UNIVERSIDADE FEDERAL DA GRANDE DOURADOS-UFGD FACULDADE DE CIÊNCIAS EXATAS E TECNOLÓGICAS-FACET
LIN MING FENG
DISTÂNCIAS ASTRONÔMICAS E GEOMETRIA
DISSERTAÇÃO DE MESTRADO PROFISSIONAL EM MATEMÁTICA
LIN MING FENG
DISTÂNCIAS ASTRONÔMICAS E GEOMETRIA
ORIENTADOR: PROF.DR. ROGÉRIO DE OLIVEIRA
Dissertação apresentada ao final do Programa de Mestrado Profissional em Matemática da Universidade Federal da Grande Dourados (UFGD) como exigência parcial para a obtenção do título de Mestre em Matemática.
Ficha catalográfica elaborada pela Biblioteca Central - UFGD
510 L735d
Lin, Ming Feng.
Distâncias astronômicas e geometria / Lin Ming Feng – Dourados-MS : UFGD, 2013.
63 f.
Orientador: Prof. Dr. Rogério de Oliveira.
Dissertação (Mestrado Profissional em Matemática) Universidade Federal da Grande Dourados.
, Dedico este trabalho a Deus, aos meus pais,
AGRADECIMENTOS
Agradeço primeiramente aos Professores Doutores que são exemplos de profissionais a serem seguidos, especialmente a Irene Magalhães Careiro,Sérgio Rodrigues, Lino Sanábria e a Rogério de Oliveira cuja dedicação para com as aulas foram visíveis e me inspiram ainda mais à carreira docente.
Agradeço a Deus pelo dom da vida que tem guiado meus caminhos dando-me a fé e perseverança para concluir o curso.
Agradeço aos meus pais Lin Shou Jen & Huang Yueh Shuang, a minha tia Sonia pelo incentivo e pela presença constante em minha vida. A vocês, minha eterna gratidão.
Agradeço a minha namorada Elena pelo apoio e paciência nos momentos de inquietação e cansaço.
Aos meus amigos, que sempre me deram apoio e muito companheirismo, um agradecimento especial ao amigo João Henrique, Roney Garcia e a professora Irene pela revisão e correção deste trabalho
Agradeço ao amigo e professor Rogério de Oliveira pela orientação e paciência.
"Há três maneiras de conquistar sabedoria: por reflexão, a mais nobre; por imitação, a mais fácil; e por experiência, a mais amarga.”
❘❡s✉♠♦
❆ ❝❛❞❛ ✐♥st❛♥t❡ ♥♦s ❞❡♣❛r❛♠♦s ❝♦♠ s✐t✉❛çõ❡s q✉❡ ♥♦s ❧❡✈❛♠ ❛ r❡✢❡t✐r s♦❜r❡ ❝♦♥❝❡✐t♦s✱ ❝á❧❝✉❧♦s ❡ ♣r♦❝❡ss♦s r❡❢❡r❡♥t❡s ❛♦ ❝♦♥❤❡❝✐♠❡♥t♦ ♠❛t❡♠át✐❝♦✳ ❆ss✐♠✱ ♦ t❡♠❛ ♣❛r❛ ❛ r❡❛❧✐③❛çã♦ ❞❡st❡ tr❛❜❛❧❤♦ s✉r❣✐✉ ❛♣ós ❛ ❖❧✐♠♣í❛❞❛ ❞❡ ❆str♦♥♦✲ ♠✐❛ r❡❛❧✐③❛❞❛ ♥❛ ❡s❝♦❧❛✳ ❆ ♣r♦❢❡ss♦r❛ ❞❡ ●❡♦❣r❛✜❛ ♠♦str♦✉✲s❡ ♣r❡♦❝✉♣❛❞❛ ❝♦♠ ❛s ❞✐✜❝✉❧❞❛❞❡s ❡♥❝♦♥tr❛❞❛s ♣❡❧♦s ❛❧✉♥♦s ♥❛ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s q✉❡ ❡①✐❣❡♠ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❞❡ ♠❛t❡♠át✐❝❛ ❜ás✐❝❛✳ P❛rt✐♥❞♦ ❞❛ ✐❞❡✐❛ ❞❡ q✉❡ ♦ ❡st✉❞♦ ❞❡ tr✐❣♦♥♦♠❡tr✐❛ ❡stá r❡❧❛❝✐♦♥❛❞♦ às ❛♣❧✐❝❛çõ❡s✱ ✐st♦ ♣❡r♠✐t❡ ❡①♣❧♦r❛r ❛ ✐♥t❡r❞✐s✲ ❝✐♣❧✐♥❛❧✐❞❛❞❡ ❞❡st❡ ❝♦♥t❡ú❞♦ ✐♥t❡❣r❛♥❞♦ ❝♦♠ ❛ ❆str♦♥♦♠✐❛✱ ár❡❛ q✉❡ ❞❡s♣❡rt❛ ♠✉✐t❛ ❝✉r✐♦s✐❞❛❞❡ ❡♥tr❡ ♦s ❛❧✉♥♦s✳
❊st❡ tr❛❜❛❧❤♦ ❛♣r❡s❡♥t❛ ✉♠❛ ❡①♣❡r✐ê♥❝✐❛ ♣❡❞❛❣ó❞✐❝❛ r❡❛❧✐③❛❞❛ ❡♠ s❛❧❛ ❞❡ ❛✉❧❛ ❝♦♠ ❛❧✉♥♦s ❞❛ ❡❞✉❝❛çã♦ té❝♥✐❝❛✱ ♦ q✉❛❧ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ❞❡ ♠❛♥❡✐r❛ r❡✢❡✲ ①✐✈❛ s♦❜r❡ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ✐♥t❡r♣r❡t❛r ❡ r❡s♦❧✈❡r ♠❛t❡♠❛t✐❝❛♠❡♥t❡ ♣r♦❜❧❡♠❛s q✉❡ ❡♥✈♦❧✈❡♠ ❞✐stâ♥❝✐❛s ✐♥❛❝❡ssí✈❡✐s✳ P❛r❛ ✐ss♦ ❢♦✐ ♥❡❝❡ssár✐♦ tr❛❜❛❧❤❛r ✐♥✐❝✐❛❧✲ ♠❡♥t❡ ✉♠❛ s❡q✉ê♥❝✐❛ ❞❡ ❝♦♥t❡ú❞♦s✿ t❡♦r❡♠❛ ❞❡ ❚❛❧❡s✱ r❛③õ❡s tr✐❣♦♥♦♠étr✐❝❛s✱ ❣❡♦♠❡tr✐❛ ♣❧❛♥❛ ❡ ❣❡♦♠❡tr✐❛ ❡s♣❛❝✐❛❧✱ ♣❛r❛ ❡♥tã♦ ❛♣r❡s❡♥t❛r ♦ ♣r♦❜❧❡♠❛ ❞♦ ❝á❧✲ ❝✉❧♦ ❞♦ ❞✐â♠❡tr♦ ❞❛ ❚❡rr❛✱ ❞❛ ❞✐stâ♥❝✐❛ ❡♥tr❡ ❛ ❚❡rr❛ ❡ ▲✉❛ ❡ ❞❛ ❞✐stâ♥❝✐❛ ❡♥tr❡ ❛ ❚❡rr❛ ❡ ❙♦❧✳ ❈♦♠ ❡st❛ ♣r♦♣♦st❛ ♦s ❛❧✉♥♦s t✐✈❡r❛♠ ❛ ♦♣♦rt✉♥✐❞❛❞❡ ❞❡ s✉♣❡r❛r ❛❧❣✉♠❛s ❞✐✜❝✉❧❞❛❞❡s q✉❡ ❡st❛✈❛♠ ❡♥❢r❡♥t❛♥❞♦ ❝♦♠ ❛ ❣❡♦♠❡tr✐❛ ❡ ♠❛t❡♠át✐❝❛ ❜ás✐❝❛ ✉t✐❧✐③❛❞❛s ♥❛ ❆str♦♥♦♠✐❛✳ ❉✉r❛♥t❡ ♦ ♣r♦❝❡ss♦ ♦s ❛❧✉♥♦s ❛♣r❡s❡♥t❛r❛♠ s♦❧✉çõ❡s ❞✐❢❡r❡♥t❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ ✐❧✉str❛çã♦ ❝♦♠♣❛r❛t✐✈❛ ❡♥tr❡ ❛s ❞✐stâ♥✲ ❝✐❛s ❛str♦♥ô♠✐❝❛s ♠❡♥❝✐♦♥❛❞❛s ❛❝✐♠❛✳ P❛r❛ ✐❧✉str❛r ♦s t❛♠❛♥❤♦s ❞❛ ❚❡rr❛✱ ▲✉❛ ❡ ❙♦❧ ❡ s✉❛s r❡s♣❡❝t✐✈❛s ❞✐stâ♥❝✐❛s ❡♠ ❡s❝❛❧❛✱ ❝r✐♦✉✲s❡ s✐t✉❛çõ❡s ❡♠ q✉❡ ♦s ❛❧✉♥♦s ❢♦r❛♠ ❝❛♣❛③❡s ❞❡ ♠♦str❛r ❝r✐❛t✐✈✐❞❛❞❡ ❡ ❝❛♣❛❝✐❞❛❞❡ ❞❡ r❛❝✐♦❝í♥✐♦✳
❈♦♠♦ ✐♥str✉♠❡♥t♦ ❛✈❛❧✐❛t✐✈♦ ❢♦r❛♠ ❛♣❧✐❝❛❞❛s ❛t✐✈✐❞❛❞❡s ❝♦♠ q✉❡stõ❡s ❞❛ ❖❧✐♠♣í❛❞❛ ❞❡ ❆str♦♥♦♠✐❛ ❡♠ s❛❧❛ ❞❡ ❛✉❧❛ ❛♣ós ❛ ❡①♣❡r✐ê♥❝✐❛ ♣❡❞❛❣ó❞✐❝❛✳ ❖ r❡s✉❧t❛❞♦ ❞♦s ❛❧✉♥♦s ❢♦✐ ❜❛st❛♥t❡ s❛t✐s❢❛tór✐♦✱ ♣♦✐s ♠♦str❛r❛♠ ♠❡❧❤♦r✐❛ ♥❛ ✐♥t❡r✲ ♣r❡t❛çã♦ ❡ ♥❛ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s q✉❡ ❤❛✈✐❛♠ s✐❞♦ ❛♣♦♥t❛❞♦s ♣❡❧❛ ♣r♦❢❡ss♦r❛ ❞❡ ●❡♦❣r❛✜❛✳
P❛❧❛✈r❛s✲❝❤❛✈❡✿ ❛str♦♥♦♠✐❛✳ ❞✐stâ♥❝✐❛s ✐♥❛❝❡ssí✈❡✐s✳ ❣❡♦♠❡tr✐❛✳♠❛t❡♠át✐❝❛
❆❇❙❚❘❆❈❚
