Name: launching a satellite beyond gravity
Uploaded: 2025-05-22T09:05:41.000Z
Duration: 1 min 26 s
Channel: JoVE

K12 Standards

Pennsylvania State Academic Standards

9-12

Earth and Space Science

Space Systems

3.3.9-12.A

Escape Velocity

Considere um objeto de massa m a uma distância r1 do centro da Terra. Como esse objeto está no campo gravitacional da Terra, ele possui energia potencial gravitacional U1.
Suponha que o objeto se afaste a uma distância r2 de modo que sua energia potencial mude para U2.
Seguindo a lei de conservação de energia, a soma da energia cinética e da energia potencial em r1 é igual à soma da energia cinética e da energia potencial em r2.
Considerando a distância r2 como infinito, onde o campo gravitacional da Terra é insignificante, a energia potencial U2 é zero.
Teoricamente, K2 é igual a zero, uma vez que o objeto se torna estacionário no infinito. Substituindo a energia cinética e a energia potencial em r1, a velocidade do objeto em r1 é igual à raiz quadrada de duas vezes o produto da constante gravitacional e da massa da Terra, dividida por r1.
Aproximando-se r1 igual ao raio da Terra, obtém-se uma expressão para a velocidade de escape do objeto. É a velocidade inicial mínima que um objeto requer para escapar do campo gravitacional da Terra.

velocidade de escape

A velocidade de escape de um objeto é definida como a velocidade inicial mínima que ele precisa para escapar da superfície de outro objeto ao qual está gravitacionalmente ligado e nunca retornar. Por exemplo, qual seria a velocidade mínima com a qual um satélite deveria ser lançado da superfície da Terra para que ele escape minimamente do campo gravitacional da Terra?

Para calcular a velocidade de escape, assume-se que nenhuma energia é perdida devido a forças de atrito. Na prática, um satélite lançado da superfície da Terra não só precisa escapar do campo gravitacional da Terra, mas também é desacelerado pela atmosfera da Terra. Assim, a velocidade de escape calculada puramente a partir de considerações de energia gravitacional é menor do que a velocidade de escape real.

Também é assumido que o satélite possui velocidade zero no infinito, onde a força gravitacional da Terra é zero. Como a velocidade de escape não depende da massa do satélite, ela seria a mesma para qualquer objeto, seja um satélite ou uma bola.

Se um objeto estiver a uma maior distância da superfície da Terra, por exemplo, a Lua, ele precisaria de uma velocidade menor para escapar do campo gravitacional da Terra. A menos que a massa esteja diretamente indo em direção à Terra e colida com ela, dando origem a forças que não são apenas gravitacionais.

Alternativamente, a velocidade de escape pode ser calculada igualando a energia total de um sistema, digamos a Terra e um satélite, a zero. A energia potencial gravitacional em grandes distâncias é convencionalmente assumida como zero. Como a velocidade de escape é definida como a velocidade mínima com a qual um satélite deve ser lançado da superfície, sua energia cinética no infinito também pode ser assumida como zero. Claro, se for positiva, o satélite se afastará cada vez mais e nunca retornará. Assim, a velocidade de interesse é quando a energia cinética no infinito é zero; ou seja, o corpo acaba de escapar do campo gravitacional.

Cálculos revelam que a velocidade de escape da superfície da Terra, assumindo nenhuma atmosfera, é de aproximadamente 11 km/s. Em comparação, a velocidade de escape do campo gravitacional do Sol é de cerca de 42 km/s na distância da Terra. Para escapar do sistema solar, as espaçonaves lançadas da Terra precisariam considerar ambos os fatores.

Este texto foi adaptado de <a href="https://openstax.org/books/university-physics-volume-1/pages/13-3-gravitational-potential-energy-and-total-energy">Openstax, University Physics Volume 1, Section 13.3: Gravitational Potential Energy and Total Energy.</a>

Velocidade de escape

A velocidade de escape de um objeto é definida como a velocidade inicial mínima necessária para escapar da superfície de outro objeto para o qual está ...

Education

JoVE Core

Physics

Física

Unit 1

Unidade 1

Gravitation

Gravitação

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

launching a satellite beyond gravity

Launching a satellite beyond gravity requires enough escape velocity to leave a planet or other body and never return. Escape velocity is the minimum initial speed needed to break free from the gravitational pull of an object that is holding the satellite in orbit or near its surface.

