ wk Aqt³ Anh .z z stk§ , wk ww Xb r z w¤ CAbt .(annihilation) ¨ ¤ Tm§dq dnh ryVAF ¨ CwOt @¡ Yl Cw` km§ .T§C¤d Ty}A .(cosmology) Aywk l w r}A`m Am± {` ¨ ryt ,¨¶A§zy º¨J w¡ z : w T® y TfF®f ©C C w AJAq AS§ d Am .¨¶A§zy ry z ,¨¶A§zyf º¨K w¡ z T§C@ T§r\n Cwh\ Tyt- T`Wqt rmts Tyn Ð z A Ð A £A kl .A§C¤ ,¯ Ayhtn z A Ð A ¤ - Am Tynb (atomism) .¨fsl £A ©± Tbl k k ,£¤dAs ¤ ¢
.rK FAt rq ºAml ¢l` A ¤ wq wWFC ¢ A A y ¢AKt ^¯(16)
14 d ¢ ¤ ,yAn§dl ¢ny w TAy} (Newton 1642-1726) wy ¤A Adn :Ahn AyAkJ .¢ny w ¢y qt ©@ , (inertial frame) ¨AW` l`m ,QA l` w¤ • Tmyqtsm Tr ¨ mt ¨t ¤ (perputual motion) Tb¶ Tr w¤ • .(rectilinear uniform motion) Tm\tnm E A ¤ .{`b AhS`b TbsnA TtA Trs rt ¨t A`m ¥Ak • .Twms Trs y ,Tl yW (space) Akm ¤ (time) Az TyRr ®W³ Y wy }w Ay¶A§zy An¶A ¢y TbsnA Akm ¤ AzA .(absolute) AqlW Awhf zynby rVAK§ .Ty¶A§zyf r¡ w\ ¢y d ©@ rsm Am¡ ¤ ©r wy (Immanual Kant 1724-1804) XA ¤ (Gottfried Leibniz 1646-1716) .(intellectual concepts) Tylq y¡Af - d± ¤ Akm @ ¤- z rbt y ¯ ¤ ºAyJ± ¤ d± ¢® rt © A d` Y Az ryK§ ¯ Amh TbsnAb .(entity that flows) dt§ Ay (general relativity) TA` Tybsn CwhZ Yt A @¡ Yl Ab§rq Cw± lZ Amy TWqn £@¡ Y w`nF . Akm ¤ Az Y Ar\ Tyfy ry ¨t Martin) rd§A¡ CA wslyfl z w ©r @h rqf £@¡ t .d` :(Heidgger 1889-1976 .«¢sf z ,z Ly` ¯ »
(The Solar System) TysmK Twmm 4 gravitational) TyÐA wA AKt ¨ AA¡ C¤ wk Tr TF C b` Trtqm ÐAmn CwW At ¤AnF .d§d y¡Af ¢bA} A ¤ (law ºAml` h ¤ ¨t AKm ¤ ,T¤rWm Tl·F± Tyw ,Tr £@¡ }w , wk r T`Atm Tlm`tsm Tq§rW }w ¯¤ dbnF .r ¨ .ÐAmn £@¡ Ahyl yn ¨t TyFAF± CAk± CwWt Stq §CA Yl r` Adn d wt A ¨t T® Tm\± yOft º¨K LAnnF Ð d` :¨¡ ¤ ¯ lf ¨ ¢lm (Johannes Kepler 1571-1630) rlb d rbt`§ w¡ ¤ T® y A\ d :(Ptolemaic system) xwmylW A\ • . wk zr w¡ A¡zr ¤ rt ¯ TtA |C± wk zr ¨¡ HmK rbt`§ :(Copernican system) yrw A\ • .HmK w C¤d wk ym ¤ y rt s T® Tm\± r :(Tychonic system) ¨¡ r A\ • |C± rbt`§ y .yqAs yA\n AWyl £CAbt km§ .¨nz A¡C¤d ¨¡ ¨t HmK w C¤d «r± wk k wk zr .|C± w C¤d
15 Tr ¢ny w Y w}w dh Tyklf rlb Am TKAnm Ð bt ¤ Trl ¢¶ Abm y`ts ¤ wy P J PmqtnF ry± ¨ ¤ . wk . wk Tr ¨¶A§zy rysf Y w}wl wk Tr rlb y w ¤ ,rlb ¢ A A T}A ,CAk± CwW TF C w¡ And¡ Y CAJ³ Cd§ w ¤ Ð ` yWts ¤ ¨ §CAt A ¨ ry m`t n @h w§dyf VAq E wmA ¨l§ Am º z º r AS§ § . w yS A C :TfO Yl wwm (video clips) http://science.larouchepac.com/kepler/astronomianova/home/1 :fO AS§ km§ http://science.larouchepac.com/kepler/newastronomy/newastronomy.html
http://www.keplersdiscovery.com/Intro.html :Y wr km§ ,Ty §CAt Awl`m d§zm ¤ .y}Aft d§zm https://en.wikipedia.org/wiki/Geocentric_model
https://en.wikipedia.org/wiki/Heliocentrism .¨l§ Amy ry Ahd tsnF ¨t AlWOm {` r@nF º¨J b
(Some Terminology) AlWOm {` 1.4 yhst T§zyl³ ¤ Tyr` ytlA AlWOm {`b Tm¶A ¨l§ Amy ¤d .£® Cw@m rm T`AW
(Planets) wk 1.1.4
y`A «r§ - (light polution) ¨¶wS wlt Ay ¨ - As³ yWts§ :¨¡ ¤ ¯ (planets) w TtF rm . CAW :Mercusry • .r¡z :Venus • . §rm :Mars • .©rtKm :Jupiter • .E :Saturn • .xw C¤ :Uranus •
16 xw C¤ «r yWts An C .(moon) rmq ¤ (sun) HmK Y TAR³A .¢tmt ¤ ¢tr ºWb (17)Abw £¤rbt`§ ºAdq ¯ rm y`A w d` ¤ r .(telescope) CA\nmA Ktk§ w ¤ xw C¤ rbt`§ yWts ¯ w wh .(Neptune) wtb w¡ TysmK Twmm ¨ ¤r` b T§r\n Am`tF £ ww wy¶A§zyf bn d ¤ dAs ¤d ¢t§¦C .CA\nm Am`tF ¢t\®
(Some Terms for Orbits) CAsm }w AlWOm {` 2.1.4 Trtqm Tm\± }¤ dn Ah AOnF ¨t AlWOm ¡ ¨l§ Amy P lnF rqf ¨ «rnF Am- Tm\± £@¡ yn .rlb b wk Tr }w Tr }w dyw Tq§rW (Aristotle) wWFC | rt Yl -Ty wm .Ahn §z ¤ Tm\tnm T§r¶ d Tr Am`tF ¨¡ wk .HmK ºAntF wn ym ¨¡ ¤ :TtA wn = fixed stars • Tr wk Ahyl rt§ r¶ CAb w¡ :r§¤dt l = epicycle • .Tm\tn T§r¶ r¶ zr Ahyl rt§ «r r¶ CAb w¡ :An = deferent • r§¤dt l .|C± lt § ¤ An r¶ zr :An zr = eccentric • ^® An`R¤ .xwmylW ¢rt ¨Ay zr :CAsm d` = equant • .Tm\tn Tr r§¤dt l zr Tr ^®yF TWqn £@¡ ¨ TWqn £@¡ dn HmK wk§ A d` wk wk§ :¤± = aphelion • .Ayd ¢trs rt§ ¤ £@¡ dn HmK wk§ A r wk wk§ :{yS = perihelion • .«wOq ¢trs rt§ ¤ TWqn .{yS ¤ ¤± y O§ ¨Ay X :Abq X = line of apsides • . wk C d kJ :PA W = ellipse • ® T§¤Ams Tbq Yl HmK AhmFr r¶ w¡ :HmK C d = ecliptic • .TnF Arbt Tywy ºAms Tb Tr ¨¡ ¤ :Y¤± Tr = first motion • .rt A¡Arbt Ayw§ Ahsf w |C± C¤ ¤ TtA |C± TbsnA wkl Tybsn Tr ¨¡ ¤ :TyA Tr = second motion • .TtA wnl . wk Tr TF C w Ty §rt AntlC µ db Aw
¤ (wondering star) w n ¨n` ¤ Tyq§r³ Tl Ahl} (planet) w Tymst (17) .(wonderer) w
