"!$#%
&('()*)+-,/.0'
=;C@Q7:13n?9B7:O62-2R4646GBDJK58;I9K7:4f9<@:D-46;/9(HI=-HU=F[2;C9B5Q>?Ga5:7:;HI9%VWF/@:9B7:AF9B2>X9K;C>o@E2-D>X2-;C>P>OY;CF5QHI9B589B7:G<=Z46F[HUHID-F/;U9(7:D-F*\]FC9h@:DJ@:^6469p4_\q9<4L@:O6=9B46HI9K>?;/7Q>-46@E>?4L;/7:7:GB9NFI9aM`9KO6>-FbN4LceHI@:df^6M-4P9K;/>O6GBFC4;/7:5Q4g5QF2GB=4g=R=Z;SO6F/@QF>7:>9B46O6D->F9B^6D-GK;C9BF[F@:>-4TOE9hrDJ4_9B>46GKG9B;I^6HI9K;C5QF/GKFC93@:7:A/cSF*i 46jk>?DJ4P7:94l i 2-jDJ>Rm 46; G
O6;I;/5QHI2-=Z==ZF-M/F/DJ@Q@:9?4}HU9BG~;/5Q5Q5:F;GB4st\q4LM/@:5QHI9K;<FuR4Y5QD€5:;<9a>=469KGB;/Nv>-F/4L@:7:9BA9~9B9B>->o4HID-46F/G?7:5QF[9B58@:7:9B465QHU=Z4L;w7Qma7:Fx3;4LG?D€OY46;/5Q5Q5QFgF-DJm_46‚$G?>€HI=-F/@:7:9BF<HUDJ;U469?;/==-9K=-;/@:>-F4L5Q7:5Q9w9BHUO69zF3;Cy ^64Y9B{?F2->9K4/|/Mh;/5QGB44
DJs„46G?ƒ…‹‰5Q9B@:58FC7:V46|HU4LM-@:GK;k46;[HInw5QFF[F/GB@:4LOEAŠ$r4L‹"4_>w4L7:@QGB4}4@E;DJFC46{?@:Ghœ29pO6467:;/5847EHI;D-=Z469B=ZF[9hF/==-7:9K462a;/5QF>-y 9Z4L4ˆ4Ly 7:5Q9a|e5Q4f4L5Q@:F@:F4}>-5QFU@:9BHI9p7:5Q46469BGK>wHI42J=-9K7E>@:;}4_{?\]2R4fDJ@:;C46HU>wGBK7:4};F3O6@:sF/9K5Q>=ZŒS9BVOf4fr-7Q7:4Ž‘FIm<;/‚ZGB>P’NK;“6=”;C•†=Rj@Q7:Œ/;S9B–Z@QO67:F/’N9B“YG0O6;S”e46@:—8GB4˜kK;/Ž‘5Q‡-F/mˆ>”wx3FU™ š46šZ46G‰GB’NOY“Y9K;/5Q”5Q5Q›w9NF Mm
=;C@E;CœZFGB4gFwDX9B=Z4L@:œZFGB9";5Q46O6F/>RD;Ofr-4gGv 46>-4L@:A9K;7:FC7E;/GB4}žW5Q90;>46A;C7:9B|;wMR>w2GBK;F[=ZF/5Q9p7:9K|/;Jm
Ÿ ¡I¢ˆ¡¤£¥§¦¨*©«ª*©I¬¢ˆ¥S­g®¯C¯S©°¥C¨±¦¨­g©U²¤ª¡¤£¥´³w¡¬%µg®¶­g®}¨X¢¬%©U¯/¥
ºqÃ/·Ä̾f¸JÅ(¼C¹P½JÂLº0¹Xºq¹P»‰Å"¼SÃ/¸oº]Âf½wÃIÁZ¹Pºqº~ÄÒ¸P͝¹P¸-½PÂf¸wξ:¿L½P¿L¸€À‰¾EÁZº0º]»½€º]½w¼CÂL¼S¸ÃÃ/¸-»-ºqÂL¿LÄ~Á(ÂLÅ(½Jº0»‰ÂLÄ0Ã-¸J½wÏ%Æ(¿fÃIÄqÐQÃC»¹€Å"Ñ-¸J½PÄ]À‰½wÁ(Ã/ÂL¾E½Jº¿fÄ~¸€ÓzÔ?Å(¼CÕfÀ(ֈ½-»¾EÕf¿f¸P×%¸€ØYÃ/ÁZÏk¾Lº~¾fÙ̸XÇR½Xº]Ëh¾:ډ¿6½€½É-¾EÀ(ʼnºq¹PÂ6ºE½*À*È ¹XÛIÉJÃCÃ/¿fº0»(»ÂLºq¿fÃC½PÂLÂ6¸Z½w¾EÁZÄq͝ÃÃCÀ‰ÂLÅh¼CºqÃI¼/¸½(¾fÄ0¾fÊ(ú0Å"Ɖ¼CÃCº0¸JÄqÂÃJ»RÊZÇJ¼SÀ(ÂLÃ/ºq»(º¼6ÎCˉÃÈ ºqº0¸JÃʼn»‰ÁZºEÀºÒÈÃC»‰¼6¼SË(Á(¸-ÃI¸X»RÇJÀ‰¾fÃC¸J¾f»‰ÃCÄq¸XÂLº0Ã/ÃC¼6»-¹Pˉ¿L¸ÃÃ
Å"ÔZӝÃCÜEˆØSÊhÄ0Ã3Ö%¼Sӝ¸RÜEØ_¸JÂ6ÃÁZºq×k»‰Ó½?ÜE¿LØSÃJÊ"ϼCÐQ¸-Ä-¾»(Ý ¸¼S¾:¸-¿L¹XÂf¸ÃI¸JÄ]Æ(½XºqÃS¿f¿fÂ6¿f½wºqºqÇJÃS¸¿f¿fÃȸ-ÂfÁZº]ÃC½(¿fÏ3Ã/Âf߈¹PÃCÂgºq»‰Íz½w½JÂLÂ}ÃÑÄqÀ(ÃÃ/þEÑ-¿fÀh¸o½w½JÎCÅ(ºq¸JÅ(»‰Äqºº-¼6¸-Ë(ÂLÃ/½JÂfÂfÃ/ºq¹PÃJʸX¸?ÇRºÇJÅ(ÃCÂLÂLº0¸g»‰¼CÄqÃ<º0ʼn͝ºÀ(»‰ÁZÎCººq¼S¸J¸J»(»hºZ¾EÁZÃ/Ã/ÂfÄ-Ç?¿L½wÃCÎ/¹Pº0¸-Å"»(¸Ã
ÁZ¼SÀ‰Ã/º~Ä0Ä$à Ã/à ÃC»(»(ÃCÃ/ÂLÂfÉJÉ-º]½ºq½¹P¹PÃ/Ã/¼C¼/¼/¼C½w½w»(»‰º]ºq¼CÞ ¼/½*½Ãoâ„Á(ÃCÁZÄ<ÃCÄq¹P]½¸-Åh¹X½wÃ/Âf»¿fº]¿f¼S¸ÃCÄq½w]½(»‰ÊZÉJÁ(¸J½?Ä]½w¿6ÂL½PÃJÏoÁ(½wá}Äq »‘½X¾f¼C¸J½J¹P¹X¹€Å"¸½ÁZÁZº<Ã/Ä0͝¸Jà ÃCÂL»(ÎCÃ/ÀÂfÉ-¼SÃ/ºq½X»-¿L¼SÂLºq½J»(Ä0ÃSº_¿LÀºqÈ ¼/½X¼S¸Jãä»h¾EÃIÃ/ÂfÁZÇ?ÃC½?Äq¿Lº0à Ã/Ç-»(¸‰ÃCÊÒÂLÅ"ÉJÃCº]½Â
Å"¸w¿fÃ/»(ÎCº]½wÄqÃåPӝÔwØSÊ
âçætã‘èéåPÓzÔ?ØSÕ
Ó:ÛeØ
ÂLÇJº0Ã/¹€Ä0¸Z½w¼C»‰ºK¿?ý(È ÊZ¼C¸-¸?¾EÇR¿LÇJ½wÃ/»Âf¿L¸XÃTÁ(»(½wÃ/º~ÄÇ?¿L½wÃCÄq¹P¸JÂLÅ"ºk¸‰ÔCë Ï´ì[æíÐQÄgÔ(ë ¾fӝÀ(ܸæäÇeî-½JØÄ0¸-Ã*ÂfÃêë ìÃÈ æWÁ(ÃSë ¿fӝÃ/Ü<Âf¹Pæðºq»‰î-½?ØYʉ¿L¸ÃÇ?Á‰½J½wÄ0Äqà 0Ã*¼S¸-»‰ÁZºqÎCºq¸J»(ºkºq»(º0Î/ºq½JÄ0ºg¾fÀ´Å"¸-¾fº0Î/º0¸-»(ÃÃ
ï ï
âñæ ò~Û ó ïìô è§åPÓzÔ ì Ø Ó$¼S¸¾:¿6½w»¿fÃeØ6õ
ÐQÁZ»ºqÅhÀ(Ã/»»‰ÁZ¼/ÃU½w¹P¾f¸JÅhÄq¸€¸oÁ(Á(½wºÒÄq͝0ÃI¸JÂL¼CÎC¸JÃU»‰¼CÁZÃCºq»ÎCºq¿f¸JÂ6»‰½wÄqº~ºÌº0»(½J»‰ºqÎC¼6º]Ë(½wÃIÄqºÏºqÄÌÙ̹P½P¸J¾E¹PÀh½XÃC»Á(¿LÃS¸oډ½w»(»(ºqÎCÉ-ºq¸J¸JÄ]»‰½wÃXÂLÁÃÈ ÃUÈ ¼C¸J»‰¾fÃCÂLÇ?½?¿L¸‰Ê(ÑÀ(ºq»‰ÁZº½J»‰¼6Ë(ÃIºqľfÀ(¸€Ç?½wÄq¸JÂLÃ
ö ë æíÔCë ì÷ ó ï ë ìæ öXù"ø ú Ó$¼S¸¾:¿6½w»¿fÃeØ6õ
ë ºq¹XʼnÄ0º]¼C½û¼6Ë(þf¸J»(¸¼S¸¾:¿6½w»¿fºk»(Ã/Äg¿fÃ/¹PÅh¸¾fºq½ºqÄ}¾EÀ‰¸¹P¸ZÁZÀ(Äq¸ ö ¼6Ë(Ã*Äq½û¾fÀ‰½
Ì
Ù

½
S
¼
¸
‰
»
f
¾
C
Ã
L
