{"id":1456,"date":"2015-10-13T03:47:10","date_gmt":"2015-10-13T03:47:10","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=1456"},"modified":"2024-08-23T14:23:24","modified_gmt":"2024-08-23T14:23:24","slug":"exercicios-de-vestibulares-sobre-satelites-em-orbitas-circulares","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/mecanica\/gravitacao\/satelites-em-orbitas-circulares\/exercicios-de-vestibulares-sobre-satelites-em-orbitas-circulares\/","title":{"rendered":"Sat\u00e9lites em \u00f3rbitas circulares – Exerc\u00edcios"},"content":{"rendered":"

Exerc\u00edcios de vestibulares sobre<\/b><\/span><\/span><\/span><\/p>\n

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

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

01-(UNICAMP-SP)<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Observa\u00e7\u00f5es astron\u00f4micas indicam que as velocidades de rota\u00e7\u00e3o das estrelas em torno de gal\u00e1xias s\u00e3o incompat\u00edveis com a distribui\u00e7\u00e3o de massa vis\u00edvel das gal\u00e1xias, sugerindo que grande parte da mat\u00e9ria do Universo \u00e9 escura, isto \u00e9, mat\u00e9ria que n\u00e3o interage com a luz. O movimento de rota\u00e7\u00e3o das estrelas resulta da for\u00e7a de atra\u00e7\u00e3o gravitacional que as gal\u00e1xias exercem sobre elas.<\/b><\/span><\/span><\/p>\n

A curva no gr\u00e1fico abaixo mostra como a for\u00e7a gravitacional<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>F=<\/b><\/i><\/span><\/span>GMm\/r<\/b><\/span><\/span>2<\/b><\/span><\/span><\/sup>que uma gal\u00e1xia de massa<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>M<\/b><\/i><\/span><\/span>\u00a0<\/b><\/i><\/span><\/span><\/span>exerce sobre uma estrela externa \u00e0 gal\u00e1xia, deve variar em fun\u00e7\u00e3o da dist\u00e2ncia<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>r<\/b><\/i><\/span><\/span>\u00a0<\/b><\/i><\/span><\/span><\/span>da estrela em rela\u00e7\u00e3o ao centro da<\/b><\/span><\/span> <\/b>gal\u00e1xia, considerando-se<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>m<\/b><\/i><\/span><\/span>=1,0.10<\/b><\/span><\/span>30<\/b><\/span><\/span><\/sup>\u00a0<\/b><\/span><\/span><\/span>kg<\/b><\/i><\/span><\/span>\u00a0<\/b><\/i><\/span><\/span><\/span>para a massa da estrela. A constante de gravita\u00e7\u00e3o<\/b><\/span><\/span>\u00a0<\/b><\/i><\/span><\/span><\/span>G<\/b><\/i><\/span><\/span>\u00a0<\/b><\/i><\/span><\/span><\/span>vale<\/b><\/span><\/span><\/p>\n

10<\/b><\/span><\/span>\uf020<\/b><\/span><\/span>6,7.<\/b><\/span><\/span>-11<\/b><\/span><\/span><\/sup>\u00a0<\/b><\/span><\/span><\/span>m<\/b><\/span><\/span>2<\/b><\/span><\/span><\/sup>.F\/kg<\/b><\/span><\/span>-2<\/b><\/span><\/span><\/sup>.<\/b><\/span><\/span><\/p>\n

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

\"\"<\/p>\n

\u00a0Calcule a velocidade de uma estrela em \u00f3rbita circular a uma dist\u00e2ncia<\/b><\/span><\/span>r<\/b><\/i><\/span><\/span>=1,6\u00d710<\/b><\/span><\/span>20<\/b><\/span><\/span><\/sup>\u00a0<\/b><\/span><\/span><\/span>m do centro da gal\u00e1xia.<\/b><\/span><\/span><\/p>\n