17 (Where Are the Planets?) ? wk ¨¡ § 2.4 :X r Yl wwm w§dyf Wq º z m`tsnF http://science.larouchepac.com/kepler/astronomianova/part1/2 km§ .¨l§ Amy (vd1) : ¢ §z C ,CwOt Yl ¹CAq dAsm ¨¶r rm :Ty¤rtk³ AfO Yl d wtm AWW m ¤ CwO Am`tF AS§ http://www.keplersdiscovery.com/Intro.html http://www.keplersdiscovery.com/Intro2.html http://science.larouchepac.com/kepler/newastronomy/newastronomy.html db ¤ Tyml` Tyhnm wW -¨ml A ©- AnAKktF ¨ btnF .T\®mA
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wn £@¡ ymF .(vd1 8:55-9:38) ºAms Tbq TbsnA rt w An¡ • .Ah w bs (planets) w T·yW Tr ¨¡ ¤ (first motion) Y¤± Tr T§¤Ams Tbq Tr Yms wn Ty`R¤ CAq km§ k . rm y`A Aht\® `O§ d Tr £@¡ dtl (vd1 8:34-8:54) TynE rt Yl TtA TyRC A` .®` ww xwl µ Annkm§ ,(18)z rbt` dm Tylyl ºAms An\¯ d` . wk Tr (pattern) Xm bn .T\®m A¤r q wq lkt (18)
18 (Lokking for Patterns) AyW`m y\n 2.2.4
Tmhm Awl`m r ts § ,A r¡AZ w (data) AyW` m d` ry§A` s AhfnO ¤ An A\® \n § Ð kmtn .Tyqb .T§¤Ams r± Tr TF C w¡ And¡ .TF Cd r¡A\ Pl ts :¢sf rW§ ©@ ¥sA «?T§¤Ams r± Tr ¤d ¤ O y»
.(vd1 10:40-12:33) d¡AJ ¢f}¤ ¤A A T§¦r . rm Ahlm`ts TtA A` Y At ,Tr © }w ,¤r` w¡ Am ?m` Am ,rt§ ºAms ¨ º¨J ¨¡ Ahth w Anyl ¨t TyAkJ³ k .(19)Ah TbsnA «r± Ar O ¤ Tm\tn Tr Yl b Annkm§ Annkm§ ¨t (vd1 8:08-8:17) Tywy T§¤Ams Tbq Tr An¡ An\ s T§¤Ams r± Ab§rq ,Ð Yl E .(background) rm AhAm`tF Ankm ©¤AmF r © Tr }¤ Annkmy .(20)Tr £@h TbsnA TtA Hipparcus of Nicaea 190-120) Lr A .TtA wn £@h TW§r R¤ ¨t ¤ TtA wnl T§¤AmF (catalogue) TW§r w`R¤ §@ ¶ ¤± (BC AnAmt¡ w Annkm§ ,TW§r £@¡ ºAht³ d` . 1000 Yl wt .(vd1 8:18-8:34) TyA Tr ¤ wn £@h TbsnA rt ¨t r± Y .Aw§ 29, 5 A¡C¤ ¨t T§r¶ d rmq Tr An¡ •
(vd1 A ¨l}± AhAk Y w` ¤ r¶ ¤ HmK rt • .(ecliptic) HmK CAs Yms§ C dm @¡ .6:46-7:40) (vd1 10:40- §rm w Tr wk Tr Am @n • ¤ ,T`§rF wk AAy Tm\tn ry Tr £@¡ Ayl rh\§ .12:33) CAs Ab§r Yqb§ CAsm k . Tql Fr «r AAy ¤ ,T·yW AAy .«r± wk Yl ¢sf º¨K bWn§ .(21)HmK .Tl·F± rV ¤ A ,T§¤Ams r± Tr }¤ ºAht³ d` .¢ wqnF ©@ whm £A ¤ w d§ ¤rWm ¥s T`ybV ^¯ :Am§d rV ¨t Tl·F±
?Y¤± Tr bF A • ?¯ |C± T§¤Ams r± ¢bK ¡ • ?A¡d` Tr` km§ ¡ ¤ ?|C± Y r T§¤Ams r± © • ?rmq ¤ HmK @ ¤ wk wm bnt km§ ¡ •
,ybq @¡ º¨J ¤ TyAkJ An AO Adn .Tywy An Ay ¨ ry Tq§rW £@¡ m`ts(19) .y}AftA th rybk CwO A`tA ¯¤ db .Y¤± Tr :Tymst bF w¡ @¡(20) .HmK ¢r ¯ ¤ ¢tr TrF Hy ¤ ¢mFr§ ©@ CAsm dOq(21)
19 ¨t dm ¨¡ A ¤ ?Tyql ¢tr §rm w wq§ r • ?¢n d ©@ ¢Ak Y w`y §rm Ahrts§ ? wk Tr bF A • Y rAs Aw .AhtA`m ¨ §CAt y rt s Ab§rq Tl·F± Anb C dq .Trtqm AA³ CwW Tq rm An T¤A ¨ ¨RAm
(Where to Start?) ?db § 3.4 ^®m TbsnA A £And ©@ T§¤Ams r± Tr Anf}¤ ^¯ A AnAmt¡ .TtA |C± Arbt An ¨n`§ Am ,|C± WF Yl Ly`§ º¨J -l` Am- (movement) Tr k .Tylyl ºAms ¨ £ r A } ¤ ¥sA .(absolute) AqlW Yn` ®m§ ¯ rtm ¤ AsA (relative) ¨bs dt y ± Yl «?r± ¨ Ofn Tq§rV An¡ ¡» :¤rWm . rt ¨t AyRrf lt Yl r\ ¨ql Aw .T§¤Ams r± Tr
(The First Movement) Y¤± Tr 1.3.4 :Am¡ Ay`ybV rysf An¡ .Y¤± Tr TKAnm ¯¤ db
An Amb .Tqyq w¡ £ rA :TA ¨ CAyt³ @¡ nO km§ :TtA |C± yWts ,yO w Yl And ¨t -yAkym y w- ¹ Abm lm ¯ wks » :(22)wWFC db Yl Amt³ AS§ Annkm§ Am .Tys An Awl`m TfF®f {` dqt .|C± Ab r§rbt «As° Ty`ybW TA ¨¡ :(23)TyAt r¡ w\ Y © ¥§ § Ahsf w |C± Tr .d ¤ £A ¨ T§w A§C • .£zf Ak Aflt ¢VwqF Ak wk§ ºAms ¨ Ad zf • .d ¤ £A ¨ wk s Tr ¤ CwyW ryV £A • .TnAF |C± ¨n`§ r¡ w\ £@¡ Ay
C¤d ¨t ¨¡ |C± :AAm HA`m CAyt³ An¡ :Ahsf w C¤d |C± w |C± C¤ wrt §@ ¶ ¤± TfF®f .TtA T§¤Ams Tbq ¤ dR wm @¡ |CA` C ¤ .(Heraclides of Pontus 390-310 BC) dylr¡ Ahsf (astronomers) yyklf {` Am ¨ Cw@ £d An ¯ (intuition) AnFd
wkt ¨t T§¤Ams r± Hk ,|C± Yl d wt ¨t As±A l`t§ dbm @¡ ^¯(22) .Tflt Ahl`§ Am (Ether) ry± A .TAW` db bs T·VA ¨¡ £@¡ ^¯(23)
20 LA Am .(Aryabhata 476-550) A AhA§C ©dnh lf A` TfF®f ¤ ¨Jw ¨l ¤ (al-Tusi 1201-1274) ¨FwW A ymlsm yyklf {` yrw ¨klf w¡ º¯¥¡ rhJ k .TyAk³ £@¡ (Ali-Qushji 1403-1474) .HmK w |C± C¤ rt Ð Yl E ©@ (Copernicus 1473-1543) ¨b§rt Ab³ ºAW³ (Foucault 1819-1868) ww CA\t Anyl A k .(Foucault pendulum) ww x wn Trt £@¡ r` .Ahsf w |C± C¤d :AV Awl`m d§zm https://en.wikipedia.org/wiki/Foucault_pendulum https://www.youtube.com/watch?v=aAN8yenz3nA wm A A§ (first motion) Y¤± Tr Ars An rbt`nF ¨l§ Amy (T§¤Ams Tbql Tyl` Tr ¤ Ahsf w |C± C¤ ) ¢ ¥ ©@ Tm Y rWt b .(second motion) TyA Tr TF C Y qtn ¤ Ahyl yn ¨t ¹ Abm {` ¯¤ LAnnF ,Trtqm Tm\± CwWt Ty §CA .Tm\± £@¡