❆t ❡✈❡r② ♠♦♠❡♥t ✇❡ ❤❛✈❡ t♦ ❢r♦♥t ♦✉rs❡❧✈❡s ✇✐t❤ s♦♠❡ s✐t✉❛t✐♦♥s ✇❤✐❝❤ ♠❛❦❡ ✉s t♦ r❡✢❡❝t ❛❜♦✉t ❝♦♥❝❡♣ts✱ ❝❛❧❝✉❧❛t✐♦♥s ❛♥❞ ♣r♦❝❡ss❡s r❡❧❛t❡❞ t♦ ♠❛t❤❡♠❛t✐✲ ❝❛❧ ❦♥♦✇❧❡❞❣❡✳ ❚❤❡r❡❢♦r❡✱ t❤❡ t❤❡♠❡ ❢♦r t❤✐s ✇♦r❦ ❝❛♠❡ ❛❢t❡r t❤❡ ❆str♦♥♦♠② ❖❧②♠♣✐❝ ❈♦♥t❡st✱ ❤❡❧❞ ❛t s❝❤♦♦❧✱ ✇❤❡r❡ t❤❡ ❣❡♦❣r❛♣❤② t❡❛❝❤❡r ❡①♣r❡ss❡❞ ❝♦♥❝❡r♥ ❛❜♦✉t t❤❡ ❞✐✣❝✉❧t✐❡s ❢♦✉♥❞ ♦✉t ❜② t❤❡ st✉❞❡♥ts t♦ s♦❧✈❡ ♣r♦❜❧❡♠s ✇❤✐❝❤ r❡q✉✐r❡ ❜❛s✐❝ ❦♥♦✇❧❡❞❣❡ ✐♥ ♠❛t❤❡♠❛t✐❝s✳ ❈♦♥s✐❞❡r✐♥❣ t❤❡ ✐❞❡❛ t❤❛t t❤❡ tr✐❣♦♥♦♠❡tr② st✉❞✐❡s ❛r❡ r❡❧❛t❡❞ t♦ ❛♣♣❧✐❝❛t✐♦♥s✱ ✐t ✐s ♣♦ss✐❜❧❡ t♦ ❡①♣❧♦r❡ t❤❡ ✐♥t❡r❞✐s❝✐♣❧✐♥❛r✐t② ♦❢ t❤✐s ❝♦♥t❡♥t ✐♥t❡❣r❛t✐♥❣ ✐t t♦ ❆str♦♥♦♠②✱ ✇❤✐❝❤ ✐s ❛♥ ❛r❡❛ t❤❛t ❛r♦✉s❡s ♠✉❝❤ ❝✉r✐♦s✐t② ♦♥ st✉❞❡♥ts✳ ❚❤✐s ✇♦r❦ ♣r❡s❡♥ts ❛ ♣❡❞❛❣♦❣✐❝❛❧ ❡①♣❡r✐❡♥❝❡ ❝❛rr✐❡❞ ♦✉t ✐♥ ❛ ❝❧❛ssr♦♦♠ ✇✐t❤ st✉❞❡♥ts ♦❢ ❛ t❡❝❤♥✐❝❛❧ s❝❤♦♦❧✱ ❛♥❞ ✐t ✇❛s ❞❡✈❡❧♦♣❡❞ ✐♥ ❛ r❡✢❡①✐✈❡ ✇❛② ❛❜♦✉t t❤❡ ♥❡❡❞s ♦❢ ✐♥t❡r♣r❡t✐♥❣ ❛♥❞ s♦❧✈✐♥❣ ♠❛t❤❡♠❛t✐❝❛❧❧② ♣r♦✲ ❜❧❡♠s ✇❤✐❝❤ ✐♥✈♦❧✈❡ ✐♥❛❝❝❡ss✐❜❧❡ ❞✐st❛♥❝❡s✳ ❋♦r t❤❛t ✐t ✇❛s ♥❡❝❡ss❛r② t♦ ✇♦r❦ ✐♥✐t✐❛❧❧② ✇✐t❤ s❡q✉❡♥❝❡❞ ❝♦♥t❡♥ts✿ ❚❤❛❧❡s ❚❤❡♦r❡♠❡✱ tr✐❣♦♥♦♠❡tr✐❝ ❡q✉❛t✐♦♥s✱ ♣❧❛♥❡ ❣❡♦♠❡tr② ❛♥❞ s♣❛t✐❛❧ ❣❡♦♠❡tr② ❛♥❞ t❤❡♥ ♣r❡s❡♥t t❤❡ ♣r♦❜❧❡♠ ✇✐t❤ t❤❡ ❝❛❧✲ ❝✉❧❛t✐♦♥ ♦❢ t❤❡ ❊❛rt❤ ❞✐❛♠❡t❡r✱ t❤❡ ❞✐st❛♥❝❡ ❜❡t✇❡❡♥ t❤❡ ❊❛rt❤ ❛♥❞ t❤❡ ▼♦♦♥ ❛s ✇❡❧❧ ❛s t❤❡ ❞✐st❛♥❝❡ ❜❡t✇❡❡♥ t❤❡ ❊❛rt❤ ❛♥❞ t❤❡ ❙✉♥✳ ❙t❛rt✐♥❣ ❢r♦♠ t❤✐s ♣♦✐♥t✱ t❤❡ st✉❞❡♥ts ❤❛❞ t❤❡ ♦♣♣♦rt✉♥✐t② ♦❢ ♦✈❡r❝♦♠✐♥❣ s♦♠❡ ❞✐✣❝✉❧t✐❡s t❤❡② ❤❛❞ ❜❡❡♥ ❢❛❝✐♥❣ ✇✐t❤ ❜❛s✐❝ ♠❛t❤❡♠❛t✐❝s ❛♥❞ ❣❡♦♠❡tr② ✉s❡❞ ✐♥ ❆str♦♥♦♠②✳ ❆❧♦♥❣ t❤❡ ♣r♦❝❡ss✱ t❤❡ st✉❞❡♥ts ❤❛✈❡ ♣r❡s❡♥t❡❞ ❞✐✛❡r❡♥t s♦❧✉t✐♦♥s ❢♦r t❤❡ ❝♦♠♣❛r❛t✐✈❡ ✐❧✲ ❧✉str❛t✐♦♥ ❜❡t✇❡❡♥ t❤❡ ❛str♦♥♦♠✐❝ ❞✐st❛♥❝❡s ✐♥❞✐❝❛t❡❞ ❛❜♦✈❡✳ ❋♦r ✐❧❧✉str❛t✐♥❣ t❤❡ s✐③❡s ♦❢ t❤❡ ❊❛rt❤✱ t❤❡ ▼♦♦♥ ❛♥❞ t❤❡ ❙✉♥ ❛♥❞ t❤❡✐r r❡s♣❡❝t✐✈❡ ❞✐st❛♥❝❡s ✐♥ s❝❛❧❡s✱ ✇❡ ❝r❡❛t❡❞ s✐t✉❛t✐♦♥s ✇❤✐❝❤ ♠❛❞❡ t❤❡ st✉❞❡♥ts ❛❜❧❡ t♦ s❤♦✇ ❝r❡❛t✐✲ ✈✐t② ❛♥❞ r❡❛s♦♥✐♥❣ ❝❛♣❛❝✐t②✳ ❋♦r ❡✈❛❧✉❛t✐♥❣✱ ❛❝t✐✈✐t✐❡s ✇✐t❤ q✉❡st✐♦♥s ♦❢ t❤❡ ❆str♦♥♦♠② ❖❧②♠♣✐❝ ❈♦♥t❡st ✇❡r❡ ❛♣♣❧✐❡❞ ✐♥ t❤❡ ❝❧❛ssr♦♦♠ ❛❢t❡r t❤❡ ♣❡❞❛❣♦✲ ❣✐❝❛❧ ❡①♣❡r✐❡♥❝❡✳ ❚❤❡ r❡s✉❧ts ♦❢ t❤❡ st✉❞❡♥ts ✇❡r❡ ✈❡r② s❛t✐s❢❛❝t♦r②✱ ♦♥❝❡ t❤❡② s❤♦✇❡❞ ❛ ❜❡tt❡r ♣❡r❢♦r♠❛♥❝❡ ✐♥ ✐♥t❡r♣r❡t✐♥❣ ❛♥❞ s♦❧✈✐♥❣ ♣r♦❜❧❡♠s ✇❤✐❝❤ ❤❛❞ ❜❡❡♥ ♣♦✐♥t❡❞ ♦✉t ✐♥✐t✐❛❧❧②✳
❑❡②✇♦r❞s✿ ❆str♦♥♦♠②✳ ■♥❛❝❝❡ss✐❜❧❡ ❞✐st❛♥❝❡s✳ ●❡♦♠❡tr②✳ ▼❛t❤❡♠❛t✐❝s✳
❙✉♠ár✐♦
✶ ❯♠ ♣♦✉❝♦ s♦❜r❡ ❛ ❤✐stór✐❛ ❞♦s ❛strô♥♦♠♦s ❞❛ ●ré❝✐❛ ❛♥t✐❣❛ ✶✺
✷ ➱ ♣♦ssí✈❡❧ ♠❡❞✐r ♦ r❛✐♦ ❞❛ ❚❡rr❛❄ ✶✼
✷✳✶ ❉✐â♠❡tr♦ ❞❛ ❚❡rr❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✷ ❱❡❧♦❝✐❞❛❞❡ ❞❡ r♦t❛çã♦ ❡ tr❛♥s❧❛çã♦ ❞❛ ❚❡rr❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✷✳✷✳✶ ▼♦✈✐♠❡♥t♦ ❞❡ ❘♦t❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✷✳✷✳✷ ▼♦✈✐♠❡♥t♦ ❞❡ ❚r❛♥s❧❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✷✳✷✳✷✳✶ ❊q✉✐♥ó❝✐♦ ✲ ♥♦✐t❡s ✐❣✉❛✐s ❛♦s ❞✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✷✳✷✳✷✳✷ ❙♦❧stí❝✐♦ ✲ ❉✐❛s ♠❛✐s ❧♦♥❣♦s ❡ ♥♦✐t❡s ♠❛✐s ❝✉rt❛s ✷✸
✸ ❉✐stâ♥❝✐❛s ❛str♦♥ô♠✐❝❛s ✷✺
✸✳✶ ❉✐stâ♥❝✐❛ ❡♥tr❡ ❛ ❚❡rr❛ ❡ ❛ ▲✉❛ ❡ ❚❡rr❛ ❡ ♦ ❙♦❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✸✳✶✳✶ ❆ ❜r✐❧❤❛♥t❡ ✐❞❡✐❛ ❞❡ ❆r✐st❛r❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✸✳✶✳✷ ❚❛♠❛♥❤♦s ❞♦ ❙♦❧ ❡ ❞❛ ▲✉❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✷ ❉✐stâ♥❝✐❛ ❞❡ ✉♠❛ ❡str❡❧❛ à ❚❡rr❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✸✳✷✳✶ P❛r❛❧❛①❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶
✹ ❈❛❧❝✉❧❛♥❞♦ ❞✐stâ♥❝✐❛s ✐♥❛❝❡ssí✈❡✐s ✸✹
✹✳✶ ❈❛❧❝✉❧❛r ❛ ❧❛r❣✉r❛ ❞❡ ✉♠ r✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✹✳✷ ❆ ❞✐stâ♥❝✐❛ ❡♥tr❡ ❞♦✐s ♣♦♥t♦s ❝♦♠ ✉♠ ♦❜stá❝✉❧♦ ♥♦ ♠❡✐♦ ✳ ✳ ✳ ✳ ✳ ✸✼
✺ P❧❛♥♦ ❞❡ ❛✉❧❛ ✹✵
✺✳✶ ❖❜❥❡t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✺✳✷ ❖❜❥❡t✐✈♦s ❡s♣❡❝í✜❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵
✻ ❊①♣❡r✐ê♥❝✐❛ ♣❡❞❛❣ó❣✐❝❛ ✹✹
✻✳✵✳✶ ❆t✐✈✐❞❛❞❡ ✶✿ ❚❛♠❛♥❤♦s ❞❛ ❚❡rr❛ ❡ ▲✉❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✻✳✵✳✷ ❆t✐✈✐❞❛❞❡ ✷✿ ❈❛❧❝✉❧❛r ♦ ❞✐â♠❡tr♦ ❞❛ ❚❡rr❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✻✳✶ ❖ r❡s✉❧t❛❞♦ ❞❛s ❛t✐✈✐❞❛❞❡s ❛♣❧✐❝❛❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✻✳✷ ❆♥á❧✐s❡ ❝rít✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼
✼ ❈♦♥❝❧✉sã♦ ✺✾
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✷✳✶ ❘❛✐♦ ❞❛ ❚❡rr❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✷✳✷ ❱❡❧♦❝✐❞❛❞❡ ❞❡ r♦t❛çã♦ ❞❛ ❚❡rr❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✷✳✸ ❱❡❧♦❝✐❞❛❞❡ ❞❡ tr❛s❧❛çã♦ ❞❛ ❚❡rr❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷
✸✳✶ ❉✐stâ♥❝✐❛ ❡♥tr❡ ❛ ❚❡rr❛ ❡ ❛ ▲✉❛ ❡ ❛ ❚❡rr❛ ❡ ♦ ❙♦❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✸✳✷ ❉✐stâ♥❝✐❛ ❡♥tr❡ ❛ ❚❡rr❛ ❡ ❛ ▲✉❛ ❡ ❛ ❚❡rr❛ ❡ ♦ ❙♦❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✸✳✸ ❆s ❞✐stâ♥❝✐❛s r❡❧❛t✐✈❛s ❞❛ ❚❡rr❛ ❛♦ ❙♦❧ ❡ à ▲✉❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✸✳✹ ❆s ❞✐stâ♥❝✐❛s r❡❧❛t✐✈❛s ❞❛ ❚❡rr❛ ❛♦ ❙♦❧ ❡ à ▲✉❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✸✳✺ ❆s ❞✐stâ♥❝✐❛s r❡❧❛t✐✈❛s ❞❛ ❚❡rr❛ ❛♦ ❙♦❧ ❡ à ▲✉❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✸✳✻ P❛r❛❧❛①❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷
✹✳✶ ▲❛r❣✉r❛ ❞❡ ✉♠ r✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✹✳✷ ❈á❧❝✉❧♦ ❞❛ ❧❛r❣✉r❛ ❞❡ ✉♠ r✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✹✳✸ ❉✐stâ♥❝✐❛ ❡♥tr❡ ❞♦✐s ♣♦♥t♦s ❝♦♠ ♦❜stá❝✉❧♦ ♥♦ ♠❡✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✹✳✹ ❚r✐â♥❣✉❧♦s s❡♠❡❧❤❛♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✹✳✺ ❚r✐â♥❣✉❧♦s s❡♠❡❧❤❛♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽
✻✳✶ ❆❧✉♥♦s ❞♦ ❝✉rs♦ ❞❡ ❚é❝♥✐❝♦ ❡♠ ❆❣r✐❝✉❧t✉r❛ ♠♦str❛♥❞♦ ❛ ❝♦♠♣❛✲ r❛çã♦ ❡♥tr❡ ♦s t❛♠❛♥❤♦s ❞❛ ❚❡rr❛✱ ▲✉❛ ❡ ❙♦❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✻✳✷ ▼♦str❛♥❞♦ ❞✐stâ♥❝✐❛ ❡♥tr❡ ❚❡rr❛✱ ▲✉❛ ❡ ❙♦❧ ❡♠ ❡s❝❛❧❛ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✻✳✸ ▼♦str❛♥❞♦ ❛ ❞✐stâ♥❝✐❛ ❡♥tr❡ ❛ ❚❡rr❛ ❡ ❛ ▲✉❛ ❡♠ ❡s❝❛❧❛ ✳ ✳ ✳ ✳ ✳ ✹✼ ✻✳✹ ●r✉♣♦s ❞❡ ❛❧✉♥♦s ❛♣r❡s❡♥t❛♥❞♦ ♠❛q✉❡t❡ ❞❛ ❚❡rr❛✱ ▲✉❛ ❡ ❙♦❧ ✳ ✳ ✹✽ ✻✳✺ ❆♣r❡s❡♥t❛çã♦ ❞❡ s❧✐❞❡ ❡ ♠❛q✉❡t❡ ❞❡st❡ ❣r✉♣♦ q✉❡ ❞❡st❛❝♦✉ ♦
♣♦rq✉ê ❞❛ ❝♦r ❜r❛♥❝❛ ❞♦ ❙♦❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✻✳✻ ❖s ❛❧✉♥♦s ❞♦ ❝✉rs♦ ❞❡ ❚é❝♥✐❝♦ ❡♠ ■♥❢♦r♠át✐❝❛ ♠♦str❛♥❞♦ ♦ tr❛✲
❜❛❧❤♦ ❞♦ ❣r✉♣♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✻✳✼ ❆❧✉♥♦s ❛♣r❡s❡♥t❛♥❞♦ ♦s ❝á❧❝✉❧♦s ❞❛ ❡s❝❛❧❛✱ ❡ ❞✐stâ♥❝✐❛ ❡♥tr❡ ❚❡rr❛
✲ ▲✉❛ ❡ ❚❡rr❛ ✲ ❙♦❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✻✳✽ ●r✉♣♦ ❡①♣❧✐❝❛♥❞♦ ❛ ♦r✐❣❡♠ ❞❛ ▲✉❛ ❡ ♦ ❡✐①♦ ❞❛ ❚❡rr❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✻✳✾ ▼♦str❛♥❞♦ ❛ ❞✐stâ♥❝✐❛ ❡♥tr❡ ❛ ❚❡rr❛ ❡ ❛ ▲✉❛ ❡♠ ❡s❝❛❧❛ r❡❛❧✳ ✳ ✳ ✺✸
■♥tr♦❞✉çã♦
❆ ▼❛t❡♠át✐❝❛ ❢♦✐ ❝r✐❛❞❛ ♣❡❧♦ ❤♦♠❡♠ ❞❡✈✐❞♦ às ♥❡❝❡ss✐❞❛❞❡s s♦❝✐❛✐s✳ ❍á ♠✐❧❤õ❡s ❞❡ ❛♥♦s ❛trás ♦ ❤♦♠❡♠ ✈✐✈✐❛ ❞❛ ❝❛ç❛ ❡ ❞❛ ❝♦❧❡t❛ ❡✱ ♣❛r❛ ✐ss♦✱ ❡❧❡ ♣r❡❝✐s❛✈❛ ❛♣❡♥❛s ❞❛s ♥♦çõ❡s ❞❡ ♠❛t❡♠át✐❝❛ ♠❛✐s ✲ ♠❡♥♦s✱ ♠❛✐♦r ✲ ♠❡♥♦r✳
▼❛✐s t❛r❞❡✱ q✉❛♥❞♦ ❝♦♠❡ç♦✉ ❛ ❝♦♥str✉✐r ❤❛❜✐t❛çõ❡s✱ ♣❛ss♦✉ ❛ ♣r❡❝✐s❛r ❞❡ ❛❧❣✉♥s ♥ú♠❡r♦s ❡ ✜❣✉r❛s✳ ❊ ❝♦♥str✉✐♥❞♦ ❡s❝♦r❛s✱ tr❛✲ ✈❡ss❛s✱ ❝✉♥❤❛s ❡ ❞❛r ✐♥❝❧✐♥❛çõ❡s✱ ✉t✐❧✐③❛✈❛ ♦ ❝♦♥❝❡✐t♦ ❞❡ tr✐â♥❣✉❧♦✳ ❆♦ ❛rr❡❞♦♥❞❛r ♦❜❥❡t♦s✱ ❣✐rá✲❧♦ ♣❛r❛ ❛❝❡♥❞❡r ♦ ❢♦❣♦ ♦✉ ❢❛③❡r ❢✉r♦s✱ ❝❤❡❣♦✉ à ❝✐r❝✉♥❢❡rê♥❝✐❛✳ ❖s sí♠❜♦❧♦s ♣❛ss❛r❛♠ ❛ s❡r ✉t✐❧✐③❛❞♦s ❝♦♠ ♠❛✐♦r ❢r❡q✉ê♥❝✐❛✱ s✉r❣✐♥❞♦ ❛ ✐❞❡♦❣r❛✜❛ ❡✱ ❛ ♣❛rt✐r ❞❛í✱ ♦ s✉r❣✐♠❡♥t♦ ❞♦s ♥ú♠❡r♦s✳ ❆ ▼❛t❡♠át✐❝❛✱ ❡♥tã♦✱ s❡♠♣r❡ ❡st❡✈❡ ♣r❡s❡♥t❡ ♥❛ ✈✐❞❛ ❞♦ ❤♦♠❡♠✱ ♠❡s♠♦ q✉❡ ❡st❡s ❝♦♥❝❡✐t♦s ❢♦ss❡♠ ❢♦r♠❛❧✐③❛❞♦s ♠✉✐t♦ t❡♠♣♦ ❞❡♣♦✐s✳
❖s ❛♥t✐❣♦s ❡❣í♣❝✐♦s✱ ❜❛❜✐❧ô♥✐♦s ❡ ❝❤✐♥❡s❡s ❥á ❝♦♥s❡❣✉✐❛♠ ❡❢❡t✉❛r ❝á❧❝✉❧♦s ❡ ♠❡❞✐❞❛s ❝♦♠ ❣r❛♥❞❡ ♣r❡❝✐sã♦✳ ▼❛s ❢♦r❛♠ ♦s ❣r❡❣♦s q✉❡ ✐♥tr♦❞✉③✐r❛♠ ♣r♦✈❛s r✐❣♦r♦s❛s ❡ ♦ ❡♥❝❛❞❡❛♠❡♥t♦ s✐st❡♠át✐❝♦ ❞❡ t❡✲ ♦r❡♠❛s✱ q✉❡ ✜③❡r❛♠ ❝♦♠ q✉❡ ❛ ▼❛t❡♠át✐❝❛ s❡ t♦r♥❛ss❡ ✉♠❛ ❝✐ê♥✲ ❝✐❛✳ ❆♥t✐❣❛♠❡♥t❡✱ ♦s ❣r❡❣♦s ❝♦♥s✐❞❡r❛✈❛♠ ❛♣❡♥❛s ❛ ❆r✐t♠ét✐❝❛ ❡ ❛ ●❡♦♠❡tr✐❛ ❝♦♠♦ ❝✐ê♥❝✐❛s ♣✉r❛♠❡♥t❡ ♠❛t❡♠át✐❝❛s✱ ♠❛✐s t❛r❞❡ ❛ ❆str♦♥♦♠✐❛ ❡ ❛ ▼❡❝â♥✐❝❛ t❛♠❜é♠ ❢♦r❛♠ ✐♥s❡r✐❞❛s✳
❆ ♣r♦♣♦st❛ ❞❡st❡ tr❛❜❛❧❤♦ é ❥✉st❛♠❡♥t❡ ✐♥t❡❣r❛r ♦ ❡♥s✐♥♦ ❞❡ ▼❛✲ t❡♠át✐❝❛ ❝♦♠ ❛ ❆str♦♥♦♠✐❛ ♣❛r❛ ❞❡s♣❡rt❛r ♦ ✐♥t❡r❡ss❡ ❞♦s ❛❧✉♥♦s ♥❛ ▼❛t❡♠át✐❝❛✱ ❛ ♣❛rt✐r ❞❛ ❞❡t❡r♠✐♥❛çã♦ ❞❡ ❞✐stâ♥❝✐❛s ❝♦♥s✐❞❡r❛✲ ❞❛s ✐♥❛❝❡ssí✈❡✐s✳ ❈♦♠ ❛ r❡✈✐sã♦ ❞❛ ♠❛t❡♠át✐❝❛ ❜ás✐❝❛✱ s❛♥❛♥❞♦ ❛s ❞ú✈✐❞❛s✱ ❛♣r♦❢✉♥❞❛♥❞♦ ♦s s❛❜❡r❡s✱ ❝❤❡❣❛✲s❡ ❛♦s r❡s✉❧t❛❞♦s ♣♦s✐t✐✈♦s ❡ ❝❛rr❡❣❛❞♦s ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦✳ ❆ ✐♥t❡r❞✐s❝✐♣❧✐♥❛r✐❞❛❞❡ ❞❡✈❡ s❡r ❛♣❧✐✲ ❝❛❞❛✱ ♣♦✐s ❢❛③ ❝♦♠ q✉❡ ♦s ❛❧✉♥♦s ♦❜t❡♥❤❛♠ ♥♦✈♦s ❝♦♥❤❡❝✐♠❡♥t♦s ❛ ♣❛rt✐r ❞♦ q✉❡ ❥á s❛❜❡♠✳
❙❡❣✉♥❞♦ P❈◆❊▼✴P❛râ♠❡tr♦ ❈✉rr✐❝✉❧❛r ◆❛❝✐♦♥❛❧ ❞❡ ❊♥s✐♥♦ ▼é✲ ❞✐♦ ✭♣á❣✐♥❛ ✼✮ ❬✶❪✿
▲■❙❚❆ ❉❊ ❋■●❯❘❆❙ ✶✸
✏❯♠ ❊♥s✐♥♦ ▼é❞✐♦ ❝♦♥❝❡❜✐❞♦ ♣❛r❛ ✉♥✐✈❡rs❛❧✐③❛çã♦ ❞❛ ❊❞✉✲ ❝❛çã♦ ❇ás✐❝❛ ♣r❡❝✐s❛ ❞❡s❡♥✈♦❧✈❡r ♦ s❛❜❡r ♠❛t❡♠át✐❝♦✱ ❝✐❡♥✲ tí✜❝♦ ❡ t❡❝♥♦❧ó❣✐❝♦ ❝♦♠♦ ❝♦♥❞✐çã♦ ❞❡ ❝✐❞❛❞❛♥✐❛ ❡ ♥ã♦ ❝♦♠♦ ♣r❡rr♦❣❛t✐✈❛ ❞❡ ❡s♣❡❝✐❛❧✐st❛s✳ ❖ ❛♣r❡♥❞✐③❛❞♦ ♥ã♦ ❞❡✈❡ s❡r ❝❡♥tr❛❞♦ ♥❛ ✐♥t❡r❛çã♦ ✐♥❞✐✈✐❞✉❛❧ ❞❡ ❛❧✉♥♦s ❝♦♠ ♠❛t❡r✐✲ ❛✐s ✐♥str✉❝✐♦♥❛✐s✱ ♥❡♠ s❡ r❡s✉♠✐r à ❡①♣♦s✐çã♦ ❞❡ ❛❧✉♥♦s ❛♦ ❞✐s❝✉rs♦ ♣r♦❢❡ss♦r❛❧✱ ♠❛s s❡ r❡❛❧✐③❛r ♣❡❧❛ ♣❛rt✐❝✐♣❛çã♦ ❛t✐✈❛ ❞❡ ❝❛❞❛ ✉♠ ❡ ❞♦ ❝♦❧❡t✐✈♦ ❡❞✉❝❛❝✐♦♥❛❧ ♥✉♠❛ ♣rát✐❝❛ ❞❡ ❡❧❛❜♦r❛çã♦ ❝✉❧t✉r❛❧✳✑
❊ ♥❛ ♣á❣✐♥❛ ✶✷✱ ✈❡♠♦s ♦ t❡①t♦ ❛❜❛✐①♦ q✉❡ ❝✐t❛ ❛❧❣✉♥s ✐t❡♥s q✉❡ ❡①♣❧♦r❛r❡♠♦s ♥❡st❡ tr❛❜❛❧❤♦✿
✏❉❡s❡♥✈♦❧✈❡r ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ q✉❡st✐♦♥❛r ♣r♦❝❡ss♦s ♥❛t✉✲ r❛✐s ❡ t❡❝♥♦❧ó❣✐❝♦s✱ ✐❞❡♥t✐✜❝❛♥❞♦ r❡❣✉❧❛r✐❞❛❞❡s✱ ❛♣r❡s❡♥✲ t❛♥❞♦ ✐♥t❡r♣r❡t❛çõ❡s ❡ ♣r❡✈❡♥❞♦ ❡✈♦❧✉çõ❡s✳ ❉❡s❡♥✈♦❧✈❡r ♦ r❛❝✐♦❝í♥✐♦ ❡ ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❛♣r❡♥❞❡r✳
✯ ❋♦r♠✉❧❛r q✉❡stõ❡s ❛ ♣❛rt✐r ❞❡ s✐t✉❛çõ❡s r❡❛✐s ❡ ❝♦♠♣r❡❡♥❞❡r ❛q✉❡❧❛s ❥á ❡♥✉♥❝✐❛❞❛s✳
✯ ❉❡s❡♥✈♦❧✈❡r ♠♦❞❡❧♦s ❡①♣❧✐❝❛t✐✈♦s ♣❛r❛ s✐st❡♠❛s t❡❝♥♦❧ó❣✐❝♦s ❡ ♥❛t✉r❛✐s✳