Â
e
Ç
J
½
C
Î
q
º
J
¸
(
»
*
Ã
Z
Á
º
ö
ÁZºqÂfÃ/ÎCºq¸J»(à ù ø ú Ê(¸?ÇRÇJÃCÂL¸¼6ˉúqÄÒ¹P¸w¿L¸Ã[È Å(ºq½J»(¸‰ÏˆÐQ»¿fÃ/Âf¹Pºq»(ºÌÁZÃ/Ä0qÃI¼S¸R¸JÂ6ÁZºq»‰½?¿LÃ[Åh¸-Äq½JÂfº~¼SºQ¸€È ºq¹XʼnÄ0º]¼C½P¼6Ë(Ã
×kӝÜEØæð×ì Óz¼S¸¾:¿6½w»¿fÃeØYÕ
Å"ӝÇ-ÃCÃ/ÂfÁZ¿L½wÃ/»ÂfÃ*¿L¸IÚhÄqÉJ½À(¿LÂ6ÂL½t½Jº0ÃCÛ¿EØS¿fÏý¸-Âfüº]½[º]¾LÁZ¾fÃC½wÄq¿f]¸´½[Å‰× ½wì ÂfÊ}¿fº]Äq¼S½Ã/Ä0¿L]½ÂL½JÉJº0ÃCº]½J¿E¿f¼S¸-Ã_Âf¾fº]À(½ûÄ(Å(ʼnÀºq½J¸´È »(¸IÃ/¾L»(¾EÃ/¸JÂfÂLù€Ã½w¾EÄqÃ_Å(ÂL½wÃ/Äq¾L½[¾L½ÁZºq¼SÂL¸JÃC¹PÎCºq¸Jû‰À‰Ã_»‰ÁZ½ûÃCÄ(͝À(¹P»(¸-Î/¹Xº0¸-Ã/»(»Ãê¿f¸UÁZ½wÃ/Ä0»‰]½‘ÉJ¸J¾fÄ]½w¸JÂLÄ]½Ã
¼S¸R¸-ÂL·ÁZ¸Jºq»‰¹P½wºq¿L»‰½X¼Sº]½w½w»(¹PÉ-¸[¸JÄ]¼S½w¸-ÂLÄRÃ}Á(ֈÃSþ(¿fÃ/»(ÂfÃ/¹PÄ̺q¾E»‰Ã/½wÉJÂLÀ(Ã3º0¿fÄ$¸Pà Ã/Ä]ѽXÀ‰½Jº0»‰ÎCÁ(ºq¸Jºq¼6»(Ë(Ã3Ã/¸JÂfÂ6Ã/½w¹PÂL¸Pºq½}¾fÔZÃCӝ¹PÜEØYÅ(Ï%Äqº]ÿ¼SÃCÃ/¹P¼C¸JÃ/¹P»-¿LÅhÃI¸-»(¼S¸Jº]½w¹P¹PÃI¸[ÔZÄqӝ½ÖÒÇJØSÃ/Ï Ä0¸Z¼Sº0¿e½È ÁZÃ/Ä0]½Å‰½wÂf¿fº]¼SÃ/Ä0]½
ºq»Ç-ÃCÄq¸Z¼Sº0¿e½XÈ ÂL½-ÁZº]½wÄqÃï ë Ã[»(¸-Âf¹€½wÄqÃï ë Ê
ï ë æíï ë èýï ë æ Ô ù ø èÔ Ö ù ø Õ
Û
z
L
r
y
r
ϑ
ϕ
x
centro di forza
ü¼S¸Rº0É-¸-À(ÂLÁZÂ6½Tºq»‰Û½w¿f·ÃXÅh¸J¸-»RÄqÇJ½JÃ/Âf»(º%ÎC¼6ºqË(¸JÃP»(º"¼CÅ"½JÂEÃC¿LÂgÃ/ľfà ºqÀ‰½J¾f»(¸€ÃJÏÁZÃCÙ<Äq à ÃU½-¾f¼S¾f¸Rà ¸JÂ6ø ÁZÃXȺq»‰ÁZ½?ºq¿LÂLÃJÃSÏ¿E¿LÐQ¸Ä̼SÄqÃ/À(»-»(¿LÉ-Âf¸*¸Pº0ÁZÄ%Ã/¹PÄ0]½¸J¹P͝¸JÃ/ÂL»-Î/¿L½T¸ÃÈ ½J¾f»(º0¿fÉJÀ‰¸-½wÄq½J¿f¸PÂfû(ÂfÃCÃ/ÄqÄq½wà ¸-¿fÂfºqÇJºqÉJ¸‰ºqþ»(ÃJ¾Eº]ÊZ¼C¾f¼Cºq¸J½X¹Pºq» Ã
Ã/ÐQ»¾L¾f¸Iʼn½JÃ<È ÂE¼C¿L¸-ºq¼C¾E¸J¿LÄ]½w½w»ÂL¿LÁúq»(Ä<ÃC¹PÄ-¿f¸wÃ/¿L¹P¸ÅhÂf¸ºq¹€Åh½wÃ/»(ÂÃoÀ‰»U¾fÃC¹P¹P¸wÅ(¿fÂL¸ÃPº0»»(ÃCÀ(Ä»Å(¼/º]½w½w¹P»(¸‘Åh¸ÓzÖ ¼SÃCæí»¿LÂLî½JÄ0à Ã-ʺqÄæíÂfº0͝îÃCÂLº0½J¹PÁûÃ/¸-»-ÉJ¿L¸»(º%¼6Ë(º]¾EÿL½w¾f¼C»ÃC¿LÉJÀÄqº]»(½wÃC¹PÄ<¸U¿fÃCÃÈ ¹Pºq»(Å"Ã/¸ÂfØSÎ/Ϻq½JÙÌÄ0Ã-à Ï
¿fÃ/Â6Á*½J¾E×û͝¸JæðÂL¹€½J½wÂLÎ/¼S¿Lº0¸-½w»(»Òº?Ó ÍÂ6½_"¼SØS¸RÏ ¸JÂ6ÁZºq»‰½?¿LÃÅ"¸JÄ]½wÂLºJÃ<¼/½wÂf¿fÃ/¾fº]½w»(Ã<¾L½wÂ6½w»‰»(¸ æðԈ¼C¸-¾/Óz×%ØYÊ €ætԈ¾Eºq»ÌÓ$׈ØSÊ?ÔIæ ô è ô
ÄqÁZ½wÃPÄq¸?Ç-¸JÁ(ÃÂ6ÃC½€ÂLù øº0Ç?Ã/½?¾L¾EÿLÃ/ÃPÁ ÂfÃÂfù ø º]¾EÂfÅ"º]¾fÂLÃS¼C½J¿fÂf¿fÅ(º0¸¿EÅ(¿6ÂL½T½wÃ/ľf¼CÃC¿L¸JÃC»¹P¹P¿L½JÃÅh»(Ä]¸¸‰½TÊ"Á(¾fÂfÃC¸Jº]Äq¾f¹P0ÅhÃX¹€ÃC͝¿EÀ(½T¿f»(ºqÇ?ÁZÎ/½wºˆº0¹P¸-ÁZ»(ÃCÀ(º%»ÃÔZ¿LÃJ¿fӝÜEÃ/Ê~Ø[Âfºq¹PÄÃPÇ-ºqÖ%»(ÃCºÂ6ӝ}ÑÜE¾EØS¸-πÂfÀ(ÃÙÃCÂLÄqà 0½-ÃC¸»(ÁZÃ/ºqÂL½JÂf½-Ä0É-ÁZÁºqº]½½wÃXÄq¼SÃUѺq»(À(ã ÃSÃ/¿LÄ0Êaqºq¸¼/Á½»(Ñã¸JÀ(ÂLÃ/¹€ÁZÄ0qÃC½w¸TÄqÄq]ÃJ»(½Êa¸-ÅhÃ/ÂfÁ¹€½wÂf½J¿fÔoº]Ä0¼SÁà ÃCãÄq֑]½T¾EÅ(¸-Ó$¼SÀ»(ºQ¸¸¸ÈÈ
»(¸-»¾fº0É-»(º0Úh¼C½X¸?ÇRÇRºq½J¹XÃ/»¿fÃ[¼6Ë(ÃIÄ$à ÃC»‰ÃCÂLÉJº]½¾fºq½XÀ(»*Ç-ÃS¿E¿L¸JÂLà pØYÏ%Ùà Ã/¾fÅ(ÂLÃ/¾L¾Eºq¸J»‰ÃÁZºÌã ÁZºqÇJÃ/»¿L½
ãtæ òÛ ó ïô æ òÛ ó Ô ô è òÛ ó Ô ô Ö ô æðã èã Õ
¹P¼S¸-¸J»¹Pã ÃC»¿Læ ¸Pô½Jó»(ÉJÔ ¸-ô Äq½JÃIÂfà ã ö Ï%æ ÐQ»Zô Ízó ½w¿EÔ ¿Lôº Ö ô Ï<Ùà À(Ä0¿fºq¹X¸P¿LÃCÂL¹Pº0»(ÃIʼnÀ¸PÈ Ã/¾L¾EÃ/ÂfÃ[Ã/¾fÅ(ÂLÃ/¾L¾E¸Xºq»ÍÀ‰»(ÎCºq¸J»(ÃUÁ(ÃCÄÒ¹P¸ZÁZÀ(Äq¸oÁZÃCÄ
ö ë æíԁë ÷ ó ï ë æíÔXë ÷ ó ÓSï ë èýï ë Ø<æíÔXë ÷ ó ï ë èýÔXë ÷ ó ï ë æíÔXë ÷ ó Ô Ö ù ø õ
ÐQÄ~¿LÃCÂL¹Xºq»(ÃI¼S¸-»¿fÃC»‰ÃC»¿fÃÔPë ÷´ï ë ÃIÈ ¾E¿L½w¿f¸PÃCÄqº0¹Pºq»‰½?¿L¸€¾Eº]¼C¼C¸J¹PÃ*Ô ë ï ë þZº0»(¸-ÄK¿LÂfÃ[þf¾fÃC»‰Á(¸ûÔ ë ù ø ʉ¾fºÒˉ½P¼6Ë(Ã
Óò Ø
ö æ ó Ô ô ֈõ
R¸¾:¿LºK¿LÀ(ÃC»‰Á(¸X¸-ÂL½XÔ ô Öº0»*ã ¾fº~ÂLºq¼/½eÇe½
ã æ ò óö ôÔ ô õ
È ºq¹PÅh¸-ÂE¿6½w»¿fø-¾L¾EÃ/ÂfÇ?½wÂLü6Ë(Ãã ÁZºqÅhÃ/»‰ÁZÃ3Ã/¾L¼SÄqÀ‰¾fº0Ç?½w¹PÃ/»-¿LÃÁ(½_ÔgÃJÊw¼S¸-¹PÿL½JÄ0Ã-ÊeÂL½JÅ(Å(ÂLÃ/¾fÃC»¿L½kÀ(»Ìà Ã/»(ÃCÂLÉJº]½
ÁZ¼Sºqºˆ»(Å"ÃC¿f¸-º]¾f¼Cº0½Î/º0¿f¸-¸J»(¿LÃJ½wþÌÄqÃX½ÃÈ ¼C½JÀ‰¾f½ÁZº¼SºQ¸TÈ ÇRºqÃC»(ÃPÁZÃ/»(¸J¹Pºq»‰½?¿L¸½J»‰¼6Ë(Ã
?ÏUÐQ»ûÁZÃCډ»(º0¿fºqÇe½Äà Ã/»(ÃCÂLÉJº]½
ãtæ òÛ ó Ô ô è ò ó ö ô Ô ô õ
Ó Ø
