{"id":3137,"date":"2017-08-19T02:28:42","date_gmt":"2017-08-19T02:28:42","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=3137"},"modified":"2024-09-04T14:43:56","modified_gmt":"2024-09-04T14:43:56","slug":"resolucoes-gravitacao","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/vestibulares-recentes\/mecanica\/gravitacao\/resolucoes-gravitacao\/","title":{"rendered":"Resolu\u00e7\u00f5es – Gravita\u00e7\u00e3o"},"content":{"rendered":"

Resolu\u00e7\u00f5es<\/span><\/span><\/span><\/p>\n

Gravita\u00e7\u00e3o Universal \u2013 2017, 2016 e 2015<\/span><\/span><\/span><\/p>\n

LEIS DE KEPLER<\/span><\/span><\/span><\/p>\n

01- <\/span><\/span><\/span><\/span><\/span><\/p>\n

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

Marte\u00a0<\/b><\/span><\/span>n\u00e3o \u00e9 o maior planeta\u00a0<\/b><\/span><\/span>do sistema solar, nem o de\u00a0<\/b><\/span><\/span>maior massa<\/b><\/span><\/span>. Ambos os t\u00edtulos s\u00e3o de\u00a0<\/b><\/span><\/span>J\u00fapiter<\/b><\/span><\/span>\u00a0que possui 2,5 vezes a massa de todos outros somados.<\/b><\/span><\/span><\/span><\/span><\/p>\n

O fato de o\u00a0<\/b><\/span><\/span>campo gravitacional\u00a0<\/b><\/span><\/span>ser intenso\u00a0<\/b><\/span><\/span>n\u00e3o influencia nesse tipo de coordenada<\/b><\/span><\/span>, e mesmo que influenciasse Marte tem um\u00a0<\/b><\/span><\/span>campo gravitacional\u00a0<\/b><\/span><\/span>da ordem de\u00a0<\/b><\/span><\/span>3,711 m\/s\u00b2<\/b><\/span><\/span>. Enquanto que o da\u00a0<\/b><\/span><\/span>Terra<\/b><\/span><\/span>\u00a0\u00e9 de\u00a0<\/b><\/span><\/span>9,807 m\/s\u00b2.<\/b><\/span><\/span><\/span><\/span><\/p>\n

A\u00a0<\/b><\/span><\/span>composi\u00e7\u00e3o atmosf\u00e9rica\u00a0<\/b><\/span><\/span>tamb\u00e9m\u00a0<\/b><\/span><\/span>n\u00e3o influencia\u00a0<\/b><\/span><\/span>nas coordenadas, por\u00e9m a composi\u00e7\u00e3o atmosf\u00e9rica de Marte realmente \u00e9 bem diferente da Terra, sendo mais rarefeita e com uma porcentagem muito grande de CO2.<\/b><\/span><\/span><\/span><\/span><\/p>\n

A\u00a0<\/b><\/span><\/span>hidrosfera tampouco influencia nas coordenadas<\/b><\/span><\/span>.<\/b><\/span><\/span><\/span><\/span><\/p>\n

Sendo assim a\u00a0<\/b><\/span><\/span>alternativa correta \u00e9 a B<\/b><\/span><\/span>, como podemos observar na imagem\u00a0<\/b><\/span><\/span>o formato da Terra e de Marte \u00e9 parecido<\/b><\/span><\/span>, sendo assim o\u00a0<\/b><\/span><\/span>sistema de coordenadas efetivo para ambos<\/b><\/span><\/span>.<\/b><\/span><\/span><\/span><\/span><\/p>\n

02<\/span><\/span><\/span>– <\/span><\/span><\/span>Vamos come\u00e7ar pelo\u00a0<\/b><\/span><\/span>tempo total\u00a0<\/b><\/span><\/span>da viagem:<\/b><\/span><\/span><\/p>\n

Tempo total = 365*6 (dias para sa\u00edrem da Terra) + 210 (dias equivalentes ao percurso)<\/b><\/span><\/span><\/p>\n

Tempo total = 2400 dias terrestres<\/b><\/span><\/span><\/p>\n

Para calcularmos em\u00a0<\/b><\/span><\/span>anos marcianos<\/b><\/span><\/span>, precisamos fazer uma\u00a0<\/b><\/span><\/span>propor\u00e7\u00e3o<\/b><\/span><\/span>:<\/b><\/span><\/span><\/p>\n

1 ano marciano -> 687 dias terrestres<\/b><\/span><\/span><\/p>\n

x anos marcianos -> 2400 dias terrestres<\/b><\/span><\/span><\/p>\n

Multiplicando em cruz:<\/b><\/span><\/span><\/p>\n

2400.1 = 687.x<\/b><\/span><\/span><\/p>\n

Isolando o x:<\/b><\/span><\/span><\/p>\n

x =\u00a0\"\"<\/b><\/span><\/span><\/p>\n

x = 3,4934<\/b><\/span><\/span><\/p>\n

O resultado mais pr\u00f3ximo \u00e9 o da letra E.<\/b><\/span><\/span><\/p>\n

03- <\/span><\/span><\/span><\/p>\n

Se voc\u00ea n\u00e3o domina a teoria ela est\u00e1 a seguir:<\/b><\/span><\/span><\/p>\n

Segunda lei de Kepler (lei das \u00e1reas)<\/b><\/span><\/span><\/p>\n

\u201c<\/span>\u00a0<\/span>O<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>segmento de reta imagin\u00e1rio<\/b><\/span><\/span>\u00a0que une\u00a0<\/b><\/span><\/span>o<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>centro do Sol ao centro do planeta varre \u00e1reas iguais em per\u00edodos de tempo iguais\u201d\u00a0\u00a0<\/b><\/span><\/span><\/p>\n

A figura abaixo representa um\u00a0<\/b><\/span><\/span>planeta em \u00f3rbita el\u00edptica ao redor do Sol.<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

V12\u00a0> V34<\/b><\/span><\/span><\/p>\n

Essa\u00a0<\/b><\/span><\/span>constante K depende do planeta<\/b><\/span><\/span>\u00a0e recebe o nome de\u00a0<\/b><\/span><\/span>velocidade areolar (velocidade escalar orbital)..<\/b><\/span><\/span><\/p>\n