✯ ❯t✐❧✐③❛r ✐♥str✉♠❡♥t♦s ❞❡ ♠❡❞✐çã♦ ❡ ❞❡ ❝á❧❝✉❧♦✳ ✯ Pr♦❝✉r❛r ❡ s✐st❡♠❛t✐③❛r ✐♥❢♦r♠❛çõ❡s r❡❧❡✈❛♥t❡s ♣❛r❛ ❛ ❝♦♠♣r❡❡♥sã♦ ❞❛ s✐t✉❛çã♦✲♣r♦❜❧❡♠❛✳
✯ ❋♦r♠✉❧❛r ❤✐♣ót❡s❡s ❡ ♣r❡✈❡r r❡s✉❧t❛❞♦s
✯ ❊❧❛❜♦r❛r ❡str❛té❣✐❛s ❞❡ ❡♥❢r❡♥t❛♠❡♥t♦ ❞❛s q✉❡s✲ tõ❡s✳
✯ ■♥t❡r♣r❡t❛r ❡ ❝r✐t✐❝❛r r❡s✉❧t❛❞♦s ❛ ♣❛rt✐r ❞❡ ❡①✲ ♣❡r✐♠❡♥t♦s ❡ ❞❡♠♦♥str❛çõ❡s✳
✯ ❆rt✐❝✉❧❛r ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❝✐❡♥tí✜❝♦ ❡ t❡❝♥♦❧ó✲ ❣✐❝♦ ♥✉♠❛ ♣❡rs♣❡❝t✐✈❛ ✐♥t❡r❞✐s❝✐♣❧✐♥❛r✳
✯ ❊♥t❡♥❞❡r ❡ ❛♣❧✐❝❛r ♠ét♦❞♦s ❡ ♣r♦❝❡❞✐♠❡♥t♦s ♣ró✲ ♣r✐♦s ❞❛s ❈✐ê♥❝✐❛s ◆❛t✉r❛✐s✳✑
❖ tr❛❜❛❧❤♦ ❢♦✐ ❡str✉t✉r❛❞♦ ❡ ♦r❣❛♥✐③❛❞♦ ❞❡ ❢♦r♠❛ q✉❡ ♦ ❈❛♣ít✉❧♦ ✶ t❡♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ❛♣r❡s❡♥t❛r ✉♠ ♣♦✉❝♦ ❞❛ ❤✐stór✐❛ ❞♦s ❛strô♥♦♠♦s ❞❛ ❛♥t✐❣✉✐❞❛❞❡✳
▲■❙❚❆ ❉❊ ❋■●❯❘❆❙ ✶✹
❖ ❝❛♣ít✉❧♦ ✸ ♠♦str❛ ❛s ❞✐stâ♥❝✐❛s ❡♥tr❡ ❛ ❚❡rr❛ ❡ ❛ ▲✉❛✱ ❡♥tr❡ ❛ ❚❡rr❛ ❡ ♦ ❙♦❧ ❡ ❞✐stâ♥❝✐❛ ❞❡ ✉♠❛ ❡str❡❧❛ à ❚❡rr❛
❖ ❝❛♣ít✉❧♦ ✹ ❛♣r❡s❡♥t❛ ❝♦♠♦ ❝❛❧❝✉❧❛r ❞✐stâ♥❝✐❛s ✐♥❛❝❡ssí✈❡✐s ❛tr❛✲ ✈és ❞❡ ❡①❡♠♣❧♦s ❞❛ ♠❡❞✐çã♦ ❞❛ ❧❛r❣✉r❛ ❞❡ ✉♠ r✐♦ ❡ ❞❛ ❞✐stâ♥❝✐❛ ❡♥tr❡ ❞♦✐s ♣♦♥t♦s ❝♦♠ ✉♠ ♦❜stá❝✉❧♦ ❡♥tr❡ ❡❧❡s✳
❖ ❝❛♣ít✉❧♦ ✺ ❛♣r❡s❡♥t❛ ♦ ♣❧❛♥♦ ❞❡ ❛✉❧❛ ❝♦♠ ♦s ♦❜❥❡t✐✈♦s ❡ ❞❡ ❝♦♠♦ ❛s ❛✉❧❛s ♣♦❞❡♠ s❡r tr❛❜❛❧❤❛❞❛s✳
❖ ❝❛♣ít✉❧♦ ✻ ♠♦str❛ ❛ ❡①♣❡r✐ê♥❝✐❛ ♣❡❞❛❣ó❣✐❝❛ ❡ ❛s ❛t✐✈✐❞❛❞❡s ❛♣❧✐❝❛❞❛s ❡♠ s❛❧❛✱ ❛♣r❡s❡♥t❛ ❛ ❛✈❛❧✐❛çã♦ ✜♥❛❧✱ ♦ r❡s✉❧t❛❞♦ ❡ ❛♥á❧✐s❡ ❞❛s ❛t✐✈✐❞❛❞❡s ❛♣❧✐❝❛❞❛s✳
❈❛♣ít✉❧♦ ✶
❯♠ ♣♦✉❝♦ s♦❜r❡ ❛ ❤✐stór✐❛ ❞♦s
❛strô♥♦♠♦s ❞❛ ●ré❝✐❛ ❛♥t✐❣❛
❈á❧❝✉❧♦s ❡ ❡st✉❞♦s ♣❛r❛ r❡s♣♦♥❞❡r ♣❡r❣✉♥t❛s s♦❜r❡ ❛s ❞✐stâ♥❝✐❛s ❛s✲ tr♦♥ô♠✐❝❛s s❡♠♣r❡s ❢♦r❛♠ ❢❡✐t❛s✳ ❉❡s❞❡ ❛ ❛♥t✐❣✉✐❞❛❞❡✱ sé❝✉❧♦s ❛♥t❡s ❞❡ ❈r✐st♦✱ ♦♥❞❡ ♠✉✐t♦s ❝✐❡♥t✐st❛s ❝♦♠♦ ❆r✐st❛r❝♦✱ ❊r❛stót❡♥❡s✱ Pt♦✲ ❧♦♠❡✉ ❡ ♦✉tr♦s✱ ❜❛s❡❛❞♦s ❡♠ ✐❞❡✐❛s ♠✉✐t♦ s✐♠♣❧❡s ❡ s✉st❡♥t❛❞♦s ♣♦r ♥♦çõ❡s ❞❡ ●❡♦♠❡tr✐❛ ❝❤❡❣❛r❛♠ ❛ ❜r✐❧❤❛♥t❡s r❡s✉❧t❛❞♦s✳
❖s ❛strô♥♦♠♦s ❞❛ ●ré❝✐❛ ❛♥t✐❣❛
❙❡❣✉♥❞♦ ♦ s✐t❡ ❤tt♣✿✴✴❛str♦✳✐❢✳✉❢r❣s✳❜r✴❛♥t✐❣❛✴❛♥t✐❣❛✳❤t♠ ❛♣r❡s❡♥t❛ ❤✐stór✐❛s ❞❡ ❛❧❣✉♥s ❛strô♥♦♠♦s ✐♠♣♦rt❛♥t❡s ❞❛ ●ré❝✐❛ ❛♥t✐❣❛✳
❚❛❧❡s ❞❡ ▼✐❧❡t♦ ✭✻✷✹✲✺✹✻ ❛✳❈✳✮ ♣❡♥s❛✈❛ q✉❡ ❛ ❚❡rr❛ ❡r❛ ✉♠ ❞✐s❝♦ ♣❧❛♥♦ ❡ ✐♥tr♦❞✉③✐✉ ♥❛ ●ré❝✐❛ ♦s ❢✉♥❞❛♠❡♥t♦s ❞❛ ❣❡♦♠❡tr✐❛ ❡ ❞❛ ❛s✲ tr♦♥♦♠✐❛✳ P✐tá❣♦r❛s ❞❡ ❙❛♠♦s ✭✺✼✷✲✹✾✼ ❛✳❈✳✮ ❛❝r❡❞✐t❛✈❛ q✉❡ ❛ ❚❡rr❛ ❡ ♦✉tr♦s ❝♦r♣♦s ❝❡❧❡st❡s ❢♦ss❡♠ ❡s❢ér✐❝♦s ❡ ❢♦✐ ♦ ♣r✐♠❡✐r♦ ❛ ❝❤❛♠❛r ♦ ❝é✉ ❞❡ ❝♦s♠♦s✳ ❆r✐stót❡❧❡s ❞❡ ❊st❛❣✐❛✭✸✽✹✲✸✷✷ ❛✳❈✮ ❡①♣❧✐❝♦✉ q✉❡ ❛s ❢❛s❡s ❞❛ ▲✉❛ ❞❡♣❡♥❞❡♠ ❞❡ q✉❛♥t♦ ❞❛ ♣❛rt❡ ❞❛ ❢❛❝❡ ❞❛ ▲✉❛ ✐❧✉♠✐♥❛❞❛ ♣❡❧♦ ❙♦❧ ❡stá ✈♦❧t❛❞❛ ♣❛r❛ ❛ ❚❡rr❛✳ ❊①♣❧✐❝♦✉✱ t❛♠❜é♠✱ ♦s ❡❝❧✐♣s❡s✿ ✉♠ ❡❝❧✐♣s❡ ❞♦ ❙♦❧ ♦❝♦rr❡ q✉❛♥❞♦ ❛ ▲✉❛ ♣❛ss❛ ❡♥tr❡ ❛ ❚❡rr❛ ❡ ♦ ❙♦❧❀ ✉♠ ❡❝❧✐♣s❡ ❞❛ ▲✉❛ ♦❝♦rr❡ q✉❛♥❞♦ ❛ ▲✉❛ ❡♥tr❛ ♥❛ s♦♠❜r❛ ❞❛ ❚❡rr❛✳ ❆r✐stót❡❧❡s ❛r❣✉♠❡♥t♦✉ ❛ ❢❛✈♦r ❞❛ ❡s❢❡r✐❝✐❞❛❞❡ ❞❛ ❚❡rr❛✱ ❥á q✉❡ ❛ s♦♠❜r❛ ❞❛ ❚❡rr❛ ♥❛ ▲✉❛ ❞✉r❛♥t❡ ✉♠ ❡❝❧✐♣s❡ ❧✉♥❛r é s❡♠♣r❡ ❛rr❡✲ ❞♦♥❞❛❞❛✳ ❆✜r♠❛✈❛ q✉❡ ♦ ❯♥✐✈❡rs♦ é ❡s❢ér✐❝♦ ❡ ✜♥✐t♦✳ ❆♣❡r❢❡✐ç♦♦✉ ❛ t❡♦r✐❛ ❞❛s ❡s❢❡r❛s ❝♦♥❝ê♥tr✐❝❛s ❞❡ ❊✉❞♦①✉s ❞❡ ❈♥✐❞✉s ✭✹✵✽✲✸✺✺ ❛✳❈✳✮✱ ♣r♦♣♦♥❞♦ ♦ s❡✉ ❧✐✈r♦ ❉❡ ❈❛❡❧♦✱ q✉❡ ✧♦ ❯♥✐✈❡rs♦ é ✜♥✐t♦ ❡ ❡s❢ér✐❝♦✱
❈❆P❮❚❯▲❖ ✶✳ ❯▼ P❖❯❈❖ ❙❖❇❘❊ ❆ ❍■❙❚Ó❘■❆ ❉❖❙ ❆❙❚❘Ô◆❖▼❖❙ ❉❆ ●❘➱❈■❆ ❆◆❚■●❆✶✻
♦✉ ♥ã♦ t❡rá ❝❡♥tr♦ ❡ ♥ã♦ ♣♦❞❡ s❡ ♠♦✈❡r✳✧
❍❡r❛❝❧✐❞❡s ❞❡ P♦♥t✉s ✭✸✽✽✲✸✶✺ ❛✳❈✳✮ ♣r♦♣ôs ❛ ❡①✐stè♥❝✐❛ ❞❡ ❡♣✲ ❝✐❝❧♦s ❡ q✉❡ ❛ ❚❡rr❛ ❣✐r❛ ❞✐❛r✐❛♠❡♥t❡ s♦❜r❡ s❡✉ ♣ró♣r✐♦ ❡✐①♦✱ q✉❡ ❱ê♥✉s ❡ ▼❡r❝úr✐♦ ♦r❜✐t❛♠ ♦ ❙♦❧✱
❆r✐st❛r❝♦ ❞❡ ❙❛♠♦s ✭✸✶✵✲✷✸✵ ❛✳❈✳✮ ❞❡s❡♥✈♦❧✈❡✉ ✉♠ ♠ét♦❞♦ ♣❛r❛ ❞❡t❡r♠✐♥❛r ❛s ❞✐stâ♥❝✐❛s r❡❧❛t✐✈❛s ❞♦ ❙♦❧ ❡ ❞❛ ▲✉❛ à ❚❡rr❛✱ ❢♦✐ ♦ ♣r✐♠❡✐r♦ ❛ ♣r♦♣♦r q✉❡ ❛ ❚❡rr❛ s❡ ♠♦✈✐❛ ❡♠ ✈♦❧t❛ ❞♦ ❙♦❧✱ ❛♥t❡❝✐♣❛♥❞♦ ❈♦♣ér♥✐❝♦ ❡♠ q✉❛s❡ ✷✵✵✵ ❛♥♦s ❡ ♠❡❞✐✉ ♦s t❛♠❛♥❤♦s r❡❧❛t✐✈♦s ❞❛ ❚❡rr❛✱ ❞♦ ❙♦❧ ❡ ❞❛ ▲✉❛✳ ❊r❛tóst❡♥❡s ❞❡ ❈✐rê♥❝✐❛ ✭✷✼✻✲✶✾✹ ❛✳❈✳✮ ❢♦✐ ♦ ♣r✐♠❡✐r♦ ❛ ♠❡❞✐r ♦ ❞✐â♠❡tr♦ ❞❛ ❚❡rr❛ ❡ ❢♦✐ ❜✐❜❧✐♦t❡❝ár✐♦ ❡ ❞✐r❡t♦r ❞❛ ❇✐❜✐❧♦t❡❝❛ ❆❧❡①❛♥❞r✐♥❛ ❞❡ ✷✹✵❛✳❈✳ ❛ ✶✾✼ ❛✳❈✳
❍✐♣❛r❝♦ ❞❡ ◆✐❝é✐❛ ✭✶✻✵✲✶✷✺ ❛✳❈✳✮ ❝♦♥s✐❞❡r❛❞♦ ♦ ♠❛✐♦r ❛strô♥♦♠♦ ❞❛ ❡r❛ ♣ré✲❝r✐stã✱ ❝♦♠♣✐❧♦✉ ✉♠ ❝❛tá❧♦❣♦ ❝♦♠ ❛ ♣♦s✐çã♦ ♥♦ ❝é✉✳ ❊❧❡ ❞❡❞✉③✐✉ ❝♦rr❡t❛♠❡♥t❡ ❛ ❞✐r❡çã♦ ❞♦s ♣ó❧♦s ❝❡❧❡st❡s✱ ❡ ❛té ♠❡s♠♦ ❛ ♣r❡❝❡ssã♦✱ q✉❡ é ❛ ✈❛r✐❛çã♦ ❞❛ ❞✐r❡çã♦ ❞♦ ❡✐①♦ ❞❡ r♦t❛çã♦ ❞❛ ❚❡rr❛ ❞❡✈✐❞♦ á ✐♥✢✉ê♥❝✐❛ ❣r❛✈✐t❛❝✐♦♥❛❧ ❞❛ ▲✉❛ ❡ ❞♦ ❙♦❧✱ q✉❡ ❧❡✈❛ ✷✻✵✵✵ ❛♥♦s ♣❛r❛ ❝♦♠♣❧❡t❛r ✉♠ ❝✐❝❧♦✳ ❍✐♣❛r❝♦ ❛✐♥❞❛ ❞❡❞✉③✐✉ ♦ ✈❛❧♦r ❝♦rr❡t♦ ❞❡ ✽✴✸ ♣❛r❛ ❛ r❛③ã♦ ❡♥tr❡ ♦ t❛♠❛♥❤♦ ❞❛ s♦♠❜r❛ ❞❛ ❚❡rr❛ ❡ ♦ t❛♠❛♥❤♦ ❞❛ ▲✉❛ ❡ t❛♠❜é♠ q✉❡ ❛ ▲✉❛ ❡st❛✈❛ ❛ ✺✾ ✈❡③❡s ♦ r❛✐♦ ❞❛ ❚❡rr❛ ❞❡ ❞✐stâ♥❝✐❛❀ ♦ ✈❛❧♦r ❝♦rr❡t♦ é ✻✵✳ ❊❧❡ ❞❡t❡r♠✐♥♦✉ ❛ ❞✉r❛çã♦ ❞♦ ❛♥♦ ❝♦♠ ✉♠❛ ♠❛r❣❡♠ ❞❡ ❡rr♦ ❞❡ ✻ ♠✐♥✉t♦s✳
❈❛♣ít✉❧♦ ✷
➱ ♣♦ssí✈❡❧ ♠❡❞✐r ♦ r❛✐♦ ❞❛
❚❡rr❛❄
❍á q✉❛♥t♦s ❛♥♦s q✉❡ ✈✐✈❡♠♦s ♥❛ ❚❡rr❛❄ ❙❡rá q✉❡ ❛ ❝♦♥❤❡❝❡♠♦s s✉✜❝✐❡♥t❡❄ ❚rês sé❝✉❧♦s ❛♥t❡s ❞❡ ❈r✐st♦✱ ✉♠ ❣r❡❣♦ ♠❛t❡♠át✐❝♦ ❞❡s✲ ❝♦❜r✐✉ ✉♠ ♠ét♦❞♦ ♣❛r❛ ♠❡❞✐r ❛s ❞✐stâ♥❝✐❛s r❡❧❛t✐✈❛s ❞❛ ❚❡rr❛ ❛♦ ❙♦❧ ❡ ❞❛ ❚❡rr❛ à ▲✉❛ ❡ ❝♦♠♣❛r♦✉ ♦ t❛♠❛♥❤♦ ❞❛ ❚❡rr❛ ❝♦♠ ♦ ❞❛ ▲✉❛✳ ▼❛✐s ♦✉ ♠❡♥♦s ❝❡♠ ❛♥♦s ❞❡♣♦✐s✱ ♦✉tr♦ ❜r✐❧❤❛♥t❡ ♠❛t❡♠át✐❝♦ ❣r❡❣♦ ❝♦♥s❡❣✉✐✉ ❝♦♠♣❛r❛r ♦ t❛♠❛♥❤♦ ❞❛ ▲✉❛ ❝♦♠ ♦ t❛♠❛♥❤♦ ❞♦ ❙♦❧✳ P❡r❣✉♥t❛✲s❡✿ ❈♦♠♦ ❢♦✐ ♣♦ssí✈❡❧ ♦❜t❡r t♦❞❛s ❡st❛s ♠❡❞✐❞❛s ❞❡ ❞✐stâ♥❝✐❛s ✐♥❛❝❡ssí✈❡✐s❄