(Movement) Tr bF 2.3.4 }¤ Y dh T§¤Ams r± Tr TF Cd Y¤± ¯¤Am A d¡± k .¨®f Fwm XbR ¤ wk w w dh Tr ¦AstA .Trl bF A§ w¤A §@ (24)§r³ TfF®f E¤r ry :rV ©@ XFw Tyt rt Ah ?Ahsf ºAql rt ¨t ¨¡ wk ¡» «?r bF An¡ ?¢y Ly` ©@ ÐA , rt ¨t (first motion) Y¤± Tr rysf lt AnKA dq TtA |C± rbt T§ db ¨ ?(second motion) wkl TyA Tr ^¯ .XFw Tr Tyt ¨¡ (first motion) Y¤± Tr ¨n`§ Am Am`tF ¤A Annkm§ .Ahsf ºAql rt ¯ (fixed stars) TtA wn sy TyA Tr k .(second motion) TyA Trl rysft Hf y rt §dq TyAR³ dyq`t £@¡ A`tl .Y¤± Tr TVAsb ¤ AAR XFwA Tyl Tr XC An¡ :Tr £@¡ rysft wWFC rysf Y Am ybF Yl r\nn .yn³ Xyl A¡rbt An¡ : wk Tr ©rOn Tbs ¨t As±A .A¡r¡w Yl As° Ty`ybW Tr dmt` • TbsnA Hk` ¤ |C± zr w Xqs TbA ¨¡ Ahy |C± ¤ ºAm wk Tr k .CAn ¤ º wh Am¡ ybA Ah§rOn ¨t As° HA rOn w¤ rt Y wWFC Am bF Am A§C@ lt .ºAms ¤ T§¤Ams r± ® wk§ ©@ (Ether) ry± Am± TybA ¯ ¥s @h wmt¡ §@ ¶ ¤± ¡ wA §r³ z Annkm§ ¯(24) . AR d «r±
21 T§¤Ams r± Hk wks ¨¡ |C± Yl As° Ty`ybW TA • .(perputual motion) Tb¶ d Tr ¨¡ Ty`ybW AhtA ¨t
,z d d` Tyl}± Ahty`R¤ Y w` T§¤Ams r± Am • .T§r¶ Ahtr § wk Tr -|C± Hk- (ideal) ¨A Ak ºAms Am • .Tm\tn T§r¶ wk ysq ,TyAkJ³ £@¡ .T\®m wt ¯ Ty¶Ahn Tytn k ,|C± (concentric) zrmtm (spheres) rk Twm Y ºAms sy rk £@¡ .(crystalline spheres) T§Cwlb rk F Ahyl lV ¨t ¤ £@¡ FAn d` w XC .TtA Trs C¤d Ahnk TnAF Xyl ¨¡ TyA TrA .T\®m w Tr Yl wO dh rk wk Tr rbt` Annkm§ .Ty @ wk Tr ¤ XFw Tr y wk TA £@¡ ¨ .Ahyl wm wk «r r Tr Tyt Ty @ .Tyl XFw Tyt TyA Tr rysft @¡ ¯ , wk Tr wWFC rysf Anmlk An C .(Ty wm rqf AV) ¢lb d r rysf P¶AO ry ¨ rtK§ T}A ,Ahn lW ¨t ¢¶ Ab ¨¡ wWFC rysf Yl zr Anl` ©@ bs :§dbm uniform circular) Tm\tnm T§r¶ d Tr ¨¡ Tnkmm dyw Tr • .Ahn §z ¤ ,(motion .Ahy A ¤ |C± r¡w T§¤Ams r± lt • Yt- wk Tr rysft Trtqm Tm\± q TybA yn .§dbm §@¡ Yl -rlb Am A§ d Y ¢bK º C ww Y rhZ ,Ty®F³ CASl Tyb¡@ CwO` ºAn wWFC rt ¨ r\n dy Adn @¡ d .T§d r\n dy` d YFw dm |rt ,FAt rq ¨f .|C± Tflt T§¤Ams r± T§ d ¨ ¤ .T§¤Ams r± y TyÐA w w¤ -YFw wn w³ rb- Am .tk y TyÐA w w¤ w T§r\ yh LA rK © A rq w¤ C .TyRC± ºA§zyf y w Hfn S T§¤Ams r± A r\ Yl AFAF dmt ymlsm dn wk Tr }¤ ¯ CAk± £@¡ £@h ¨FAF± wkm ¨¡ Tm\tnm T§r¶ d Tr Aqt³ T}A wWFC .Tr r\ ¨ql Aw , wk Tr }w Tlm`tsm HF± AnKA d` .Trtqm Tm\° ¨ §CAt CwWt Yl TfVA
(Geocentrism) wk zr |C± 3.3.4 CwWt rWt b rt ¯ |C± Aqt³ º C¤ bs LAn Aw w |C± C¤ dR d ¨t AqAF AnKA dq .Trtqm Tm\± TAR³A .HmK w |C± Tr dR Yl ¨l§ Amy zrnF .Ahsf
22 An¡ ,wm @¡ ¨ Ah d tF km§ ¨t r@ TfAs Y :¨¡ ¨t ¤ «r
,TtA wnl (relative position) Tybsn Ty`Rw ¨ ry © w¤ d • .(Polaris) AmK T}A
.(Venus) r¡z wk (apparent luminosity) ©r¡A\ A`ml wb • .An Tb§r wn rbt Y¤± TA .Tmh AVAq lf £@¡ k At ¤ Tlmh ryt £@¡ `§ An wn d`b ,Ð Hk Tqyq k A`ml wb ,TyA Tl TbsnA A .Aht§¦r ©w (telescope) CA\n Y A¡d` ¤ rmq r ¢bK ¨t r¡z r :ylA rA\ Y r§ w A Aml ry} HmK T`J Hk`§ ©@ Ws A Amlk .|C± ¨t Tynz rtf ® A¤r` §rysft ® k§ .An Ab§r r¡z .Anmh ¶Aw \` ± wk Tr }w rt A\ ¤ XbSA r`§ ¯ A`± Ty® TyFdnh Tm\± ¤ y . fl ¤ AR d Ty §CAt Eudoxus of Cnidus) xws¤ w§ (25)¢rt ©@ A\n wk Tr }w A\n @¡ dmt .(Callipus of Cyzicus 370-300 BC) xwbyA ¤ (390-337 BC wWFC A . wk zr ¨¡ ¨t ¤ |C± zrm dt r 27 Yl .r 55-47 Y rk d r (Aristotle 384-322 BC) ¯ T`C± wOf Ð Yl E .Ttb Tylm k Tm\± £@¡ k .wWFC A\n Anys b Y AyAkJ³ £@¡ .(26)dm Hfn rmts wOf TyAkJ (27)|C± zr T§Cwlb rk zr zE TAR .¨RC ^®m TbsnA Tm\tn ry HmK Tr `§ Am . T`C± ¤ (deferent) An : w k y r¶ d T§Cwlb rk dbtF , @¡ Y Apollonius) ©¤Arb xwywl A\n @¡ rt ¤ .(epicycle) r§¤dt l d` .(Hipparchus of Nicaea 190-120 BC) Lr £CwV (of Perga 262-190 BC mtm ¤ ry± §d`t TAR (Claudius Ptolemy 100-170) xwmylW A Ð Ptolemaic) xwmylW A\ ww Y Er @k¡ ¤ .(equant) Tr d` ¨ º¨K A\n @¡ Y w`nF .rlb Am T§A Y rmtF ©@ ¤ (system .¢ TOO m rqf ¨ yOft dmt`§ ¨t (parametrs) ®A`m y yO Yl wyklf zC ,T§ db ¨ ¨ ¤d ¤ hAmt¡ ¤ry Ð d` .¢tynb xAsm ¤ xwmylW A\ Ahyl Tr O TyAkJ TA³ ¨ On§ hAmt¡ A y Tynb £@¡ dq km§ .CAbt³ y` wkl Tyql Tr @ Ahnk A\n @¡ d Tm\ An¡(25) :¨¤rtk³ wm Yl ®V³
http://www.astronomy.ohio-state.edu/~pogge/Ast161/Unit3/greek.html .Awl`m d§zm T§r¶ d TrA .Any` ®O w§ HmK CAs r¶ C @ Aqt³ A(26) .T§¤Ast rtf bnt Tm\tnm |C± d`b . rt³ @¡ ¨ ºAtK ¤r ¤ yO C r A ¦Ast An §(27) .Tns wV Yl Aflt wkyF HmK
23 A ©@ ¦AstA .(eccentrics problem) T§zr® TyAkJ ¤ (equant problem) :w¡ A¤rW «?T§zr® ¤ Tr O ¤d A\ ºAn Annkm§ ¡» :y ¥s TA³ nt T¤A A ©@ ¤ TyAy TWqn TbsnA A\t rt § Ah wk r` y • ?((equant) Tr O) ?Tm\tnm T§r¶ d Tr Y w` km§ ¡ • ¹ Abm lW xwmylW C .TyAt A\®m Tyt Tl·F± £@¡ A @¡ ¢A\ ¯ wk Tr ¢A\ ºAnb wWFC Ah`R¤ ¨t Ty¶A§zyf E ,(|C± ) wk zr lt § An zrm :¹ Abm £@¡ |CA`t§ xwmylW @ .A¡zrm TbsnA Tm\tn sy An Yl Tr ,Ð Yl Yl wOl wWFC ¹ Ab Yl y (pragmatic approach) Aylm Afw . wk Tr O§ Xys A\ AnA ll ¤ £® ¦Ast Yl TA² ¡ wh wmlsm } wbsn§ §@ yyklf y .(Maragha school) T rm TFCd CwW ¤ E¤r §d W ,1274-1201 ¨FwV §d ryO ,1266-1200 ¨Rr` §d d§¥ Ahy §dq ¨ TFCdm £@¡ .1375-1304 rVAK ¤ ,1311-1236 ©E ryJ Y |C± A ¤ (equant) Tr O ¤d wk Tr Tm\ Awl`m d§zm .r¶ ¤d d A§E w¡ ¢` ¤ ©@ m k .zrm : rm Yl ®V³ km§ http://www.encyclopedia.com/science/encyclopedias-almanacs-transcripts- and-maps/ptolemaic-astronomy-islamic-planetary-theory-and-copernicuss- debt-maragha-school