È ºq»¿fÃCÂLÃ/¾L¾L½w»¿fÃ-ʈ½êÑ-À‰Ã/¾E¿f¸êʼnÀ(»¿f¸‰Ê¼6ˉº0ÃÁZÃCÂ6¾Eº3¼S¸-¹XÃT¹P½Jº3¼C¸J¹Pʼn½Jºq½Äà ½wÉJÉ-ÃS¿f¿fºqÇJ¸
À(¸-¾L»é¾fÃC¾EÂLº]Çe¾:¿L½wÃC¿f¹€¸-Âf½ºkºqÁZ»(ºkÃCÂLÂLÎCºK͝º]Ã/½wÂfÄqºqº$¹PÏ ÃCÿ}»¿fº}¸êÍz½?»(¿f¸J¿f»‘¸‰Êkºq»(»(Ã/Ã/ÂfÄÎ/ÁZºq½JÃCÄ0¿fÃ-Ã/ÊÂf¹PÑ-Àhºq»‰½w»‰½wÂLÁZÃ*¸hʈ㠺0»RÇJ½?ÿf¼S¿fÃ-Â6ʈ½eÇJ½JÃ/Æ(ÂLÆ(¾fº]¸ê½w¹PÄ]½¸ ¼S¼C¸¸J¾:¹P¿6½wºq»»‰¿f¼Sú]½?ÁZ¿L¸Ã/Ä_º¹P»‰¸w¸-¿L¾E¸ ¿fÂLº3?ö ʼ/½w¿f¼SºqÄ]ºÅ(¼S¸J¾fºq¼Cº]Äq½w¸º¹PÁ‰ÁZ¸½ º
¾fÁZƉÃ/½wÄ0]Â6½ ½wÎ/¾fÎ/¸J½?Ä]½¿LºÌÇ?ÁZ½JÃ/ÂfÄ0º]]½w½oÆ(Ç?ºqĽwÃÂLº]ÁZ½wºkÆ(ºqÅ"Ä0Á¸-¾fÁZº0Î/ºº0Å"¸-»(¸-¾fúqÎCÔºq¸JÏt»(Á·ºgÖ¾EÊ"º]ډ½w¹P»‰¸T¸û½J¼SÁ¸-¾ÃÝ ¾EʼnÂfº0Âf¿fºqÂL¹P¸?ÃCÇ?ÂL½?ÃU¿fºgÄ$à ¼CÃC¸J»‰¹PÃCÂLÃTÉJº]¸½o¾f¾f¼SÃCºq»(ÂLÇ?ÃS½?¿Lºq¿f¼/¸-½€Âfº¿L¸w»(¿L¸J½J»éÄ0úq»(ãÃCÂLº0ÎC»º]½w͝ÄqÀ(º»(ºqÎC»éºq¸JÀ(»‰» Ã
¾fºq¾E¿fÃ/¹P½*ÁZº<Âfº0͝ÃCÂLº0¹PÃ/»-¿L¸¾E¸-Ä0º]Á(½wÄqÃP½wÄ%Â6½wÉJÉ-º0¸ÇJÃC¿E¿L¸JÂLà ù ø Þ Ï€ÿÃCÂLº0Ç?½w»hÁZ¸*ã Âfº]¾fÅhÃC¿E¿f¸½-ÁêÔÀ¼C½w¹Æ(º]½w»‰ÁZ¸ÁZº
"! #$%&(')*+-,.# /)012
3
4')*+-,.# /)012
ò
ZÔ¾fÃCӝÉJÜEØS»‰Ï ¸XR¾f¸-ºÒ¾E¸w¿fº0¿f¿f¿fÀ‰ºqÃCÃC»(»‰Ã[ÁZ¸€ºq»ZÄÍzà½?Ã/¿fÑ¿fÀ‰ºÒ½wºqÄÒÎ/º0Ç?¸-½w»(ÄqøJÂLPÃ[»(ÁZÃCÃCÄqÄq ½½ÛI͝¸-¾fÂfºÒνXˉ½ ¼CÃC»¿fÂLº0͝À(É-½‰Ïgº0¿f¸-Âf»‰ºq½J¹X¸€½JÄÒ¼C½wÄ]¼S¸-Ä0¸PÁZÃ/Ä0à ÃÑÀ‰½wÎ/º0¸-»(ø-ÂL½JÂfº]½
âçæ òaÛ ó Ô ô è ò ó ö ô Ô ô èéåPÓzÔ?Ø Iõ
Ó RØ
ÐQÀ(ĻҿLà ÃCÃC»‰ÂL¹PÃCÂLº0ÉJ»(º]ÃT½X¿fÁ(Â6º~½*Åhʼn¸½w¾EºqÂLÎCÃCºq»¸J¿L»(Ã/ÃI¾fº<¼6Ë(ÑÃIÀ‰½JʼnÁZÂfÂLÃ/ÃJ»‰ÊˆÁZ¼6Ã[Ë(º0ÃoÄÌ»(É-¸Jº0¸Z¹P¼6Ë(ÃIÃ/ÁZÂeºÒ½È Ã/À(»(»´ÃCÂLÂfÉJÀ(º]½¸-Ä0Å"¸¸wºq¿L¹PÃC»(ÅhÎ/¸-ºq½JÂE¿6Ä0ÃI½w»Ã ¿foÀ¼C»‰½JÃC¼CÄqÃI½å Á(
Ã/¾L¼SÂLº0Î/º0¸-»(ÃoÁZÃCÄ3¹P¸w¿L¸‰ÊÃÈ
å æ ò ó ö ô Ô ô è§å€ÓÔwØYõ
Ó -Ø
"!#$&%'()+*,%.-/01,+02431+* ¾fÅ(Äqº ¼CºK¿Lºq½J¹P¸X¸-ÂL½€åPÓzÔ?Øg»(ÃCÄq ½Í¸-Âf¹€½PÁZÃCÄqà Ã/»(ÃCÂLÉJº]½Å"¸w¿LÃC»(Î/ºq½JÄ0ÃIÉ-ÂL½eÇRº0¿L½JÎCºq¸J»‰½JÄ0Ã
åPӝÔwØ<4æ 576 9ó Ô 8 4æ 5;:Ô Õ
=Ó <Ø
Å"Å"ÁZ¸?¸-¸wÇ-¿f¾EÃ/¿fà ¸»(8 ÎC:º]½wÄqÃÈ ?æ Ã[Ä]Ný6o¹P9ó ¼C½-½-8 ¾f¼S¾LýX¼Cå ÁZ¸J
@»ÃC ÄÌ6B¼CÓzÃCÃ/»ACÑ¿fÀ‰ÂL½w¸P<‰Î/õ <&º0ÁZ¸-DFºa»(͝EaOà ¸JÛ/ÂLJÎ/î ؽXG Å"¾EÃCIº0¿fHÂ_Àh¹ºq½?ÄÒ¿fKôÅ"¸PJM¸wL »(¿fÉÃ/Ã/»(ôÄ0ÏtÎCà ¸Jº]½wÂLÐQÄqº0»éÃ[É-º0ÉJ»(ډÂ6#ÃÉ-½eÀ(>…ÇRÂLºK½ ¿6ӝ½wÇJòÎCúq¸JÁZÃ*È »hÃCÂL½wÂfúqÄqÅ"Ã[ډ¸JåPÉJÂfÀ(¿LÓz½?Â6Ô?¿L½Ø[¸ûÓzÛÃ/º0ØYÄgÑÏ%À‰É-߈½JÂLÃ/½wÎCÂ3ºqÚh¸JƉ¼S»(¸ûÂf#à Ã/ÇÁZ<-º0ÃCØS¿eÄqÏ ½Èà Ã/ÃIÈ »(¾EÃC¿LÂL½?ÉJ¿Lº]¸½
¼¹PS¸-¸wÀ(¿LÄqÐg¸€¸JÂL¹Âfºq¾fÃ/ƉÀ(Äqºq½wÄ0½J¿L¿f»‰½?ºqÇJ½¿L¸‰º¿fUÏ ¼6Â6Ë(½[T_ÃÀ(»‰¿f»‰¼6ÂLˉ½U¸?ÃUÇJ¼/Ã/½wº0»ÂfÂLÃ/ºq¼/ѹX½IÀ(¸€ÃQè ¾:Å"¿LP€ÃC¸TÂÊ-¼C¼Sºq½-ÄÃ/¾E»Å"¸P¿f¸wÂLºq¿L¸UÄÌÃCÅ"»(ÁZ¸wÎ/º(ºq¿L͝½JÃC¸-Ä0»(ÂfÁÎÎ/½(ºqÉJ½JÊ-Â6Ä0½e¾fÀǺ0¿fÃUȺ0À‰¿L½J½wÁ(ÎC¿LÃC½[ºqÄÒ¸J¿Lºq»‰;»º0½JÅ"Ä0>¸*Ã[å€Å"Ã/ÁP¸wӝ¿LÔwÀ(ÂLØ3½J»‰Væ»(½I»(¼/5¸o½wÂLúq?¾f¼/¾fÔR½IÃCÊhÂLÁZÁZÃUºh¸?Ã/¾fÇ-ÃC¾EÃI¿fÉ-û(Åh¾E¸[Ã/ºˆÂe¸J½w¸È Å(ÄqÅ"à ºq»¸-æ ¿f¾E¿fÃCR¸Â6½w5Î/º0S¸-P#»(ºq»SÃ
WYXMZ[
:
:
¼S¸-» WYXMZ [ A]\QEwÛî_^ H ¹ ô Ïÿ½wÄq$à Ã/ÑÀ‰½JÎCºq¸J»(ÃQPÅ"¸-¾L¾Eº]½w¹P¸XÂfº]¼C½eÇ?½wÂLÃ
ÓgDJØ
ÔUæ.`ba dó ò c âe5 ò ó ö ô Ô ô 5‘åPӝÔwØfõ
ºqÿ»(ÃCº0Î/ºßˆºq½JÁ(¸JÄ0À(ú]¼6ÃT%ºËÒ0¾fÃÈÄ~ÃCÇ-ÉJÔTÃC»‰Â6ÂLººq¾E¾f¸PÅ(À(ÂLÁZÄ0ÃC¿LºÒ»‰½*ÁZÂL¸w¾fÃ/¸J¿6Âf½wÄqÃ/¸Î/¹Pº0͝¸-¸*À‰»(»(ÑÃÎCÀ(ºqÁ(¸JÃ/ÃCÄ0»(Äqq¸Ão½XÁ(Å"¹€ÃC¸-Äq½J¾fºK¾L½¿L¾fº0½ Ç?Ç-½w¸‰ó ÂLþ%ºq½JÏÑÆ(À(ºqÃ/Ä0ÃP¾E¿L½ÔRʾL½J¼SÄ%Ã/ÄKډ¿6½»(Ão¼S¸JÁZÂLº%ÂLºqÂL¾fº]Åh¼C½e¸-Ç?»‰½wÁZÂLÀÁ½JÔZÁûÓzÖ~ºqØP¹PÃ€È Åh¸-¾EÀÂfÂLoÃP¼CÀ(º0Ã/»‰»-½¿LÃP¼C¸J¸-»‰¾LÁ(¾EÃ/º0Î/ÂfÇ?º0¸-½w»(ÂLÃÃ
¼6Ë(Ã
h
Ôh Ö æ hh ÖÔ hh ÜÜ æ Ô õ
=Ó iØ
Ö
ÐQ»ZÍz½w¿E¿fºÊ‰¾f¸-¾E¿fº0¿fÀ(Ã/»‰ÁZ¸PÄqÃIÃ/ÑÀ‰½wÎ/º0¸-»(º ò Fà DRÊZ»(¸-»‰¼6ËÒÃÈ Ä]½ÄqÃCÉ-ÉJÃIÁZºq»‰½w¹Pº]¼Cj½ <(ÊZ»‰ÃCÄq j½ i€¾fºa¿fÂL¸?Çe½
h
Ó$â 5 ö ô ò ó Ô ô è : eÔwØ õ
ô
h Ô æ Ô ?