✷✳✶ ❉✐â♠❡tr♦ ❞❛ ❚❡rr❛
❖ ♣r✐♠❡✐r♦ ❝á❧❝✉❧♦ ❞♦ t❛♠❛♥❤♦ ❞♦ ❞✐â♠❡tr♦ ❞❛ ❚❡rr❛ ❢♦✐ ♦❜t✐❞♦ ♣♦r ❊r❛stóst❡♥❡s ✭✷✼✼✲✶✾✻ ❆✳❈✮ ✜❧ós♦❢♦✱ ❛strô♥♦♠♦ ❡ ♠❛t❡♠át✐❝♦ ❣r❡❣♦ ❞❛ ❡s❝♦❧❛ ❞❡ ❆❧❡①❛♥❞r✐❛✱ ❇✐❜❧✐♦t❡❝ár✐♦✲❈❤❡❢❡ ❞♦ ▼✉s❡✉ ❞❡ ❆❧❡①❛♥✲ ❞r✐❛✳ ❖ ♠ét♦❞♦ q✉❡ ❡❧❡ ✉t✐❧✐③♦✉ ❝♦♥s✐st❡ s❡❣✉✐♥t❡✿ ♦ sá❜✐♦ s♦✉❜❡ q✉❡ ♥♦ s♦❧stí❝✐♦ ❞❡ ✈❡rã♦✶♥♦ ❞✐❛ ✷✶ ❞❡ ❥✉♥❤♦ ✉♠ ❣♥♦♠♦♠✷♥ã♦ ❛♣r❡✲ s❡♥t❛✈❛ s♦♠❜r❛ ♥❛ ❝✐❞❛❞❡ ❞❡ ❙✐❡♥❛ ✭❤♦❥❡ ❆s✉❛♠✮✱ ♠❛s ♥❛ ❝✐❞❛❞❡ ❞❡ ❆❧❡①❛♥❞r✐❛ ✉♠ ❡st✐❧❡t❡ ♥❛s ♠❡s♠❛s ❝♦♥❞✐çõ❡s ❛♣r❡s❡♥t❛✈❛ ✉♠❛ s♦♠❜r❛✳ ❊st❡ ❢❛t♦ ❡❧❡ ❛tr✐❜✉✐✉ à ❡s❢❡r✐❝✐❞❛❞❡ ❞❛ ❚❡rr❛✳ ❈♦♥t❛ ❛ ✏❤✐s✲ tór✐❛✑ q✉❡ ❊r❛tóst❡♥❡s ♠❛♥❞♦✉ ✉♠ ❡s❝r❛✈♦ ❛ ♣é✱ ♠❡❞✐r ❛ ❞✐stâ♥❝✐❛ ❡♥tr❡ ❛s ❞✉❛s ❝✐❞❛❞❡s✳
◆♦ ♠❡s♠♦ ❞✐❛ ❞❡ ✷✶ ❞❡ ❥✉♥❤♦✱ ❊r❛stóst❡♥❡s ♠❡❞✐✉ ♦ ❝♦♠♣r✐♠❡♥t♦
✶s♦❧stí❝✐♦ ❞❡ ✈❡rã♦✿ ❞✐❛ ♠❛✐s ❧♦♥❣♦✲ ♥♦✐t❡ ♠❛✐s ❝✉rt❛
✷❣♥♦♠♦♠✿ ✉♠ ❡st✐❧❡t❡ ✈❡rt✐❝❛❧ ✜♥❝❛❞♦ ♥♦ s♦❧♦ ♥❛ ❞✐r❡çã♦ ♣❡r♣❡♥❞✐❝✉❧❛r
❈❆P❮❚❯▲❖ ✷✳ ➱ P❖❙❙❮❱❊▲ ▼❊❉■❘ ❖ ❘❆■❖ ❉❆ ❚❊❘❘❆❄ ✶✽
❞❛ s♦♠❜r❛ ❞❡ ✉♠ ♦❜❡❧✐s❝♦ ❡♠ ❆❧❡①❛♥❞r✐❛ ❡ ✈❡r✐✜❝♦✉ q✉❡ ♥❛q✉❡❧❡ ❡①❛t♦ ♠♦♠❡♥t♦ ♦ r❛✐♦ s♦❧❛r ♣r♦❥❡t♦✉ ✉♠ â♥❣✉❧♦ ❞❡ ✼✱✷➸ ❛♦ s✉❧ ❞♦ ③ê♥✐t❡✸✳ ❈♦♠ ❛ s✐♠♣❧❡s ♣r♦♣♦rçã♦ ❞❡ q✉❡ ❛ ❝✐r❝✉♥❢❡rê♥❝✐❛ ❞❛ ❚❡rr❛ ❡stá ♣❛r❛ ❛ ❞✐stâ♥❝✐❛ ❡♥tr❡ ❛s ❞✉❛s ❝✐❞❛❞❡s ❛ss✐♠ ❝♦♠♦ ♦ â♥❣✉❧♦ ❞❛ ❝✐r❝✉♥❢❡rê♥❝✐❛ ✭✸✻✵➸✮ ❡stá ♣❛r❛ ♦ â♥❣✉❧♦ ♠❡❞✐❞♦✱ ♦ sá❜✐♦ ❞❡t❡r♠✐♥♦✉ ❛ ❝✐r❝✉♥❢❡rê♥❝✐❛ ❞❛ ❚❡rr❛ ✭✈❡❥❛ ✜❣✉r❛ ✷✳✶✮✳
❋✐❣✉r❛ ✷✳✶✿ ❘❛✐♦ ❞❛ ❚❡rr❛
❋♦♥t❡✿❤tt♣✿✴✴♣r♦❢❡❜❧♦❣✳❡s✴❜❧♦❣✴❥❝❛r♣✐♥t✴✷✵✶✷✴✵✾✴✶✻✴✪❈✷✪❇❋❝♦♠♦✲♠✐❞✐♦✲❡r❛t♦st❡♥❡s✲❡❧✲r❛❞✐♦✲❞❡✲ ❧❛✲t✐❡rr❛✴
❆ ✉♥✐❞❛❞❡ ❞❡ ♠❡❞✐❞❛ ✉t✐❧✐③❛❞❛ ♥❡st❛ é♣♦❝❛ ❡r❛ ❡♠ ❡stá❞✐♦s ❡ ♦ ♠❛t❡♠át✐❝♦ ❝♦♠♣✉t♦✉ ✷✺✷✳✺✷✵ ❡stá❞✐♦s✱ ♦ q✉❡ ❡q✉✐✈❛❧❡♥t❡ ❛ ✹✵✳✵✵✵ ❦♠✳ ♦ q✉❡ r❡s✉❧t♦✉ ♣❛r❛ ♦ r❛✐♦ ❞❛ ❚❡rr❛ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ✻✹✵✵❦♠✳ ➱ ❝❡r❝❛ ❞❡ ✻✸✼✽❦♠✳
❖❜s❡r✈❡ ❝♦♠♦ ♦s r❛✐♦s s♦❧❛r❡s sã♦ ♣r❛t✐❝❛♠❡♥t❡ ♣❛r❛❧❡❧♦s ❡♥tr❡ s✐✱ ❡♥tã♦ ♦ â♥❣✉❧♦ ❝❡♥tr❛❧ t❛♠❜é♠ ♠❡❞❡ ✼✱✷➸✳
❙❡❥❛CT erra❛ ❝✐r❝✉♥❢❡rê♥❝✐❛ ❞❛ ❚❡rr❛ ❡ ❞ ❛ ❞✐stâ♥❝✐❛ ❡♥tr❡ ❛ ❝✐❞❛❞❡
❆❧❡①❛♥❞r✐❛ ❡ ❙✐❡♥❛✳
❯s❛♥❞♦ ❛ ♣r♦♣♦r❝✐♦♥❛❧✐❞❛❞❡ ❡♥tr❡ ❛r❝♦s ❡ ã♥❣✉❧♦s ♦ sá❜✐♦ ❝❤❡❣♦✉ ❛ s❡❣✉✐♥t❡ r❡❧❛çã♦✿
✸③ê♥✐t❡✿ ♦ ♥♦♠❡ ❞❛❞♦ ❛♦ ♣♦♥t♦ ♠❛✐s ❡❧❡✈❛❞♦ ❞♦ ✜r♠❛♠❡♥t♦✱ ❛q✉❡❧❡ q✉❡ ♠✐r❛♠♦s ❛♦ ♦❧❤❛r
❈❆P❮❚❯▲❖ ✷✳ ➱ P❖❙❙❮❱❊▲ ▼❊❉■❘ ❖ ❘❆■❖ ❉❆ ❚❊❘❘❆❄ ✶✾
CT erra d =
360➸
7,2➸
CT erra
800km = 50
❘❡s♦❧✈❡♥❞♦ ❛ ✐❣✉❛❧❞❛❞❡ ❝❤❡❣❛✲s❡ ❛♣r♦①✐♠❛❞❛♠❡♥t❡CT erra❂ ✹✵✵✵✵
❦♠✱ ♦♥❞❡ CT erra❂✷πr✱ ❧♦❣♦ t❡♠♦s ♦ r ❂ ✻✸✻✻✱✷✵✸❦♠ ♦ q✉❛❧ é ♦ t❛✲
♠❛♥❤♦ ❞♦ r❛✐♦ ❞❛ ❚❡rr❛✳
✷✳✷ ❱❡❧♦❝✐❞❛❞❡ ❞❡ r♦t❛çã♦ ❡ tr❛♥s❧❛çã♦ ❞❛ ❚❡rr❛
❈♦♠♦ t♦❞♦s ♦s ❝♦r♣♦s ❞♦ ❯♥✐✈❡rs♦✱ ❛ ❚❡rr❛ t❛♠❜é♠ ♥ã♦ ❡stá ♣❛r❛❞❛✳ ❊❧❛ r❡❛❧✐③❛ ✐♥ú♠❡r♦s ♠♦✈✐♠❡♥t♦s✳ ❖s ❞♦✐s ♠♦✈✐♠❡♥t♦s ♣r✐♥❝✐♣❛✐s ❞♦ ♥♦ss♦ ♣❧❛♥❡t❛ sã♦ ♦ ❞❡ r♦t❛çã♦ ❡ ♦ ❞❡ tr❛♥s❧❛çã♦✱ ❝✉❥♦s ❡❢❡✐t♦s s❡♥t✐♠♦s ♥♦ ❝♦t✐❞✐❛♥♦✳
❋✐❣✉r❛ ✷✳✷✿ ❱❡❧♦❝✐❞❛❞❡ ❞❡ r♦t❛çã♦ ❞❛ ❚❡rr❛
❋♦♥t❡✿❤tt♣✿✴✴❞✐❝❛s❝✉r✐♦s✐❞❛❞❡s❡♠❛✐s✳❜❧♦❣s♣♦t✳❝♦♠✳❜r✴✷✵✵✾❴✵✹❴✵✶❴❛r❝❤✐✈❡✳❤t♠❧
✷✳✷✳✶ ▼♦✈✐♠❡♥t♦ ❞❡ ❘♦t❛çã♦
❈❆P❮❚❯▲❖ ✷✳ ➱ P❖❙❙❮❱❊▲ ▼❊❉■❘ ❖ ❘❆■❖ ❉❆ ❚❊❘❘❆❄ ✷✵
❞✐❢❡r❡♥t❡s ♣♦♥t♦s ❞❛ s✉♣❡r❢í❝✐❡ ❞❛ ❚❡rr❛✳ ✏❉✉r❛♥t❡ ✉♠ ❛♥♦✱ ♦ ❙♦❧ ♥ã♦ ✐❧✉♠✐♥❛ ✐❣✉❛❧♠❡♥t❡ ❡♠ t♦❞♦s ♦s ❧✉❣❛r❡s ❞❛ ❚❡rr❛✱ ♣♦rq✉❡ ♦ ❡✐①♦ ✐♠❛❣✐♥ár✐♦✱ ❡♠ t♦r♥♦ ❞♦ q✉❛❧ ❛ ❚❡rr❛ ❢❛③ ❛ s✉❛ r♦t❛çã♦✱ t❡♠ ✉♠❛ ✐♥❝❧✐♥❛çã♦ ❞❡ ✷✸➸✷✼✱ ❡♠ r❡❧❛çã♦ ❛♦ ♣❧❛♥♦ ❞❛ ♦r❜✐t❛ ❞❛ ❚❡rr❛✳
❖ ♠♦✈✐♠❡♥t♦ ❛♣❛r❡♥t❡ ❞♦ ❙♦❧ ♦❝♦rr❡ ❞♦ ❧❡st❡ ♣❛r❛ ♦ ♦❡st❡✱ ♣♦r ✐ss♦ q✉❡ ❤á ♠✐❧❤❛r❡s ❞❡ ❛♥♦s✱ ♦ ❙♦❧ s❡r✈❡ ❝♦♠♦ r❡❢❡rê♥❝✐❛ ❞❡ ♣♦s✐✲ çã♦✳ ❆♣❛r❡❝❡ ♣❡❧❛ ♠❛♥❤ã ❛ ❧❡st❡ ♦✉ ♥❛s❝❡♥t❡ ❡ ❛♦ ✜♥❛❧ ❞❛ t❛r❞❡ ❞❡s❛♣❛r❡❝❡ ♥♦ ♦❡st❡ ♦✉ ♣♦❡♥t❡✳
❉❡t❡r♠✐♥❛✲s❡ ❛ ✈❡❧♦❝✐❞❛❞❡ ❞❡ r♦t❛çã♦ ❝♦♠ ♦s s❡❣✉✐♥t❡s ❞❛❞♦s✿ ✶✮ ❆ ❚❡rr❛ é ✉♠❛ ❡s❢❡r❛❀
✷✮ ❖ r❛✐♦ ❡q✉❛t♦r✐❛❧ é ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ✻✳✸✼✽❦♠❀ ✸✮ ❯♠ ❞✐❛ sã♦ ✷✹ ❤♦r❛s✳
Pr✐♠❡✐r♦ ♣❛ss♦✿ ✈❛♠♦s ❞❡t❡r♠✐♥❛r ❛ ❝♦♠♣r✐♠❡♥t♦ ❞❛ ❝✐r❝✉♥❢❡✲ rê♥❝✐❛ ❡q✉❛t♦r✐❛❧✿
CT erra = 2πr
CT erra = 2π·6378km
t♦♠❛♠♦s ♦ ✈❛❧♦r ❞♦ π ❂ ✸✱✶✹
CT erra ∼= 40053,84km
❆ ✈❡❧♦❝✐❞❛❞❡ ♠é❞✐❛ é ❞❡✜♥✐❞❛ ♣❡❧♦ q✉♦❝✐❡♥t❡ ❞❛ ✈❛r✐❛çã♦ ❞♦ ❡s✲ ♣❛ç♦ ♣❡❧♦ t❡♠♣♦✿
V m = △x △t
♦♥❞❡ ̀① é ♦ ❝♦♠♣r✐♠❡♥t♦ ❞❛ ❝✐r❝✉♥❢❡rê♥❝✐❛ ❡q✉❛t♦r✐❛❧ ❡ ̀t é ♦ t❡♠♣♦ ❡♠ q✉❡ ❛ ❚❡rr❛ ❧❡✈❛ ♣❛r❛ ❝♦♠♣❧❡t❛r ✉♠❛ ✈♦❧t❛ ❞❡ ✸✻✵➦ ❡♠ t♦r♥♦ ❞❡ s❡✉ ❡✐①♦✳ ❊♥tã♦ t❡♠♦s✿
V m = 40074,16
24 = 1669,76km/h
❈♦♠♦ ✶ ❤♦r❛ ❡q✉✐✈❛❧❡ ❛ ✸✳✻✵✵s✱ ♣♦❞❡♠♦s ✈❡r✐✜❝❛r ❛ ✈❡❧♦❝✐❞❛❞❡ ❡♠ ♠✴s✿
V m ⋍463m/s
❈❆P❮❚❯▲❖ ✷✳ ➱ P❖❙❙❮❱❊▲ ▼❊❉■❘ ❖ ❘❆■❖ ❉❆ ❚❊❘❘❆❄ ✷✶
✉♠ ✈❡í❝✉❧♦ q✉❡ s❡ ❞❡s❧♦❝❛ ♥✉♠❛ ✈❡❧♦❝✐❞❛❞❡ ❝♦♥st❛♥t❡✳ ❙❡ ❡st✐✈❡r♠♦s ❞❡♥tr♦ ❞❡st❡ ✈❡í❝✉❧♦✱ ♥ã♦ ♣❡r❝❡❜❡r❡♠♦s ♦ s❡✉ ♠♦✈✐♠❡♥t♦✱ ♣♦rq✉❡ ❛❞q✉✐r✐♠♦s ❛ ♠❡s♠❛ ✈❡❧♦❝✐❞❛❞❡✳ ❙❡ ♦❧❤❛r♠♦s ♣❡❧❛ ❥❛♥❡❧❛✱ ✈❛♠♦s ✈❡r ❛ ♣❛✐s❛❣❡♠ s❡ ♠♦✈✐♠❡♥t❛♥❞♦✳
