Trabalho De FÍsica - GravitaÇÃo Universal - 1º Ano

1. A tabela resume alguns dados importantes sobre os satélites de Júpiter

Ao observar os satélites de Júpiter pela primeira vez, Galileu Galilei fez diversas anotações e tirou importantes conclusões sobre a estrutura de nosso universo. A figura abaixo da tabela reproduz uma anotação de Galileu referente a Júpiter e seus satélites.

De acordo com essa representação e com os dados da tabela, associe os pontos indicados por 1, 2, 3 e 4 ao satélite correspondente:

1

2

3

4

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2. Qual é a figura geométrica que mais se assemelha à órbita de um dos planetas em torno do Sol

reta

elipse

hipérbole

parábola

circunferência

An ellipse is the geometric shape that most closely resembles the orbit of a planet around the Sun. The orbit of a planet is not a straight line (reta), a hyperbola, a parabola, or a circle (circunferência). The shape of an ellipse is elongated and slightly flattened, just like the shape of a planet's orbit around the Sun.

Explanation

An ellipse is the geometric shape that most closely resembles the orbit of a planet around the Sun. The orbit of a planet is not a straight line (reta), a hyperbola, a parabola, or a circle (circunferência). The shape of an ellipse is elongated and slightly flattened, just like the shape of a planet's orbit around the Sun.

3. Observe atentamente a figura a seguir. Ela nos permite concluir que:

A exemplo dos outros planetas do sistema solar, a Terra descreve ao redor do Sol uma órbita circular.

Entre 21 de março e 21 de junho, o hemisfério Sul encontra-se no verão

A inclinação do eixo da Terra juntamente com o movimento de translação explicam a existência das estações do ano.

Em face de sua órbita, a Terra mantém sempre a mesma distância do Sol.

Quando o plano da órbita terrestre corta o Equador, ocorrem os solstícios.

The correct answer is that the inclination of the Earth's axis, along with its movement of translation, explains the existence of the seasons. This means that the Earth's axis is tilted relative to its orbit around the Sun, causing different parts of the Earth to receive varying amounts of sunlight throughout the year. This tilt, combined with the Earth's movement around the Sun, leads to the changing of seasons.

Explanation

The correct answer is that the inclination of the Earth's axis, along with its movement of translation, explains the existence of the seasons. This means that the Earth's axis is tilted relative to its orbit around the Sun, causing different parts of the Earth to receive varying amounts of sunlight throughout the year. This tilt, combined with the Earth's movement around the Sun, leads to the changing of seasons.

4. É bem conhecida a lei das áreas, de Kepler, segundo a qual "o segmento que liga um planeta ao Sol varre áreas iguais em tempos iguais". Esta lei é obedecida pelos outros corpos que orbitam o Sol, como é o caso do cometa Hale-Bopp, que passou nas proximidades da Terra. Na figura, estão esquematizados o Sol e a órbita do cometa.O ponto em que o cometa desenvolve a maior velocidade é:

A

C

E

B

D

The correct answer is D. In this question, it is stated that the comet obeys Kepler's law, which states that the segment connecting a planet to the Sun sweeps equal areas in equal times. This means that the comet moves faster when it is closer to the Sun and slower when it is farther away. In the given figure, point D is the closest point to the Sun, indicating that the comet will be moving at its highest speed at this point.

Explanation

The correct answer is D. In this question, it is stated that the comet obeys Kepler's law, which states that the segment connecting a planet to the Sun sweeps equal areas in equal times. This means that the comet moves faster when it is closer to the Sun and slower when it is farther away. In the given figure, point D is the closest point to the Sun, indicating that the comet will be moving at its highest speed at this point.

5. Adotando o Sol como referencial, aponte a alternativa que condiz com a primeira lei de Kepler da gravitação universal:

As órbitas planetárias são curvas quaisquer, desde que fechadas.

As órbitas planetárias são espiraladas

As órbitas planetárias não podem ser circulares

As órbitas planetárias são elípticas, com o Sol ocupando o centro da elipse.

As órbitas planetárias são elípticas, com o Sol ocupando um dos focos da elipse

The correct answer states that the planetary orbits are elliptical, with the Sun occupying one of the foci of the ellipse. This is in accordance with Kepler's first law of universal gravitation, which states that the planets move in elliptical orbits around the Sun, with the Sun located at one of the foci of the ellipse. This law describes the shape of the orbits and the position of the Sun within them.