æ
k l
Ö Ö
ö ó Ôô
h
gº]¾E¸-Ä0Ç-ÃC»‰Á(¸ÂLºq¾fÅ"ÃS¿E¿L¸o½ ֈʉÁZ¸-Åh¸€ÑÀ‰½JÄq¼6Ë(h ÃI¾fÃC¹PÅ(Äqº ¼CÃIʼn½J¾L¾L½wÉJÉ-º0¸½wÄqÉJÃCƉÂfº]¼S¸Ph ¾EºÌ¸w¿E¿Lº0Ã/»(Ã
h
Öæ Ô ô Ózâ5 ö ö Ô ò Ô è eÔwØ æ Ô ô lUm Ô è Ô ôqp l Ô15éÛ õ
ô k l ô ó ô : k oú n ô rú n
ó
Ù̽oæ ͝¸Jò ÂL¹â À(Ä]½€ö Å(ÂLÊuÃ/tg¼CÃ/æ ÁZÃ/ò »¿fþföº¾fÃCÃ#¹Pv_Å(ÄqæBº0Úh¼C5I½TÛ »(¸w¿LÃCÇJ¸-Ä0¹PÃ/»-¿LþfÃÂ6½wÉJÉ-ÂfÀ‰Å(Å(º]½w¹P¸PÄ0ÃX¼S¸-¾E¿L½J»¿fºÁ(ÃCĈ¹P¸w¿f¸TÅh¸-»(ÃC»‰Á(¸
s
ó ô ó: ô
h
h
Öæ Ô_w s Ô ô èxÔ tYÔgèxv õ
=Ó \Ø
ºˆÅ‰y½J¹P¾LÂE¾E¿LÃCÃ/Ã[¹ÂfÇRÁ(Ɖº]ÃC½wÂfÄqº%¹P0Ã[ÁZ¸Ã/¿6Ä0½e¼6ÇJˉà øJÃJÑÄqÊÃ[À‰Åh½wÁZ¸-Î/ºÒº0ºq¸-¼6ºq»-ËÒ»(¿LÃÈFà ÃCÉ-ö\ÂL½JӝÃÄÄ0ÁûºNà ºqØ<»â¾f¿fºÒÃ/ÉJ¸J¾fÂ6¿E¸J½w¿f»‰ºqÄqÃCÁ¸»‰ÁZüSÃ/¸-Ĉ¾E¿L¾f½JÃ/»¼C¿f¸Jº»‰Ê Á(s ¸T;à ¹PtÃC¹»(¸-Æ(»‘Âf¸ÁZ¾EºqºˆÅhÃ/Å(»‰ÀÁZ¸TÈ ¸J¿L»‰Âf¸¸?Ç?Á(½w½*ÂLÃIÔR¿6ϽwÆ(ÐQ»À(¿fÄ]Ã/½?ÉJ¿LÂ6¸½w»‰¾fÀ(Á(Äq¸½TÃ/¹€»¿f½wÂ6ÉJ½wÉ-¹º0¸-Ɖ º
½wÂ6¼C¾fº0{» z Ô t6Ôt ô Mò #|è 5 v s v&} æt~Ö 5 Ö ì õ
ÓEÛ/îØ
3
(
3
Energia
Potenziale ~ r−2
centrifugo
Potenziale
efficace
r
Potenziale
−1
coulombiano ~ r
ü¼SÃ/º0»É-¿fÀ(ÂLÂ6ºK½ÍÀ(ò É-¸ÂÃ%È 6Åh½?¸Úh¾E¼Cº0¿f¸ºqÇJѸgÀ‰Ã½wÄq¼Sº0ÂL¿LÃ/½?¾L¿L¼Sº0Ç-Ã%¸¼S¸-ÁZ¹XÃ/Ä"Ã%Å"Ô ¸wG ¿LÃC»(Êe¹PÎ/ºq½JÃC»Ä0ÿfÂLÃNÃ%oºqÄJ¼/Å"½J¼S¸wÿfÃ/»(»(ÃCÎCÄ~º]½w¼/Äq½Jþf¼S¸¸-¼SÀ(¸-Äq¸JÀ(¹Ä0¸-Ɖ¹ºqÆ(½J»(º]½w¸g»‰¾E¸¸-Ä0½?¸g¿f¿f¼SÂ6¸-½?¹P¿E¿Lú0Ç-Ô ¸‰G ÏÐQÏÄaÅhÀ(¸J¿fºq»‰ÃC»‰ÁZÎCºJº]Å"½wÃCÄqÃÂ
Å(¾fºaº]¼C͝¼C¸J¸JÂL¹PÄqÃ[½PÁ(ºq½J¾EÄ0¿Lq½J¸J»(Â6½ÎCÃIÀ‰Å(»‰ÂL½ÃCÇ?E½JÆ(Ä0ÀhÃ[¼CĽXà ÃÁZ"ºÒÃC¿EÅ"¿f¸w¸¿fÃ/¼S»(ÃCÎC»º]¿L½wô ÂfÄqº0Ã͝À(‰ÉJÏ ¸hÊZÅhÃ/Â_ÉJÂ6½w»hÁZºÒÑÀ(ÃCÄq0¸€¼C¸JÀ(Äq¸J¹Æ(ºq½J»(¸‰þZ½€ÁZº]¾E¿L½w»‰Î/½Xº0»¿LÃCÂL¹XÃÁZºqÃ
»(ÁZÃ/Ã/Ä0Ä0]]Ù̽½½Í¾fÀ(¸J¼S»(Äq¸À(ÎC¾:ÎCºq¿6¸Jºq½w¸J»‰»»(ÃU¿fÃýwÂ6ÛÁZ¼Sîºg¸-¾fº<ºqÃC»-Ç?»‰¿L½JÃC¸‰Ä0É-ÊZ¸-ÂLÂf½w½Jº<Æ(ÎCƉÁ(ºq¸Jºqº ½J»(s¹XÃÊ$¸ Ö tXì Ã;ÃÈ v?ÁZÊ%ÃSÁZ¿L¸-ÃCÅhÂL¹P¸º0À‰»‰»‰½w½¿L½¾fÃCÁ(¹P½wÄqÅ(]½êÄqº ¼CÅ"Ão¸-¹€¾fº0Î/½wº0»(¸-ºq»(ÅhÃ*¸-Äq½w½J»(ÎCÉ-ºq¸J¸J»(Ä]½wÃoÂLÃT½JÄ0É-ºq»(ÃCº0Æ(Î/ÂLºq½Jº]¼CÄ0½*Ã-Ï ÃoRÄ¸à ºq¾:»R¿LÇJºK¿LÃ/À(ÂL¾fÃCº0»‰¸-Á(»(¸Ã
¾fº0»ÌÓz~Ö 5Ö ì Ø<æ _Ô w ó ô : ô Ô è 5 ò ö ô â ö ô õ
gº]¾E¸-Ä0Ç-ÃC»‰Á(¸ÂLºq¾fÅ"ÃS¿E¿L¸o½JÁԁ¾fºÒ¸w¿f¿fºqÃC»(ÃIÄ]½PÁZºqÅhÃ/»‰ÁZÃC»‰Î/½€ó ÁZºÒ: ÔXÁ(½XÖ ó
ÔZӝÖÒØ<æ Û5 Ûè ö mô úró n :¾Eºq»ÌӝÖ~5 Ö ì Ø õ
ÓEÛJÛeØ
ô
l pn
k
ÔZӝÖÒØk ¸JÅ"É-ÃCÄ0Â_º]½wÖ¹Pæ ¸XÖ¸JÂ6ì ½ÃUÂLº]¼6¾fË(¼Cº]Âf½wºq¹PÇJÃ/º]Âf½wÃ[¹PѸJÀ(ÄqÃ/¸¾E
"¿L½XÏ%À(ÐQÄÌÉ-¾fÀ‰ÃC½w»(É-¸€Ä0º]½w¾fºÒ»(½wνU»(»Rºq»*À(Äq]À(½»‰Ã½XÁ͝¸J¸wÂL¿E¹€¿LÃC½X»(º]Å(½wºE¹PÀÈ ¸ ¾fÃC¹PÅ(Äqº ¼CÃJÏ·3½JÄq¼C¸JÄqº ½J¹X¸XºqÄ~Çe½JÄ0¸-ÂfÃIÁZº
ÔZÓÖ ì Øæ ó ö ô: æ "õ
ÓEÛ ò Ø
T_ƉÆ(ºq½J¹P¸´ÇRºq¾E¿f¸§¼6Ë(ÃÄ]½‘¼S¸-»(¸-¾L¼SÃ/»(Î/½ÁZÃ/Ä0qà ¼C¸J»‰Á(º0Î/º0¸-»(º}ºq»(ºqÎCº]½wÄqººq¹PÅ(Ä0º]¼C½´Äq½´¼S¸J»‰¸-¾L¼SÃC»‰Î/½ÁZº ö à ÑÀ(ºq»‰ÁZº
ÁZ¾fº0º »Ì
"ÓzÖ€Ï èZºq ½J¹Xò ¸ Ø%æBÄ0ºqÆ"5ÃCÂL¼Sºk¸Á(¾Zºkֈ½-Ͼf߈¾fÀ(¸J»(¹Pº]ÃC½wÂL¹PÃT¸XºqÄ3½w»‰Çe½J¼C¸JÄ0¸-Â6Âf½ ú0»‰º0Î/ºq½JÄ0ÃÖ ì æ 5 ò þÑ-À‰Ã/¾E¿f¸º0¹PÅ(Äqº ¼/½ê¼6Ë(Ã*¾fº0»ÌÓzÖ 5éÖ ì ØPæ
æ Ûè ò ó â : ö ô ô õ
ÓEÛ Ø
ÐQ»ÑÀ(Ã/¾E¿f¸P¹P¸ZÁZ¸PÄ$à Ã/ÑÀ‰½JÎCºq¸J»(ÃPÛJÛ[¾fºÒÂfº]¾L¼SÂLº0Ç-üC¸J¹PÃ
ÔZӝÖÒØæ Ûè ¼S¸¾ZÖ õ
ÓEÛ RØ
ÁZÃÀ(¼Sú]ÁZ¾:¿6ÃC½ûÂLÃÃoÈ ÁZĺà ü6ÑË(À‰ÃI½w¿fÎ/ºqº0Å"¸-¸»(ÃoÁZºÁZº3¼S¸JÀ(»‰»‰ºq½¼/½€¾EºÌ¿fÂ6½?o¿E¿6ºq»´½ÃIȼC¸ºq¸-ÄÂLÇ?Á(½Jº0Ä0»‰¸-½wÂf¿fÃUÀÁZÅ"º ¸J Ä]½w¼6ÂLˉº$ÃJÏ Êh ½TÃȾEÀ‰ÁZ½oÃS¿fÇJ¿L¸J½ Ä0¿L½‰ÊÒÃÈ Á(ÃS¿fÃ/Âf¹Po ºq»‰ÁZ½?Ã/¿LÄ0]¸o½Á(¼S½o¸-»(â º]¼C½(ÃÏ Á Tö