Observa\u00e7\u00e3o importante:\u00a0<\/b><\/span><\/span>Observe que, quando\u00a0<\/b><\/span><\/span>A1\u00a0= A2\u00a0\u00a0\"\"\u00a0\u2206t1\u00a0=\u00a0\u2206t2,<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>ou seja, para o\u00a0<\/b><\/span><\/span>arco maior (1,2),<\/b><\/span><\/span>\u00a0ser percorrido no\u00a0<\/b><\/span><\/span>mesmo intervalo de tempo que o arco menor (3,4)<\/b><\/span><\/span>,\u00a0<\/b><\/span><\/span>a\u00a0<\/b><\/span><\/span>velocidade em (1,2)<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>(<\/b><\/span><\/span>mais perto do Sol,\u00a0<\/b><\/span><\/span>peri\u00e9lio<\/b><\/span><\/span>)<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>deve ser maior que a velocidade em (3,4)\u00a0<\/b><\/span><\/span>(<\/b><\/span><\/span>mais afastado do Sol,\u00a0<\/b><\/span><\/span>af\u00e9lio<\/b><\/span><\/span>).<\/b><\/span><\/span><\/p>\n

Ent\u00e3o, V12\u00a0> V34.<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

Portanto<\/b><\/span><\/span>\u00a0os\u00a0planetas aceleram do af\u00e9lio para o peri\u00e9lio e retardam do peri\u00e9lio para o af\u00e9lio.<\/b><\/span><\/span><\/p>\n

Ainda, de\u00a0<\/b><\/span><\/span>acordo com essa lei<\/b><\/span><\/span>,\u00a0<\/b><\/span><\/span>se as\u00a0<\/b><\/span><\/span>\u00f3rbitas forem circulares<\/b><\/span><\/span>\u00a0a\u00a0<\/b><\/span><\/span>velocidade de transla\u00e7\u00e3o ser\u00e1<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>constante\u00a0<\/b><\/span><\/span>e se a \u00f3rbita do planeta tiver\u00a0<\/b><\/span><\/span>raio R<\/b><\/span><\/span>\u00a0e seu\u00a0\u00a0<\/b><\/span><\/span>per\u00edodo de transla\u00e7\u00e3o for T<\/b><\/span><\/span>,\u00a0<\/b><\/span><\/span>sua<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>velocidade\u00a0areolar<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>(velocidade escalar orbital)<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>ser\u00e1 constante\u00a0<\/b><\/span><\/span>e dada por:\u00a0<\/b><\/span><\/span>K = V = A\/\u2206t = \u03c0R2\u00a0\/T.<\/b><\/span><\/span><\/p>\n

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

 <\/p>\n

04- <\/span><\/span><\/span>De acordo com a\u00a0<\/b><\/span><\/span>primeira lei de Kepler<\/b><\/span><\/span>\u00a0as\u00a0<\/b><\/span><\/span>\u00f3rbitas s\u00e3o el\u00edpticas ao redor do sol, sendo que o sol est\u00e1 localizado em um dos focos. Alternativa B.<\/b><\/span><\/span><\/span><\/span><\/p>\n

No caso de A,\u00a0<\/b><\/span><\/span>a velocidade do planeta aumenta quando o corpo se aproxima do sol.<\/b><\/span><\/span><\/p>\n

No caso de C e D,\u00a0<\/b><\/span><\/span>o per\u00edodo de transla\u00e7\u00e3o s\u00f3 depende da dist\u00e2ncia entre o planeta e o sol<\/b><\/span><\/span>.<\/b><\/span><\/span><\/p>\n

 <\/p>\n

05- <\/span><\/span><\/span>A trajet\u00f3ria da Lua\u00a0<\/b><\/span><\/span>ao redor da Terra\u00a0<\/b><\/span><\/span>n\u00e3o \u00e9 circular, \u00e9 el\u00edptica.<\/b><\/span><\/span><\/p>\n

Quando o\u00a0<\/b><\/span><\/span>dia em que ocorre uma Lua Cheia coincide com o dia em que ela passa pelo perigeu\u00a0<\/b><\/span><\/span>(mais pr\u00f3xima da Terra)\u00a0<\/b><\/span><\/span>ela pode se apresentar at\u00e9 cerca de 30% mais brilhante que uma Lua Cheia no<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

apogeu<\/b><\/span><\/span>\u00a0(mais afastada da Terra).<\/b><\/span><\/span><\/p>\n

Nesse caso,\u00a0<\/b><\/span><\/span>ela aparenta ter um aumento de 14% em rela\u00e7\u00e3o ao seu tamanho real.<\/b><\/span><\/span><\/p>\n

Essa\u00a0<\/b><\/span><\/span>Lua Cheia mais pr\u00f3xima da Terra\u00a0<\/b><\/span><\/span>\u00e9 chamada de\u00a0<\/b><\/span><\/span>Super Lua.
\n<\/b><\/span><\/span>R- E<\/b><\/span><\/span><\/p>\n

06- <\/b><\/span><\/span><\/span>O\u00a0<\/b><\/span><\/span>tempo total T<\/b><\/span><\/span>\u00a0para a\u00a0<\/b><\/span><\/span>Lua\u00a0<\/b><\/span><\/span>efetuar\u00a0<\/b><\/span><\/span>uma volta completa ao redor da Terra<\/b><\/span><\/span>(\u201cvarrer\u201d um\u00a0<\/b><\/span><\/span>\u00e2ngulo de 360o<\/b><\/span><\/span>) vale\u00a0<\/b><\/span><\/span>T = t1\u00a0+ t2<\/b><\/span><\/span>\u00a0= 14,9 + 14,8\u00a0<\/b><\/span><\/span>= 29,7 dias.<\/b><\/span><\/span>\u00a0(I)<\/b><\/span><\/span><\/p>\n

O tempo\u00a0<\/b><\/span><\/span>t2\u00a0= 14,8 dias<\/b><\/span><\/span>\u00a0que \u00e9 aquele\u00a0<\/b><\/span><\/span>decorrido de uma lua quarto minguante a uma lua quarto<\/b><\/span><\/span><\/p>\n

crescente<\/b><\/span><\/span>e que<\/b><\/span><\/span>\u00a0\u00e9 o mesmo que a Lua demora para \u201cvarrer\u201d um \u00e2ngulo 2\u03b1.<\/b><\/span><\/span>(II)<\/b><\/span><\/span><\/p>\n

Como, pelo enunciado voc\u00ea deve supor que o\u00a0<\/b><\/span><\/span>movimento \u00e9 uniforme<\/b><\/span><\/span>\u00a0voc\u00ea pode utilizar uma\u00a0<\/b><\/span><\/span>regra de tr\u00eas com\u00a0<\/b><\/span><\/span>(I) e (II):<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