https://www.cambridge.org/core/services/aop-cambridge- core/content/view/S0957423900001429
http://paperity.org/p/51456472/the-role-of-maragha-in-the-development-of- islamic-astronomy-a-scientific-revolution http://qisar.fssr.uns.ac.id/wp-content/uploads/2015/04/Qisar-Roshdi-Rashed- Encyclopedia-of-the-History-of-Arabic-Science.pdf
º¨K .TFCdm £@¡ Am (Copernicus) yrw r TyAk wC¥m LA ,|C± T§zr rk nb T rm TFCd ¨ykl Am w¡ ¢n dtm ¤ Tr O Yl ºASq Tq§rV T}A) hAm± TyRA§r Tynb k :Am ybF Yl AV .yrw A\ dy` d Y ¢bK (T§zr® http://www.ub.edu/arab/suhayl/volums/volum7/paper%203.pdf
24 (Heliocentrism) wk zr HmK 4.3.4 TShn Tyt «( wk ¤) TysmK Twmm zr ¨¡ HmK » rk sy d` wbq ® Ahnk Tm§d rkfA .xAn TybA dqt`§ Am Ty¤C¤± E .£@¡ r\n Th¤ Ab³ Tml`tsm T}A ,y}Aft AyR Ahn AbF dR ¤ (|C± T§zr) ¢yl CA`tm ¢wt dR ¢wt @¡ w Ð Yl .Tywy hCA xAn ¢`wt§ A zr ¨¡ HmK ¤rbt §@ TfF®f ¤ ,Tyqbtm Awl`m s ,d§dK F° .(Aristarchus of Samos 310-230 BC) ¨FwAs HrWFC w¡ wk xdymC AAt VAq A ¢ml` A ¤ Tyl}± ¢ AAt n «r xwmJ CAb ¨¡ TtA wn HrWFC dqt .(Archimedes) rt Am Ah` w ¨ ry © «r ¯ bs @h ¤ ,An d dy` Ahnk HmK wb HrWFC Aqt º C¤ bs yC¥m {` rt .|C± Am`tF |C± HmK d` ¤ xAyq A dq .rybk Ahm w¡ . rm A·m |C± rb HmK ¢Am tntF .rmq Tr Amt rb -Am r}± - |C± Tr Amt ¨n`§ Am : rm T`AW km§ Awl`m d§zm .HmK https://en.wikipedia.org/wiki/On_the_Sizes_and_Distances_(Aristarchus) https://ia600502.us.archive.org/17/items/aristarchusofsam00heat/aristarchusofsam00heat.pdf w¡ ¤ ¯ ,HmK T§zrm dqt -HrWFC Y TAR- r ¨kl An¡ HrVwl C¥m z§ .(Seleucus of Seleucia 190-150 BC BC) ¨wls HwlF Annk ,rt |C± ¤ TtA HmK b HwlF (Plutarch 46 -120) ©E ryJ §d W lsm ¨klf AS§ An¡ .y ¤ Ð ` Anyq§ l` ¯ .Ahn Yl ¢nk wk zr HmK w TyAk LA ©@ (1311-1236) T§zr T§r\ `b (Copernicus 1473-1543) yrw CA\t Anyl A ym Yqb§ wm @¡ £ÐA º C¤ bs k .Ay Y HmK ¢nk ¢t§r\n ¨b§r y © ¨W`§ ¢At ¨ kmt§ .yC¥m rV TVAsb rsf§ ¢A\n .(elegance) ¢tA ¤ A\n TVAs w Yl dmt ¨ wk AhmFr ¨t (retrograde motion) Ty`r Tr ¤ Aql .HmK w wk ¤ |C± C¤ TrF ®t Tyt Ah Yl ºAms A Ab³ ¤ wylyA d .|C± C¤ Cw ym T`C± wOf XC Am r r¡z wk ^¯ wh HmK w wk C¤d Tyb§rt .rmq r
(Hybrid Proposal) yh A\n 5.3.4 ¨t dyw ¨¡ HmK ¤ |C± T§zr Yl dmt` ¨t Tm\± k d A .Amhny Tny¡ Tm\ Anh , wk Tr rysft rt y` @± k |C± T§zr ¨l t d Tm\± £@¡ m ¨FAF±
25 r¡z :Tyl d wk T}A ,Lms w wk C¤ TyAk CAbt³ -AyR q - Cd TlkK «r r ¢ w .(mercury) CAW ¤ (venus) dylr¡ wslyf Aqt An¡ Am ybF Yl` .Tm§dq wh` AAt .HmK w C¤d Tyl d wk ` (Heraclides of Pontus 390-310 BC) .Ð b§ ¨`W y ©± w¤ ¯ ¢nk ¨klf A Am ybF Yl` .£A ³ @¡ ¨ ¯Am T§dnh CAS ¨ d .HmKl TbsnA wk (period) C¤ ºAW (Aryabhata 476-550) A AhA§C {` ¯ (geocentric) zrm ¨¡ |C± rbt ¢ Y ryK ¢ AAt C zrm ¨¡ HmK rbt ¤ Any¡ AA\ m`tF ¢ ¤dqt`§ yC¥m rt (Nilakantha Somayaji 1444-1544) ¨AywF AtA®y A .(heliocentric) C¤d ¨t HmK w @ T¤r`m wk ym C¤d y y¡ A\ .|C± w A¡C¤d .¢·W ¤ ¢y ¡Ð A T} w ºAml` lt ,¢A\n yrw rK d` .(Tycho Brahe 1546-1601) ¨¡ r w y ¢·W Ab w¤A §@ yyklf y Oty -¢ ¢tRCA` C- yrw A\n TyA§³ ªAqn @ ¨¡ r A @ .r@ µ (Somayaji) ¨AywF A\ ¢bK§ ©@ ¤ yh ¢A\ Yl wk Hk ,|C± Tr rysf © dw§ ¯ ¢± wm @¡ ¨¡ r `§ ©@ º¨K ,ry± A wkt ¨t (rmq ¤ HmK Ahy Am) «r± .Tb¶ d Tr Ty`ybW AhtA (representative) m Cz Aw ,CAk° ¨ §CAt CwWt Yl Anmlk d` (second motion) TyA Tr Yl Xq zrnF .yOft º¨K A\ . wkl
(Ptolemaic system) xwmylW A\ 4.4 Tm\ mm (Claudius Ptolemy 100-170) xwmylW A\ An§d db :w§dyf VAq Yl ¨l§ Amy dmt`nF .(Geocentrism) |C± T§zr http://science.larouchepac.com/kepler/astronomianova/part1/4 :w§dyf ¤ (vd2) :¢ zrnF ©@ http://science.larouchepac.com/kepler/astronomianova/part1/5 .¢A\ ¨n Adn xwmylW rykf AA ¤A Aw .(vd3) :¢ zrnF ©@
wk Ak w xwmylW d¡ A :(Two Circles) w k y r¶ Tr w¡ ¢yl wO Anyl § ©@ ¤± º¨KA .ºAms Y Ar\ y vid2) wkl (retrograde motion) Ty`r Tr ¤ (looping) Tyql T§r¶ d Tr Am`tF -wWFC s- wzl An r@ .(2:29-2:45 Y At An Y (28)xwmylW Pl .Xq (uniform circular motion) Tm\tnm xwmylW A\ -|C± T§zr Tm\± ¨ §CAt CwWt And dn- AqAF AnflF Am(28) .wRw ¤ TVAsb d¶Af TdA ¨SnF ¨l§ Amy .yykl d Am rA\ Tyt A