Explanation

The correct answer states that the planetary orbits are elliptical, with the Sun occupying one of the foci of the ellipse. This is in accordance with Kepler's first law of universal gravitation, which states that the planets move in elliptical orbits around the Sun, with the Sun located at one of the foci of the ellipse. This law describes the shape of the orbits and the position of the Sun within them.

6. Um satélite (S) gira em torno de um planeta (P) numa órbita circular. Assinale, dentre as opções abaixo, aquela que melhor representa aresultante das forças que atuam sobre o satélite

Option 1

Option 2

Option 3

Option 4

The correct answer, Option 2, represents the resultant of the forces acting on the satellite. In a circular orbit, the gravitational force between the satellite and the planet provides the centripetal force necessary to keep the satellite in its orbit. This force acts towards the center of the planet, perpendicular to the velocity vector of the satellite. Therefore, the resultant of the forces acting on the satellite is directed towards the center of the planet.

Explanation

The correct answer, Option 2, represents the resultant of the forces acting on the satellite. In a circular orbit, the gravitational force between the satellite and the planet provides the centripetal force necessary to keep the satellite in its orbit. This force acts towards the center of the planet, perpendicular to the velocity vector of the satellite. Therefore, the resultant of the forces acting on the satellite is directed towards the center of the planet.

7. A lei da gravitação universal de Newton diz que:

os corpos se atraem na razão direta de suas massas e na razão inversa do quadrado de suas distâncias

os corpos se atraem na razão direta de suas massas e na razão inversa de suas distâncias

The correct answer is that bodies attract each other in direct proportion to their masses and in inverse proportion to the square of their distances. This is known as Newton's law of universal gravitation. According to this law, the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This means that the larger the masses of the objects and the closer they are to each other, the stronger the gravitational force between them.

Explanation

The correct answer is that bodies attract each other in direct proportion to their masses and in inverse proportion to the square of their distances. This is known as Newton's law of universal gravitation. According to this law, the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This means that the larger the masses of the objects and the closer they are to each other, the stronger the gravitational force between them.

8. Imagine que desapareça repentinamente a força de gravitação entre a Terra e o Sol, e que seja desprezível a força de atração de qualquer outro astro sobre ela. Então, a Terra

continuará girando em torno do Sol

ficará parada em relação ao Sol

passará a deslocar-se em movimento retilíneo uniformemente retardado em relação ao Sol.

passará a deslocar-se em movimento retilíneo uniforme em relação ao Sol.

cairá em direção ao Sol.

If the gravitational force between the Earth and the Sun suddenly disappears and the attraction force from any other celestial body is negligible, the Earth will start moving in a straight line with a constant velocity (uniform motion) in relation to the Sun. This is because without the gravitational force, there is no centripetal force acting on the Earth to keep it in orbit, so it will continue moving in a straight line.

Explanation

If the gravitational force between the Earth and the Sun suddenly disappears and the attraction force from any other celestial body is negligible, the Earth will start moving in a straight line with a constant velocity (uniform motion) in relation to the Sun. This is because without the gravitational force, there is no centripetal force acting on the Earth to keep it in orbit, so it will continue moving in a straight line.

9. Satélites utilizados para telecomunicaçõe ssão colocados em órbitas geoestacionárias ao redor da Terra, ou seja, de tal forma que permaneçam sempre acima de um mesmo ponto da superfície da Terra. Considere algumas condições que poderiam corresponder a esses satélites e marque a que é incorreta:

ter o mesmo período, de cerca de 24 horas

ter aproximadamente a mesma massa

estar aproximadamente à mesma altitude

manter-se num plano que contenha o círculo do equador terrestre

The explanation for the correct answer is that satellites in geostationary orbits do not need to have approximately the same mass. The key factor for a satellite to maintain a geostationary orbit is its altitude, which should be approximately the same. The period of the orbit should also be approximately 24 hours to match the rotation of the Earth. However, the mass of the satellite does not have a significant impact on its ability to remain in a geostationary orbit.

Explanation

The explanation for the correct answer is that satellites in geostationary orbits do not need to have approximately the same mass. The key factor for a satellite to maintain a geostationary orbit is its altitude, which should be approximately the same. The period of the orbit should also be approximately 24 hours to match the rotation of the Earth. However, the mass of the satellite does not have a significant impact on its ability to remain in a geostationary orbit.