▼❛s ❛ ❚❡rr❛ ❞❡s❡♥✈♦❧✈❡ ✉♠❛ ✈❡❧♦❝✐❞❛❞❡ ✉♥✐❢♦r♠❡✱ ♣♦r ❡st❛r♠♦s ✏♣r❡s♦s✑ ❛ ❡❧❛ ♣♦r ❝❛✉s❛ ❞❛ ❢♦rç❛ ❣r❛✈✐t❛❝✐♦♥❛❧✳ P♦r ✐ss♦ ❣✐r❛♠♦s ♥❛ ♠❡s♠❛ ✈❡❧♦❝✐❞❛❞❡✱ ❢❛③❡♠♦s ♣❛rt❡ ❞❡ ✉♠ só s✐st❡♠❛✳
◆ã♦ ♣❡r❝❡❜❡♠♦s s✉❛ r♦t❛çã♦ ♣♦rq✉❡ ♥ã♦ ❡①✐st❡ ♥❡♥❤✉♠ ❝♦r♣♦ r❡❢❡r❡♥❝✐❛❧ ♣❡rt♦ ❞❛ ❚❡rr❛✳ ❈♦♠♦ ❡ss❡ ♠♦✈✐♠❡♥t♦ é ❝✐r❝✉❧❛r✱ é ✐♥✲ t❡r❡ss❛♥t❡ ❝❛❧❝✉❧❛r s✉❛ ✈❡❧♦❝✐❞❛❞❡ ❛♥❣✉❧❛r✳ ❈♦♥s✐❞❡r❡ ✉♠ ♣♦♥t♦ P q✉❡ s❡ ❡♥❝♦♥tr❛
❈♦♥s✐❞❡r❡ ✉♠ ♣♦♥t♦ P q✉❡ s❡ ❡♥❝♦♥tr❛ ❡♠ θ0 ♥♦ ✐♥st❛♥t❡ ✐♥✐❝✐❛❧
t0❂ ✵✳ ◆✉♠ ♦✉tr♦ ✐♥st❛♥t❡ q✉❛❧q✉❡r t✱ ♦ ♣♦♥t♦ P ❡♥❝♦♥tr❛✲s❡ ❡♠θ✱
❡♥tã♦ ♦ ♣♦♥t♦ ❞❡s❧♦❝♦✉✲s❡ ❞❡θ0 ❛té θ✱ ♦✉ s❡❥❛✿
△θ =θ−θ0
♥✉♠ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦✿
△t=t−t0
P♦❞❡♠♦s ❞❡✜♥✐r ❛ ✈❡❧♦❝✐❞❛❞❡ ❛♥❣✉❧❛r ❝♦♠♦✿
ω= △θ △trad/s
P❛r❛ ✉♠❛ ♣❛rtí❝✉❧❛ q✉❡ r❡❛❧✐③❛ ♠♦✈✐♠❡♥t♦ ❝✐r❝✉❧❛r✱ ♥♦t❛♠♦s q✉❡ ❡st❛ ♣❛rtí❝✉❧❛ ♣❡r❝♦rr❡ ✉♠❛ ❞✐stâ♥❝✐❛ ❧✐♥❡❛r ❞❛❞❛ ♣❡❧♦ ❝♦♠♣r✐♠❡♥t♦ ❞♦ ❛r❝♦✿
V = ∆x △t =
r·∆θ
∆t =r·
∆θ
△t =r·ω
❊♥tã♦✱ ❛ ✈❡❧♦❝✐❞❛❞❡ ❛♥❣✉❧❛r ❞❛ r♦t❛çã♦ ❞❛ ❚❡rr❛ s❡rá✿
ω= v rrad/s
ω= 463m/s
166976000m
ω = 7,259×10−5
❈❆P❮❚❯▲❖ ✷✳ ➱ P❖❙❙❮❱❊▲ ▼❊❉■❘ ❖ ❘❆■❖ ❉❆ ❚❊❘❘❆❄ ✷✷
✷✳✷✳✷ ▼♦✈✐♠❡♥t♦ ❞❡ ❚r❛♥s❧❛çã♦
❯♠ ❣r❛♥❞❡ ♠❛t❡♠át✐❝♦ ❝❤❛♠❛❞♦ ❑❡♣❧❡r ✭✶✺✼✶ ✕ ✶✻✸✵✮ ❞❡❞✐❝♦✉ ❛ ♠❛✐♦r ♣❛rt❡ ❞❡ s✉❛ ✈✐❞❛ ❛♥❛❧✐s❛♥❞♦ ❛s ♣♦s✐çõ❡s ❞❛s ♣❧❛♥❡t❛s✳ ❊❧❡ ❞❡s❝♦❜r✐✉ q✉❡ ♦s ♣❧❛♥❡t❛s ❞❡s❝r❡✈❡♠ ór❜✐t❛s ❡❧í♣t✐❝❛s ❡ ♥ã♦ ❝✐r❝✉❧❛r❡s ❝♦♠♦ ❡r❛♠ r❡❝♦♥❤❡❝✐❞❛s✳ ❈♦♠ ❡ss❛ ❝♦♥tr✐❜✉✐çã♦ ❛ ❝✐ê♥❝✐❛ t❡✈❡ ✉♠ ❛✈❛♥ç♦ ✐♥❝rí✈❡❧ ♥❛ ❆str♦♥♦♠✐❛✳
❖ ♠♦✈✐♠❡♥t♦ q✉❡ ❛ ❚❡rr❛ r❡❛❧✐③❛ ❛♦ r❡❞♦r ❞♦ ❙♦❧ ❥✉♥t♦ ❝♦♠ ♦s ♦✉tr♦s ♣❧❛♥❡t❛s é ❝❤❛♠❛❞♦ ❞❡ ▼♦✈✐♠❡♥t♦ ❞❡ ❚r❛♥s❧❛çã♦✱ ♥♦ q✉❛❧ ❛ ❚❡rr❛ ♣❡r❝♦rr❡ ✉♠ ❝❛♠✐♥❤♦ ♦✉ ór❜✐t❛ ❡♠ ❢♦r♠❛ ❞❡ ✉♠ ❡❝❧✐♣s❡✳ ❆ ✈❡❧♦❝✐❞❛❞❡ ♠é❞✐❛ ❞❛ ❚❡rr❛ ❛♦ ❞❡s❝r❡✈❡r ❡ss❛ ór❜✐t❛ é ❞❡ ✶✵✼✳✵✵✵ ❦♠✴❤ ❡ ❡❧❛ ❝♦♠♣❧❡t❛ ✉♠❛ ✈♦❧t❛ ❛♦ r❡❞♦r ❞♦ ❙♦❧ ❡♠ ✸✻✺ ❞✐❛s✱ ✺❤♦r❛s ❡ ❝❡r❝❛ ❞❡ ✹✽ ♠✐♥✉t♦s✳ ➱ ♦ ❝❤❛♠❛❞♦ ❛♥♦✳ ❆❞♦t❛❞♦ ♣♦r ❝♦♥✈❡♥çã♦✱ ♦ ❛♥♦ ❝✐✈✐❧ t❡♠ ✸✻✺ ❞✐❛s ❡ ❛ ❝❛❞❛ ✹ ❛♥♦s t❡♠♦s ✉♠ ❛♥♦ ❞❡ ✸✻✻ ❞✐❛s✱ ❝❤❛♠❛❞♦ ❛♥♦ ❜✐ss❡①t♦✳
❋✐❣✉r❛ ✷✳✸✿ ❱❡❧♦❝✐❞❛❞❡ ❞❡ tr❛s❧❛çã♦ ❞❛ ❚❡rr❛
❈❆P❮❚❯▲❖ ✷✳ ➱ P❖❙❙❮❱❊▲ ▼❊❉■❘ ❖ ❘❆■❖ ❉❆ ❚❊❘❘❆❄ ✷✸
✷✳✷✳✷✳✶ ❊q✉✐♥ó❝✐♦ ✲ ♥♦✐t❡s ✐❣✉❛✐s ❛♦s ❞✐❛s
❖ ❞✐❛ ❡ ❛ ♥♦✐t❡ ❞❡ ✷✶ ❞❡ s❡t❡♠❜r♦ t❡♠ ❛ ♠❡s♠❛ ❞✉r❛çã♦ ♥❛ ♠❛✐♦r ♣❛rt❡ ❞♦s ❧✉❣❛r❡s ❞❛ ❚❡rr❛✱ ♣♦rq✉❡ ♦s r❛✐♦s ❞♦ ❙♦❧ r❡✢❡t❡♠ ♣❡r♣❡♥✲ ❞✐❝✉❧❛r♠❡♥t❡ s♦❜r❡ ❛ ❧✐♥❤❛ ❞♦ ❊q✉❛❞♦r✳ ◆❡ss❡ ❞✐❛ é ♦ ❡q✉✐♥ó❝✐♦ ❞❛ ♣r✐♠❛✈❡r❛ ♥♦ ❤❡♠✐s❢ér✐♦ ♥♦rt❡ ❡ ❡q✉✐♥ó❝✐♦ ❞❡ ♦✉t♦♥♦ ♥♦ ❤❡♠✐s❢ér✐❝♦ s✉❧✳ ❏á ♥♦ ❞✐❛ ✷✸ ❞❡ s❡t❡♠❜r♦ ❛❝♦♥t❡❝❡ ♦ ❝♦♥trár✐♦❀ é ♦ ❡q✉✐♥ó❝✐♦ ❞❡ ♣r✐♠❛✈❡r❛ ♥♦ ❤❡♠✐s❢ér✐❝♦ s✉❧ ❡ ❞❡ ♦✉t♦♥♦ ♥♦ ❤❡♠✐s❢ér✐❝♦ ♥♦rt❡✳
✷✳✷✳✷✳✷ ❙♦❧stí❝✐♦ ✲ ❉✐❛s ♠❛✐s ❧♦♥❣♦s ❡ ♥♦✐t❡s ♠❛✐s ❝✉rt❛s
❖s s♦❧stí❝✐♦s ❛❝♦♥t❡❝❡♠ ♥♦s ❞✐❛s ✷✶ ❞❡ ❥✉♥❤♦ ❡ ✷✶ ❞❡ ❞❡③❡♠❜r♦✳ ◆♦ ❞✐❛ ✷✶ ❞❡ ❥✉♥❤♦✱ ♦s r❛✐♦s ❞♦ ❙♦❧ r❡✢❡t❡♠ ♣❡r♣❡♥❞✐❝✉❧❛r♠❡♥t❡ s♦❜r❡ ♦ tró♣✐❝♦ ❞❡ ❈â♥❝❡r q✉❡ s❡ s✐t✉❛ ❛ ✷✸➸ ✷✼✱ ✸✵ ♥♦ ❤❡♠✐s❢ér✐❝♦ ♥♦rt❡✳ ➱ ♦ s♦❧stí❝✐♦ ❞❡ ✈❡rã♦✱ ♦♥❞❡ s❡ t❡♠ ♦ ❞✐❛ ♠❛✐s ❧♦♥❣♦ ❡ ❛ ♥♦✐t❡ ♠❛✐s ❝✉rt❛ ❞♦ ❛♥♦✱ ✐♥í❝✐♦ ❞♦ ✈❡rã♦✳
◆♦ ❤❡♠✐s❢ér✐❝♦ s✉❧ ♦❝♦rr❡ ♦ s♦❧stí❝✐♦ ❞❡ ✐♥✈❡r♥♦✱ ❝♦♠ ❛ ♥♦✐t❡ ♠❛✐s ❧♦♥❣❛ ❞♦ ❛♥♦✱ ✐♥í❝✐♦ ❞❛ ❡st❛çã♦ ❢r✐❛✳
◆♦ ❞✐❛ ✷✶ ❞❡ ❞❡③❡♠❜r♦ ♦s r❛✐♦s ❞♦ ❙♦❧ ✜❝❛♠ ❡①❛t❛♠❡♥t❡ ♣❡r✲ ♣❡♥❞✐❝✉❧❛r❡s ❛♦ tró♣✐❝♦ ❞❡ ❈❛♣r✐❝ór♥✐♦✱ q✉❡ s❡ s✐t✉❛ ✷✸➸ ✷✼✱ ✸✵✱ ♥♦ ❤❡♠✐s❢ér✐❝♦ s✉❧ ❡ ♦❝♦rr❡ ❛í ♦ s♦❧stí❝✐♦ ❞❡ ✈❡rã♦✳ ❆ ♣❛rt❡ s✉❧ ❞♦ ♣❧❛✲ ♥❡t❛ ♥❡ss❡ ❞✐❛ r❡❝❡❜❡ ♠❛✐♦r q✉❛♥t✐❞❛❞❡ ❞❡ ❧✉③ ❞♦ ❙♦❧ ❞♦ q✉❡ ❛ ♣❛rt❡ ♥♦rt❡✱ é ♦ ❞✐❛ ♠❛✐s ❧♦♥❣♦ ❞♦ ❛♥♦ ❡ ❝♦♠❡ç❛ ♦ ✈❡rã♦✳ ❏á ♥♦ ❤❡♠✐s❢ér✐❝♦ ♥♦rt❡ é ♦ ✐♥í❝✐♦ ❞♦ ✐♥✈❡r♥♦ ❡ ❛❝♦♥t❡❝❡ ❛ ♥♦✐t❡ ♠❛✐s ❧♦♥❣❛ ❞♦ ❛♥♦✳
❆ ❚❡rr❛ ❞❡s❡♥✈♦❧✈❡ s✉❛ ór❜✐t❛ ♣♦r ❝❛✉s❛ ❞❛ ❛tr❛çã♦ ❣r❛✈✐t❛❝✐♦♥❛❧ q✉❡ ♦ ❙♦❧ ❡①❡r❝❡✳ ◗✉❛♥t♦ ♠❛✐s ♣❡rt♦ ❞♦ ❙♦❧✱ ♠❛✐♦r é ❛ ✈❡❧♦❝✐❞❛❞❡ ♦r❜✐t❛❧✱ ♣♦rq✉❡ s❡❣✉♥❞♦ ❛ ▲❡✐ ❞❛ ●r❛✈✐t❛çã♦ ❞❡ ◆❡✇t♦♥✱ ❛ ❢♦rç❛ ❞❡ ❛tr❛çã♦ é ✐♥✈❡rs❛♠❡♥t❡ ♣r♦♣♦r❝✐♦♥❛❧ ❛♦ q✉❛❞r❛❞♦ ❞❛ ❞✐stâ♥❝✐❛ ❡♥tr❡ ❞♦✐s ❝♦r♣♦s✳
❉❡t❡r♠✐♥❛✲s❡ ❛ ✈❡❧♦❝✐❞❛❞❡ ♠é❞✐❛ ♦r❜✐t❛❧ ❝♦♥s✐❞❡r❛♥❞♦✿ ✶✮ ❆ ór❜✐t❛ ❞❛ ❚❡rr❛ ❝♦♠♦ s❡♥❞♦ ✉♠❛ ❝✐r❝✉♥❢❡rê♥❝✐❛❀ ✷✮ ❖ r❛✐♦ ♦r❜✐t❛❧ ♠é❞✐♦ s❡♥❞♦ ✶✺✵✳✵✵✵✳✵✵✵❦♠❀
✸✮ ❯♠ ❛♥♦ ❝♦♠♦ ❡q✉✐✈❛❧❡♥❞♦ ❛ ✸✻✺ ❞✐❛s✱ ♦✉ ✽✳✼✻✵ ❤♦r❛s✳ ❱❛♠♦s ❞❡t❡r♠✐♥❛r ♦ ❝♦♠♣r✐♠❡♥t♦ ❞❛ ❝✐r❝✉♥❢❡rê♥❝✐❛ ♦r❜✐t❛❧✿
Co = 2π❘
Co = 2π·150.000.000
❈❆P❮❚❯▲❖ ✷✳ ➱ P❖❙❙❮❱❊▲ ▼❊❉■❘ ❖ ❘❆■❖ ❉❆ ❚❊❘❘❆❄ ✷✹
❚♦♠❛♠♦s ❛ ❢ór♠✉❧❛ ♣❛r❛ ❝á❧❝✉❧♦ ❞❛ ✈❡❧♦❝✐❞❛❞❡ ♠é❞✐❛✿
V m = △x △t
♦♥❞❡̀① é ♦ ❝♦♠♣r✐♠❡♥t♦ ❞❛ ❝✐r❝✉♥❢❡rê♥❝✐❛ ♦r❜✐t❛❧ ❡̀t é ♦ t❡♠♣♦ ❡♠ q✉❡ ❛ ❚❡rr❛ ❧❡✈❛ ♣❛r❛ ❝♦♠♣❧❡t❛r ✉♠❛ ✈♦❧t❛ ❞❡ ✸✻✵➦ ❡♠ t♦r♥♦ ❞♦ ❙♦❧✳ ❊♥tã♦ t❡♠♦s✿
V m= 942.477.796
8.760 = 107.588.79km/h
V m= 29.885.775m/s
❱❛♠♦s ❝❛❧❝✉❧❛r✱ ❛❣♦r❛✱ ❛ ✈❡❧♦❝✐❞❛❞❡ ❛♥❣✉❧❛r ❞❛ ❚❡rr❛ ❡♠ s✉❛ ór❜✐t❛✿
ω = 29.885.775
150.000.000.000 = 1,992385×10
−7
❈❛♣ít✉❧♦ ✸
❉✐stâ♥❝✐❛s ❛str♦♥ô♠✐❝❛s
✸✳✶ ❉✐stâ♥❝✐❛ ❡♥tr❡ ❛ ❚❡rr❛ ❡ ❛ ▲✉❛ ❡ ❚❡rr❛ ❡ ♦
❙♦❧
✸✳✶✳✶ ❆ ❜r✐❧❤❛♥t❡ ✐❞❡✐❛ ❞❡ ❆r✐st❛r❝♦