3
') #')$
)')')*+-,.#' # $
S¼ÓÃ¸RѸ-À‰ÂLÁZ½wÎ/ºq»‰º0¸-½w»(¿fÃ[ÃT¼CÛ ½w-ÂfØg¿fÃÃP¾Eº]ѽwÀ(»‰ºqÃJ»‰þ(ÁZÁ(º%½JÁ(Ä0]½w½Äq ډÁÉJ¼SÀ(¸-Â6»‰½ÁZºqÛ[ÎCºq¾f¸JºÌ»(ÁZºÃºqÁZ»(À‰º0Î/¼CºqÃ[½JÄ0¼6ºË‰Ï#à T ÑÀ(þ:¿L¸TÅ(À‰»-¿L¸Å‰À¸TÈ Ã¾f¾fÃCÂLÁ¼C¸J¹P¸ZÁZ¸Tʼn½-¾f¾L½wÂLÃU½wÄq Ã
*æ Ô%¼S¸¾ZÖ €æ Ô%¾fº0»gֈõ
ÎCRºq¸¸J¾:»‰¿Lº$ºK¿LÊ(À(¾fº~ÃC»‰¿fÂLÁ(¸?¸ Ç?½Ã/Á €»(ÃCÄq$à Ã/ÑÀ‰½JÎCºq¸J»(ÃÛ hʼCÛ¸J5 »‰¾fºqÁ(ÃCÂ6è ½w»‰ò ÁZ¸X
¼6Ë(è Ã}ÔUæ æ Õ ô è ô ÊRÁ(¸JÅ"¸Ã/Ä0Ã/¹XÃ/»¿L½wÂLº"¹P½J»(ºqÅhÓE¸-ÛKÄq-½ Ø
ô ô ô ô
¼6Ë(ÃPÃ[È Äà ÃÑ-Àh½wÎCºq¸J»‰Ã[Á(º~À(»‰½€¼S¸-»(º]¼C½º0»¼S¸R¸-ÂLÁZºq»‰½w¿fÃI¼C½JÂE¿LÃ/¾fºq½J»(ÃJÏ ¾fºq¾E¿f¸-»(¸¿fÂLÃIÅh¸¾f¾fº0Ɖº0ÄqºK¿?½È
ÅhÅhÃ/Ã/Â_Â_Ä0Ä0Ã[Ã[¸-¸-ÂfÂfÆ(Æ(º0º0¿f¿fÃ[Ã[ºqʼnÅh½JÃ/ÂLÂf½JÆ"Æh¸J¸-ÄqÄ0º]º]¼6¼6Ë(Ë(ÃJÃ-þ þ
Û
æýÛ
î Û ÅhÃ/Â_Ä0Ã[¸-ÂfÆ(º0¿fÃ[Ã/Ä0qºK¿f¿fº]¼6Ë(ÃJÏ
¼SÁZÃ/ºqÂf»Ã/¿fÐQÎCÂLÄkºq¸o¸J¼C»(½JÁZÃI¾fºÒ¸ ͝ÁZ¸-º_ö ÂfÔÎë ì½ æ ÄÃ]îé½Pë ì ÓzÅ‰Ï ¼C½wº0H ¸‰Âf¿fÃÈÃCº]Ä̼S
§Ã/¾fÄ0ÃC]æ É-½€À(¼Cº0î ¿f½-¸PÁZÃ/ÃIÁ Ã/¾LÇJ¼S Ã/ÄqÀ‰ÂL愾fÁZ¸PÃ/ÛÂfº0Ã/Ä؁¹X¼S¼SÃ/¸-¸P»-Âf¿LÑÂLÂfºqÀ(¸o¾fÃ/Å"¾EÁ(¸J¿LºÒ»‰½X͝ÁZ¸JÅ"ÃÂL¸-Î/½J¾L½P¾EÁ‘ºq¾fÆ(Ã/À‰ºq¼CÄ0»Òº ¸J¿eà »‰¸-½‰È ÂfÁZÏ Æ‰¸€ºK¿6À‰½»‰½€ÂLÃS¿EÄqº0¿L»(º0Äqú ½P»(Ã/Âf½êÃC¿E»(¿6½€ÃCÄq½e½ÇJÃCÁZ»ºq¿LÂfÃIÃ/ÎCÄqºq½€¸J»(¾EÿfþfÁZ¾LÃC½ Ä
ï
ÓÄzà¼Cú0Ñ-¸‰ÀhÃ_È ½wâ ÎCºq¸J»‰ÃXîIÛ ÃÁ Á(ö º0Ç-æðÃC»î¿L½Ø%¾Eºhˉ»‰½ ÃC ļ/½J¾fÛJ¸€Ê-¸?¼6ÇRË(ÇJÃUÃCÄÂLà ¸PÃ/»('Û ÃC5ÂLÉJ º]½Pô ¾Eº]½Pî(Åhψ¸ßˆ¾E¸Jº0¿f»(ºqÇ?º]½w½€¹PÃ/¸UÁ*½JºqÄ0ÄÌq¸J¹PÂ6½X¸-¹X'Û Ã/5 »¿f¸oô Bæ½w»‰ÉJ5 ¸JUÄ]½wÊRÂL¼SÃ[¸J»(» ¸Jä»Åh¾fºq¸½P¾Eº0»R¿fÀ(ºqÇJÄq¸h¸ þ
5
ô è ò è ô æ ô õ
ÐQ¾f»ûº<¿LÑ-ÂLÀ‰½w¿EÃ/¿L¾E½¿L½ÁZÃ/ÃCÑÄqÀ‰à ýwÑ-Î/Àhº0¸-½w»(ÎCÃXºq¸Jºˆ»‰Ã¼C¸RÁZNà ºkoÀ(¼S»ÒºqÃCà »ºqÅh¿fÃ/ºÂfÁ(Æ"ÃC¸JºˆÄqÃJ¿fύÃ/Âf¹PÐQ»‘ºq»(ډºÉ-ÑÀ(À‰Â6½J½ Á(ÂLQ½½w-¿fØTº]¼Sº ÓN¿fÂ6ô½?¿fÿf¸ô¼S¸J¾f»¸J¿L»(º0»R¸*À(ÁZ¸Rºq؀ÇJÃ/ÃoÈ ÂL¾fÂLºˆºqÅhÃX¸-ÂEÁZ¿6º½?¾f¿fÃC¸ É-»(º0Ä3¸ÉJ¸JÂ6½?Å(Ú"Å"¼S¸-¸ê¾E¿fÁZ¸ º
À(»Òà ºqÅhÃ/ÂfÆ"¸JÄqÃU½eÇJÃ/»-¿Là æ Û-õ ò à XæýÛJÏ%ÐQÄ̼CÃC»¿fÂL¸XÁ(º~͝¸JÂLÎ/½TÃ[È Åh¸¾:¿L¸P»(ÃCÄq$à ¸JÂLºqÉJºq»(ÃJÏ
Óz¼Cº0¸‰Ã[È âñæäîXÃ/Á ö æðîØ3¾EºÒËh½»(ÃC Äkæý¼C½-Û-¾E¸êψÐQ¼6»*ˉÃTÑÀ(ÄÃà Ã/¾:»(¿LÃC¸€ÂLÉJ¼C½Jº]½¾f¸X¾fºqÄ$½êà Ã/Ñ»À‰À‰½JÄ0]ÎC½ºq¸Jû(ÁÃPº0KÛ ÄkX¹PÁZ¸JºqÇJ¹PÃ/»Ã/»-¿L½X¿L¸ ¾EÃ/½J¹X»(ÉJʼn¸-Ä0º]Äq¼S½JÃ/Âf¹XÀÃ/»(»¸-¿f»´Ã ¾fºq½»RÀ(Äq ¸
æ ò Û Ó ô 5 ô ØYÕ
¼6¼SË(¸-»ÃÃ_È Äæýà ÃÑ-Û[Àhà ½wÎC
Xºq¸J揻‰Ã}ÛJÁZÏ ºaÀ(»‰½ʼn½wÂ6½wÆ"¸JÄ]½(ÏÐQ»€Ú‰ÉJÀ‰ÂL½ 8½Ø_ӝ¿fÂ6½?¿E¿LÃCÉ-ÉJºq¸Ø3ÃÈ ÂfºqÅh¸-ÂE¿6½?¿L¸Uº0Ä"ÉJÂ6½?Ú"¼S¸UÁZºaÀ(»‰½ʼn½wÂ6½wÆ"¸JÄ]½
¾fºq½X»RÀ(Äq0¸Óz¼Cº0¸‰ÃIÈ â îXÃ/Á ö æðîØk¾Eº~Ëh»(½XÃ/îÄa¼/½J¾f ¸¼6Ë(ÛJÃψÄ$ÐQà ÃC»»‰ÃCÑÂLÀ(ÉJÃ/º]¾E½U¿f¸€¾Eº]½U¼C½-»‰¾EÃC¸PÉ-Ľwà ÿfºqÑÇ?À‰½U½wÃ/Î/ÁTº0¸-»(º0ÄaÁ¹PÛ ¸JX¹P½JÃ/¾L»-¾EÀ(¿L¸¹P½JÃ[»(Ä]ÉJ½¸-͝Äq¸-½JÂfÂf¹€Ãg»(½ ¸-»
è ô è Pè ô æ ô Õ
¼S¾f¸J¸-»(» ¸€…ÁZº~æ À(É-Û À‰5 ½wÄÒ ¾fô ÃCÉ-»(¸ îo%¾Ã fº~í¿fÂ6½?æ ¿f¿Lò ½P ÁZ
"Ã/Ï[Ä0ÐQà » ÃÑÑÀ‰À(½wÃÎ/¾:º0¿6¸-½o»(ÃÃ/ÑÁ(À‰ºÒ½JÀ(ÎC»Òºq¸Jà ÃC»(ÄqÁ0º]¾Lº%¾EÃ-¼SϸRNà H oÃC¼Sĺq¼CÃC½J»¾f¿L¸XºˆÁ(º0»ÃCº¼S¿fÀ‰Ã/º Âf¹Pºq»(º%Ñ-Àh½JÁZÂ6½?¿Lºq¼Cº ô à ô
âçæ 5 ó ò ö : ô ô
¾fº~ˉ½PÃ/¾L½?¿f¿L½w¹PÃ/»-¿Là ætî‰ÊZÃIÄ$à Ã/ÑÀ‰½JÎCºq¸J»(ÃPÛ ¾fºÒÂLºqÁZÀh¼SÃI½PÑ-À‰ÃCÄq ½PÁZºÒÀ‰»‰½€¼SºqÂL¼C¸J»Z͝Ã/ÂfÃ/»(Î/½
ô è ô æ ô õ
