{"id":1458,"date":"2015-10-13T03:47:40","date_gmt":"2015-10-13T03:47:40","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=1458"},"modified":"2015-10-13T03:48:54","modified_gmt":"2015-10-13T03:48:54","slug":"resolucao-comentada-dos-exercicios-de-vestibulares-sobre-satelites-em-orbitas-circulares","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/mecanica\/gravitacao\/satelites-em-orbitas-circulares\/resolucao-comentada-dos-exercicios-de-vestibulares-sobre-satelites-em-orbitas-circulares\/","title":{"rendered":"Resolu\u00e7\u00e3o comentada dos exerc\u00edcios de vestibulares sobre Sat\u00e9lites em \u00f3rbitas circulares"},"content":{"rendered":"

Resolu\u00e7\u00e3o comentada dos exerc\u00edcios de vestibulares sobre<\/b><\/span><\/span><\/span><\/p>\n

Sat\u00e9lites em \u00f3rbitas circulares<\/b><\/span><\/span><\/span><\/p>\n

01-<\/b><\/span><\/span><\/span> F=mV<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/r\u00a0 —\u00a0 4.10<\/b><\/span><\/span><\/span>19<\/b><\/span><\/span><\/sup><\/span>.1,6.10<\/b><\/span><\/span><\/span>20<\/b><\/span><\/span><\/sup><\/span>=10<\/b><\/span><\/span><\/span>30<\/b><\/span><\/span><\/sup><\/span>V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 V=\u221a64.10<\/b><\/span><\/span><\/span>8<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 V=8,0.10<\/b><\/span><\/span><\/span>4<\/b><\/span><\/span><\/sup><\/span>m\/s<\/b><\/span><\/span><\/span><\/p>\n

02-<\/b><\/span><\/span><\/span> Observe pela express\u00e3o E<\/b><\/span><\/span><\/span>P<\/b><\/span><\/span><\/sub><\/span>= – GMm\/R que, como GMm \u00e9 constante, a energia potencial \u00e9 m\u00e1xima no af\u00e9lio (maior R) e m\u00ednima no peri\u00e9lio (menor E). R D<\/b><\/span><\/span><\/span><\/p>\n

03-<\/b><\/span><\/span><\/span> m<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>=81m<\/b><\/span><\/span><\/span>L<\/b><\/span><\/span><\/sub><\/span>\u00a0 —\u00a0 Terra V<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>=\u221aGm<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>\/R =\u221aG81m<\/b><\/span><\/span><\/span>L<\/b><\/span><\/span><\/sub><\/span>\/R\u00a0 —\u00a0 V\u00ad<\/b><\/span><\/span><\/span>L<\/b><\/span><\/span><\/sub><\/span>=\u221aGm<\/b><\/span><\/span><\/span>L<\/b><\/span><\/span><\/sub><\/span>\/R\u00a0 —\u00a0 V<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>\/V<\/b><\/span><\/span><\/span>L<\/b><\/span><\/span><\/sub><\/span>=9\u221aGm<\/b><\/span><\/span><\/span>L<\/b><\/span><\/span><\/sub><\/span>\/Rx1\/\u221aGm<\/b><\/span><\/span><\/span>L<\/b><\/span><\/span><\/sub><\/span>\/Rx\u00a0 —\u00a0 V<\/b><\/span><\/span><\/span>L<\/b><\/span><\/span><\/sub><\/span>=V\/9<\/b><\/span><\/span><\/span><\/p>\n

04-<\/b><\/span><\/span><\/span><\/span> a) V=\u221aRg\u00a0 —\u00a0 V=\u221a(64.10<\/b><\/span><\/span><\/span><\/span>5<\/b><\/span><\/span><\/span><\/sup><\/span>.10)\u00a0 —\u00a0 V=8.10<\/b><\/span><\/span><\/span><\/span>3<\/b><\/span><\/span><\/span><\/sup><\/span>m\/s=8km\/s.<\/b><\/span><\/span><\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 b) V=2\u03c0R\/T\u00a0 —\u00a0 T=2.3.6400\/8\u00a0 —\u00a0 T=6800s=1he20nin<\/b><\/span><\/span><\/span><\/span><\/p>\n