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

02-(UFRS)<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>O cometa de Halley atingiu, em 1986, sua posi\u00e7\u00e3o mais pr\u00f3xima do Sol (peri\u00e9lio) e, no ano de 2023,\u00a0 atingir\u00e1 sua posi\u00e7\u00e3o mais afastada do Sol (af\u00e9lio).<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Assinale a op\u00e7\u00e3o correta:
\n<\/b><\/span><\/span><\/span>a)<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Entre 1986 e 2023 a for\u00e7a gravitacional que o Sol aplica no cometa ser\u00e1 centr\u00edpeta<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>
\n<\/b><\/span><\/span><\/span>b)<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Entre 1986 e 2023 o cometa ter\u00e1 movimento uniforme<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>
\n<\/b><\/span><\/span><\/span>c)<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>No ano de 2041 a energia potencial do sistema Sol-cometa ser\u00e1 m\u00e1xima
\n<\/b><\/span><\/span><\/span>d)<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Ao atingir o af\u00e9lio, no ano de 2023, a energia potencial gravitacional do sistema Sol-cometa ser\u00e1\u00a0m\u00e1xima<\/b><\/span><\/span><\/span><\/p>\n

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

03-(INATEL-MG)<\/b><\/span><\/span><\/span> Um sat\u00e9lite permanece em \u00f3rbita circular terrestre\u00a0 de raio R com velocidade tangencial V. Qual dever\u00e1 ser a velocidade tangencial desse sat\u00e9lite para permanecer em \u00f3rbita circular lunar de mesmo raio R? Considere a massa da Lua 81 vezes menor que a massa da Terra.<\/b><\/span><\/span><\/span><\/p>\n

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

04-(UNICAMP-SP)<\/b><\/span><\/span><\/span> Um m\u00edssil\u00a0 \u00e9 lan\u00e7ado horizontalmente em \u00f3rbita circular rasante \u00e0 superf\u00edcie da Terra. Adote o raio da Terra\u00a0 R=6400km, massa da Terra M=6,0.10<\/b><\/span><\/span><\/span>24<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/span>kg, a constante de gravita\u00e7\u00e3o G=6,7.10<\/b><\/span><\/span><\/span>-11<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/span>Nm<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/kg<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/sup><\/span>\u00a0e, para simplificar, tome 3 como valor aproximado de<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>p.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

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

a) Qual \u00e9 a velocidade de lan\u00e7amento?<\/b><\/span><\/span><\/span><\/p>\n

b) Qual \u00e9 o per\u00edodo da \u00f3rbita?<\/b><\/span><\/span><\/span><\/p>\n

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

05-(FUVEST-SP)<\/b><\/span><\/span><\/span> Se fosse poss\u00edvel colocar um sat\u00e9lite em \u00f3rbita rasante em torno da Terra, o seu per\u00edodo seria T. Sendo G a constante de gravita\u00e7\u00e3o universal, expresse a massa espec\u00edfica (densidade m\u00e9dia) da Terra em fun\u00e7\u00e3o de T e G.<\/b><\/span><\/span><\/span><\/p>\n

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

06-(UF-ES)<\/b><\/span><\/span><\/span> Dois sat\u00e9lites descrevem \u00f3rbitas circulares em torno da Terra.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

O raio da \u00f3rbita do sat\u00e9lite mais afastado da Terra \u00e9 o dobro do raio da \u00f3rbita do sat\u00e9lite mais pr\u00f3ximo. Considere que V<\/b><\/span><\/span><\/span>a<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span>e V<\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span>s\u00e3o, respectivamente, os m\u00f3dulos das velocidades do sat\u00e9lite afastado e do sat\u00e9lite pr\u00f3ximo. A rela\u00e7\u00e3o entre esses m\u00f3dulos \u00e9:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

07-(UF-MG)<\/b><\/span><\/span><\/span> Dois sat\u00e9lites artificiais, R e S, est\u00e3o em \u00f3rbitas circulares de mesmo raio, em torno da Terra.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