͝¿fÀ(Â6½?¸Z¿f¼6ÐQ¿fË(»ºNºØYډÊ}ÃgÈ ÉJ½-»(À‰Á Ã/ÂLÄ0½ à ¸-Âfæ¶ÆºqhÉJØkºqî(»(¾fõ Ã}¸Jî(»‰ÛMÁ(D¸XÃCÉJÂLÀ(Äqºqºa»ÒÅh½J¸-à ¸J¾LÂEÂL¾E¿6Æ(º½?Ï º0¿f¿LTºÌ½‘ºÌÁ ¼CÉJ¸JÂ6»t½?æäÚ"Ä]¼SîU½´ºÒ¼SÁZ¾E¸-¿fºÂfÃÃCÂL¾fÄqº]¾L0¾E½º]Å"¾f¾f¸JÃ/ºÌ»‰¼/½eÁ(¼SÇ-Ã/ÃgÃC»-Ä$»¿Là ¸J¿fÂfºº]ÂL¼SÆ(
€º0¿eº0¿L½´æÈ ½UÁZ¼CÛIº0ºÂ6üSѸ-ÁZÀ(ÄqºÃ/½J"Ä0Âf]Ã/ÃU½ÂfÃ/Ó$¿L»-¼SÃCÀ(¿LÂLºÌÂLÂfÇ?Ç?ý[¾:½w¿LÄq¿fÂf¸JÂ6ÑÂL½?ºÒ¿fÓ$ÁZ¿f¼SÃCºÀ(É-ÂL ÉJÇ?þhº]½´½?À(¿6»(¼C½I¸o¸J½I»ÁZ¿fÅ(Ã/ºq»Rº]º¼CÀ‰ÁZ¼S½-¸-À‰ØSÄ0à ºÏ
R¼S¸-ºÂf¸-ÂLº]¾L¾E¾EÅ"Ã/¸JÂfÇR»‰ºÁ(ÃU¼S ¸JÀ(¹P»ÒÃà ¸JÂL¾EÆ(º]½‘º0¿L½TÁZº ¼Co¸J»¼SºqÄ0Ä]Ãû½TÁZ¾E¿fº]¾:ÿL¾fº0¾L»(½€É-À(üCÃC¼SÂLÃ/ûĿfàÂL¸-ºqÂf¼CƉºK¿?ºK½TÈ¿6½‘ÁZºˆÁZÃCÑÄqÀ(]½ÃCÄq ¿f½Ã/ÂfÁZÂ6ÃC½‘ĈÁ(Å(½Jº]½wÄ0»‰à ¸JÃS¿LÂL½Æ(ºK¿6ß½‘ÄqÀZ¼S¿fºq¸-Â6»(¼S¸JÃÄ]½wÓ$¼SÂLÃÀ(ÂLÇ?½€T}¿LÁ ÂL½w ¿E¿fÃ/æ ÉJÉ-q½wõ ò ¿L½
3
"!
$#
$# %#
2 3&
+
'()&()*+,-
"!
3
,.,-'/0&1()&2
"!
43
73
65 %5
3
ε =1
ε =1.2
ε =0.017
1
1
ε =0.25
0.5
0.5
ε =0
−1
−0.5
0
0.5
1
−1
−0.5
0
0.5
−0.5
−0.5
−1
−1
1
üÓN¿Lº0ÂLÉ-½wÀ(¿EÂ6¿L½ÃCÉJÉ-ºq½w¿L½‰Ê æ Û ØSϾf¸J»(¸*Â6½wÅ(Å(ÂL Ã/¾f¾fÃC¸J»»‰¿6¸T½?¿fÂ6ÃP½wÅ(À(Å(»ÂLÃ/ºqÅ"¾fÃCÃC»ÂL¿6Æh½?¸-¿fÄ0ÃÃêÀ(ӝ¿f»‰Â6½*½?¿f¼S¿fºq¸ÂL¼C¼S¸J¸-»Z»ÍÃ/¿fÂfºq»Ã/À‰»(¸‰Î/½êÊ ÓN¿fÂ6æ ½?¿fÛ-¿fÃ/õ0ÛeÉJØ[ÉJºqÃ/¸oÁÚhÀ(»(»hÃJ½Ê ʼn½wæ Â6½wî-Æ"ØS¸JÊ~Ä]½Ã
ÁZÑÀ(À(Ã/ÃI¾EÃ/¿fÃ[Ä0qº]¼S¾f¸-¾fºÌ»(º]¼S¼6¸-Ë(»Ã üC¼C¸J¼CÂLÃCÂf»º]¾E¿fÅ"ÂLºq¸J¼C»hºK¿?ÁZ½PÈ ¸J»(ÁZ¸º0Ç-ÃC½wÂ6Äq$¾fà ½Ã/ÑÓNÀ‰¿LÂL½J½wÎC¿Eºq¸J¿L¸o»(à ¼S¸J»¿LÓEº0Û0»RÀ(5 ¸hÊ Øaæäè ò î(õ î(
Û[DUè ÿfÂ6½?æ ¿f¿f
ÃCÉ-ÉJ¼Sºq¸J¸P» Äq½J
XÂfÉ-æ ¸‰Ê Û- ÊZÑ-æäÀ‰º0î(»‰õ Á(ò -º~ ØYʼnϽJ̾L¾fÀ(½J¿E»(¿f¸Ã
ô ô ô ô
¿fÀ(¿E¿fÃÅhÃ/ÂgºÒÅ(À(»¿fºÓzî(Õ/ÛØÃoÓzî‰Õ5IÛeØYÏ
3
()7(
()/
2
UýI¿LÑÂLÀ(ÐQ½w»*ÃC¿EÄq¿Lډºh¸PÉ-Äq¼CÀ(À(¸J»(ÂL»½bÉ-Ë(Äq ½Xº]ÆØSÏÅ(ºEH¾fÀ*È ¸JÃ/»(ÉJÄ"¸€Â6¾f½wºqÂL¾E»‰º0¿fÅ"Á(Ã/Á¸J¹€ÂfÃIÈ ¿L½½wß<¾f¿f¸JÃIÄ0ÀZÄ]½wÄq¿LÃUÂL¸JÃ_»(¸JÃ-º0ÂLÄ"Æ(Ï Å(º0¿fº]ÃU½w»(ÁZÃCÃ/¿LºÌ½Å(¼Sº]¸J½w»T»‰ÃSÄq¿f½ºÅ(Ã/ºE¾EÀÈ¿fÃ/Å(Âf»(º]¼Cº¼S½w¸-ÄqÄq½U½XÃ/¿L¼CÃC¼CÂLÃCÂL»½P¿fÂL»‰º]ÃC¼Sĺ0¿e¾f½€È º]¾:ÃÈ ¿LÃCH ¹€ÃC½€¿E¿f¾EÀ‰¸-»(Äq¸½JÂfÓÃ[ ÃUæäÄà î(¸JÂLõ îJÆ(î_ºK¿6½ Ø
ÁZ¾f¸JÃ/Ä]Ä0½w]½ÂLÃX¼C¸JÓ ¹PAäÃS¿6î(½ õ \-ØY½wÏ Äq0
à "þÒÑÀ(þ:¿6½oÅ(ÂLÃ/¾fÃC»¿6½oÀ(»Òà Ã/¼/¼SÃ/»-¿LÂfº]¼Sº0¿e½TÈ ¹P¸JÄ0¿f¸Å(ºEÀÈ ½wÄ0¿L½ÁZºˆ¿fÀZ¿f¿fº%ºˆÅ(º]½w»(ÃC¿fº%ÁZÃ/Ĉ¾fº]¾:¿LÃC¹€½
<
Ð
/
¼
J
½
f
¾
½ÂLwºq»‰½-ÉJ¾f¸J¾fÀ(Ä]½w»ÂL¿fà º~º"ºqöÂL»TÃCÄ]ÓzÚh½?Ñ¿LÉJÀ(º0À(ÇRºqÂ6»‰º~R½ ÁZ½wºÄqÃ¾:½w¿LÅ"¿EÃ/¿L¾L¸-ÂL¾E¾L½e¸¾EÇ-ºqÆ(ÃCÇ?Â6½wºqÄ0¾EÄqº~¸¸J¸-ÂLº0ÃÂfÄÌƉÁ(Å"ºK¿LºqÃC½JÃÂIÉJÁZÂ6Ä]½Ã/½wÄa¹P
"¹X¹€ÊÒ¸JÇ-½¿fÃ/¸PÁZÁZÃ/ºqÃ/»ÂfÄ0ÃXàÀ(Ã/Ã/»»(ÑÃCÀ‰¼CÂL½JÉJ½J¹Xº]ÎC½XºqÅ"¸JÅh»(¸P¸JÃÉJ¿fÃ/Â6Û »(½eò ÇRÎCØ_º]ºK½w¿6À½wÄqÃ[ÎCÁZºqºqNøJÇJo»hÃ/ÂL½w¼C¾LÄq½-ÃJ½o¼SÊ-ÃÃ/½e»(Ç-å ÃCÃC
ÂL» ÉJ¿fº]ºaÓz½oÔw¾EØY¿f¿LÏ Ã/¸w¾L¿6¾f½w¸ÄqÃX¹Pâ¸J¹PʾEÃ/¸-»-»(¿L¸¸
1
%' *% ,, r
qºÙÒÄÌÃUÃCÅ(ÂL¼Cº]ÂL½w¸J½T»(»‰À(ÃC¼C¿L»Ä0Àh½P¾E¾LÉ-ºq½?¸Jº0¿L¸Z»(ÃC¼CºÌÄq½X0ºÅ(¿fºqÂfÃ-ÄÌÃÊ̼SÂL½JÀ(ÃÁÁZ¸JÃCÄq¸oÀ‰»»‰¿fÁZºÌ½*ºÅhÁZ¼S¸ÃCºq¾f¾E»¾f¿L¿L¸J½JÂf»(»(¸€¸€Î/ÁZ½TÃÃ/¾fÔCÄ0¾f]쀽XÃCÂLÁ(͝ÃI¸J½JÂL½wĈÎ/Å(¼C½‰Å‰ÃCÏ »Ä0º]R¿f¼CÂLÀ(½w¸¿fʼnÃUÅhÁ(½w¸-ÃCÄq»h»(½¼6ºq½JË(¹PÌÃUÃ/¸T½wÂfºÌÂ6ÁZ½(¾LºÒ½?ÏUÇ-¿LÙ¸JÃCÄqÄq½T0ÃCº Â_¿fÇ-ºÃCÄ]½wÁZÄq¸Z»‰ºÌ¼S¼CÀ‰º0ºq¿e½J»½oÈ ÂfÃ[Å(ºq»(ºqºq½J»ºq»(ÎCº]ÃS¸J½w¿6ÂLÄq½(ÃXÆ(þ(º0Á(¿Lºq½P»ÃCÄ%½?Ѿf¿fÀ(½w¿fÃ/¸J¿f¾EÃ/ÂL¿fÄ0»(q¸oºK¸o¿L¼/à ½J½JÄ0¾fë]¸½ì