07- <\/b><\/span><\/span><\/span>Terceira lei de Kepler (lei dos per\u00edodos)<\/b><\/span><\/span><\/p>\n

\u00a0<\/span>\u201c\u00a0<\/span>Os\u00a0<\/b><\/span><\/span>quadrados dos\u00a0<\/b><\/span><\/span>per\u00edodos\u00a0T<\/b><\/span><\/span>\u00a0de revolu\u00e7\u00e3o dos planetas<\/b><\/span><\/span>\u00a0(tempo que demora para efetuar uma volta completa em torno do Sol)\u00a0<\/b><\/span><\/span>s\u00e3o <\/b><\/span><\/span>proporcionais<\/b><\/span><\/span>\u00a0aos cubos das suas\u00a0<\/b><\/span><\/span>dist\u00e2ncias m\u00e9dias R\u00a0ao Sol<\/b><\/span><\/span>\u201d<\/b><\/span><\/span><\/p>\n

T<\/b><\/span><\/span>2<\/b><\/span><\/sup><\/span>\/R<\/b><\/span><\/span>3<\/b><\/span><\/sup><\/span>=constante=K\u2019<\/b><\/span><\/span><\/p>\n

O mesmo \u00e9 v\u00e1lido para Terra-Lua.<\/b><\/span><\/span>\u00a0Se a\u00a0<\/b><\/span><\/span>dist\u00e2ncia m\u00e9dia R da Lua \u00e0 Terra aumenta<\/b><\/span><\/span>, e ela \u00e9\u00a0<\/b><\/span><\/span>proporcional ao per\u00edodo de transla\u00e7\u00e3o da Lua ao redor da Terra<\/b><\/span><\/span>, este <\/b><\/span><\/span>per\u00edodo tamb\u00e9m deve<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>aumentar.<\/b><\/span><\/span><\/p>\n

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

08- <\/b><\/span><\/span><\/span>a)<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>confirmaram as teorias definidas por Cop\u00e9rnico<\/b><\/span><\/span>\u00a0e s\u00e3o exemplos do<\/b><\/span><\/span>modelo cient\u00edfico que passou a vigorar a partir da Alta Idade M\u00e9dia.<\/b><\/span><\/span><\/p>\n

a) Falsa<\/b><\/span><\/span>\u00a0\"\"\u00a0<\/b><\/span><\/span>foi por volta do s\u00e9culo XVI<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>(e n\u00e3o na Alta idade m\u00e9dia (do s\u00e9culo V ao s\u00e9culo X)<\/b><\/span><\/span>\u00a0que,\u00a0<\/b><\/span><\/span>Nicolau Cop\u00e9rnico\u00a0<\/b><\/span><\/span>(1473-1543) apresentou um<\/b><\/span><\/span>modelo<\/b><\/span><\/span>helioc\u00eantrico<\/b><\/span><\/span>, em que o\u00a0<\/b><\/span><\/span>Sol estava no centro<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>do universo<\/b><\/span><\/span>, e os<\/b><\/span><\/span>planetas descreviam \u00f3rbitas circulares ao seu redor.<\/b><\/span><\/span><\/p>\n

b)<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>confirmaram<\/b><\/span><\/span>\u00a0as teorias defendidas por Ptolomeu<\/b><\/span><\/span>\u00a0e permitiram a produ\u00e7\u00e3o das cartas n\u00e1uticas usadas no per\u00edodo do descobrimento da Am\u00e9rica.<\/b><\/span><\/span><\/p>\n

b) Falsa<\/b><\/span><\/span>\u00a0\"\"\u00a0<\/b><\/span><\/span>Ptolomeu\u00a0<\/b><\/span><\/span>apresentou e desenvolveu argumentos a favor da<\/b><\/span><\/span>teoria geoc\u00eantrica na qual o universo os planetas, o Sol e a Lua giravam em torno da Terra.<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

c)<\/b><\/span><\/span>\u00a0s\u00e3o a\u00a0<\/b><\/span><\/span>base do modelo planet\u00e1rio geoc\u00eantrico<\/b><\/span><\/span>\u00a0e se tornaram as premissas cientificas que vigoram at\u00e9 hoje.<\/b><\/span><\/span><\/p>\n

c) Falsa<\/b><\/span><\/span>\u00a0\"\"\u00a0as\u00a0<\/b><\/span><\/span>leis de Kepler n\u00e3o s\u00e3o a base do<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>modelo geoc\u00eantrico proposto por Pttolomeu (veja b acima).<\/b><\/span><\/span><\/p>\n

d)<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>forneceram subs\u00eddios<\/b><\/span><\/span>\u00a0para demonstrar o modelo planet\u00e1rio helioc\u00eantrico<\/b><\/span><\/span>\u00a0e\u00a0<\/b><\/span><\/span>criticar as posi\u00e7\u00f5es<\/b><\/span><\/span><\/p>\n

defendidas pela Igreja naquela \u00e9poca.<\/b><\/span><\/span><\/p>\n

d) Correta<\/b><\/span><\/span>\u00a0\"\"\u00a0as\u00a0<\/b><\/span><\/span>leis de Kepler confirmaram o sistema\u00a0<\/b><\/span><\/span>helioc\u00eantrico <\/b><\/span><\/span>defendido por Nicolau Cop\u00e9rnico e\u00a0<\/b><\/span><\/span>contrariaram a teoria do\u00a0<\/b><\/span><\/span>geocentrismo defendida pela igreja.<\/b><\/span><\/span><\/p>\n

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

09-<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

10- <\/span><\/span><\/span><\/p>\n

C\u00e1lculo da acelera\u00e7\u00e3o da gravidade na superf\u00edcie do planeta.<\/b><\/span><\/span><\/p>\n