26 An Y¤± r¶ d Yms . w Tr }w (vid2 2:46-3:03) y r¶ (epicycle) r§¤dt l TyA r¶ d Yms ¤ .|C± A¡zr ¤ (deferent) Trs rty wk A .An Yl Tm\tn Trs rt§ A¡zr ¤ yr At ¨¡ |C± A¡ r ¨t TrA .r§¤dt l Yl Tm\tn An rWq TCAq r§¤dt l rW Tbs ry Adn .btr y A¡ rtq§ A¡ºAn ¤ ,(vid2 3:04-3:31) Tyql Tr Yl O yWts ¨ wk§ (Mars) §rm w ± T\®m w§ @¡ .|C± wk d¡AK km§ .(retrograde motion) Ty`r ¢tr ºAn (brightest) ¢A`m ¤ .(vid2 3:32-3:54) Wqm ¨ -Ak Hy ¤- An xwmylW A\ r Adn A w Ak w xwmylW d¡ A ,AqAF AnflF Am ©@ dyw º¨K ¨n`§ @¡ .¨qyq wk w ¯ ,ºAms Y Anny rW Y r§¤dt l rW y Tbsn w¡ T\®m §rV ¢FAy Annkm§ r§¤dt l ©rW ry§ y (vid2 3:55-4:11) Wqm d¡AJ ,An ®tF Annkm§ . wk ¢y «r ©@ £A ³ Yl Ð r¥§ ¤ An ¤ (Mercury) CAW ¤ (Venus) r¡z ybwkl An rW ryyt Ty}A £@¡ Amh ¤ rh\§ Abwk @¡ `n ,HmK C d rWq A§¤As ¢l` ¤ .(vd2 5:29-5:51) HmK w C¤d§
Tyql Tr A@ d` :(Irregular Motion) Tm\tn ry Tr ¨t Aql :TyAt TyAkJ³ Th w Anyl ¤ CAbt³ y` wkl .(vd3 0:12-1:33) Wqm d¡AJ . Hfn sy A w AhmFr§ vd3) T§¤Ast wk Aql AqAF ¢y Anl}w ©@ A\n Yl Xq Admt (vd3 1:46-2:16) An zr |C± Tzz ¯¤ xwmylW A .(1:35-1:44 TbsnA Tm\tn ry r§¤dt l zr Tr `§ Am .TyAkJ³ £@¡ d¡AKm Aql Hf Yl xwmylW O§ @¡ C ¤ .|C± rm .(vd3 2:18-2:36) ºAms ¨ Tr O :d§d TWq AR y ¢A\ ¨ d§d ryyt xwmylW A Tm\tn Tr An Yl r§¤dt l zr Tr wk y ,(equant) xwmylW R¤ .Tr O dn q§ ^®m TbsnA (vd3 2:37-3:30) @h km ¤ ,|C± ¤ Tr O y TAsm Otn An zr km§ .(vd3 3:31-3:43) T\®m Aqll Ab§rq TqAW Aql Yl wO ¨ TqAs rqf A\ Y TAR Aqll d ¨t ryt d¡AK .(vd3 3:44-4:02) Wqm
:TyAt Abrm Yl xwmylW A\ dmt`§ :(Conclusion) T}® .rt HmK ¤ TtA |C± • (epicycle) r§¤dt l zr Ahyl rt§ r¶ w¡ ¤ (deferent) An • .|C± lt § A¡zr ¤ .TtA Trs wk Ahyl rt§ r¶ w¡ ¤ (epicycle) r§¤dt l •
27 zr Tr ¤db y TyAy TWq ¨¡ ¤ (equant) Tr O • xwmylW R¤ .Ah TbsnA Tm\tn Tr An Yl r§¤dt l .Tr O ¤ |C± y TAsm Otn An r¶ zr
.(vd3 4:03-4:42) Wqm ¨ ¨lk xwmylW A\ d¡AK km§
(Copernican system) yrw A\ 5.4 :w§dyf m`tsnF ¨l§ Amy http://science.larouchepac.com/kepler/astronomianova/part1/6 .(vd4) :¢ zr ¤ ©rO rm ¤ rt |C± ` (Nicolaus Copernicus 1473-1543) yrw Y sn§ :®¶A t y . wk zr ¨ HmK R¤ Ak ¨ ym db` xwA S§ yWts§ m .k XF¤ ¨ HmK dw » ¤ º¨J º¨S§ xwAfl km§ An¡ , Akm @¡ s ¤ r Tl¶A ,¨klm AhJr Yl TsA Ah ¤ ,HmK k @k¡ ¤ ? w Hf ¨ « .Ahw w ¨t wk
“In the center of all rests the sun. For who would place this lamp of a very beautiful temple in another or better place than this, from which it can illuminate everything at the same time?... And so the sun, as if resting on a kingly throne, governs the family of stars which wheel around.” .AqAF £An§C A ºwR Yl d§d yrw A\ ¢ Y A LAnn
Tr yrw rsf§ y :(Retrograde Motion) Ty`r Tr ybF Yl @n ?|C± A¡d¡AK ¨t wkl (looping motion) Tyql :yt\®m Yl dmt`§ rysft .(Mars) §rm w Am
.T§r¶ Tr ¨ HmK w C¤d§ |C± ¤ §rm •
.HmK w ¢ C¤ Am ³ |C± wV At¤ §rm rts§ • `§ Am ,T§¤Ast TynE rt ¨ §rm E¤AttF |C± ¨n`§ @¡ TA ® .(vd4 1:00-1:21) º Cw Y w`§ ¢ ¤ §rm d¡AK§ AyRC A\® .y r¶ Am`tF³ An¡
Tr rysf Ankm dq :(Irregular Motion) Tm\tn ry Tr AnA\ ¢`wt§ A Hk A ry kJ Ð Aql £@¡ k TVAsb Tyql .(equal) Tr O yS ¤ xwmylW ¢ A A Hfn wq Annkm§ .Xysb Trl yRCA`m dJ A ¢± @¡ m`ts§ yrw k
28 (double epicycles) (29) ¤ z r§¤d l yS§ yrw Cr .Tm\tn ry Am`tF k .yrw A\ T§¦r (vd4 1:27-1:47) Wqm d¡AJ . w k vd4) T\®m TyA r © kK§ ¯ Tr O ¤ ¤ z r§¤d l .(1:47-2:40
:TyAt Awkm Yl yrw A\ dmt`§ :(Conclusion) T}® .HmK w C¤d |C± ¤ TtA HmK • .(double epicycle) ¤ z r§¤d l ¤ (deferent) A w k • .Tm\tn T§r¶ Ar ¨¡ Ar ym •
Om (double epicycle) ¤ zm r§¤dt l dbtF km§ ,AqAF AnflF Am zr yrw m`tF .ry} T\®m rqf £@¡ t .(equant) Tr yrw r .¢A\ ¢yl ¨nby -HmK lt § ©@ - |C± C d .¢A\ ¨ C¤ © `l ¯ HmK ¯ C¤d |C± ` ¤ HmK b
(Tychonic system) ¨¡ r A\ 6.4 :X r Yl w§dyf m`tsnF http://science.larouchepac.com/kepler/astronomianova/part1/7 .(vd5) :¢ zr ¤ ©rO rm yA\n y y¡ A\ rt (Tycho Brahe 1546-1601) ¨¡ r w y A w C¤d A¡C¤d ¨t ¤ HmK w C¤d wk ` y ,yqAs Awk Ahsf ¨¡ ¢A\ Awkm .(vd5 1:14-1:48) Wqm d¡AJ .TtA |C± .rt HmK ` ¤ TtA |C± ` ºAntF yrw A\ .«r± wk Tr zrm HmK ¨¡ r m`ts§ ,Tqyq ¨ Tr |C± w rt§ ¤ HmK Ab§r (mean sun) zr m`tF A\ ¨ C¤ © `l ¯ (true sun) HmKA .(vd5 1:49-2:13) Tm\tn T§r¶ .yrw A\ ¨ AhA Hf w¡ ¤ ¨¡ r
(Laws of Planetary Motion) wk Tr y w 7.4 An¡ ^¯ ¨¡ r ¢lm (Johannes Kepler 1571-1630) rlb d Adn bF ¨¡ HmK An¥ rlb A . wk Tr rK Tm\ T® wk @ y HyVAnm ¢bK HmK dqt`§ A . wk Tr ¤ rlb Am ¨ rm ¡ bt ¨l§ Amy ¤AnF .Ahw C¤d Ahl` ¤ . wk Tr ® ¢ny w R¤ Y ¨t
TFCd Tm\ .d§d rkfA sy Tr O d ¤ z r§¤d l Am`tF(29) .Tr O Pl tl ThAK Tly lm`tF T rm