10. O texto foi extraído da peça Tróilo e Créssida de William Shakespeare, escrita, provavelmente, em 1601. "Os próprios céus, os planetas, e este centroreconhecem graus, prioridade, classe,constância, marcha, distância, estação, forma,função e regularidade, sempre iguais;eis porque o glorioso astro Solestá em nobre eminência entronizadoe centralizado no meio dos outros,e o seu olhar benfazejo corrigeos maus aspectos dos planetas malfazejos,e, qual rei que comanda, ordenasem entraves aos bons e aos maus."(personagem Ulysses, Ato I, cena III).SHAKESPEARE, W. Tróilo e Créssida: Porto: Lello & Irmão, 1948.A descrição feita pelo dramaturgo renascentista inglês se aproxima da teoria

geocêntrica do grego Claudius Ptolomeu.

da reflexão da luz do árabe Alhazen

heliocêntrica do polonês Nicolau Copérnico.

da rotação terrestre do italiano Galileu Galilei

da gravitação universal do inglês Isaac Newton.

The passage describes the celestial bodies recognizing degrees, priority, class, distance, and regularity, with the Sun being in a central and noble position among the other planets. It also mentions the Sun's beneficial influence on the other planets. This aligns with the heliocentric theory proposed by Polish astronomer Nicolaus Copernicus, which states that the Sun is at the center of the solar system and the planets revolve around it.

Explanation

The passage describes the celestial bodies recognizing degrees, priority, class, distance, and regularity, with the Sun being in a central and noble position among the other planets. It also mentions the Sun's beneficial influence on the other planets. This aligns with the heliocentric theory proposed by Polish astronomer Nicolaus Copernicus, which states that the Sun is at the center of the solar system and the planets revolve around it.

11. A órbita de um planeta é elíptica e o Sol ocupa um de seus focos, como ilustrado na figura (fora de escala). As regiões limitadas pelos contornos OPS e MNS têm áreas iguais a A.Se top e tmn são os intervalos de tempo gastos para o planeta percorrer os trechos OP e MN, respectivamente, com velocidades médias vop e vmn, pode-se afirmar que

top > tmn e vop < vmn.

top = tmn e vop > vmn.

top = tmn e vop < vmn.

top > tmn e vop > vmn.

top < tmn e vop < vmn.

The statement "top = tmn e vop > vmn" means that the time interval spent by the planet to travel from point O to point P is equal to the time interval spent to travel from point M to point N, and the average velocity from O to P is greater than the average velocity from M to N. This implies that the planet covers equal areas in equal amounts of time, but it covers the distance from O to P at a faster rate than the distance from M to N.

Explanation

The statement "top = tmn e vop > vmn" means that the time interval spent by the planet to travel from point O to point P is equal to the time interval spent to travel from point M to point N, and the average velocity from O to P is greater than the average velocity from M to N. This implies that the planet covers equal areas in equal amounts of time, but it covers the distance from O to P at a faster rate than the distance from M to N.

12. Um planeta descreve uma órbita elíptica em torno do Sol. Pode-se dizer que a velocidade de translação desse planeta é:

maior quando se encontra longe do Sol

maior quando se encontra perto do Sol

menor quando se encontra mais próximo do Sol

Constante ao longo da órbita

A planet's speed of translation is greater when it is closer to the Sun. This is because the gravitational force between the planet and the Sun is stronger when they are closer together. According to Kepler's laws of planetary motion, a planet moves faster in its orbit when it is closer to the object it is orbiting. Therefore, the planet's speed is highest when it is closest to the Sun and decreases as it moves further away.

Explanation

A planet's speed of translation is greater when it is closer to the Sun. This is because the gravitational force between the planet and the Sun is stronger when they are closer together. According to Kepler's laws of planetary motion, a planet moves faster in its orbit when it is closer to the object it is orbiting. Therefore, the planet's speed is highest when it is closest to the Sun and decreases as it moves further away.

13. Assinale a alternativa correta, com relação às leis de Kepler para o movimento dos planetas

A primeira lei de Kepler diz que as órbitas descritas pelos planetas são circunferências perfeitas

The correct answer is the second law of Kepler states that the module of the translational velocity of a planet (areolar velocity) around the Sun varies during the orbit. This law is known as the law of areas, which states that a line that connects a planet to the Sun sweeps out equal areas in equal times. It means that a planet moves faster when it is closer to the Sun and slower when it is farther away. This law is based on observations and is consistent with Newtonian mechanics.