❆r✐st❛r❝♦ ❞❡ ❙❛♠♦s ✭✸✶✵✲✷✸✵ ❛✳❈✳✮ ❝❛❧❝✉❧♦✉ ❛s ❞✐stâ♥❝✐❛s r❡❧❛t✐✈❛s ❡♥tr❡ ❛ ❚❡rr❛ ❡ ❛ ▲✉❛ ❡ ❛ ❚❡rr❛ ❡ ♦ ❙♦❧✱ ✈❡r✐✜❝♦✉ q✉❡ ♥♦ q✉❛rt♦ ❝r❡s✲ ❝❡♥t❡ ✭ ♦✉ ♥♦ q✉❛rt♦ ♠✐♥❣✉❛♥t❡✮✱ q✉❛♥❞♦ ♦ ❞✐s❝♦ ❧✉♥❛r ❛♣r❡s❡♥t❛✲s❡ ♣❛r❛ ✉♠ ♦❜s❡r✈❛❞♦r t❡rr❡str❡✱ ❝♦♠ ♠❡t❛❞❡ ✐❧✉♠✐♥❛❞❛ ❡ ♦✉tr❛ ♠❡✲ t❛❞❡ ❡s❝✉r❛✳ ◗✉❛♥❞♦ ✐ss♦ ❛❝♦♥t❡❝❡✱ ❛ ❚❡rr❛✲▲✉❛✲❙♦❧✱ ❡ss❡ tr✐â♥❣✉❧♦ é r❡tâ♥❣✉❧♦✱ ❝♦♠ â♥❣✉❧♦ r❡t♦ ♥♦ ✈ért✐❝❡ ♦❝✉♣❛❞♦ ♣❡❧❛ ❧✉❛✳ ◆❡ss❛ ❝♦♥✜❣✉r❛çã♦ ♦ â♥❣✉❧♦ α = ∠LT S ✭✜❣✉r❛ ✸✳✷✮ é ♠✉✐t♦ ♣ró①✐♠♦ ❞❡
✾✵➦ ❡ ✐ss♦ ✐♥❞✐❝❛ q✉❡ ♦ ❙♦❧ ❡stá ♠✉✐t♦ ♠❛✐s ❧♦♥❣❡ ❞❛ ❚❡rr❛ q✉❡ ❛ ▲✉❛✳ P♦❞❡✲s❡ ♥♦t❛r ❢❛❝✐❧♠❡♥t❡ ❛♦ ♥❛s❝❡r ❡ ❛♦ ♣ôr ❞♦ ❙♦❧✳ ▼❛s ✐ss♦ s❡ ❛ ▲✉❛ ❡st✐✈❡r ❡♠ q✉❛rt♦ ❝r❡s❝❡♥t❡ ♦✉ q✉❛rt♦ ♠✐♥❣✉❛♥t❡✳❬✶✵❪
❈❆P❮❚❯▲❖ ✸✳ ❉■❙❚➶◆❈■❆❙ ❆❙❚❘❖◆Ô▼■❈❆❙ ✷✻
❋✐❣✉r❛ ✸✳✶✿ ❉✐stâ♥❝✐❛ ❡♥tr❡ ❛ ❚❡rr❛ ❡ ❛ ▲✉❛ ❡ ❛ ❚❡rr❛ ❡ ♦ ❙♦❧
❋♦♥t❡✿❤tt♣✿✴✴✇✇✇✳❢✉♥❞✶✾✽✳✉❢❜❛✳❜r✴tr✐❣♦✲♣❛✴✺✲✶❛♣❧✐❝✳♣❞❢
❋✐❣✉r❛ ✸✳✷✿ ❉✐stâ♥❝✐❛ ❡♥tr❡ ❛ ❚❡rr❛ ❡ ❛ ▲✉❛ ❡ ❛ ❚❡rr❛ ❡ ♦ ❙♦❧
❋♦♥t❡✿❤tt♣✿✴✴✇✇✇✳❢✉♥❞✶✾✽✳✉❢❜❛✳❜r✴tr✐❣♦✲♣❛✴✺✲✶❛♣❧✐❝✳♣❞❢
P❛r❛ ❝❛❧❝✉❧❛r ♦ â♥❣✉❧♦ α ❜❛st❛ ♦❜s❡r✈❛r ♦ t❡♠♣♦ ♥❡❝❡ssár✐♦ ♣❡❧❛
❈❆P❮❚❯▲❖ ✸✳ ❉■❙❚➶◆❈■❆❙ ❆❙❚❘❖◆Ô▼■❈❆❙ ✷✼
tr❛♥s❧❛çã♦ ❞❛ ❚❡rr❛✳ ❈♦♠ ❡st❡ ❢❡♥ô♠❡♥♦ ❆r✐st❛r❝♦ ❛✐♥❞❛ ♦❜s❡r✈♦✉ q✉❡ ❛ ♣❛ss❛❣❡♠ ❞❡ ♠✐♥❣✉❛♥t❡ ♣❛r❛ ❝r❡s❝❡♥t❡ ❞✉r❛✈❛ ✶✹✱✷✺ ❞✐❛s✳ ❆❞✲ ♠✐t✐♥❞♦ q✉❡ ❛ ✈❡❧♦❝✐❞❛❞❡ ❞❛ ▲✉❛ é ✉♥✐❢♦r♠❡ ❡♠ s✉❛ ór❜✐t❛✱ ♣♦❞❡♠♦s ❡s❝r❡✈❡r ❛ ♣r♦♣♦rçã♦
360
2α =
29,5 14,25 ❉♦♥❞❡ ♦❜t❡♠♦s
2α = 14,25·360
29,5
❧♦❣♦
α= 86,95➸
P♦rt❛♥t♦ T L
T S = cosα = 0,053✳ ■st♦ é✱ ❚▲❂✵✱✵✺✸ ❚❙✳ ❊♥tã♦✱ ❛
r❡❧❛çã♦ ❡♥tr❡ ❛s ❞✐stâ♥❝✐❛s ❞❛ ❚❡rr❛ ❛♦ ❙♦❧ ❡ ❞❛ ❚❡rr❛ à ▲✉❛ ❞❡✈❡ s❡r ❚❙❂✶✽✱✽ ❚▲✳ ❖✉ s❡❥❛✱ ❛ ❞✐stâ♥❝✐❛ ❞❛ ❚❡rr❛ ❛♦ ❙♦❧ é ❛♣r♦①✐♠❛❞❛✲ ♠❡♥t❡ ✷✵ ✈❡③❡s ❛ ❞✐stâ♥❝✐❛ ❞❛ ❚❡rr❛ à ▲✉❛✳
❍♦❥❡ s❛❜❡♠♦s q✉❡ ❛ ❞✐stâ♥❝✐❛ ❞♦ ❙♦❧ ❛ ❚❡rr❛ é ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ✹✵✵ ✈❡③❡s à ❞❛ ▲✉❛ ❛ ❚❡rr❛✱ ♦ q✉❡ ❡stá ♠✉✐t♦ ❧♦♥❣❡ ❞♦ r❡s✉❧t❛❞♦ ❞❡ ❆r✐st❛r❝♦✳ ❊♥tr❡t❛♥t♦✱ ❡st❡ ❡rr♦ s❡ ♦r✐❣✐♥♦✉ ♥❛ ♠❡❞✐❞❛ ❞♦ â♥❣✉❧♦
α✱ q✉❡ é ❜❡♠ ♣ró①✐♠♦ ❞❡ ✽✾✱✽✻➸✱ ♦✉ s❡❥❛✱ ✉♠ ❡rr♦ ♥❛ ♣r❡❝✐sã♦ ❞❛
♠❡❞✐❞❛ ❞♦ â♥❣✉❧♦ r❡s✉❧t♦✉ ♥❡st❛ ❞✐s❝r❡♣â♥❝✐❛✱ ♠❛s ❝♦♠♦ ❞✐ss❡ ♦ ●❡r❛❧❞♦ ➪✈✐❧❛✱ ✏✐ss♦ ♥ã♦ ❡♠♣❛♥❛ ♦ ♠ér✐t♦ ❞❡ ❆r✐st❛r❝♦✑✱ q✉❡ ❡stá ♥♦ r❛❝✐♦❝í♥✐♦ ✉t✐❧✐③❛❞♦✳❬✸❪
✸✳✶✳✷ ❚❛♠❛♥❤♦s ❞♦ ❙♦❧ ❡ ❞❛ ▲✉❛
❯♠❛ ❝♦✐♥❝✐❞ê♥❝✐❛ ♠✉✐t♦ ✐♥t❡r❡ss❛♥t❡ é ♦ ❢❛t♦ ❞♦ ❙♦❧ ❡ ❛ ▲✉❛ t❡r❡♠ ♦ ♠❡s♠♦ t❛♠❛♥❤♦ ❛♥❣✉❧❛r✳ ❈♦♠♦ ✐❧✉str❛ ❛ ❋✐❣✉r❛ ✸✳✸✱ ♦ â♥❣✉❧♦ ✷γ s♦❜ ♦ q✉❛❧ ✈❡♠♦s ❛ ▲✉❛ é ♦ ♠❡s♠♦ s♦❜ ♦ q✉❛❧ ✈❡♠♦s ♦ ❙♦❧✳ ❆
♣ró♣r✐❛ ◆❛t✉r❡③❛ ❡①✐❜❡ ♣❛r❛ ♥ós ❡ss❛ ❝♦✐♥❝✐❞ê♥❝✐❛ ❡①❛t❛ q✉❛♥❞♦ ❤á ❡❝❧✐♣s❡ t♦t❛❧ ❞♦ ❙♦❧✳
❆r✐st❛r❝♦ ❢❡③ ❛ ❡st✐♠❛t✐✈❛ s♦❜r❡ ♦ â♥❣✉❧♦ ✷γ✱ ❝♦♠♦ s❡♥❞♦ ✷➦✱ ♠❛s
♥❛ ✈❡r❞❛❞❡ é ❞❡ ❝❡r❝❛ ✵✱✺➦✳ ▼❛s ✐ss♦ ♥ã♦ ❛❧t❡r❛ ♦ r❡s✉❧t❛❞♦ q✉❡ s❡ ♦❜té♠✱ ❜❛s❡❛❞♦ ♥❛ s❡♠❡❧❤❛♥ç❛ ❞♦s tr✐â♥❣✉❧♦s r❡tâ♥❣✉❧♦s ❚▲▲✬ ❡ ❚❙❙✬✳ ❊st❛ s❡♠❡❧❤❛♥ç❛ ♣❡r♠✐t❡ ❡s❝r❡✈❡r
SS′
LL′ =
T S T L DS❂ ❞✐stâ♥❝✐❛ ❞❛ ❚❡rr❛ ❛♦ ❙♦❧❀
❈❆P❮❚❯▲❖ ✸✳ ❉■❙❚➶◆❈■❆❙ ❆❙❚❘❖◆Ô▼■❈❆❙ ✷✽
RS❂ r❛✐♦ ❞♦ ❙♦❧❀
RL❂ r❛✐♦ ❞❛ ▲✉❛❀
RT❂ r❛✐♦ ❞❛ ❚❡rr❛
❱❛♠♦s ✐♥tr♦❞✉③✐r ♦s ♣❛râ♠❡tr♦s ❛ ❡ ❜ ❛ss✐♠ ❞❡✜♥✐❞♦s✳ ❱❡❥❛ ❛ ❋✐❣✉r❛ ✸✳✸ ♣❛r❛ ❡♥t❡♥❞❡r ❛ ✐❣✉❛❧❞❛❞❡ ❞❛s r❛③õ❡s RS
DS ❡
RL DL✳
a= RS DS
= RL
DL
;
b= DS DL
❋✐❣✉r❛ ✸✳✸✿ ❆s ❞✐stâ♥❝✐❛s r❡❧❛t✐✈❛s ❞❛ ❚❡rr❛ ❛♦ ❙♦❧ ❡ à ▲✉❛
❋♦♥t❡✿❤tt♣✿✴✴✇✇✇✳✐♠❡✳✉s♣✳❜r✴⑦♣❧❡✐t❡✴♣✉❜✴❛rt✐❣♦s✴❛✈✐❧❛✴r♣♠✺✺✳♣❞❢
P❛r❛ ❆r✐st❛r❝♦✱ ❝♦♠♦ b ≈ 20. P❛r❛ ♦❜t❡r ♦ ♣❛râ♠❡tr♦ ❛✱ ❝♦♠♦ ♦ â♥❣✉❧♦ γ ❡r❛ ❝♦♥❤❡❝✐❞♦✱ ❡❧❡ t❡r✐❛ ❞❡ ♠❡❞✐r ♦s ❧❛❞♦s ❙❙✬ ❡ ❚❙ ♥♦
tr✐â♥❣✉❧♦ ❚❙❙✬ ✭✜❣✉r❛ ✸✳✸✮ ❍♦❥❡ ❛ r❛③ã♦ ❙❙✬✴❚❙ é ♦ q✉❡ ❝❤❛♠❛♠♦s ❞❡ s❡♥♦ ❞♦ â♥❣✉❧♦ ❣✱ ❞❡ s♦rt❡ q✉❡ ❛ ❂ s❡♥γ✳ ❊❧❡ ❝♦♠♣❧❡t♦✉ ❛ ❞❡✲
t❡r♠✐♥❛çã♦ ❞❛s ❣r❛♥❞❡③❛s DT✱ DL✱ RS ❡ RL ❡♠ t❡r♠♦s ❞♦ r❛✐♦ ❞❛
❚❡rr❛ RT✱ ♦❜s❡r✈❛♥❞♦✲s❡ ❞❡ ✉♠ ❡❝❧✐♣s❡ ❞❛ ▲✉❛✳ ❬✸❪
❈❆P❮❚❯▲❖ ✸✳ ❉■❙❚➶◆❈■❆❙ ❆❙❚❘❖◆Ô▼■❈❆❙ ✷✾
❋✐❣✉r❛ ✸✳✹✿ ❆s ❞✐stâ♥❝✐❛s r❡❧❛t✐✈❛s ❞❛ ❚❡rr❛ ❛♦ ❙♦❧ ❡ à ▲✉❛
❋♦♥t❡✿❤tt♣✿✴✴✇✇✇✳✐♠❡✳✉s♣✳❜r✴⑦♣❧❡✐t❡✴♣✉❜✴❛rt✐❣♦s✴❛✈✐❧❛✴r♣♠✺✺✳♣❞❢
❖ t❡♠♣♦ q✉❡ ❛ ▲✉❛ ❧❡✈♦✉ ♣❛r❛ ❛tr❛✈❡ss❛r ♦ ❝♦♥❡ ❞❡ s♦♠❜r❛ ❞❛ ❚❡rr❛✱ ❆r✐st❛r❝♦ ❞❡t❡r♠✐♥♦✉ ♦ ❞✐â♠❡tr♦ ❞❡ss❡ ❝♦♥❡ ♥❛ ❛❧t✉r❛ ❞❛ ▲✉❛✲ ▲❉ ♥❛ ✜❣✉r❛ ✸✳✺ ❝♦♠♦ s❡♥❞♦ ✽✴✸ ❞♦ ❞✐â♠❡tr♦ ❞❛ ▲✉❛✳
❋✐❣✉r❛ ✸✳✺✿ ❆s ❞✐stâ♥❝✐❛s r❡❧❛t✐✈❛s ❞❛ ❚❡rr❛ ❛♦ ❙♦❧ ❡ à ▲✉❛
❋♦♥t❡✿❤tt♣✿✴✴✇✇✇✳✐♠❡✳✉s♣✳❜r✴⑦♣❧❡✐t❡✴♣✉❜✴❛rt✐❣♦s✴❛✈✐❧❛✴r♣♠✺✺✳♣❞❢
◆❛ ✜❣✉r❛ ✸✳✺✱ ▲✱ ❚ ❡ ❙ sã♦ ♦s ❝❡♥tr♦s ❞❛ ▲✉❛✱ ❞❛ ❚❡rr❛ ❡ ❞♦ ❙♦❧✱ r❡s♣❡❝t✐✈❛♠❡♥t❡❀ ▲❍❂RT✱ ❚❈❂RT ❡ ❙❆❂RS sã♦ r❡s♣❡❝t✐✈♦s r❛✐♦s✳
❉❡ ❛❝♦r❞♦ ❝♦♠ ❆r✐st❛r❝♦✱ ▲❉❂✽RL✴✸✳ ❉❛ s❡♠❡❧❤❛♥ç❛ ❞♦s tr✐â♥✲
❣✉❧♦s ❉❋❈ ❡ ❈❊❆ r❡s✉❧t❛ ❈❋✴❉❋❂❆❊✴❈❊✳ ❖❜s❡r✈❡ q✉❡
CF =T C−T F =RT −LD,=RT −8RL/3, DF =DL,
AE =AS−SE =RS−RT, CE =DS
❙✉❜st✐t✉✐♥❞♦ ❡ss❡s ✈❛❧♦r❡s ♥❛ ♣r♦♣♦rçã♦ ❛♥t❡r✐♦r✱ ♦❜t❡♠♦s
RT −8RL/3
DL
= RS−RT
DS
❈❆P❮❚❯▲❖ ✸✳ ❉■❙❚➶◆❈■❆❙ ❆❙❚❘❖◆Ô▼■❈❆❙ ✸✵
DS =bDL, RS =aDS =abDL=aDL,
t❛♠❜é♠ ❛ ✐❣✉❛❧❞❛❞❡ ❛♥t❡r✐♦r ♣♦❞❡ s❡r ❡s❝r✐t❛ ❛ss✐♠✿
RT −8aDL/3
DL
= abDL−RT
bDL , ❞♦♥❞❡ RT DL − 8a
3 =a−
RT
bDT
q✉❡ t❛♠❜é♠ s❡ ❡s❝r❡✈❡
(1 + 1/b)RT
DL
= 11a/3
❞♦♥❞❡
DL=
3(b+ 1)RT
11ab
P♦rt❛♥t♦
DL=
3(b+ 1)RT
11ab
DS =bDL=
3(b+ 1)RT
11a ,
RS =abDL=
3(b+ 1)RT
11 ,
RT =aDL =
3(b+ 1)RT
11b ,
❈♦♠ ♦s ❞❛❞♦s ❞❡ ❆r✐st❛r❝♦✱
DL≈16,8RT,
DS ≈337RT,
❈❆P❮❚❯▲❖ ✸✳ ❉■❙❚➶◆❈■❆❙ ❆❙❚❘❖◆Ô▼■❈❆❙ ✸✶
RL ≈0,29RT.