29 (Equivalence of the Three Systems) ® Tm\± ¥Ak 1.7.4 :w§dyf rqf £@¡ ¨ m`tsnF http://science.larouchepac.com/kepler/astronomianova/part1/8 .(vd6) :¢ zr ¤ ©rO rm Td ¤ TnF 40 dm wk Tr §¤d Tyklf ¨¡ r Am ¡ ¥§ A ¨¡ r m`A rlb t Adn .¢t¤ ¨ S± A Ab³ ¨¡ r A\® m`ts§ C @h ¤ . wk Tr bF ¨¡ HmK Y Pl ¢nk £ºAOqtF rlb d .yO A\n w¡ yrw A\ :Tb§r Tyt ,ºAms Y Anwy r Adn A w Ak A§ w¡ And¡ A » .«Trt ºAW ¤d ¨ wt Hf ¨W` T® Tm\±A d¡AJ .TyRC± A\®m A®W T® Tm\± y zyymt km§ ¯ ¢ © A¡d¡AKyF ¨t §rm w Ty`R¤ TCAq t§ y (vd6 2:03-2:17) Wqm !!!r © dw§ ¯ :T® Tm\± A`w s ¨RC r :Ty}A ®tF T® Tm\± ¥Ak Ab Annkm§ r¶ ¤d lt CAW s ¨¡ ,T\®m ¶At Am`tF ¢FAy yWts A .A\ ¨ d wtm ym Yl OnF sn £@¡ ryy ¤ r¶ ¤d £@¡ CAW ryyt Anm A®W (vd6 2:28-4:53) Wqm ¨ ¢l` t§ A @¡ .TF Cd A\nl wbq ºAn § .yrw A\ Y On ¨¡ r A\n C¤r xwmylW A\ TS§Aq xwmylW A\ ¨ (eccentric) T§zr® Pl t Tylm` £@¡ .(double epicycle) ¤ z r§¤d lf (equant) Tr O A ©@ ¥s w ¨ q TyAkJ³ £® TKAnm Ayl rh\§ :Tm\± lt ºAn dn A¤rW «?ºAms Y Anny r Adn wk d §» :w¡ ¢rV w ¥sA «?AhbbF A ¤ ? wkl (actual motion) Tyqyq Tr ¨¡ A» Yl O§ ¢ A\ © Am`tF wk Tr bt ¢ rlb ^¯ ¨A sq ¨ AWW m ^¯ .r ¤ w (absurdities) AA F :Ty¤rtk³ TfO http://www.keplersdiscovery.com/Hypotheses.html A .HmK A¡zr w tn§ km§ ¯ dq`m CAsm @¡ A\ b Anyl § , wk Tr bF ¨¡ HmK :w¡ AnqlWn §rm w ¨l§ Amy An§d rOtqyF . wk Tr }w d§d .d§d © yS§ ¯ «r± wk §d ± (Planet Mars)
30 (Re-observing) T\®m T` r 2.7.4
¨ lWn§ b ¢ A A ¤ .¢Am ¨ (meticulous) Td d§dJ rlb A AyAkJ³ ¢ w§ ¢yl Ak .T\®m ¶At dt w¡ ©rkf £ wh :TyAt Tr TlO ¨¡ wkl T§r¡A\ Tr rt |C± Am • .|C± Tr ¤ Ty @ wk . §rm Tr ©wts lt § |C± Tr ©wts • .TqAs AFAyq ¨ Tyqyq HmK Am`tF d • Yl ¤ §rm ¤ HmK y |C± wk Adn §rm w xAyq rlb A q .|C± Tr Pl tl (Measurement at opposition) TAqtF³ Hf .Hk` ¤ rK Th §rm wk§ ¤ HmK r Adn AFAyq @ Ð ®t CAbt¯ y` @ Ahnk dq @n Tlm`ts A Tq§rW £@¡ :AV .¢yOt A ¤ W @¡ rlb ^¯ . §rm ¤ |C± Tr ¨§wts http://www.keplersdiscovery.com/Observations.html Tr Aqt³ A .Ahth w rlb Yl A «r TyAkJ An¡ zr Am`tF Y « @¡ .Tm\tn T§r¶ Tr ¨¡ HmK w |C± lt § Tyqyq HmK w k .AFAyql rm (mean sun) Tr £@¡ :TfO T`AW km§ .zrm @¡ http://www.keplersdiscovery.com/MeanSun.html kK bO§ ,CAbt³ y` §rm ¤ |C± Tr ¨§wts ®t @ dn .T\®m ¶At yl Yl rb ry ¤Ð (mean sun) |C± Tr zr ¢yl A @h , wk Tr bF ¨¡ HmK TyRrf rlb lW :AV Awl`m d§zm .Tyqyq HmK Am`tF A\®m rysf A http://www.keplersdiscovery.com/CorrectedTable.html ,xAyq ºAW± (potential sources) Tnkmm V wm Yl rlb YS d` .©r\n ¢lm ¨ lW
(Reviewing the Hypothesis) AyRrf T` r 3.7.4 {Ant ¯ AyRr -d§d T§r\ ¤ A\ ºAn ºAn- lWn § :ytyRrf rlb lW .T\®m .HmK lt § km§ zr Ð T§r¶ Tr ¨¡ §rm Tr •
¢ TbsnA §rm Tr rh\ y (equant) dy¤ Tr O An¡ • .Tm\tn
31 ºAW ¤d ¨- ¸Ak AyRrf £@¡ Wftm ¹CAq ^®§ § yrw A\ ± @¡ .yrw A\ Ahyl ¨n ¨t AyRrf -Trt ¨ mk§ ®t³ k .Tr bF ¨¡ HmK :rlb lWn Y r± w¡ @¡ ¢rO rlb d¡ A .T\®m Yl rlb Ahl ¨t AyOt ¨ ®W³ b (push to the limit) A¡AO Y @ d wtm Tm\± .r± zltF d§d A\ b rA .Ayb§r (equant) Tr O Ak d§ rlb C ,Ð Yl A§E wk ± (line of upsides) Abq X Yl -A T`ybW- wm @¡ wkyF :AV .Ahn d`tb§ Am AW ¤ HmK rtq§ Am rF wk§ http://www.keplersdiscovery.com/Equant.html .Tr O ry rk §wkt r¶ An¡ r@ ?Tr O Ak yy`t rlb A y k Y At An ¨n`§ @¡ .d ¤ TAqtF Yl sy ªAq T® rm dy¤ rlb C .r¶ CAb CAsm dt A C Ð ± Yl ªAq T`C TynE rt Yl §rm wk R w T`C CAt ¤ ¢ A\® ¤d Y zl C¤A T`C :T`VAqt C¤A T`C A¤E £AW Am .T§¤Ast VAqt §rm Ty`Rw C¤A T`C ¤ (equant) Tr O dn VAqt C¤A z C¤Am VAq Ð d` .(sun) HmK dn £@¡ rk §wkt .d ¤ r¶ d ¨mtn ªAq T`C Yl wOl Ty`Rw : ¤± sq AV TynSm Tylm` http://www.keplersdiscovery.com/Vicarious.html Yl wOl r d (guess and check) d ¤ m Tq§rV rlb m`tF d¤ ¤ T\®m §rm w ¢A\ A`w CA Ð d` .r¶ d .¸VA ¢A\ ¨n`§ Am . @ T\®m T «d`t§ rf xAyq wq§ Cr @h .¢Am ¨ Td d§dJ rlb A AqAF AnflF Am wt§ ¯ ® Tm\± ¹ Ab Hf Yl ¨nbm ¢A\ dtl r km§ ¢ rlb l .T·VA Tm\± ¨n`§ Am ,Tyklf A\®m {yS ¤ (aphelion) ¤± ¨`Rw dn HmK §rm d` Hyq§ ¢ : ¨A sq AV .¢A\ Am`tF ¤ T\®m Am`tF (perihelion) http://www.keplersdiscovery.com/Vicarious.html lt ¢A\ ¶At rlb d¤ .¢ A ©@ As T`ybV Tr`m ytyRrf ® ¤ «d ¨n`§ @¡ .T\®m T E¤At Tmyq T\®m .T·VA Amhn lW ¨t © Yl t§ rlb Cr ?m` Am ¤ds §rW Anl}¤ An rh\§ An§C Am- k .T\®m A®W §rm C d Fr§ ¤ T§db TyRr Anyl § :Ty @ ¢tr sy |C± Ah\® ¨t §rm Tr -AqAF TqAs Tly Hf m`ts Annkm§ ¯ .|C± Tr l`tm ºz Tr` CAs r` Ð Anyl § . §rm R w km d rb d§r An± .Td |C±
32 (The Orbit of Earth) ?|C± CAs w¡ A 4.7.4 .|C± CAs d§d ¢yl ¤ ¤ CAy rlb lm§ ,r@ AnflF Am (Hipparchus) Lr A§ A` r ?CAsm @¡ d§ ¨k db§ y k £@¡ ¶At A .Tm\tn T§r¶ Tr (HmK ¤) |C± Tr rbt` ¨t rlb TyO J k .xAyq T ¤d ¨ T\®m Tqft TyRrf ¢tr k ©r¶ |C± CAs TyRr ®W³ Y ¢ A Td b Ahlm`tF ¨t Ahsf ¨¡ TyRrf £@¡ ^¯ .Tm\tn sy CAsm @¡ Yl ¢¶dbm TyqWn Tyt ¢ Yl rOt @¡ h km§ . §rm CAs TF C ¨ A ¨t TyAkJ³ k .« wk Tr bF ¨¡ HmK » :¢n lW ©@ yWts yk .|C± WF A\®m ym wq An ¨¡ Ahth w ¢yl ?Ah C A ¤ |C± CAs d§d A§ Anyl @h ymyqts VAq §rV TWq Ak d§d km§ @ ¤d |C± dn VAqt Yl O Annk .|C± dn A`VAqt§ ymyqts T§dyl³ TFdnh ¨ AnFC l` ¤ .|C± t§ AnFAy ± wh © ©- ¢ ©E wm A`K ¤ TWq Tr` ¨¡ yqts d§dt rW y yWts ,ºAms ¨ Ah`Rw xAyqb HmK ¨¡¤ TtA TWq An¡ .-£A ³ Ahl wkA ?TyA T\qn d y k .¤± yqtsm Yl O §rV Tl\`m £@¡ rlb A . d dy` TtA wn ¤ rt .Aw§ 687 §rm Tr C¤ l`§ rlb A . §rm w yb .¨A yqtsm Yl O w§ 687 ºAms ¨ §rm Ak T\®m Anm .AmhAk ry§ ¯ §rm ¤ HmK ± |C± CAs Tr` km§ Tq§rW £@h xAy Am`tF ¢tyt d r¶ d d§dt AFAy T® rlb m`tF :TfO AV . C http://science.larouchepac.com/kepler/newastronomy/part3/24/index.html ©r¶ |C± C d Y rlb Pl .rlb Tq§rW ¨yRw XW T§¦r zr lt (equant) Tr Om TbsnA Tm\tn |C± Tr ¤ TF C Y wr -(30)Td |C± CAs d§d d`- rlb Ak b}.C dm . §rm w C d