¾fѺqÀ‰½U½wÁ(ÄqÃTº0ÂLÃSÁZ¿fÃ/¿LÇJ½Iø-Ã/ÂE¾L¿L¾E¸JÃ/ÉJÂf¸-Ão»‰ºq½wÄ3Äq¹PÇe½JÃCÄ0»¸-¿fÂfÃkýwÁZÄhº ÂL½JÉJì É-M½ º0¸[€ÇJ»‰ÃC¼6¿EËk¿L¸JÃ€Ý ÂLº0ÀÄkÔCë ¾Lì½?¿f¼6Ã/ˉÄ0Ã_qº0¿f»(ÃTÃ}Å"ºq»‰ÃCÂ6ÁZ¼SºqÇR¸-ÂfºqÁ(Â6½*À‰½IÀ(Ä]»Ò½Ià ¸JÅhÂL¸Æ(¾Eº0ºq¿LÎC½ ºq¸J¼S»‰ºqÃgÂL¼Cº0¸J»(Ä]ºq½wÎCÂLº]½wÀÄqÃJÃTÏ<Ñ·À‰º"½w¼6ÄqÃTË(º0ºqÃÄÁZÇ?º]½w½J¹PÄ0ï¸-¸ Â
¹Pº0»‰º0¹P¸oÁZº ï ì ½ €»‰¼6ËkÃÝ Ã/¾L¾E¸€½JÆ(Æ‰ï ½w»hÁZ¸J»(ºaÅ"ÃCÂ}¾fÃC¹PÅ(ÂLÃ[Äq½ÃCÂLÂL½‰Ï
ºqÁZ¹XÃ/ÄaÅ"¾L¸J½?»‰¿LÃCÃC»‰Äq0ÁZº ¿f¸PÃ-ÊZ¼6Ë(¼S¸Jû Ä$à ½J¼/¼SÑÃ/Ä0À(Ã/ÃCÂLÄ]Äq½½J½XÎC¼Cºq¸J¸JÁZ»(»‰Ã/ÃÁ(Ä0]º0½ ÉJÎ/Â6º0¸-½eÃC»(ÇÂLÃ}º0ÂL¿L½½JÅ"ÎCÃCúqÂk¸J¼C»‰Ä¸Jà ½J¸-» Ä0ÂfÃgÆ(º0Ã/¿LÉJ½À‰º0Äa¼S½JÇ?ºqÉJÂL½wÄq¼Cº"Äq¸J¸JÑÄ]ÂL½wÀ(ÃÂLÃ/Ã_Á(Ä0]º ¾E½Xºa¼SìÂLÃCºq¼/»ÁZ½e¿LÃCÇ?Âf¿fº0½UÃ/͝ÂfÀ(Á(¹PÉ-½w½‰ºqÄq»‰]Ͻ½?ÐQ¿L»h¾f¸Ã/ÁZ¼SÁ(ºq¸-¼/½X»‰½w»‰Á(ÑÁ(½IÀ(¸XÃ/Äq¾EÃC¼C¿LÉ-¸J½ÉJ» ÃÀ(óÉJÁZÀ‰º ½JÄ]H ½ÉJÃÄq¹€º k½J½-»(¿L¸J¾fÎ/¾L»Ò½‰½ ÊÊ
ï ï
8
¾fº~ˉ½
ó ï ÔC ì ô @æ 6 ó Ô ì8 ô Õ ï æ 6 8Ô/ì õ
¾fÃC¹PÅ(ÂLÃUÁ(½wÄq ½ ÃCÂLÂ6½ÃUÈ Ñ-À‰ÃCÄqÄ]½P½o¹X¼6ˉºq»(ÃUºq¹€Á̽€È ½PÄqÀ(ÇJÃC¸JÄqÉ-¸Z¸P¼Sº0½-¿e½XÁ*È ºqÀ(»(»Òº0Î/à ¸Jºq½JÂLÄ0Æ(à º0¿Lï ½P ʼn¼6½JË(ÂLÃI½JÆhÇJ¸-ÃÄ0ÁZº]¼CÂL½‰ÃCÆ(Ï Æ"Ã[¾L¾LÄq½X½X¹€¾fºÌ½J¸J¾L¿E¾f¿L½ º0Ã/ó »(ÃU½JºqÄ0¹Xq¸JÅ"»¸J¿6»‰½w»‰ÃC»‰½JÁZÂL¾f¸oºhÅ"¼6ˉÃCÃÂ
( 0&1()&
(7()&(),1(
<
Terra
ρ
1
v0 < vC
Urano
2
ellisse a
Marte
Terra
Saturno
3
Giove
moto circolare
v0 = vC
Nettuno
Cometa
di Halley
ellisse b
vC < v0 < vP
üò º0à É-À(PÂ6½RÁZº~ ډÉ-À(ÂL½R(ÏÙ̽PR¼S¸-À(»(ÂL¸oÇ?½¹PÛ[¸-¾E¼C¿f¸JÂ6½?ÂLÂf¿Lº]þfÅhÄqÁ¸-»‰ÁZÁZºqÇJÃ[Ã/½wÂLÄ̾fü/½J¸-¾fÂf¸ Æ(º0¿fìÃÅhÃ/Â[¾LÊ(½?¿Lºq»*ÃCÄq0¼Sº À(¿fººÒ¿fÄ]½PÃ/ÂfÅ"ÂLÃ/¸-¾E¾f¿fº0ÂLÎ/ºˆº0¸-¼S»(¸JÃ[ÂLÂLº0ºq»(¾fÅhºqÎC¸-º]½w»‰ÄqÁZà Ã/
ê»-¿LӝºÃ½JѺÀ‰¼/½w½JÎ/¾fº0¸-º<»(ÛJà Ê
Û ò Ø<¼C¸Jºq»‰ì ¼Sº]ÁZüS¸J»ÊºqÄ$»´à ½?͝¼SÃ/À(Ä0ºqºk¸‰Ä]Ï%½ÙÅ"½¸-¼C¾fÀ(º0Î/Âfº0Ç?¸-½ »(ÃTò ¼Cºq»(¸JºqÂLÎCÂfº]º]½w¾EÄqÅ"à ¸J»h
ÁZӝÃÃѽJï À‰Ä"½w¹PÎ/¸Jº0¸-ï¿f»(¸P Ãê¼SºqÛ ÂLò¼CØU¸JÄ]¼C½w¸JÂLÃJºq»‰Ï¼SÙº]ÁZ½Ã¼CÀ(¼S¸JÂL»´Çe½ º0ÄkÅ"¼CÃC¸JÂLÂLº0ÂfÃ/º]Ä0¾fºqÅh¸‰¸-Ïû»‰ÁZÐQ»Ã}½J¿LÀZÄa¿E¼/¿L½Jºg¾f¸Ã
¿fï¸JÂLÂLÃXÆ(º0º¿fÀ¼C½Jï ÁZ¾fÃ/ºˆºº0Ä%Å(º]Ç?ï½w½J»(Ä0¸-ÃC¿fÂfºÃXÁZÁZÃ/ºÄ<
*¾Eº]ÃP¾E¿fÑÃC¹€À(ºq½*»‰ÁZ¾fº¸JÄ]Á(½wÃCÂLĈùPÃ/¾E¸J¿f¹PÃ/ÂfÃC»‰»º<¿f¸*½wÄq½w½ »‰ÉJ¸JÃCÄ]ÂL½wÂLÂL½‰ÃoÊÒÃÈ ½J¾LÚh¾E¾LºqÃC¾f¹P½w¿fÀ¸hϽwÄq ½*¼C¸J¹PÃS¿6½ R¸J»‰½w¸Äq0Â6
à ½wJÅ(ÊÌʼn¼6ˉÂfÃÃX¾EÃ/ʼn»-Âf¿6ý?¾E¿LÃ/û-¿6Äq½Ã
À(»‰½XüC¼SÃ/»¿fÂLºq¼CºK¿?½È ¹P¸-ÄK¿L¸X¹€½JÉJÉJºq¸JÂLÃJÏ
Äà Ã/»(ÃCÂLÉJº]½¹PüC¼C½J»(º]¼C½Pâ ¾fº]½»RÀ(Äq]½
âçæ òÒÛ ó ï ô 5{6 9ó ÔC8ì æäî ï æ ò 6 8Ô/ì æ w ò ï õ
ÐQÄ3Çe½JÄ0¸-ÂfÃ ï ¼S¸-ÂfÂLºq¾fÅ"¸J»‰ÁZýwÄq ½êÇJÃCÄq¸Z¼Sº0¿e½È Á(º<͝À(ɽê½êʼn½wÂf¿fºqÂfÃÁ(½wÄq ½ ÑÀ(¸w¿6½Ô ì È Ï ZÃÔ ì ¼C¸Jºq»‰¼Sº]ÁZÃ/¾L¾fÃT¼S¸-»‘º0Ä
Â6¸J½wÂ6ÉJ½XÉ-Ñ-º0¸oÀh½wÁ(ÄqÃCÃ[Äq¾f½ º]½ÌºqÃ/Ä~Âf¿LÂ6º0½Å"¸o ÁZÊ~ºÒ¾E¸-º%Âf½eÆ(ÇRº0ÂL¿LÃC½XÆ(Å"Æ"ÃCà Âgï Ç- ÃCÄq¸Ræ ¼CºKk¿?½È ò 6ì æ w ÃIò Åh Ã/  Aíì Û-ÛJõ [Ï ¹ J ¾/Ï º0»¿fÃ/Âfþf¾L½w»¿LÁÁZ¸-¹P½J»‰Á(½JÂL¾fº
ï ï ï ï
ÄqÃì ¸Jæ ÂLÆ(º0¿fÃXÓz¾E¸J¸-ÂL»(Æ(¸ºK¿6½XÁZºÅ‰¿f½wºqÂ6Å"½w¸Æ"¸JºqÅhÄqº Ã/¼/Âf
½-Æ"ظJ¹PÄqº]¼SÃC¸ »¿fӝÂLډÃ[ÉJÅhÀ‰Ã/ÂL½Â JÅ"ì ØYÃCÏQæ T_ï Ɖì Æ(ºq½J¹Pï ¸o¿f¾fӝÂL¸Jº¸?ÂLËhÇ?Æ(½?½ º0¿L¿L½P¸T¼6Ë(¼S¼6úqË(Â6ÃÄ$¼Sà ¸JÃCÄÄ]»‰à ½wÃCÃC»(ÂLÂLÃÃ/ÉJØ<Âfº]É-½‘¾EºqºÌ½€ÃÈ Ë‰¹P½PÅh¸Ã¼6¼CË(¾Eº0¼Cà ¿f½JºqÇ?»(½º]¼C½Ã*ÃÈ Ñ-À‰»Rº0À(»‰Ä0Á(]½oºkÅ"¼6ˉÃCÃÂ