A\u00a0<\/b><\/span><\/span>Terra (ou qualquer outro planeta)<\/b><\/span><\/span>\u00a0origina ao seu redor um\u00a0<\/b><\/span><\/span>campo gravitacional<\/b><\/span><\/span>\u00a0de maneira que qualquer\u00a0<\/b><\/span><\/span>corpo de massa m<\/b><\/span><\/span>, quando colocado no interior desse campo fica sujeito \u00e0<\/b><\/span><\/span>uma for\u00e7a de atra\u00e7\u00e3o gravitacional Fg=GMm\/r2,\u00a0sendo,\u00a0<\/b><\/span><\/span>G\u00a0<\/b><\/span><\/span>a constante de gravita\u00e7\u00e3o universal,\u00a0<\/b><\/span><\/span>M<\/b><\/span><\/span>a massa da Terra ou do planeta e\u00a0<\/b><\/span><\/span>r\u00a0<\/b><\/span><\/span>a dist\u00e2ncia do centro da Terra ou do<\/b><\/span><\/span>centro do planeta at\u00e9 o corpo<\/b><\/span><\/span>\u00a0de massa\u00a0<\/b><\/span><\/span>m.<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

Mas, esta\u00a0<\/b><\/span><\/span>for\u00e7a que age sobre o corpo<\/b><\/span><\/span>\u00a0ou sat\u00e9lite corresponde ao seu<\/b><\/span><\/span>pr\u00f3prio peso, tal que, P=mg.<\/b><\/span><\/span><\/p>\n

Portanto\u00a0 \u2014\u00a0Fg=P\u00a0 \u2014 \u00a0GMm\/r2=mg\u00a0 \u2014 \u00a0<\/b><\/span><\/span>g=GM\/r2<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

11- <\/span><\/span><\/span>Heliocentrismo\u00a0<\/b><\/span><\/span>\u00e9 a teoria a respeito do sistema cosmol\u00f3gico, segundo a qual a\u00a0<\/b><\/span><\/span>Terra e os demais planetas giram em torno do\u00a0<\/b><\/span><\/span>Sol<\/b><\/span><\/span><\/a>.
\n<\/b><\/span><\/span>Nicolau Cop\u00e9rnico, um polon\u00eas que viveu entre 1453 \u2013 1543<\/b><\/span><\/span>, \u00e9 considerado o fundador da astronomia moderna e pai do heliocentrismo.<\/b><\/span><\/span><\/p>\n

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

12- <\/span><\/span><\/span>A seguir, a teoria:<\/b><\/span><\/span><\/p>\n

Primeira lei de Kepler (lei das \u00f3rbitas)<\/b><\/span><\/span><\/p>\n

\u201cAs\u00a0<\/b><\/span><\/span>\u00f3rbitas<\/b><\/span><\/span>\u00a0que os planetas descrevem ao redor do Sol s\u00e3o\u00a0<\/b><\/span><\/span>el\u00edpticas<\/b><\/span><\/span>, com o\u00a0<\/b><\/span><\/span>Sol\u00a0<\/b><\/span><\/span>ocupando um dos\u00a0<\/b><\/span><\/span>focos\u00a0<\/b><\/span><\/span>da elipse\u201d.<\/b><\/span><\/span><\/p>\n

\"\"\"\"\"\"<\/p>\n

Numa\u00a0<\/b><\/span><\/span>elipse<\/b><\/span><\/span>\u00a0(figura acima), para qualquer posi\u00e7\u00e3o do ponto P a soma das dist\u00e2ncias FP com PF\u2019 \u00e9 sempre a mesma.<\/b><\/span><\/span><\/p>\n

Segunda lei de Kepler (lei das \u00e1reas)<\/b><\/span><\/span><\/p>\n

\u201c\u00a0<\/span>O\u00a0<\/b><\/span><\/span>segmento de reta\u00a0<\/b><\/span><\/span>imagin\u00e1rio que\u00a0<\/b><\/span><\/span>une o centro do Sol ao centro do planeta<\/b><\/span><\/span>\u00a0descreve \u00e1reas\u00a0<\/b><\/span><\/span>iguais\u00a0 em intervalos de tempo iguais<\/b><\/span><\/span>\u201d<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

Sejam:<\/b><\/span><\/span><\/p>\n

A1\u00a0<\/b><\/span><\/span>\u2014 \u00e1rea entre 1,2 e o Sol<\/b><\/span><\/span><\/p>\n

A2\u00a0<\/b><\/span><\/span>\u2014 \u00e1rea entre 3, 4 e o Sol<\/b><\/span><\/span><\/p>\n

\u2206<\/span>t1\u00a0<\/b><\/span><\/span>\u2014 tempo que o planeta demora para ir de 1 a 2<\/b><\/span><\/span><\/p>\n

\u2206<\/span>t2\u00a0<\/b><\/span><\/span>\u2014 tempo que o planeta demora para ir de 3 a 4<\/b><\/span><\/span><\/p>\n

\u00a0<\/span>Ent\u00e3o:<\/b><\/span><\/span><\/p>\n

A1\/\u2206t1~A2\/\u2206t2\u00a0=\u00a0<\/b><\/span><\/span>constante = K<\/b><\/span><\/span><\/p>\n

Terceira lei de Kepler (lei dos per\u00edodos)<\/b><\/span><\/span><\/p>\n

\u201c\u00a0<\/span>Os\u00a0<\/b><\/span><\/span>quadrados dos per\u00edodos\u00a0T\u00a0<\/b><\/span><\/span>de revolu\u00e7\u00e3o dos planetas (tempo que demora para efetuar uma volta completa em torno do Sol) s\u00e3o proporcionais aos\u00a0<\/b><\/span><\/span>cubos das suas dist\u00e2ncias m\u00e9dias\u00a0R\u00a0<\/b><\/span><\/span>ao Sol\u201d<\/b><\/span><\/span><\/p>\n

T2\/R3\u00a0= constante = K\u2019<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

O\u00a0<\/b><\/span><\/span>raio m\u00e9dio R\u00a0<\/b><\/span><\/span>da \u00f3rbita de um planeta corresponde \u00e0\u00a0<\/b><\/span><\/span>m\u00e9dia aritm\u00e9tica <\/b><\/span><\/span>entre a dist\u00e2ncia do Sol ao af\u00e9lio e a dist\u00e2ncia do Sol ao peri\u00e9lio. Observe que esse valor \u00e9 o mesmo que a medida do semi-eixo maior da elipse, que na figura acima seria\u00a0<\/b><\/span><\/span>a<\/b><\/span><\/span>.<\/b><\/span><\/span><\/p>\n