Explanation

The correct answer is the second law of Kepler states that the module of the translational velocity of a planet (areolar velocity) around the Sun varies during the orbit. This law is known as the law of areas, which states that a line that connects a planet to the Sun sweeps out equal areas in equal times. It means that a planet moves faster when it is closer to the Sun and slower when it is farther away. This law is based on observations and is consistent with Newtonian mechanics.

14. Um astronauta flutua no interior de uma nave em órbita circular em torno da Terra. Isso ocorre porque naquela altura:

não há gravidade

a nave exerce uma blindagem à ação gravitacional da Terra

existe vácuo.

o astronauta e a nave têm aceleração igual à gravidade, isto é, estão numa "queda livre"

o campo magnético terrestre equilibra a ação gravitacional

The correct answer is that the astronaut and the spaceship are in a state of "free fall" where their acceleration is equal to gravity. This means that they are constantly falling towards the Earth, but their forward motion keeps them in orbit, creating the sensation of weightlessness. This is why the astronaut is able to float inside the spaceship.

Explanation

The correct answer is that the astronaut and the spaceship are in a state of "free fall" where their acceleration is equal to gravity. This means that they are constantly falling towards the Earth, but their forward motion keeps them in orbit, creating the sensation of weightlessness. This is why the astronaut is able to float inside the spaceship.

15. A figura abaixo representa o Sol, três astros celestes e suas respectivas órbitas em torno do Sol: Urano, Netuno e o objeto recentemente descoberto de nome 1996 TL66.

Analise as afirmativas a seguir e marque a(s) correta(s):

Essas órbitas são elípticas, estando o Sol em um dos focos dessas elipses.

Dentre todos os astros representados, quem gasta menos tempo para completar uma volta em torno do Sol é Urano

The correct answer states that the orbits represented in the figure are elliptical, with the Sun being one of the foci of these ellipses. This means that the orbits are not perfect circles, but rather elongated and slightly off-center. Additionally, the answer states that among all the represented celestial bodies, Uranus takes the least amount of time to complete one orbit around the Sun. This implies that Uranus has the shortest orbital period compared to Neptune and the recently discovered object named 1996 TL66.

Explanation

The correct answer states that the orbits represented in the figure are elliptical, with the Sun being one of the foci of these ellipses. This means that the orbits are not perfect circles, but rather elongated and slightly off-center. Additionally, the answer states that among all the represented celestial bodies, Uranus takes the least amount of time to complete one orbit around the Sun. This implies that Uranus has the shortest orbital period compared to Neptune and the recently discovered object named 1996 TL66.

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16. Dois satélites,1 e 2,giram em torno da Terra em órbitas circulares idênticas,sendo que m1> m2. Pode-se afirmar que:

a velocidade escalar de 1 é maior que a de 2

o período de 1 é maior que o de 2

a força de atração entre a Terra e os satélites 1 e 2 tem mesma intensidade

as acelerações de 1 e 2 são diferentes

The correct answer is that the velocities and the periods of satellites 1 and 2 are respectively equal. This is because the satellites are in identical circular orbits around the Earth. In a circular orbit, the speed of the satellite remains constant, so the velocities of both satellites would be the same. Additionally, the period of an object in a circular orbit is determined solely by the radius of the orbit and the mass of the Earth, not the mass of the satellite. Therefore, the periods of both satellites would also be equal.

Explanation

The correct answer is that the velocities and the periods of satellites 1 and 2 are respectively equal. This is because the satellites are in identical circular orbits around the Earth. In a circular orbit, the speed of the satellite remains constant, so the velocities of both satellites would be the same. Additionally, the period of an object in a circular orbit is determined solely by the radius of the orbit and the mass of the Earth, not the mass of the satellite. Therefore, the periods of both satellites would also be equal.

17. Na figura, representamos a trajetória do planeta Marte em torno do Sol. Como se sabe, esta trajetória é elíptica e AB eCD representam, respectivamente, o eixo maior e o eixo menor da elipse. É correto afirmar que:

O Sol está localizado exatamente no ponto de concorrência das retas AB e CD (centro da elipse).

Sendo vA e vB os valores da velocidade de Marte em A e B, tem-se VA = VB.