ï ï ï ï ï âçæ òÒÛ ó ï ô 5{6 ó9ÔC8ì æ45 òÛ 6 ó9ÔC8ì î(õ
ÐQ¼6»oË(ºqÉ-À‰ÃC¾f»(ÃPÃ/ӝÂLډ½JÉJÄ0Ã_À‰ÂLÅ"½RÃC JØSï ʉì ÑÀ(ºq»‰ï ÁZº~¾fÅ"ºhÃCˉ ½â î(þZ½-Á€ÃC»(Ã/ÂfÉ-º0Ã}¹XüC¼/½w»(º]¼6Ë(Ã}»‰ÃCÉ-½w¿fºqÇJÃ}¼C¸JÂLÂfº]¾fÅh¸-»‰ÁZ¸J»‰¸U¾EÃ/¹XʼnÂføJÂLÆ(ºK¿LÃ
ïì ï Ã ï ïì ï
ºq½eÄ3ÇJ¾LÃ/½?»¿L¿fÃCº~ÄqÄ0ºà ½w¿fÃo͝ÃCÄqÅ"º0¸TÃCÂ6¼C¼S¸J¸-ºqÂf»‰ÂLÀ¼Sº]ÁZ¸JÃ/ÂL»-Æ(¿Lº0¿fÃUÃo¼SÃ/¸-Ä0»qº0¿EÄ]¿f½€º]¼6Å"Ë(¸-Ã-¾fϺ0Î/ÐQº0¸-»‘»(ʼnÃI½JºqÂE»(¿Lº0ºqÎ/¼Cºq¸J½JÄ]Ä0½wÃIÂLÔ/ÃJìTÊÌÅ"ӝÇ-ÃCÃ/ ÁZï ºÌì ډÉJÀ‰ÂLï ½R €Êˆºq¼CÄ3À(¾LÂf½?Ç?¿L½*ÃCÄqÛ-0ºÊ(¿fʼnýw¾EÂfº3¿fÃU¹¾fÀ(Å"¸?Ã/Ç-¾LÃo¾f½¾EØ3À´¹X¸JÃ/ÂL»Æ(¿fºKÂL¿LÃÃ
ÃXºqÄgÅhÅhÃ/Ã/ Âfºqï ÃCÄqº0¸tÓzÇJï Ã/ì Á(ºkډï ÉJ À(Â6ºq½ ľLê½?¿f¼CÃ/À(Ä0qÂLº0Çe¿f½ÃXÅh‰Ã/Ê<ÂLʼn¼C¸J½JÂLÂEÂf¿LÃUÃ*¸-¾fÂfÅ"ƉÃ/ºK¾L¿L¾fýØYÃCÏéÄq ºK¿fÐQ¿f»§º]¼6ÚhË(ÉJÀÀ(¼SÂ6¸J½ » Äq½T¾f¸JÅh»(¸¸¾EºqÎC¹Pºq¸J¸-»‰¾EÁ¿fÂ6ºq½?»(¿LºqÃÎCº]Äq½wÃÄqÃX¼SÀ(¼C¸JÂLºqÇJ»‰Ã*¼Sº]ÁZÁZºgÃC»Ã/¿L»(ÁÃCÂL¼SÉJ¸-º]»½
Å"¼SÂL¸wÃ/¿f¾LÃ/¼S»(Ã/ÎCÂfº]ÃX½wÄqÁZú ÃNoì ¼/À½J¼SÑ-à À‰º0廉Á(
XºÁZӝÔwº Øêö ӝÇJæ ÃÁZÃCÂLÔ Ãì ½wì »hÊ~¼6ÄË(à Ã/û(ÄqÃC½ÂLÉJÚhº]½ÉJÀ(¼CÂ6ÃC½ »¿fò ÂLØXº0͝À(¸JÉ-¿E½¿fÃ/»Rö ÀZ¿fÃò Å"ÃCÔ ÂTì º½JÁZÀ(º¹P"Ã/ÃCÂf»Ã/¿L»½¿fº}¹PÇ?ÃC½J»Ä0¿f¸-ÂLÂfÀº_å€ÁZº ӝÔwï Øì ÂfÏ Ã¾:T_¿6½ Ä
ºq¼S»À‰Ç?Âf½JÇ?Âf½º]½?¼C¿6¸J½(ÂLþÂf»(º]¾EÃï Å"¼C¸J¸J»h»‰ÁZ¾fÃPÃCÉ-À(À(»‰Ã½¼6ÁZˉºqÃ}ÇJÃ/ÄqÃÂL¾L¼C½À(Âfó¿fÇ-Â6½wúqÃSÁZï ¿fÃ/¿fÄa¸-ÅhÂfº]¸J½ ¿f½ÃC»‰JÎCÄ0º]]½w½ÄqüCÀ(à Âf€Ç?½¼/½Jò¼CÃ[ʈ¼Cå ¸J
ÂLXÂfô º]ӝ¾fÔwÅhØkó¸-¾E»‰ºaÁZ¾fô ÃPÅh¸Äq½¾:¿6¿f½wÂ6»(½w¸ºqÃSÇJ¿EÃC¿L¸JÂ6¾fÂL¸ºq½Äà ¼C½Jº0ÄKÂ6¿L¼S¸‰¸-Ï Äq½JT}ÂfÁÃ-ʸJ½JÉJÄ0»‰]½ º
¼SÁZÀ‰ºqÇJÂfÃ/Ç?ÂLb½ ¾fÃX¸-ÑÂfÀ(ƉÃ/ºKÄ0¿L]ÃU½X¾Eʼn¸-½w»(Â6¸½wÆ"ÂLºq¸JÅhÄqº]¸-¼CÂE½(¿6ÊZ½?¿f½JÃ[Ä0qúq»¼CÀ(ډÂLÉJÇJÀ(ÃPÂ6F½ Û[ à Q½(Ï ¿LÂL½Jº0ÃC¿E¿f¸-ÂfºqÃÃCÄq0º ¿E¿Lºq¼6Ë(Ã[ÃI½wÄq]½X¼CÀ(ÂLÇej½ XÑÀ(ÃCÄq ½XºqÅhÃ/ÂfÆ"¸JÄqº]¼C½(Ï%ÙÌÃ
3
Plutone
() ( 3
()/
3
'
,,
3
3
D
Energia
5
4
3
2
1
iperbole
E5
parabola
E4
ρ
r
ellisse b
E3
cerchio
E2
E1
ellisse a
üÛ ò º0É-Ø3À(¼SÂ6¸J½~ºq»‰ ¼CºqÁZ¸ÃIw¼C¿f¸J¸*»ÁZÄ$àÃ/½?ºˆÍÃ/¾LÄ0½?ºq¸¿LÃCÄqӝ0Äqºº0¿f»(º ýP¹€ ½wÉJ Ã/»¿L ½ï º0»*ì ÉJÂ6½Jï¾L ¾fÃSÊa¿E¹X¿L¸¸JØS¿fʸÃ/Ä0ÃCqº]Äq¾f0º¾f¿Eà ¿Lºq¼C¸‰»(Ê~ÃCÄ]Äq½T½XÅ"Úh¸-ÉJ¾fÀ(º0Î/Â6º0½¸-»( Ã8½‰ºqÏ
»(ºqÎCº] ½wÄqà ӝÃÑÀ‰ì ½wæ Î/º0¸-»(à Ê
¹P¼S¸-¸wº0»h¿L¸¼Sº]ÁZ¼CÁº0Â6¼S¼C¸-¸JÄq»½JÂfºqÃ-ÄÏÅ"ÃCÂLº0 Ã/Ä0ºq¸ ÓzÄ0ºq»(Ãï½o ¹€½wÉ-ï ÃCì »¿L½Pºqï» ÉJÊ<Â6½J¹P¾L¸w¾fÃS¿L¿E¸ ¿L¸Ã/ØSÄ0qʉºK¿fÃC¿fÄqº]ºq¼S¾L¸h¾EÊ<ÃÄ]_½ê»‰Å"ÃC¸-Äq¾f½oº0Î/ډº0¸-ÉJ»(À(ÃÂ6½jº0»( ºqÎCQ½(º]½wÏÄqà ð ӝ Ã/ÑÀ‰ ½JÎCï ºq¸Jì »(æ ÍïÛ ò Ø Ê
¹Pоf¸wÃC¿LÉ-¸X¹PÅhÃC½w»Â6¿f½wºˆÆ"¸J¸JÂLÄqºqº ÎC¼CÎC¸‰¸-Ï»¿L½w Äqº ¿fÂ6½?¿E ¿LÃCï É-ì ÉJº]½?¿fï º Â6½wʉÅ(¹XÅ(¸JÂL¿fÃ/¸P¾fÃCºq»Åh¿6Ã/½wÂf»(Æ"¸o¸JÄqĺ à¼CÃC¸‰»(Ï Ã/ÂfÉ-ºq½T¿f¸J¿L½wÄqÃPâÊÒÃ/¾L¾fºˆ¾f¸J»‰¸»RÀ(¹PÃCÂ6½?¿Lº%ï Á(½êÛPï½ ¼S¼S¸-¸-¹Pº0»hüSº]ÄqÁZÃ3üC¼C¸J¸JÂL»€Âfº]¾fÄÅhà ½-¸-¾f»‰¾fÃ}ÁZÃCÁZ»Ã/¿LÄ0º-qüSÀ‰½-Âf¾fÇ-¼Cúq¾L¾EÁZÃ-ºRÊ-ÃCâ绉ÃCÂLæäÉJº]î(½_ÏÅ"ÐQ¸w»€¿fÃ/¿f»(ÀZÎC¿fº]¿f½wºaÄqºaÃ3¼CNà ½Jo¾fº‰¼Cºq½-Ä"¼SÇeÃJ½Jþ?Ä0ºq¸-ÄZÂf¾EÃÃ/ÉJÁZ¹Pº XÃC»Ã¿L¸}ÑÀ(»RºqÀ(»‰¹PÁZºaÃCÂLÁZ¸ Ã/ÄhP¹Pӝ¹P¸J¹P¸w¿LÃ/¸»-Åh¿L¸½wÂ6½w½w»‰Æ"ÉJ¸J¸JÄqÄ]º ½w¼C¸ÂLÃØ
ÃÈ Úh¾L¾f½w¿f¸hÏ
(
(
(
$
1
i
(
(
Scarica

Moto dei pianeti Giuseppe Dalba Sommario Questi appunti