(The Orbit of Mars) ? §rm CAs w¡ A 5.7.4 .TyRr © ®W³ d §rm CAs TyAkJ ¨W t rlb rk A .¢y }w ©@ |C± CAs Am`tF §rm Rw xAy dy`§ Cr dq Cr ,Ð C ¤ .ªAqn £@¡ mK§ ©@ ¨Fdnh kK d§ ¤A Ð d` Tytn k «r r ¢ AAs A .«r T}r T§r¶ d Tr ¨W`§ r¶ d ¨l t ry Cr Y r ¤ r ¢ AAs rlb A .ryt .(oval shape) ©wSy kJ Y r\n§ ¢ r ¤ ¢ ¤AK `Kq @¶dn ¤ .Ay¶Ah :TfO Yl ry± XW m d¡AJ http://www.keplersdiscovery.com/NotaCircle.html .@ £CAbt km§ @ T\®m T ¤d ¨ k A§r¶ Hy |C± CAs(30)
33 ?¢f}w T A` R¤ km§ ¡ ¤rWm ¥s k k r§ ¢ dtl r d ¢ AAs ¤ ¢ AFAy rlb A d` d§r§ m .r¶ dl TyFdn¡ AAR Am`tF kK @¡ }¤ ¤A ,W © :Yl lW§ km§ rlb ¯¤A r\ wk§ http://science.larouchepac.com/kepler/newastronomy/part4/index.html lV (refraction) ºwS CAsk r¡A\ ¢tF C ºAn ¢ ry rlb r@ Wq w (Apollonius of Perga 3th century BC) ©¤Arb xwywl Am Yl PA W w¡ §rm w CAs C .(conic sections) TyV¤r m :AV .(ellipse) http://www.keplersdiscovery.com/Elipse.html .Awl`m d§zm
(Laws of Planetary Movement) wk Tr y w 6.7.4 HmK TyRr A®W wk C d }¤ ¨ d rlb C ¢tlC rlb d Adn .rµ At³ ¨ K ¢ ¯ ,(heliocentrism) TtA Wts§ ¢nk . wk Tr bF ¨¡ HmK Ab ¢d¡ A Tyklf TA P¶AO b§ Crq .HmK T An wq £@h Af}¤ ¨W`§ bs A§ ¨ ®bqts dAs Ahl wk Tr (universal properties) TAR³A y w T® Xbnts§ rlb AWtF .Tr £@¡ º C¤ ¨¶A§zyf .d ¤ wtsm ¨mtn§ wk C d ¢tr` Y
:¤± wAq « .¢y C¥ «d ¨ HmK q AOA A`W ¢tr ºAn wk Fr§ »
“The orbit of a planet is an ellipse with the Sun at one of its two foci.”
:¨A wAq rt ºAn T§¤Ast AAs wkA HmK Xr§ ©@ A`K sm§ » « .T§¤Ast TynE
“A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.”
34 :A wAq ¨sy¶r Cwm O `k wk T§C dm rtf r FAnt§ » « .£C dm “The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.” ¨¶A§zyf Yn`m LAn Aw , wyn TA` TyÐA wA LAn b .(vector calculus) ¨A`K As ¨ ©dylq §rm ¢ .£® ¨A wAql dt TynE rt ¨ £® −→r A`K Ahsm§ ¨t TAsm b hs −→ : r`m L (Angular Momentum) Tr z A`J Tl§wV FAnt§ −→ L = −→r ∧ −→p , −→ AZwf L Tr z wk§ . wk (momentum) Tr Tym w¡ −→p y .(gravitation) TyÐA (central force) T§zrm wq A`t Adn z §r` ,Ð Yl E ._Af³ @¡ Tyt w¡ £® ¨A wAq −→ ¨n`§ Am .−→r ¤ −→p yA`K Yl © wm L tnts Tr ¨A wAq Y r\n km§ Annk .d ¤ wts Y ¨mtn wk Tr Tr ¢y yS Adn- ¨A wAq tnts @¶dn .}± w¡ ¢ Yl . A Tr Tym z Yl d§ -d ¤ wts ¨ t
(Gravitational Attraction) A` TyÐA wA 8.4 «? wk Tr bF A» :w¡ wk Tr TF C ¨qbtm ¥s ¥s @¡ ^¯ Trl ¢ny w (Newton 1642-1726) wy R¤ d` ` Am- LAnnF TA` TA A`t d k .Ahb§rt T}r ¨W`§ y wq zrnF ,¨l§ Amy .Tm\tnm T§r¶ d Trl T}A TA - wy .K3 ¤ ,K2 ,K1 : rlb y wq zrnF Am .N3 ¤ ,N2 ,N1 :EwrA wy −→ . wk Yl r¥ F w An¡ tnts (N1 + K1) • :Tmyq R rW O ¤ v TrF Ð Tm\tn T§r¶ Tr CAs @§ • v2 a = . R :TmyqA Trl T T§C dm rtf YW` • 2 π R T = . v : K3 wAq Am`tF tnts • α v2 = , R . A α y
35 Yl O ,TqAs ¶Atn Y TAR³A ,N3 ¤ N2 ywAq Am`tF • :TyÐA wA m M F = G , N R2 .HmK Tlt ¨¡ M ¤ wk Tlt ¨¡ m y @ w P¶AO Hf m§ ¢yl O ©@ wAq wy ^¯ dtl .r ªwqs O§ ¢sf wAq @¡ | rt Y @¡ ¢` .TyRC± r ªwqs |C± w rmq Tr y TCAqmA wy A ,Ð TyÐA w An¡ @h Atb Tyb§rt ¶Atn w§ ¢wA d¤ .As° .m2 ¤ m1 ytlt © y AtntF ¤A ¤ TyÐAl A` wAq lWn ¤ Arykf Tq§rV Hk`n P¶AO {` TKAnm ¨ftk ¤ An¡ Tlm £@¡ TF Cd wq .rlb y w ytlt ©¤Ð yms wkt T¤z` TykyAky Twm xCd Adn .TA` ys Tr (center of mass) q zr Tr z` ¯¤ wq ,m2 ¤ m1 −→ R ¢`Rw A`J ¤ M q zr Tlt Aty} @ .(reduced mass) A`f :kK −→ 1 M = m + m , R = (m −→r + m −→r ) , 1 2 M 1 1 2 2 −→ ¤ µ A`f s Tlt @ Aqm ¨ .mi Tltk Rw A`J w¡ ri y :TyO −→r ¢`Rw A`J
1 1 1 −→ −→ −→ = + , r = r1 − r2 . µ m1 m2 @¡ .Ahyl r¥ TyCA «w w¤ d T¤z`m TykyAkym Tlm ¨n` ¶At . wyn A wAq bs yms Twk Tlm TbsnA q . wyn ¤± wAql S § ¤ r wk§ M q zr ,Ty}A £@¡ ys Fr§ ,TyÐA w TA ¨ .wq µ A`f ys S § Aqm ¨ .¢tr ºAn PA W A`f CAbt³ y` @± § ,TysmK Twmm Yl ¶Atn £@¡ ybW dn km§ lWnm @¡ .TysmK Twmm Tlt \` kK HmK Tlt Aqm ¨ .(31)rt ¯ ¨AtA ¤ TysmK Twmm q zr HmK CAbt .Ahtr ºAn AOA A`W Fr wk CAbt km§
(Beyond Newton) wy d` A 5