R- C\u00a0<\/b><\/span><\/span><\/p>\n

LEI DA ATRA\u00c7\u00c3O UNIVERSAL<\/span><\/span><\/span><\/p>\n

01- <\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

02- <\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Observando as\u00a0<\/b><\/span><\/span>figuras<\/b><\/span><\/span>\u00a0abaixo voc\u00ea verificar\u00e1 que, tanto na\u00a0<\/b><\/span><\/span>Terra\u00a0<\/b><\/span><\/span>quanto na\u00a0<\/b><\/span><\/span>Lua,<\/b><\/span><\/span>\u00a0os corpos est\u00e3o em\u00a0<\/b><\/span><\/span>repouso<\/b><\/span><\/span>\u00a0(<\/b><\/span><\/span>equil\u00edbrio est\u00e1tico<\/b><\/span><\/span>) e a\u00a0<\/b><\/span><\/span>for\u00e7a resultante sobre eles deve ser nula.<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

ACELERA\u00c7\u00c3O GRAVITACIONAL<\/b><\/span><\/span><\/span><\/p>\n

01-<\/b><\/span><\/span><\/span> <\/b>Sendo o peso\u00a0<\/b><\/span><\/span>P = mg e a massa do objeto a mesma<\/b><\/span><\/span>, o\u00a0<\/b><\/span><\/span>peso diminuiria <\/b><\/span><\/span>se a\u00a0<\/b><\/span><\/span>acelera\u00e7\u00e3o da gravidade g diminu\u00edsse<\/b><\/span><\/span>, sendo g fornecida por\u00a0<\/b><\/span><\/span>g = GM\/r<\/b><\/span><\/span>2<\/b><\/span><\/sup><\/span>\u00a0onde:<\/b><\/span><\/span><\/p>\n

g\u00a0<\/b><\/span><\/span>\u00a0\u2014valor da acelera\u00e7\u00e3o da gravidade \u00e0 uma dist\u00e2ncia r do centro do planeta (m\/s2\u00a0ou N\/kg)<\/b><\/span><\/span><\/p>\n

G\u00a0<\/b><\/span><\/span>\u00a0\u2014\u00a0constante de gravita\u00e7\u00e3o universal (6,67.10-11\u00a0Nm2\/kg2)<\/b><\/span><\/span><\/p>\n

M\u00a0\u00a0<\/b><\/span><\/span>\u2014\u00a0massa do planeta (kg)<\/b><\/span><\/span><\/p>\n

r\u00a0<\/b><\/span><\/span>\u00a0\u2014dist\u00e2ncia do centro do planeta ao centro do corpo (m)<\/b><\/span><\/span><\/p>\n

Observe na express\u00e3o\u00a0<\/b><\/span><\/span>g = GM\/r<\/b><\/span><\/span>2<\/b><\/span><\/sup><\/span>\u00a0que, para que\u00a0<\/b><\/span><\/span>g\u00a0<\/b><\/span><\/span>e consequentemente o <\/b><\/span><\/span>peso diminua<\/b><\/span><\/span>, voc\u00ea deve\u00a0<\/b><\/span><\/span>aumentar o raio r da Terra<\/b><\/span><\/span>\u00a0(inversamente proporcional a r<\/b><\/span><\/span>2<\/b><\/span><\/sup><\/span>) e <\/b><\/span><\/span>diminuir a massa M da Terra<\/b><\/span><\/span>\u00a0(diretamente proporcional a M).<\/b><\/span><\/span><\/p>\n

R \u2013 C<\/b><\/span><\/span><\/p>\n

02-<\/span><\/span><\/span> \u00a0<\/b><\/span><\/span>A. Falsa\u00a0\"\"\u00a0gT\u00a0=GM<\/b><\/span><\/span>T<\/b><\/span><\/sub><\/span>\/R<\/b><\/span><\/span>T<\/b><\/span><\/sub><\/span>2<\/b><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span>= G.6.10<\/b><\/span><\/span>24<\/b><\/span><\/sup><\/span>\/(150.10<\/b><\/span><\/span>6<\/b><\/span><\/sup><\/span>)2\u00a0= 6<\/b><\/span><\/span>.10<\/b><\/span><\/span>24<\/b><\/span><\/sup><\/span> G\/22500.10<\/b><\/span><\/span>12<\/b><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span>= 6<\/b><\/span><\/span>.10<\/b><\/span><\/span>24<\/b><\/span><\/sup><\/span> <\/b>G\/2,25.10<\/b><\/span><\/span>16 <\/b><\/span><\/sup><\/span>\u00a0\"\"\u00a0g<\/b><\/span><\/span>T<\/b><\/span><\/span>\u00a0= 2,7 .10<\/b><\/span><\/span>8<\/b><\/span><\/sup><\/span> <\/b>G.g<\/b><\/span><\/span>M<\/b><\/span><\/span>\u00a0=\u00a0<\/b><\/span><\/span>GM<\/b><\/span><\/span>M<\/b><\/span><\/sub><\/span>\/R<\/b><\/span><\/span>M<\/b><\/span><\/sub><\/span>2<\/b><\/span><\/sup><\/span>\u00a0=\u00a0<\/b><\/span><\/span>G.6,5.10<\/b><\/span><\/span>23<\/b><\/span><\/span>\/(230.10<\/b><\/span><\/span>6<\/b><\/span><\/span>)<\/b><\/span><\/span>2<\/b><\/span><\/span>= G.6,5.10<\/b><\/span><\/span>23<\/b><\/span><\/span>\/52900.10<\/b><\/span><\/span>12<\/b><\/span><\/span>\u00a0= G.6,5.10<\/b><\/span><\/span>23<\/b><\/span><\/span>\/5,29.10<\/b><\/span><\/span>16<\/b><\/span><\/span>\u00a0\"\"\u00a0<\/b><\/span><\/span>g<\/b><\/span><\/span>M<\/b><\/span><\/span>\u00a0= 1,23.10<\/b><\/span><\/span>7<\/b><\/span><\/sup><\/span> <\/b>G.<\/b><\/span><\/span><\/p>\n

Observe que\u00a0<\/b><\/span><\/span>g<\/b><\/span><\/span>M<\/b><\/span><\/span>\u00a0< g<\/b><\/span><\/span>T<\/b><\/span><\/span>.<\/b><\/span><\/span><\/p>\n

B. Correta\u00a0\"\"\u00a0<\/b><\/span><\/span>quanto\u00a0<\/b><\/span><\/span>menor a press\u00e3o atmosf\u00e9rica no planeta, menor ser\u00e1 a temperatura de ebuli\u00e7\u00e3o<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>da \u00e1gua nele.<\/b><\/span><\/span>\u00a0Como a press\u00e3o atmosf\u00e9rica em Marte\u00a0<\/b><\/span><\/span>(PM\u00a0= 0,00 atm) \u00e9 menor que a da Terra (1 atm),<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>em Marte a \u00e1gua ferver\u00e1 a uma temperatura menor que na Terra..<\/b><\/span><\/span><\/p>\n