❆♦ ❝♦♥trár✐♦✱ ❝♦♠ ✈❛❧♦r❡s ♠❛✐s ❝♦rr❡t♦s ♣❛r❛ ♦s â♥❣✉❧♦s β ❡ γ✱
♦❜t❡♠♦s ♦s r❡s✉❧t❛❞♦s ❜❡♠ ♠❛✐s ♣ró①✐♠♦s ❞♦s ✈❛❧♦r❡s ♠♦❞❡r♥♦s✿ ❞❡ s♦rt❡ q✉❡ ❛ ✐❣✉❛❧❞❛❞❡ ❛♥t❡r✐♦r ♣♦❞❡ s❡r ❡s❝r✐t❛ ❛ss✐♠✿ ❬✸❪
DL ≈62RT,
DS ≈24855RT,
RS ≈109RT,
RL ≈0,27RT.
❆s ❞✐stâ♥❝✐❛s ❡stã♦ ❡♠ ❢✉♥çã♦ ❞♦ r❛✐♦ ❞❛ ❚❡rr❛✱ ♣♦✐s ♥❛q✉❡❧❛ é♣♦❝❛ ❛✐♥❞❛ ♥ã♦ s❡ s❛❜✐❛ ♦ s❡✉ t❛♠❛♥❤♦✳ ❖ ❝❛♣ít✉❧♦ ❛♥t❡r✐♦r ❛♣r❡✲ s❡♥t♦✉ ❛ s♦❧✉çã♦ ❞♦ ❊r❛stóst❡♥❡s✱ s❛❜❡♥❞♦ q✉❡ ♦ ✈❛❧♦r ❞♦ r❛✐♦ ❞❛ ❚❡rr❛ é ❡st✐♠❛❞♦ ❤♦❥❡ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ✻✸✼✽❦♠ ❝♦♠ ❡ss❡ r❡s✉❧t❛❞♦ t❡♠♦s✿
DL≈695.436km
DS ≈158.525.190km,
RS ≈695.202km,
RL ≈1772,06km.
✸✳✷ ❉✐stâ♥❝✐❛ ❞❡ ✉♠❛ ❡str❡❧❛ à ❚❡rr❛
✸✳✷✳✶ P❛r❛❧❛①❡
❈❆P❮❚❯▲❖ ✸✳ ❉■❙❚➶◆❈■❆❙ ❆❙❚❘❖◆Ô▼■❈❆❙ ✸✷
✈✐s✉❛❧✐③❛✲s❡ ❛ ❡str❡❧❛ ❡♠ ❞✉❛s ❞✐❢❡r❡♥t❡s ❞✐r❡çõ❡s✱ r❡❧❛t✐✈❛♠❡♥t❡ às ❡str❡❧❛s ✈✐③✐♥❤❛s ❡ ♠❛✐s ❞✐st❛♥t❡s✱ ❤á ❛ss✐♠ ✉♠ ❛♣❛r❡♥t❡ ❞❡s❧♦❝❛✲ ♠❡♥t♦ ❞❛ ❡str❡❧❛✳ ❆ ♣❛r❛❧❛①❡ ❞❡ ✉♠❛ ❡str❡❧❛ é ♠❡t❛❞❡ ❞❛ ❛♠♣❧✐t✉❞❡ ❞♦ â♥❣✉❧♦ ❞❡✜♥✐❞♦ ❡♥tr❡ ❛ ❞✐r❡çã♦ ❞❛ ♣r✐♠❡✐r❛ ♦❜s❡r✈❛çã♦ ❡ ❛ ❞✐r❡çã♦ ❞❛ s❡❣✉♥❞❛ ♦❜s❡r✈❛çã♦✳❬✷❪
❋✐❣✉r❛ ✸✳✻✿ P❛r❛❧❛①❡
❋♦♥t❡✿❤tt♣✿✴✴❡✜s✐❝❛✳✐❢✳✉s♣✳❜r✴♠❡❝❛♥✐❝❛✴❡♥s✐♥♦♠❡❞✐♦✴❞✐st❛♥❝✐❛✴❣r❛♥❞❡s✴
◆❛ ✜❣✉r❛ ✸✳✻✱ ✶ ❯✳❆✳ r❡♣r❡s❡♥t❛ ✉♠❛ ✉♥✐❞❛❞❡ ❛str♦♥ô♠✐❝❛✱ ♦✉ s❡❥❛✱ ❛ ❞✐stâ♥❝✐❛ ♠é❞✐❛ ❞❛ ❚❡rr❛ ❛♦ ❙♦❧✳ ❙❛❜❡♥❞♦ q✉❡ ✶ ❯✳❆✳∼=✶✱✺①✶✵8
❦♠ ❡ q✉❡ ✶ ♣❛rs❡❝➵ ❂ ✷✵✻✷✻✺ ❯✳❆✳
❙❡❣✉❡ ♦ s❡❣✉✐♥t❡ ❡①❡♠♣❧♦✿ ❖ ❝á❧❝✉❧♦ ❞❛ ❞✐stâ♥❝✐❛ ❡♥tr❡ ❛ ❡str❡❧❛ Pró①✐♠❛ ❞❡ ❈❡♥t❛✉r♦ ❡ ❚❡rr❛✱ ❡st❛ ❡str❡❧❛ é ❛ s❡❣✉♥❞❛ ♠❛✐s ♣ró①✐♠❛ ❞❛ ❚❡rr❛✱ ❛ ❡str❡❧❛ ♠❛✐s ♣ró①✐♠❛ é ♦ ❙♦❧✳
❈❆P❮❚❯▲❖ ✸✳ ❉■❙❚➶◆❈■❆❙ ❆❙❚❘❖◆Ô▼■❈❆❙ ✸✸
♣❡❧❛ r❡❧❛çã♦ tr✐❣♦♥♦♠étr✐❝❛ ❝♦♥❝❧✉✐✲s❡ ❢❛❝✐❧♠❡♥t❡ q✉❡
sen(α) = 1 d
❚❡♠✲s❡ q✉❡ ♦ â♥❣✉❧♦ ❞❡ ♣❛r❛❧❛①❡ ❞❛ ❡str❡❧❛ Pró①✐♠❛ ❞❡ ❈❡♥t❛✉r♦ à ❚❡rr❛ é ✵✱✼✻✹➸✱ s✉❜st✐t✉✐♥❞♦ ♦α♣♦r ❡st❡ ✈❛❧♦r ❡ ✐s♦❧❛♥❞♦ ❛ ✈❛r✐á✈❡❧
❞ s❡❣✉❡ q✉❡
d= 1
sen(0,764)
❈♦♥❝❧✉✐ q✉❡ ❞∼=✷✻✾✾✽✵ ❯✳❆✳ s❛❜❡✲s❡ q✉❡ ✶❯✳❆∼=✶✱✺×108
km✱ ✜♥❛❧✲
♠❡♥t❡ ❛ ❞✐stâ♥❝✐❛ ❞❛ ❡str❡❧❛ ❡ ❚❡rr❛ é ❞❡ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ❞∼=✹✱✵✹✾✼×1023
km
♦✉ ✶✱✸ ♣❛rs❡❝s✶✳ ❬✷❪
✶♣❛rs❡❝✿ é ✉♠❛ ✉♥✐❞❛❞❡ ❞❡ ❞✐stâ♥❝✐❛ ✉s❛❞❛ ❡♠ tr❛❜❛❧❤♦s ❝✐❡♥tí✜❝♦s ❞❡ ❛str♦♥♦♠✐❛ ♣❛r❛
❈❛♣ít✉❧♦ ✹
❈❛❧❝✉❧❛♥❞♦ ❞✐stâ♥❝✐❛s
✐♥❛❝❡ssí✈❡✐s
➚s ✈❡③❡s✱ ❛❝♦♥t❡❝❡♠ ❝♦♠ ❢r❡q✉ê♥❝✐❛ ♣r♦❜❧❡♠❛s ❝♦♠ ♠❡❞✐❞❛s q✉❡ ♥ã♦ ♣♦❞❡♠♦s r❡s♦❧✈❡r ❝♦♠ ❛❥✉❞❛ ❞❛ ❚r❡♥❛✳ ◆♦ ❝❛♠♣♦ ♣♦r ❡①❡♠♣❧♦✱ ❛ ❧❛r❣✉r❛ ❞❡ ✉♠ r✐♦✱ ❞✐stâ♥❝✐❛ ❡♥tr❡ ❞♦✐s ♣♦♥t♦s s❡ ❛❝❛s♦ ❡①✐st✐r ✉♠ ♠♦rr♦ ♥♦ ♠❡✐♦✳
✹✳✶ ❈❛❧❝✉❧❛r ❛ ❧❛r❣✉r❛ ❞❡ ✉♠ r✐♦
P❡❣❛✲s❡ ❝♦♠♦ ❡①❡♠♣❧♦✱ ✉♠❛ ❢❛③❡♥❞❛ ❝♦rt❛❞❛ ♣♦r ✉♠ r✐♦ ♠✉✐t♦ ❧❛r❣♦✳ ❈♦♠♦ ❝❛❧❝✉❧❛r s✉❛ ❧❛r❣✉r❛❄ ❈♦♠ ✉♠❛ tr❡♥❛ ❞❡ ✷✵ ♠✱ ✉♠ ❡sq✉❛❞r♦ ❣r❛♥❞❡ ❞❡ ♠❛❞❡✐r❛✱ q✉❛tr♦ ❡st❛❝❛s ❡ ✉♠ r♦❧♦ ❞❡ ❜❛r❜❛♥t❡✳
❈❆P❮❚❯▲❖ ✹✳ ❈❆▲❈❯▲❆◆❉❖ ❉■❙❚➶◆❈■❆❙ ■◆❆❈❊❙❙❮❱❊■❙ ✸✺
❋✐❣✉r❛ ✹✳✶✿ ▲❛r❣✉r❛ ❞❡ ✉♠ r✐♦
❋♦♥t❡✿ ❊❧❛❜♦r❛❞❛ ♣❡❧♦ ❛✉t♦r
❙❡❣✉❡✲s❡ ♦s s❡❣✉✐♥t❡s ♣❛ss♦s✿
Pr✐♠❡✐r♦ ♣❛ss♦✿ Pr♦❝✉r❛♠♦s ✉♠ ♣♦♥t♦ r❡❢❡r❡♥❝✐❛❧ ❞♦ ♦✉tr♦ ❧❛❞♦ ❞❡ r✐♦✱ ♣♦❞❡ s❡r ✉♠❛ ár✈♦r❡✱ ✉♠❛ ♣❡❞r❛ ❣r❛♥❞❡ ♦✉ ✉♠ tr♦♥❝♦ ❞❡ ár✈♦r❡ ❡ ❝❤❛♠❛♠♦s ❞❡ ♣♦♥t♦ P✳
❙❡❣✉♥❞♦ ♣❛ss♦✿ ✜①❛♠♦s ✉♠❛ ❡st❛❝❛ ♥♦ ♣♦♥t♦ ❆ ❡ ❛♠❛rr❛♠♦s ♥❡❧❛ ✉♠ ❜❛r❜❛♥t❡✳ ❖ ❜❛r❜❛♥t❡ é ❡st✐❝❛❞♦ ❛té ✉♠ ♣♦♥t♦ ❈ q✉❛❧q✉❡r✱ ❞❡ ❢♦r♠❛ q✉❡ ♦ â♥❣✉❧♦ P➶❈ s❡❥❛ r❡t♦✳
❚❡r❝❡✐r♦ ♣❛ss♦✿ ❋✐①❛♠♦s ♠❛✐s ✉♠❛ ❡st❛❝❛ ❡♠ ❈✳ ❙♦❜r❡ ♦ ❜❛r❜❛♥t❡ ❡st✐❝❛❞♦ ❆❈ ❞❡✈❡♠♦s ❛❣♦r❛ ❡s❝♦❧❤❡r ✉♠ ♣♦♥t♦ ❇ q✉❛❧q✉❡r✱ q✉❡✱ ❞❡ ♣r❡❢❡rê♥❝✐❛✱ ❡st❡❥❛ ♠❛✐s ♣ró①✐♠♦ ❞❡ ❈ q✉❡ ❞❡ ❆✳