For Earth, the idea is often shown with a satellite launched from the ground. The calculation assumes that no energy is lost to friction. In real life, Earth’s atmosphere also slows the satellite down, so the true launch speed must be higher than the value found from gravity alone.

The escape speed depends on gravity, not on the mass of the object being launched. That means a satellite and a ball would need the same escape velocity if they started from the same place. An object that starts farther from Earth’s surface, such as the Moon, needs a smaller speed to escape Earth’s gravitational field, unless it is moving directly toward Earth and collides with it.

Escape velocity can also be found by using energy. In this method, the total energy of the Earth-satellite system is set to zero. Gravitational potential energy is taken as zero at very large distances, and the satellite is treated as having zero speed at infinity, where Earth’s gravity is zero. The escape condition is the point where the object just makes it out, so its kinetic energy at infinity is also zero.

For Earth, the escape velocity is about 11 km/s if the atmosphere is ignored. For the Sun’s gravitational field at Earth’s distance, the escape velocity is about 42 km/s. Spacecraft leaving Earth to travel out of the solar system must take both Earth’s gravity and the Sun’s gravity into account.

Launching a Satellite Beyond Gravity

gravitation

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newton's law of gravitation

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gravitation between spherically symmetric masses

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acceleration due to gravity on earth

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acceleration due to gravity on other planets

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Measuring Gravity on Distant Planets

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apparent weight and the earth's rotation

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potential energy due to gravitation

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the-principle-of-superposition-and-the-gravitational-field

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escape velocity

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circular orbits and critical velocity for satellites

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energy of a satellite in a circular orbit

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kepler's first law of planetary motion

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kepler's second law of planetary motion

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kepler's third law of planetary motion

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tidal forces

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schwarzschild radius and event horizon

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detection of black holes

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principle of equivalence

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space-time curvature and the general theory of relativity

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key terms and concepts

Explore escape velocity, the minimum speed needed for a satellite to leave Earth or the Sun’s gravity. Learn why mass, atmosphere, and starting distance matter.

Launching a Satellite Beyond Gravity | JoVE K12

physics

JoVE Core - Fisica apresenta a teoria e a aplicação de tópicos fundamentais da física, incluindo cinemática, dinâmica, mecânica dos fluidos, estática, ondas e acústica, com vídeos animados concisos e de fácil compreensão. Além disso, os vídeos de cientistas em ação demonstram a aplicação de conceitos relacionados em experimentos de pesquisa clássica e original realizados nos laboratórios de todo o mundo hoje em dia.

3.3.9-12.D

Louisiana Student Standards for Science

High School

Earth Science

Earth’s Place In The Universe

HS-ESS1-1

HS-ESS1-2

HS-ESS1-3

Tennessee Academic Standards

motion-and-stability-forces-and-interactions

Motion and Stability: Forces and Interactions

PHYS.PS2.9

Virginia  Standards of Learning

HIgh School

ES.2

ES.2.b

ES.2.c

PH.3

PH.3.b

new-jersey-student-learning-standards-for-science

New Jersey Student Learning Standards for Science

Earth's Place in the Universe

HS-ESS1-4

Florida Department of Education

SC.912.E.5

SC.912.E.5.6

SC.912.E.5.10

Physical Science

SC.912.P.10

SC.912.P.10.6

Texas Essential Knowledge and Skills

PHYS.5

PHYS.5.H

south-carolina-college-and-career-ready-science-standards

South Carolina College and Career Ready Science Standards

Earth and Space Science (ESS)

Earth’s Place in the Universe

E-ESS1-6.

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Kepler's Third Law of Planetary Motion

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Schwarzschild Radius and Event Horizon

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Students who demonstrate understanding can construct an explanation of the Big Bang theory based on astronomical evidence of light spectra, motion of distant galaxies, and composition of matter in the universe.  Clarification Statement: Emphasis is on the astronomical evidence of the red shift of light from galaxies as an indication that the universe is currently expanding, the cosmic microwave background as the remnant radiation from the Big Bang, and the observed composition of ordinary matter of the universe, primarily found in stars and interstellar gases (from the spectra of electromagnetic radiation from stars), which matches that predicted by the Big Bang theory (3/4 hydrogen and 1/4 helium).  Assessment Boundary:

3.3.9-12.B

Launching a Satellite Beyond Gravity

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