C. Falsa\u00a0\"\"\u00a0<\/b><\/span><\/span>a\u00a0<\/b><\/span><\/span>massa\u00a0<\/b><\/span><\/span>de um corpo \u00e9 uma\u00a0<\/b><\/span><\/span>grandeza invari\u00e1vel<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>independente do lugar ou do planeta<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>onde ele esteja.<\/b><\/span><\/span><\/p>\n

D. Falsa<\/b><\/span><\/span>\u00a0\"\"\u00a0Na\u00a0<\/b><\/span><\/span>express\u00e3o<\/b><\/span><\/span>\u00a0da terceira lei de Kepler,\u00a0<\/b><\/span><\/span>T<\/b><\/span><\/span>2<\/b><\/span><\/sup><\/span>\/R<\/b><\/span><\/span>3<\/b><\/span><\/sup><\/span>\u00a0= K = constante<\/b><\/span><\/span>, observamos que\u00a0<\/b><\/span><\/span>\u00e0 medida que R<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>aumenta, T tamb\u00e9m aumenta,<\/b><\/span><\/span>\u00a0o que significa que\u00a0quanto <\/b><\/span><\/span>mais afastado o planeta estiver do Sol<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>maior ser\u00e1 seu ano<\/b><\/span><\/span>\u00a0(tempo que demora para dar um volta completa ao redor do Sol). Como Marte est\u00e1\u00a0<\/b><\/span><\/span>mais afastado<\/b><\/span><\/span>\u00a0do Sol (RM\u00a0= 230.10<\/b><\/span><\/span>6<\/b><\/span><\/sup><\/span>\u00a0km) que a Terra (RT= 150.10<\/b><\/span><\/span>6<\/b><\/span><\/sup><\/span>\u00a0km),\u00a0<\/b><\/span><\/span>seu ano ser\u00e1 maior que o da Terra.<\/b><\/span><\/span><\/p>\n

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

03-<\/b><\/span><\/span><\/span> A\u00a0<\/b><\/span><\/span>Terra (ou qualquer outro planeta)<\/b><\/span><\/span>\u00a0origina ao seu redor um\u00a0<\/b><\/span><\/span>campo gravitacional<\/b><\/span><\/span>\u00a0de maneira que\u00a0<\/b><\/span><\/span>qualquer corpo de massa m,<\/b><\/span><\/span>\u00a0quando colocado no interior desse campo fica sujeito \u00e0 uma\u00a0<\/b><\/span><\/span>for\u00e7a de<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>atra\u00e7\u00e3o gravitacional,<\/b><\/span><\/span>\u00a0dirigida para o\u00a0<\/b><\/span><\/span>centro da Terra<\/b><\/span><\/span>\u00a0e de intensidade<\/b><\/span><\/span><\/p>\n

F<\/b><\/span><\/span>G<\/b><\/span><\/sub><\/span>=GMm\/r<\/b><\/span><\/span>2<\/b><\/span><\/sup><\/span>,\u00a0sendo\u00a0<\/b><\/span><\/span>G<\/b><\/span><\/span>\u00a0a\u00a0<\/b><\/span><\/span>constante de gravita\u00e7\u00e3o universal, M a massa da Terra ou do planeta e r a dist\u00e2ncia do centro da Terra ou do planeta ao centro do corpo.\u00a0<\/b><\/span><\/span>Essas for\u00e7as que o corpo de\u00a0<\/b><\/span><\/span>massa m<\/b><\/span><\/span>\u00a0troca com o centro do\u00a0<\/b><\/span><\/span>planeta de massa M<\/b><\/span><\/span>\u00a0constituem par\u00a0<\/b><\/span><\/span>a\u00e7\u00e3o e rea\u00e7\u00e3o.<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

04- <\/span><\/span><\/span><\/span><\/span><\/p>\n

Se voc\u00ea n\u00e3o domina a teoria, leia o breve resumo a seguir:<\/b><\/span><\/span><\/p>\n

A\u00a0<\/b><\/span><\/span>massa\u00a0(m)<\/b><\/span><\/span>\u00a0de um corpo \u00e9 a medida de sua\u00a0<\/b><\/span><\/span>in\u00e9rcia<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>(resist\u00eancia de um corpo em ter seu movimento<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>acelerado ou retardado),<\/b><\/span><\/span>\u00a0sendo um\u00a0<\/b><\/span><\/span>valor num\u00e9rico<\/b><\/span><\/span>\u00a0atribu\u00eddo a<\/b><\/span><\/span>cada corpo comparando-o com outro<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>tomado como padr\u00e3o.<\/b><\/span><\/span><\/p>\n

\u00c9 uma\u00a0<\/b><\/span><\/span>grandeza escalar, positiva<\/b><\/span><\/span>\u00a0e\u00a0<\/b><\/span><\/span>invari\u00e1vel para cada corpo n\u00e3o dependendo do lugar onde ele se<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>encontra<\/b><\/span><\/span>.<\/b><\/span><\/span><\/p>\n

\u00a0<\/span>Assim, a\u00a0<\/b><\/span><\/span>massa de um corpo \u00e9\u00a0<\/b><\/span><\/span>sempre a mesma em qualquer ponto da Terra<\/b><\/span><\/span>, do\u00a0<\/b><\/span><\/span>espa\u00e7o<\/b><\/span><\/span>\u00a0ou de<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

qualquer planeta.<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

No caso do exerc\u00edcio, a massa do astronauta, incluindo seu corpo, trajes especiais e equipamento de sobreviv\u00eancia\u00a0<\/b><\/span><\/span>eram de aproximadamente\u00a0<\/b><\/span><\/span>300 kg (na Terra, na Lua ou em qualquer outro planeta).<\/b><\/span><\/span><\/p>\n

Peso total do astronauta na Lua onde gLua\u00a0= gTerra\/6 = 10\/6 m\/s2\u00a0\"\"\u00a0P = m.g = 300.\"\"<\/b><\/span><\/span>\u00a0\"\"\u00a0<\/b><\/span><\/span>P = 500 N.<\/b><\/span><\/span><\/p>\n