A massa do sat\u00e9lite R \u00e9 maior que a do sat\u00e9lite S. Com rela\u00e7\u00e3o ao m\u00f3dulo das velocidades, V<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span>e V<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>, e dos per\u00edodos\u00a0 de transla\u00e7\u00e3o, T<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span>e T<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>, pode-se afirmar que:<\/b><\/span><\/span><\/span><\/p>\n

a) V<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span><\u00a0 V<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/sub><\/span>\u00a0e T<\/b><\/span><\/span><\/span>R\u00a0<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/sub><\/span>=<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/sub><\/span>T<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

b) V<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span><<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>V<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/sub><\/span>\u00a0e T<\/b><\/span><\/span><\/span>R\u00a0<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/sub><\/span>><\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>\u00a0\u00a0<\/b><\/span><\/span><\/sub><\/span>T<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

c) V<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span>=\u00a0 V<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/sub><\/span>\u00a0e T<\/b><\/span><\/span><\/span>R\u00a0<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/sub><\/span>=T<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

d) V<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span>=\u00a0 V<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/sub><\/span>\u00a0e T<\/b><\/span><\/span><\/span>R\u00a0<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/sub><\/span>><\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/sub><\/span>T<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

e) V<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span>>\u00a0 V<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/sub><\/span>\u00a0e T<\/b><\/span><\/span><\/span>R\u00a0<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/sub><\/span>><\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/sub><\/span>T<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span><\/p>\n

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

08-(CESGRANRIO-RJ)<\/b><\/span><\/span><\/span>\u00a0 Dois sat\u00e9lites, A e B, giram ao redor da Terra em \u00f3rbitas circulares. O raio da Terra \u00e9 R e as alturas das \u00f3rbitas dos sat\u00e9lites, em rela\u00e7\u00e3o \u00e0 superf\u00edcie terrestre, s\u00e3o, respectivamente, H<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>=R e H<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>=3R. Sendo a<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span>e a<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span>os m\u00f3dulos das acelera\u00e7\u00f5es vetoriais dos sat\u00e9lites em \u00f3rbita, ent\u00e3o \u00e9 correto afirmar que:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

09-(FUVEST-SP)<\/b><\/span><\/span><\/span> Um sat\u00e9lite artificial se move em \u00f3rbita circular ao redor da Terra, ficando permanentemente sobre a cidade de Macap\u00e1. Qual \u00e9 o seu per\u00edodo?<\/b><\/span><\/span><\/span><\/p>\n

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

10-(FUVEST-SP)<\/b><\/span><\/span><\/span> Sat\u00e9lites utilizados para telecomunica\u00e7\u00f5es s\u00e3o colocados em \u00f3rbitas geo-estacion\u00e1rias ao redor da Terra, ou seja,\u00a0 de tal forma que permane\u00e7am sempre acima de um mesmo ponto da superf\u00edcie da Terra. Considere algumas condi\u00e7\u00f5es que deveriam corresponder a esses sat\u00e9lites:<\/b><\/span><\/span><\/span><\/p>\n

I.\u00a0\u00a0\u00a0 Ter o mesmo per\u00edodo, de cerca de 24 horas.<\/b><\/span><\/span><\/span><\/p>\n

II.\u00a0\u00a0 Ter aproximadamente a mesma massa.<\/b><\/span><\/span><\/span><\/p>\n

III.\u00a0 Estar aproximadamente \u00e0 mesma altitude.<\/b><\/span><\/span><\/span><\/p>\n

IV.\u00a0 Manter-se num plano que contenha o c\u00edrculo do equador terrestre.<\/b><\/span><\/span><\/span><\/p>\n

O conjunto de todas as condi\u00e7\u00f5es que sat\u00e9lites em \u00f3rbitas geo-estacion\u00e1rias devem necessariamente obedecer corresponde a:<\/b><\/span><\/span><\/span><\/p>\n

a) I e III\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

b) I, II e III\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

c) I, III e IV\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

d) II e III\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

e) II e IV<\/b><\/span><\/span><\/span><\/p>\n

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

11-(UFG)<\/b><\/span><\/span><\/span>\u00a0 Considere que a Esta\u00e7\u00e3o Espacial Internacional, de massa<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>M, descreve uma \u00f3rbita el\u00edptica est\u00e1vel em torno da<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Terra, com um per\u00edodo de revolu\u00e7\u00e3o T e raio m\u00e9dio R da<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>\u00f3rbita. Nesse movimento,<\/b><\/span><\/span><\/span><\/p>\n

(A) o per\u00edodo depende de sua massa.<\/b><\/span><\/span><\/span><\/p>\n

(B) a raz\u00e3o entre o cubo do seu per\u00edodo e o quadrado do raio m\u00e9dio da \u00f3rbita \u00e9 uma constante de movimento.<\/b><\/span><\/span><\/span><\/p>\n