The statement is correct because the force exerted by the Sun on Mars depends on the distance between them. Since the distance from Mars to the Sun is different at points A and B, the forces exerted by the Sun on Mars at these points will also be different. Therefore, FA will be different from FB.

Explanation

The statement is correct because the force exerted by the Sun on Mars depends on the distance between them. Since the distance from Mars to the Sun is different at points A and B, the forces exerted by the Sun on Mars at these points will also be different. Therefore, FA will be different from FB.

18. O astronauta brasileiro, Cel. Marcos César Pontes, esteve em órbita e passou alguns dias na Estação Espacial Internacional (EEI) a 402 km de altitude, onde experimentou um ambiente de microgravidade. O ambiente de microgravidade é a condição de quase ausência de efeitos gravitacionais que é encontrada na órbita da Terra. A falta de impacto gravitacional do ambiente espacial provoca perda de massa muscular nos astronautas, uma vez que a resistência a ser vencida, para mover-se, é sempre bem menor do que na Terra.Em relação a este assunto, analise as proposições a seguir e marque a(s) que está(ão) CORRETA(S)

No ambiente de microgravidade da EEI, não há aceleração, desta forma não existem forças atuando sobre ela

Em relação à Terra, o Cel. Marcos César Pontes, mesmo sem apresentar movimento, pode estar sob a ação de forças

Na Terra, a resistência, para mover-se e vencer nossa inércia, é maior, face os acentuados efeitos gravitacionais e atritos

The correct answer states that in relation to Earth, Colonel Marcos César Pontes, even without showing movement, may be under the action of forces, and that on Earth, the resistance to move and overcome inertia is greater due to the pronounced gravitational effects and friction. This is because in microgravity, there is a near absence of gravitational effects, causing a loss of muscle mass in astronauts as the resistance to be overcome is much lower than on Earth.

Explanation

The correct answer states that in relation to Earth, Colonel Marcos César Pontes, even without showing movement, may be under the action of forces, and that on Earth, the resistance to move and overcome inertia is greater due to the pronounced gravitational effects and friction. This is because in microgravity, there is a near absence of gravitational effects, causing a loss of muscle mass in astronauts as the resistance to be overcome is much lower than on Earth.

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19. Leia com atenção o quadrinho abaixo:



Assinale as proposições corretas:

Num planeta em que a aceleração da gravidade for menor que a da Terra, o Garfield apresentará um peso menor.

Num planeta em que a aceleração da gravidade for menor que a da Terra, o Garfield apresentará uma massa menor.

Num planeta de massa maior que a da Terra, o Garfield apresentará um peso maior

Num planeta de raio maior que a da Terra, o Garfield apresentará um peso menor

O peso de Garfield será o mesmo, independentemente do planeta pra onde ele vá

No planeta em que a aceleração da gravidade for menor que a da Terra, o Garfield apresentará um peso menor porque a força gravitacional exercida sobre ele será menor. No entanto, a massa do Garfield não será afetada, pois a massa é uma propriedade intrínseca do objeto e não depende da gravidade. Em um planeta de massa maior que a da Terra, o Garfield apresentará um peso maior, pois a força gravitacional será maior. Da mesma forma, em um planeta de raio maior que a da Terra, o Garfield apresentará um peso menor, pois a força gravitacional diminui à medida que nos afastamos do centro do planeta. Portanto, o peso de Garfield varia de acordo com a aceleração da gravidade e o tamanho do planeta.

Explanation

No planeta em que a aceleração da gravidade for menor que a da Terra, o Garfield apresentará um peso menor porque a força gravitacional exercida sobre ele será menor. No entanto, a massa do Garfield não será afetada, pois a massa é uma propriedade intrínseca do objeto e não depende da gravidade. Em um planeta de massa maior que a da Terra, o Garfield apresentará um peso maior, pois a força gravitacional será maior. Da mesma forma, em um planeta de raio maior que a da Terra, o Garfield apresentará um peso menor, pois a força gravitacional diminui à medida que nos afastamos do centro do planeta. Portanto, o peso de Garfield varia de acordo com a aceleração da gravidade e o tamanho do planeta.

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20. Associe os modelos solares:

Os planetas se movem em círculos cujos centros giram em torno da Terra

O Sol está em repouso. Os planetas (inclusive a Terra) giram em volta dele em órbitas circulares

A Terra ocupa o centro do Universo. O sol, as estrelas e os demais planetas estão incrustados em uma esfera que gira em torno dela

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