05-<\/b><\/span><\/span><\/span><\/span> T<\/b><\/span><\/span><\/span><\/span>2<\/b><\/span><\/span><\/span><\/sup><\/span>\/R<\/b><\/span><\/span><\/span><\/span>3<\/b><\/span><\/span><\/span><\/sup><\/span>=4<\/b><\/span><\/span><\/span><\/span>\u03c0<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/span><\/sup><\/span>\/GM\u00a0 —\u00a0 d=M\/V\u00a0 —\u00a0 V=4\/3<\/b><\/span><\/span><\/span><\/span>\u03c0<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/span><\/span>3<\/b><\/span><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 d=3M\/4<\/b><\/span><\/span><\/span><\/span>\u03c0<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/span><\/span>3<\/b><\/span><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 d\/3=M\/4<\/b><\/span><\/span><\/span><\/span>\u03c0<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/span><\/span>3<\/b><\/span><\/span><\/span><\/sup><\/span>=\u03c0\/T<\/b><\/span><\/span><\/span><\/span>2<\/b><\/span><\/span><\/span><\/sup><\/span>G\u00a0 —\u00a0 d=3\u03c0\/T<\/b><\/span><\/span><\/span><\/span>2<\/b><\/span><\/span><\/span><\/sup><\/span>G<\/b><\/span><\/span><\/span><\/span><\/p>\n

06-<\/b><\/span><\/span><\/span><\/span> R<\/b><\/span><\/span><\/span><\/span>a<\/b><\/span><\/span><\/span><\/sub><\/span>=2R<\/b><\/span><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span><\/sub><\/span>\u00a0 —\u00a0 V<\/b><\/span><\/span><\/span><\/span>a<\/b><\/span><\/span><\/span><\/sub><\/span>=\u221aGM<\/b><\/span><\/span><\/span><\/span>T<\/b><\/span><\/span><\/span><\/sub><\/span>\/R<\/b><\/span><\/span><\/span><\/span>a<\/b><\/span><\/span><\/span><\/sub><\/span>\u00a0 —\u00a0 V<\/b><\/span><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span><\/sub><\/span>=\u221aGM<\/b><\/span><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span><\/sub><\/span>\/R<\/b><\/span><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span><\/sub><\/span>\u00a0 —\u00a0 V<\/b><\/span><\/span><\/span><\/span>a<\/b><\/span><\/span><\/span><\/sub><\/span>\/V<\/b><\/span><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span><\/sub><\/span>=\u221aGM<\/b><\/span><\/span><\/span><\/span>T<\/b><\/span><\/span><\/span><\/sub><\/span>\/\u221a2R<\/b><\/span><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span><\/sub><\/span>\u00a0X\u221aR<\/b><\/span><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span><\/sub><\/span>\/\u221aGM<\/b><\/span><\/span><\/span><\/span>T<\/b><\/span><\/span><\/span><\/sub><\/span>\u00a0 —\u00a0 V<\/b><\/span><\/span><\/span><\/span>a<\/b><\/span><\/span><\/span><\/sub><\/span>\/V<\/b><\/span><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span><\/sub><\/span>=1\/\u221a2\u00a0 —\u00a0 V<\/b><\/span><\/span><\/span><\/span>a<\/b><\/span><\/span><\/span><\/sub><\/span>=V<\/b><\/span><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span><\/sub><\/span>\/\u221a2\u00a0 R-B<\/b><\/span><\/span><\/span><\/span><\/p>\n

07<\/b><\/span><\/span><\/span>– Como T<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/R<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>3<\/b><\/span><\/span><\/sup><\/span>=T<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/R<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0e os raios s\u00e3o iguais, conclu\u00edmos que T<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=T<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>e pela express\u00e3o V=2\u03c0R\/T, conclu\u00edmos tamb\u00e9m que as velocidades s\u00e3o iguais. R-C<\/b><\/span><\/span><\/span><\/p>\n

08-<\/b><\/span><\/span><\/span> R<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>=2R\u00a0 —\u00a0 R<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>=4R\u00a0 —\u00a0 a=GM\/R<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 a<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>=GM\/4R<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 a<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>=GM\/16R<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0\u00a0— a<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>\/a<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>=GM\/4r<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>x16R<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/GM\u00a0 —\u00a0<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

a<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>=4a<\/b><\/span><\/span><\/span>b<\/b><\/span><\/span><\/sub><\/span>\u00a0— R-D<\/b><\/span><\/span><\/span><\/p>\n

09-<\/b><\/span><\/span><\/span> 24h (vide teoria)<\/b><\/span><\/span><\/span><\/p>\n

10-<\/b><\/span><\/span><\/span> C (vide teoria)<\/b><\/span><\/span><\/span><\/p>\n

11-<\/b><\/span><\/span><\/span> E (vide teoria)<\/b><\/span><\/span><\/span><\/p>\n