F ¤ ªAK Y (32)A` ÐAtl ¢wA ¤ Trl wy y w E¤r « ¡ Yl ¨l§ Amy r`nF .Ah¶At (explore) AKktF ¤ y wq £@¡ TF Cd Tyb¡@ wns ºAn Ah`R¤ ¨t (principles) ¹ Abm ¤ (concepts) y¡Afm .Tm\tn Tmyqts Tr HmK Tr wk AS§ km§(31) Adn (Robert Hooke 1635-1703) w¡ r¤C CAk r wy A Ð A w d An¡(32) .TyÐA wA Kt
36 y w {` Y ¹CAq ¢bn § .TykyF®k yAkyml (golden ages) ºwR Yl Aht` r Xq m ¤ wy Am b T¤r` A _Af³ .¢Am
(Potential) wmk 1.5 w Yl wqf hnk Tflt TyÐA wA £A yy¶A§zyf ` ¤ C A d` r¥ wqA .(mysterious) TSA w (Gravitational Force) TyÐA w ytltk y d`b A Amh :Aw ry A ©@ º¨K ,(action at a distance) ¯ Abt§ ¤ «r± Tltk ww Ar`yF -«r ¤ Tq§rW- Amh m2 ¤ m1 dy¤ Tlt An`R¤ An y :TyAt TyAkJ³ AS§ An¡ .(interaction) ryt km§ ?¯ ºASf @¡ ¨ Tltk £@¡ A ryy © An¡ ¡ ,ºASf ¨ M :yfwm A§ @ t , @h AnmlF k .Tlt w¤ Yl dmt` wq ± ry © dw§ ¯ • ?TyA Tltk R¤ T\ ww Y wq £@¡ E¤r rsf An y ¦Ast Yl y § ,ryy ww AnmlF ¤ ¨A wm A@ • ?¢FAy Annkm§ y ¤ ryt @¡ T`ybV w ¨W`§ ¢ y ¨A ©r ©dAs (Laplace 1749-1827) x®¯ A w T\®m x®¯ ®W .TyÐAl (local description) Ay`Rw Af}¤ ry A A§ ,TyÐA xAyq @ T¤r`m dyw Tq§rW ¨¡ TyÐA :(33)T®` m`tF .wq £@h r ¤ kK l`t§ § M Tltk 1 Fi = ∂i V (x) ,V (x) ∼ , ri :T®` q§ V (x) (potential) wmk by
∆x V (x) = −4 π ρ(x) , wmk (source) CdO ¨¡ ¨t (mass distribution) Tltk §Ew w¡ ρ(x) y l`t§ ©@ £® T A`ml m§± rW .V (x) (gravitational potential) ¨lq Sim´eonPoisson) wF w wymyF ¢AR x®¯ T A` ¨ k§ ρ(x) : (quantities) Aymk Xysbt TyRA§C Tly T§ db ¨ wmk rbt .(1781-1840 .Ah` A`t § ¨t ryb`t Anyl hs§ Am (scalar quantity) ¨mlF C dq CAb wmk • .(change of coordinates) A`m ry Adn ¢n m Y (point particle) T§ Am Xqn y w ym` wmk Annkm§ • .Twhs dyq` r TykyAky .(potential energy) TnAk TAW §r` wmk Annkm§ • b} y (general relativity) TA` Tybsn T§r\ E¤r ry Cw± k .¨¶A§zy w¤ ¨lq wmkl
.T®` £@¡ rt ¤ (Alexis Clairaut 1713-1765) ¤ryl Hysk wk§ km§(33)
37 (Conservation Laws) _Af³ y w 2.5 r¡ w\ TF C ¨ Tmh TAk (conservation laws) _Af³ y w t :y wq £@¡ d¶ w y .Ty`ybW Y At ® .Trt ºAn Ah wq ¨t AFAyq _Af³ y w hs • .rmts TfO AFAyqA wq r@ .Ahf}¤ ¤ T`ybWl d§d y w bl lWnm kK km§ • .Am ybF Yl rlb ¢ A A AKt³ Am ybF Yl lm`tF .whml AKktF kK • .wn§rtn (Pauli) ¨w ` Am d§d Amys @ .TyRA§r ¶Asm Xysbt _Af³ y w Am`tF AS§ km§ • wA Am`tF ,(central force) ©zr q ¨ Tr Am ybF Yl degrees of) T§r AC d {f yWts Tr z _Af .yn Y T® (freedom y w ¡ (conservation of energy) TAW _Af wA CAbt km§ ¯ µ d ¢ rt` Anyl § k ,(fruitful) TwO A¡r ¤ _Af³ :(Hendrik Kramers 1894-1952) Er r A Am .TAWl A §r` dw§ ,T}A Ty¶A§zyf wl` ¨ ¤ ,TA ¨As³ rkf A ¨ wk§ d§ » « .Td Ahr` yts§ ¨t ¨¡ y¡Afm O ¤ ¡
“ In the world of human thought generally, and in physical science particularly, the most important and fruitful concepts are those to which it is impossible to attach a well-defined meaning. ” Annkm§ ¯ d§dK F° .Ttb A·yJ ¨n` ¯ AhZAf db ¤d TAW ^¯ .¢n rysy r@ ¨ftknF ¤ TAW _Af db §CA ¨ Qw T§r\ Am`tF T¤A ¤ (Decartes) CAk§ Am A§ db A £@¡ A .A AO y wq ºA§zyf y w TAyO dbm ¢ZAf ¤ z Tr Tym _Af y w TAyO Hnw¡ ¤ , C ,Hy ¤ ® T¤Am TAW Tym¡ ^¯ ¤ znby A .Trm A AOt ¨ Tyr TAW ¤ ¥§ A Am .A AOt ¨ AhZAf ¤ (kemitic energy) (34)Tyr TAV Y -Tr ry A AOt TA ¨- wt§ Tyr TAW ºz .(latent energy) Tyl ,{ wn ,r ªwqsA CA d` -rtf £@¡ ¨- wy¶A§zyf A y w §rV ¶Atn rysf T¤A w¡ A` £A ³ A ¤ ,A AOt .Tyr TAW T}A TAWl Ayms d CwhZ Y @¡ « ._Af³ ©@ (Willem’s Gravesande 1688-1742) dns r ¤ Tr CAt £@¡ y rf m d¤ .(soft clay) y yV Yl Tyd` r ªwqF ry xC . dW}³ dn rk TrF r FAnt§
(living force) Ty TAW F Ahyl lV(34)
38 y w CwhZ d` yAkymA wmth§ (mathematicians) wyRA§r d .T·Ak AkJ Ahny w TAy} A hq A Yl w`R¤ ¤ ,Trl wy TyA`K wy y w §w d§d ¢wt @h TrtKm P¶AO ¡ .(scalar quantities) TymlF r§ Aq Yl dmt` y w Y (vectorial equations) d’Alembert 1717-) rbm ,(Euler 1707-1783) rl§¤ :Am ybF Yl r@ .(Lagrange 1736-1813) r¯ ¤ ,(1783 scalar) ¨mlF C dqm wq {§w` Yl d§d AAyO £@¡ dmt` Xq Tnkm AAyO £@h .(potential energy) TnAk TAW Yms§ (function ® \ TylRAf ¯ A` ¨¡ Tr ¯ A` ¤ ,«wq QA w h k .(potential energy) TnAk TAW ¤ (kenitic energy) Tyr TAW ¨wA ¤ (Hamilton 1805-1865) wtlA¡ Am Y At ¯ A`m £@¡ } ytAW wm _Af T\® Y Am± £@¡ .(Jacobi 1804-1851) .TnAk ¤ Tyr yAky ,(thermodynamics) T§C r yAn§d ¨ T§r\n Am± CwW ¯µ CwhZ ¤ ,(electromagnetism) TysyVAn¤rhk ¤ ,(hydrodynamics) ¶ ws ¨ q (universal principle) A db An¡ ^w TyAnO T\hn .(conservation of total energy) Tylk TAW _Af w¡ ¤ ¯ ¯Am ym y w Xr (Emmy Noether 1882-1935) rw ¨m§ Am CA\t Anyl A :(symmetries) rZAnt _Af³ time) z ¨ As³ rZAnt ⇐⇒ Tylk TAW _Af • .(translation invariance Akm ¨ As³ rZAnt ⇐⇒ Tylk Tr Tym _Af • .(space translation invariance)
.(rotation invariance) C¤dl rZAnt ⇐⇒ Tr z _Af • .ºA§zyf y w TAyO HA`m £A ³ ¨ A rw T§r\ m`ts
39