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

05- <\/span><\/span><\/span>\u00a0<\/b><\/span><\/span>O\u00a0<\/b><\/span><\/span>menor intervalo de tempo,\u00a0<\/b><\/span><\/span>em\u00a0<\/b><\/span><\/span>minutos, para que o sat\u00e9lite\u00a0<\/b><\/span><\/span>se movimente da\u00a0<\/b><\/span><\/span>posi\u00e7\u00e3o A\u00a0<\/b><\/span><\/span>para a<\/b><\/span><\/span>\u00a0posi\u00e7\u00e3o B,\u00a0<\/b><\/span><\/span>ocorre quando o sat\u00e9lite se <\/b><\/span><\/span>move no sentido anti-hor\u00e1rio varrendo o \u00e2ngulo de 108o.<\/b><\/span><\/span><\/p>\n

Pelo enunciado,\u00a0<\/b><\/span><\/span>o per\u00edodo do sat\u00e9lite (tempo que ele demora para efetuar uma volta completa\u00a0<\/b><\/span><\/span>em torno da Terra e\u00a0<\/b><\/span><\/span>percorrer um arco de 360o) \u00e9 de 140 min,\u00a0<\/b><\/span><\/span>ent\u00e3o para\u00a0<\/b><\/span><\/span>percorrer 108o\u00a0basta utilizar uma\u00a0<\/b><\/span><\/span>regra de tr\u00eas:<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

b)\u00a0<\/b><\/span><\/span>O\u00a0<\/b><\/span><\/span>raio da \u00f3rbita do sat\u00e9lite (Ro)\u00a0<\/b><\/span><\/span>\u00e9\u00a0<\/b><\/span><\/span>medido em rela\u00e7\u00e3o ao centro da Terra,\u00a0<\/b><\/span><\/span>ou seja\u00a0<\/b><\/span><\/span>Ro\u00a0= RT\u00a0+ 2560\u00a0\"\"<\/b><\/span><\/span>\u00a0Ro\u00a0= 6400 + 2650\u00a0\"\"\u00a0<\/b><\/span><\/span>Ro\u00a0= 8960 km.<\/b><\/span><\/span><\/p>\n

Assim, o\u00a0<\/b><\/span><\/span>sat\u00e9lite dista do centro da Terra\u00a0<\/b><\/span><\/span>em\u00a0<\/b><\/span><\/span>fun\u00e7\u00e3o ao raio da Terra\u00a0<\/b><\/span><\/span>R de\"\"\u00a0<\/b><\/span><\/span>Ro<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>=\u00a0\"\"<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>= 1,4R.<\/b><\/span><\/span><\/p>\n

Veja no\u00a0<\/b><\/span><\/span>gr\u00e1fico a correspond\u00eancia<\/b><\/span><\/span>\u00a0entre essa\u00a0<\/b><\/span><\/span>dist\u00e2ncia (Ro\u00a0=1,4R) e g:<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

R\u2013 g = 5m\/s<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span><\/p>\n

VELOCIDADES EM \u00d3RBITAS CIRCULARES<\/b><\/span><\/span><\/span><\/p>\n

01- <\/span><\/span><\/span>Vamos analisar esse exerc\u00edcio estudando a f\u00f3rmula de velocidade orbital:<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

Aonde: V \u00e9 a velocidade orbital.<\/b><\/span><\/span><\/p>\n

G \u00e9 a constante de gravita\u00e7\u00e3o universal\u00a0\"\"\u00a06,67.\"\"\u00a0N.m\u00b2\/kg\u00b2<\/b><\/span><\/span><\/p>\n

M \u00e9 a massa do objeto que est\u00e1 ao centro da \u00f3rbita.<\/b><\/span><\/span><\/p>\n

r \u00e9 o raio dessa \u00f3rbita.<\/b><\/span><\/span><\/p>\n

Agora precisamos decompor essa velocidade:\u00a0\"\"\"\"<\/b><\/span><\/span><\/p>\n

Como \u00e9 um movimento circular o\u00a0\"\"<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>vai ser o comprimento do c\u00edrculo (2\u03c0r) e o\u00a0\"\"<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>vai ser o per\u00edodo (T).<\/b><\/span><\/span><\/p>\n

Substituindo:<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

Substituindo na primeira f\u00f3rmula, j\u00e1 elevando todos os componentes ao quadrado:<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

Como precisamos analisar o raio em rela\u00e7\u00e3o ao per\u00edodo, vamos isolar o T, primeiro elevando ambos os lados por -1.<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

Multiplicando ambos lados por\u00a0\"\"<\/b><\/span><\/span>:<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

Ao fazer a raiz quadrada da equa\u00e7\u00e3o, podemos notar que a rela\u00e7\u00e3o entre T e r \u00e9:<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

Se o raio \u00e9 4 vezes menor, o per\u00edodo \u00e9\u00a0\"\"<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>= 8 vezes menor<\/b><\/span><\/span>, diretamente proporcional, ou seja,\u00a0<\/b><\/span><\/span>o per\u00edodo menor \u00e9 de 28\/8 = 3,5<\/b><\/span><\/span>.\u00a0<\/b><\/span><\/span>A alternativa correta \u00e9 a A.<\/b><\/span><\/span><\/p>\n

02-<\/span><\/span><\/span> Falso\u00a0\"\"\u00a0A esta\u00e7\u00e3o espacial deve ter\u00a0<\/b><\/span><\/span>velocidade angular igual \u00e0 velocidade angular da Terra<\/b><\/span><\/span>, pois no caso da\u00a0<\/b><\/span><\/span>velocidade linear (\"\")<\/b><\/span><\/span>, ela<\/b><\/span><\/span>varia<\/b><\/span><\/span>\u00a0com a\u00a0<\/b><\/span><\/span>dist\u00e2ncia<\/b><\/span><\/span>, como a esta\u00e7\u00e3o espacial est\u00e1 em uma\u00a0<\/b><\/span><\/span>altura maior<\/b><\/span><\/span>que a da Terra, sua\u00a0<\/b><\/span><\/span>velocidade<\/b><\/span><\/span>\u00a0seria maior, com isso a esta\u00e7\u00e3o\u00a0<\/b><\/span><\/span>perderia<\/b><\/span><\/span>sua posi\u00e7\u00e3o geoestacion\u00e1ria, por terem\u00a0<\/b><\/span><\/span>velocidades diferentes<\/b><\/span><\/span>. Diferente da\u00a0<\/b><\/span><\/span>velocidade<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>angular (\"\")<\/b><\/span><\/span>, que por\u00a0<\/b><\/span><\/span>n\u00e3o<\/b><\/span><\/span>\u00a0depender da\u00a0<\/b><\/span><\/span>dist\u00e2ncia, manteria <\/b><\/span><\/span>essa\u00a0<\/b><\/span><\/span>posi\u00e7\u00e3o geoestacion\u00e1ria<\/b><\/span><\/span>, por\u00a0<\/b><\/span><\/span>manter<\/b><\/span><\/span>\u00a0sempre a\u00a0<\/b><\/span><\/span>posi\u00e7\u00e3o relativa<\/b><\/span><\/span>\u00a0com a Terra.<\/b><\/span><\/span><\/p>\n