12-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Observe na figura as for\u00e7as que atuam sobre cada estrela\u00a0 —\u00a0\"\"– for\u00e7a de atra\u00e7\u00e3o gravitacional<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

entre as duas estrelas de intensidade\u00a0 —\u00a0 F=GMm\/d<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 F=GMM\/(2R)<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 — F=GM<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/4R<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 a afirmativa 4 \u00e9 verdadeira\u00a0 —\u00a0 mas essa for\u00e7a \u00e9 tamb\u00e9m a for\u00e7a resultante centr\u00edpeta de intensidade F<\/b><\/span><\/span><\/span>c<\/b><\/span><\/span><\/sub><\/span>=F=MV<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/R (II)\u00a0 —\u00a0 igualando (I) com (II)\u00a0 —\u00a0 GM<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/R<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0= MV<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>R\u00a0 —\u00a0 V=\u221aGM\/4R\u00a0 —\u00a0 a afirmativa 8 \u00e9 falsa\u00a0 —\u00a0 V=\u0394S\/\u0394t\u00a0 —\u00a0 V=2\u03c0R\/T = \u221aGM\/4R\u00a0 —\u00a0 4\u03c0<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>R<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/T<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>=GM\/4R\u00a0 —\u00a0 T= 2\u03c0R\u221a4R\/GM\u00a0 —\u00a0 T=4\u03c0\u221aR<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>\/GM\u00a0 —\u00a0 a afirmativa 12 \u00e9 verdadeira\u00a0 — \u00a0<\/b><\/span><\/span><\/span>R- E<\/b><\/span><\/span><\/span><\/p>\n

13-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Dados\u00a0 —\u00a0 R = 6,4.10<\/b><\/span><\/span><\/span>6<\/b><\/span><\/span><\/sup><\/span>\u00a0m\u00a0 — \u00a0(GM\/4\u03c0<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>)<\/b><\/span><\/span><\/span>1\/3<\/b><\/span><\/span><\/sup><\/span>; 2,2.10<\/b><\/span><\/span><\/span>4<\/b><\/span><\/span><\/sup><\/span>\u00a0m.s<\/b><\/span><\/span><\/span>-2\/3<\/b><\/span><\/span><\/sup><\/span>\u00a0 — \u00a0T = 24 h = (24×3.600)s\u00a0 —\u00a0 (24×3.600 s)<\/b><\/span><\/span><\/span>2\/3<\/b><\/span><\/span><\/sup><\/span>\u00a0= 2,2×10<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0s<\/b><\/span><\/span><\/span>2\/3<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 a for\u00e7a gravitacional (F<\/b><\/span><\/span><\/span>G<\/b><\/span><\/span><\/sub><\/span>) sobre o sat\u00e9lite \u00e9 a for\u00e7a resultante centr\u00edpeta (F<\/b><\/span><\/span><\/span>C<\/b><\/span><\/span><\/sub><\/span>)\u00a0 —\u00a0 GMm\/r<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>=mV<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/r\u00a0 —\u00a0 V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>=GM\/r (I)\u00a0 —\u00a0 para efetuar uma volta completa ele percorre \u0394S=2\u03c0r no intervalo de tempo \u0394t=T (per\u00edodo)\u00a0 —\u00a0 V=2\u03c0r\/T\u00a0 —\u00a0 V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>=4\u03c0<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>r<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>T<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0(II)\u00a0 —\u00a0 I = II\u00a0 —\u00a0<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

r = (2,2.10<\/b><\/span><\/span><\/span>4<\/b><\/span><\/span><\/sup><\/span>).(2.10<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>) = 4,4.10<\/b><\/span><\/span><\/span>7<\/b><\/span><\/span><\/sup><\/span>\u00a0m = 44.10<\/b><\/span><\/span><\/span>6<\/b><\/span><\/span><\/sup><\/span>\u00a0m\u00a0 —\u00a0 observe na figura que\u00a0 —\u00a0 r=R + h\u00a0 —\u00a0 h=r \u2013 R\u00a0 —\u00a0 44.10<\/b><\/span><\/span><\/span>6<\/b><\/span><\/span><\/sup><\/span>\u00a0\u2013 6,4.10<\/b><\/span><\/span><\/span>6<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 h=37,6.10<\/b><\/span><\/span><\/span>6<\/b><\/span><\/span><\/sup><\/span>m\u00a0 —\u00a0 h=37,6.10<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>=37.600km\u00a0 —\u00a0<\/b><\/span><\/span><\/span>\u00a0R- A<\/b><\/span><\/span><\/span><\/p>\n