(C) o m\u00f3dulo de sua velocidade \u00e9 constante em sua \u00f3rbita.<\/b><\/span><\/span><\/span><\/p>\n

(D) a energia cin\u00e9tica \u00e9 m\u00e1xima no af\u00e9lio.<\/b><\/span><\/span><\/span><\/p>\n

(E) a energia cin\u00e9tica \u00e9 m\u00e1xima no perigeu.<\/b><\/span><\/span><\/span><\/p>\n

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

12-(UPE-PE)<\/b><\/span><\/span><\/span>\u00a0 A figura a seguir representa a trajet\u00f3ria de duas estrelas id\u00eanticas (cada uma com<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

massa M) que giram em torno do centro de massa das duas estrelas. Cada \u00f3rbita \u00e9 circular e possui raio R, de modo que as duas estrelas est\u00e3o sempre em lados opostos do c\u00edrculo. Considere G a constante de gravita\u00e7\u00e3o universal.<\/b><\/span><\/span><\/span><\/p>\n

Analise as proposi\u00e7\u00f5es que se seguem.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00a0soma dos n\u00fameros entre par\u00eanteses das proposi\u00e7\u00f5es que corresponde aos itens corretos \u00e9 igual a<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

13-(FGV-RJ)<\/b><\/span><\/span><\/span> Muitos sat\u00e9lites utilizados em telefonia, transmiss\u00f5es de r\u00e1dio e TV, internet e outros servi\u00e7os de telecomunica\u00e7\u00f5es ocupam a \u00f3rbita geoestacion\u00e1ria. Nesta \u00f3rbita, situada no plano da<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

linha do equador, os sat\u00e9lites permanecem sempre acima de um mesmo ponto da superf\u00edcie terrestre, parecendo parados para um observador no equador. A altura de um sat\u00e9lite geoc\u00eantrico, em rela\u00e7\u00e3o \u00e0 superf\u00edcie da Terra, em \u00f3rbita circular, \u00e9 aproximadamente igual a<\/b><\/span><\/span><\/span><\/p>\n

Dados: G = constante de gravita\u00e7\u00e3o universal; M = massa da Terra; R = raio da Terra = 6, 4.10<\/b><\/span><\/span><\/span>6<\/b><\/span><\/span><\/sup><\/span>m; (G M \/ 4 \u03c0<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>)<\/b><\/span><\/span><\/span>1\/3<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/span>= 2,2.10<\/b><\/span><\/span><\/span>4<\/b><\/span><\/span><\/sup><\/span>ms<\/b><\/span><\/span><\/span>-2\/3<\/b><\/span><\/span><\/sup><\/span>; (24 horas)<\/b><\/span><\/span><\/span>2\/3<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/span>= 2,0.10<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/span>s<\/b><\/span><\/span><\/span>2\/3<\/b><\/span><\/span><\/sup><\/span><\/p>\n

\"\"<\/p>\n

14-(UNICAMP-SP)<\/b><\/span><\/span><\/span> Em 1665, Isaac Newton enunciou a Lei da Gravita\u00e7\u00e3o Universal, e dela pode-se<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

obter a acelera\u00e7\u00e3o gravitacional a uma dist\u00e2ncia d de um corpo de massa M , dada por g=G.M\/d<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/span>sendo G = 6,7.10<\/b><\/span><\/span><\/span>-11<\/b><\/span><\/span><\/sup><\/span>Nm<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/span>\/kg<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/span>a constante de gravita\u00e7\u00e3o universal. Sabendo-se o valor de G, o raio da Terra, e a acelera\u00e7\u00e3o da gravidade na superf\u00edcie da Terra, foi poss\u00edvel encontrar a massa da Terra, M<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span>= 6,0.10<\/b><\/span><\/span><\/span>24<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/span>kg.<\/b><\/span><\/span><\/span><\/p>\n

A acelera\u00e7\u00e3o gravitacional sobre um determinado sat\u00e9lite orbitando a Terra \u00e9 igual a g = 0,25m\/s<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

A dist\u00e2ncia aproximada do sat\u00e9lite ao centro da Terra \u00e9 de<\/b><\/span><\/span><\/span><\/p>\n

a) 1,7.10<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/span>km.\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

b) 4,0.10<\/b><\/span><\/span><\/span>4<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/span>km.\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