02\u00a0\"\"\u00a0Falso\u00a0\"\"Ainda\u00a0<\/b><\/span><\/span>haveria atra\u00e7\u00e3o gravitacional<\/b><\/span><\/span>, que\u00a0<\/b><\/span><\/span>perderia for\u00e7as<\/b><\/span><\/span>conforme a esta\u00e7\u00e3o ganhasse\u00a0<\/b><\/span><\/span>altitude<\/b><\/span><\/span>. Por\u00e9m, devido \u00e0\u00a0<\/b><\/span><\/span>acelera\u00e7\u00e3o de subida<\/b><\/span><\/span>\u00a0da esta\u00e7\u00e3o, uma\u00a0<\/b><\/span><\/span>for\u00e7a contr\u00e1ria<\/b><\/span><\/span>\u00a0pressionaria essas pessoas contra o ch\u00e3o,<\/b><\/span><\/span>\u00a0similar<\/b><\/span><\/span>\u00a0ao que acontece nos elevadores comuns.<\/b><\/span><\/span><\/p>\n

04\u00a0\"\"\u00a0Verdadeiro\u00a0\"\"\u00a0Como j\u00e1 estudado no caso (01).<\/b><\/span><\/span><\/p>\n

08\u00a0\"\"\u00a0Falsa\u00a0\"\"\u00a0varia intensidade, dire\u00e7\u00e3o e sentido.<\/b><\/span><\/span><\/p>\n

16\u00a0\"\"\u00a0Verdadeiro\u00a0\"\"\u00a0Pois no caso da\u00a0<\/b><\/span><\/span>velocidade<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>angular (\"\")<\/b><\/span><\/span>, para\u00a0<\/b><\/span><\/span>manter <\/b><\/span><\/span>a velocidade da Terra e da esta\u00e7\u00e3o igual, o\u00a0<\/b><\/span><\/span>per\u00edodo<\/b><\/span><\/span>\u00a0deve ser o\u00a0<\/b><\/span><\/span>mesmo<\/b><\/span><\/span>, j\u00e1 que o\u00a0<\/b><\/span><\/span>\u00e2ngulo percorrido<\/b><\/span><\/span>\u00a0entre os dois \u00e9 sempre\u00a0<\/b><\/span><\/span>igual<\/b><\/span><\/span>\u00a0e de valor 360\u00b0.<\/b><\/span><\/span><\/p>\n

32\u00a0\"\"\u00a0Falso\u00a0\"\"\u00a0A for\u00e7a de\u00a0<\/b><\/span><\/span>atra\u00e7\u00e3o gravitacional da Terra<\/b><\/span><\/span>\u00a0n\u00e3o ser\u00e1 a centr\u00edfuga, que exerce uma for\u00e7a\u00a0<\/b><\/span><\/span>para fora<\/b><\/span><\/span>\u00a0do movimento circular, e sim a<\/b><\/span><\/span>centr\u00edpeta<\/b><\/span><\/span>, que exerce uma for\u00e7a\u00a0<\/b><\/span><\/span>para dentro<\/b><\/span><\/span>\u00a0do movimento circular, ou seja, em dire\u00e7\u00e3o a Terra, sendo\u00a0<\/b><\/span><\/span>similar<\/b><\/span><\/span>\u00a0\u00e0 for\u00e7a gravitacional.<\/b><\/span><\/span><\/p>\n

64\u00a0\"\"\u00a0Verdadeiro\u00a0\"\"\u00a0<\/b><\/span><\/span>A for\u00e7a gravitacional (\"\")<\/b><\/span><\/span>\u00a0varia conforme a<\/b><\/span><\/span>dist\u00e2ncia<\/b><\/span><\/span>\u00a0entre as duas massas, com isso, ao\u00a0<\/b><\/span><\/span>aumentar a altitude<\/b><\/span><\/span>, a dist\u00e2ncia\u00a0<\/b><\/span><\/span>aumenta<\/b><\/span><\/span>\u00a0e a for\u00e7a gravitacional\u00a0<\/b><\/span><\/span>diminui<\/b><\/span><\/span>,<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span>por serem inversamente proporcionais.<\/b><\/span><\/span><\/p>\n

03- <\/span><\/span><\/span>Na\u00a0<\/b><\/span><\/span>\u00f3rbita circular da figura<\/b><\/span><\/span>\u00a0abaixo,\u00a0<\/b><\/span><\/span>M<\/b><\/span><\/span>\u00a0\u00e9 a massa da Terra<\/b><\/span><\/span>,\u00a0<\/b><\/span><\/span>m\u00a0<\/b><\/span><\/span>a massa do sat\u00e9lite<\/b><\/span><\/span>,\u00a0<\/b><\/span><\/span>V<\/b><\/span><\/span>\u00a0a velocidade de<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

 <\/p>\n

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

Resolu\u00e7\u00f5es Gravita\u00e7\u00e3o Universal \u2013 2017, 2016 e 2015 LEIS DE KEPLER 01- \u00a0 Marte\u00a0n\u00e3o \u00e9 o maior planeta\u00a0do sistema solar, nem o de\u00a0maior massa. Ambos os t\u00edtulos s\u00e3o de\u00a0J\u00fapiter\u00a0que possui 2,5 vezes a massa de todos outros somados. O fato de o\u00a0campo gravitacional\u00a0ser intenso\u00a0n\u00e3o influencia nesse tipo de coordenada, e mesmo que influenciasse Marte tem um\u00a0campo gravitacional\u00a0da ordem de\u00a03,711 m\/s\u00b2.<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":3135,"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-3137","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/3137","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=3137"}],"version-history":[{"count":2,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/3137\/revisions"}],"predecessor-version":[{"id":3139,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/3137\/revisions\/3139"}],"up":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/3135"}],"wp:attachment":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/media?parent=3137"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}