14-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Dados\u00a0 —\u00a0 M<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>\u00a0=\u00a0 6,0.10<\/b><\/span><\/span><\/span>24<\/b><\/span><\/span><\/sup><\/span>\u00a0kg\u00a0 —\u00a0 G = 6,7.10<\/b><\/span><\/span><\/span>-11<\/b><\/span><\/span><\/sup><\/span>\u00a0N.m<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0\/kg<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 \u00a0g = 0,25 m\/s<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 g=GM\/d<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 25.10<\/b><\/span><\/span><\/span>-2<\/b><\/span><\/span><\/sup><\/span>=6,7.10<\/b><\/span><\/span><\/span>-11<\/b><\/span><\/span><\/sup><\/span>.6.10<\/b><\/span><\/span><\/span>24<\/b><\/span><\/span><\/sup><\/span>\/d<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 d=\u221a(16.10<\/b><\/span><\/span><\/span>14<\/b><\/span><\/span><\/sup><\/span>)\u00a0 —\u00a0 d=4.10<\/b><\/span><\/span><\/span>7<\/b><\/span><\/span><\/sup><\/span>m=4.10<\/b><\/span><\/span><\/span>4<\/b><\/span><\/span><\/sup><\/span>km\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>R- B<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

15-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Leia atentamente a teoria abaixo:<\/b><\/span><\/span><\/span><\/p>\n

Terceira lei de Kepler (lei dos per\u00edodos)\u00a0 —\u00a0 \u201cOs quadrados dos per\u00edodos\u00a0T\u00a0de revolu\u00e7\u00e3o dos planetas (tempo que demora para efetuar uma volta completa em torno do Sol) s\u00e3o proporcionais aos cubos das suas dist\u00e2ncias m\u00e9dias\u00a0R\u00a0ao Sol\u201d\u00a0 —\u00a0 T<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/R<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>=constante=K\u2019<\/b><\/span><\/span><\/span><\/p>\n

* A constante K\u2019 depende apenas da massa do Sol e n\u00e3o do planeta que gira ao seu redor<\/b><\/span><\/span><\/span><\/p>\n

* Na express\u00e3o T<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/R<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>=K\u2019, observamos que a medida que R aumenta, T tamb\u00e9m aumenta, o que significa que\u00a0quanto mais afastado o planeta estiver do Sol maior ser\u00e1 seu ano (tempo que demora para dar um volta completa ao redor do Sol)<\/b><\/span><\/span><\/span><\/p>\n

* Para dois planetas quaisquer como,\u00a0por exemplo, Terra e Marte, vale a rela\u00e7\u00e3o\u00a0 T<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/R<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>3<\/b><\/span><\/span><\/sup><\/span>= T<\/b><\/span><\/span><\/span>M<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/R<\/b><\/span><\/span><\/span>M<\/b><\/span><\/span><\/sub><\/span>3<\/b><\/span><\/span><\/sup><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

* Ao efetuar um volta completa ao redor do Sol num per\u00edodo (ano) T um planeta percorre \u2206S=2\u03c0R e sua velocidade orbital vale V=\u2206S\/T\u00a0 — \u00a0T=2\u03c0R\/V, que substitu\u00edda em T<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/R<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>=K\u2019 nos fornece\u00a0 4\u03c0<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>R<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/VR<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>=K\u2019\u00a0 —\u00a0 V=4\u03c0<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/K\u2019R\u00a0 — V=constante\/R\u00a0 —\u00a0 V \u00e9 inversamente proporcional a R ou seja, quanto mais afastado o\u00a0sat\u00e9lite ou planeta estiver, menor ser\u00e1 sua velocidade orbital.<\/b><\/span><\/span><\/span><\/p>\n

R- C<\/b><\/span><\/span><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

16-<\/b><\/span><\/span><\/span> a) Ap\u00f3s completar uma volta completa a Esta\u00e7\u00e3o Espacial Internacional percorre \u2206S=2.\u03c0.R=2.3.6800\u00a0 —\u00a0 \u2206S=40800km\u00a0 —\u00a0 aos 16 voltas completas percorre \u2206S=16×40800\u00a0 —\u00a0 \u2206S=652800km\u00a0 —\u00a0 V<\/b><\/span><\/span><\/span>m<\/b><\/span><\/span><\/sub><\/span>=\u2206S\/\u2206t=652800\/24\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>V<\/b><\/span><\/span><\/span>m<\/b><\/span><\/span><\/sub><\/span>=27.200km\/h<\/b><\/span><\/span><\/span><\/p>\n

b) E<\/b><\/span><\/span><\/span>c<\/b><\/span><\/span><\/sub><\/span>=m.V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/2=9.10<\/b><\/span><\/span><\/span>4<\/b><\/span><\/span><\/sup><\/span>.(8.10<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>)<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/2\u00a0 —\u00a0<\/b><\/span><\/span><\/span>\u00a0E<\/b><\/span><\/span><\/span>c<\/b><\/span><\/span><\/sub><\/span>\u22482,9.10<\/b><\/span><\/span><\/span>12<\/b><\/span><\/span><\/sup><\/span>J<\/b><\/span><\/span><\/span><\/p>\n