\u00a0c) 7,0.10<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/span>km.\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

d) 3,8.10<\/b><\/span><\/span><\/span>5<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/span>km.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

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

15-(UEMG-MG)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

A figura a seguir representa dois sat\u00e9lites artificiais em \u00f3rbita, em torno da Terra.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Baseando-se nas leis de Kepler, e diante da representa\u00e7\u00e3o mostrada, \u00c9 CORRETO afirmar que<\/b><\/span><\/span><\/span><\/p>\n

A) os sat\u00e9lites 1 e 2 possuem a mesma velocidade.<\/b><\/span><\/span><\/span><\/p>\n

B) o sat\u00e9lite 2 percorre uma dist\u00e2ncia maior que o sat\u00e9lite 1, num mesmo intervalo de tempo.<\/b><\/span><\/span><\/span><\/p>\n

C) o sat\u00e9lite 2 leva mais tempo que o sat\u00e9lite 1 para dar uma volta completa em torno da Terra.<\/b><\/span><\/span><\/span><\/p>\n

D) os sat\u00e9lites 1 e 2 d\u00e3o uma volta completa em torno da Terra no mesmo intervalo de tempo.<\/b><\/span><\/span><\/span><\/p>\n

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

16-(UNICAMP-SP)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Em 2011 o Atlantis realizou a \u00faltima miss\u00e3o dos \u00f4nibus espaciais, levando quatro astronautas \u00e0 Esta\u00e7\u00e3o Espacial Internacional.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

a) A Esta\u00e7\u00e3o Espacial Internacional gira em torno da Terra\u00a0 numa \u00f3rbita aproximadamente circular de raio R = 6800 km e<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

completa 16 voltas por dia. Qual \u00e9 a velocidade escalar m\u00e9dia da Esta\u00e7\u00e3o Espacial Internacional?<\/b><\/span><\/span><\/span><\/p>\n

b) Pr\u00f3ximo da reentrada na atmosfera, na viagem de volta, o \u00f4nibus espacial tem velocidade de cerca<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

de 8000 m\/s, e sua massa \u00e9 de aproximadamente 90 toneladas. Qual \u00e9 a sua energia cin\u00e9tica?<\/b><\/span><\/span><\/span><\/p>\n

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

17-(FGV-SP)<\/b><\/span><\/span><\/span><\/p>\n

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

Curiosamente, no sistema solar, os planetas mais afastados do Sol s\u00e3o os que t\u00eam maior quantidade de sat\u00e9lites naturais, principalmente os de maior massa, como J\u00fapiter e Saturno, cada um com mais de 60 sat\u00e9lites naturais.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Considere 2 sat\u00e9lites A e B de J\u00fapiter. O sat\u00e9lite A dista R do centro de J\u00fapiter e o sat\u00e9lite B dista 4R do mesmo centro. Se A demora n dias terrestres para completar uma volta em torno de J\u00fapiter, o n\u00famero de dias terrestres em que B completa uma volta em torno do mesmo planeta \u00e9<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

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

\u00a0Confira a resolu\u00e7\u00e3o comentada<\/span><\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"

Exerc\u00edcios de vestibulares sobre Sat\u00e9lites em \u00f3rbitas circulares \u00a0 01-(UNICAMP-SP)\u00a0Observa\u00e7\u00f5es astron\u00f4micas indicam que as velocidades de rota\u00e7\u00e3o das estrelas em torno de gal\u00e1xias s\u00e3o incompat\u00edveis com a distribui\u00e7\u00e3o de massa vis\u00edvel das gal\u00e1xias, sugerindo que grande parte da mat\u00e9ria do Universo \u00e9 escura, isto \u00e9, mat\u00e9ria que n\u00e3o interage com a luz. O movimento de rota\u00e7\u00e3o das estrelas resulta da<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":1454,"menu_order":0,"comment_status":"closed","ping_status":"closed","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-1456","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1456","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=1456"}],"version-history":[{"count":3,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1456\/revisions"}],"predecessor-version":[{"id":10882,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1456\/revisions\/10882"}],"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=1456"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}