17-<\/b><\/span><\/span><\/span> Terceira lei de Kepler (lei dos per\u00edodos)\u00a0 —\u00a0\u00a0 \u201cOs quadrados dos per\u00edodos\u00a0T\u00a0de revolu\u00e7\u00e3o dos planetas (tempo que demora para efetuar uma volta completa em torno do Sol) s\u00e3o proporcionais aos cubos das suas dist\u00e2ncias m\u00e9dias\u00a0R\u00a0ao Sol\u201d\u00a0 —\u00a0 T<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/R<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>=constante=K\u2019<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

O raio m\u00e9dio R da \u00f3rbita de um planeta corresponde \u00e0 m\u00e9dia aritm\u00e9tica entre a dist\u00e2ncia do Sol ao af\u00e9lio e a dist\u00e2ncia do Sol ao peri\u00e9lio\u00a0 — observe que esse valor \u00e9 o mesmo que a medida do semi-eixo maior da elipse, que na figura acima seria\u00a0a\u00a0 —\u00a0 na express\u00e3o T<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/R<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>=K\u2019, observamos que a medida que R aumenta, T tamb\u00e9m aumenta, o que significa que\u00a0quanto mais afastado o planeta estiver do Sol maior ser\u00e1 seu ano (tempo que demora para dar um volta completa ao redor do Sol)\u00a0 —\u00a0 para dois planetas quaisquer como,\u00a0 por exemplo, Terra e Marte, vale a rela\u00e7\u00e3o\u00a0 T<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>T<\/b><\/span><\/span><\/sub><\/span>\/R<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>T<\/b><\/span><\/span><\/sub><\/span>=T<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>M<\/b><\/span><\/span><\/sub><\/span>\/R<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>M<\/b><\/span><\/span><\/sub><\/span>\u00a0 —\u00a0 no caso do exerc\u00edcio\u00a0 —\u00a0 T<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>A<\/b><\/span><\/span><\/sub><\/span>\/R<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>A<\/b><\/span><\/span><\/sub><\/span>=T<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>B<\/b><\/span><\/span><\/sub><\/span>\/R<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>B<\/b><\/span><\/span><\/sub><\/span>\u00a0 —\u00a0 \u00a0n<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/R<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0= T<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>B<\/b><\/span><\/span><\/sub><\/span>\/(4R)<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 T<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>=64n<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 T<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>=8n\u00a0 —<\/b><\/span><\/span><\/span><\/p>\n

R- D<\/b><\/span><\/span><\/span><\/p>\n

 <\/p>\n

Voltar para os exerc\u00edcios<\/a><\/span><\/h3>\n","protected":false},"excerpt":{"rendered":"

Resolu\u00e7\u00e3o comentada dos exerc\u00edcios de vestibulares sobre Sat\u00e9lites em \u00f3rbitas circulares 01- F=mV2\/r\u00a0 —\u00a0 4.1019.1,6.1020=1030V2\u00a0 —\u00a0 V=\u221a64.108\u00a0 —\u00a0 V=8,0.104m\/s 02- Observe pela express\u00e3o EP= – GMm\/R que, como GMm \u00e9 constante, a energia potencial \u00e9 m\u00e1xima no af\u00e9lio (maior R) e m\u00ednima no peri\u00e9lio (menor E). R D 03- mT=81mL\u00a0 —\u00a0 Terra VT=\u221aGmT\/R =\u221aG81mL\/R\u00a0 —\u00a0 V\u00adL=\u221aGmL\/R\u00a0 —\u00a0 VT\/VL=9\u221aGmL\/Rx1\/\u221aGmL\/Rx\u00a0 —\u00a0 VL=V\/9<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":1454,"menu_order":0,"comment_status":"open","ping_status":"open","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-1458","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1458","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/comments?post=1458"}],"version-history":[{"count":3,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1458\/revisions"}],"predecessor-version":[{"id":1464,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1458\/revisions\/1464"}],"up":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1454"}],"wp:attachment":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/media?parent=1458"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}