Name: adding gravitational forces with superposition
Uploaded: 2025-05-22T09:06:10.000Z
Duration: 1 min 17 s
Channel: JoVE

K12 Standards

Pennsylvania State Academic Standards

9-12

Earth and Space Science

Space Systems

3.3.9-12.A

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

The Principle of Superposition and the Gravitational Field

O campo gravitacional experimentado por uma partícula de uma certa massa devido a outra partícula é a força gravitacional que atua sobre essa partícula dividida por sua massa.
O princípio da superposição afirma que o campo gravitacional líquido em qualquer ponto é a soma vetorial dos campos gravitacionais devidos a objetos pontuais individuais.
Um objeto real com uma forma definida pode ser dividido em partes infinitesimais, cada uma com uma massa diferencial produzindo um campo diferencial a uma certa distância. O campo resultante devido a todo o objeto é obtido de acordo com o princípio da superposição, integrando-se sobre um limite adequado.
Por exemplo, considere uma esfera com densidade constante. A massa diferencial para qualquer casca constituinte pode ser escrita como densidade vezes o volume diferencial.
A equação de campo para uma casca é conhecida, na qual a massa diferencial é substituída.
A expressão é então integrada de zero ao raio da esfera.
Como a densidade vezes o volume dá a massa, o campo final obtido é o mesmo de uma massa pontual.

<ol>
	<li>Halliday, Resnick e Walker (2014), Fundamentos da Física, 10ª Edição, Wiley and Sons Inc.: seção 13.2; página 357.</li>
	<li>Verma, H.C. (2008). Conceitos de Física. Volume 1, Bharati Bhawan Pub. & Dis.: seção 11.6; página 210.</li>
</ol>

o princípio da superposição e o campo gravitacional

O princípio da superposição se aplica às forças gravitacionais de objetos que estão suficientemente distantes. Ele afirma que a força gravitacional resultante em um objeto pontual é a soma vetorial das forças gravitacionais sobre ele devido a vários objetos. O princípio auxilia no cálculo da força listando as forças individuais e, em seguida, somando-as de forma vetorial. No entanto, deve-se observar que o princípio da superposição nem sempre é aparente. Na presença de uma segunda força, a primeira força poderia ter sido amplificada ou reduzida, ou as duas forças poderiam ter um efeito combinado que fosse uma combinação complexa das duas. Felizmente, a natureza é simples na forma como as forças afetam de forma conjunta um objeto pontual.

O princípio da superposição ajuda a conceptualizar o efeito da gravidade em termos de um novo conceito, o campo gravitacional. Na adição vetorial de forças devido a múltiplas massas, a massa de um objeto de teste é uma grandeza escalar que multiplica a aceleração de cada força. Ela pode ser retirada da soma e dividida. A força resultante por unidade de massa, então, não depende da massa de teste. Essa grandeza é chamada de campo gravitacional, uma grandeza vetorial cuja direção é a mesma que a direção da força gravitacional resultante. Por definição, o campo segue o princípio da superposição.

O campo gravitacional nos ajuda a entender o problema matemático de estudar o movimento de objetos sob a influência da força gravitacional. Vários objetos criam um campo gravitacional ao seu redor; eles se somam de forma vetorial para criar um campo gravitacional resultante no espaço. Quando uma massa de teste está presente no campo, o campo resultante cria uma força resultante sobre ela, que é o produto do campo e sua massa.

O Princípio da Superposição e o Campo Gravitacional

O princípio da superposição se aplica às forças gravitacionais de objetos que estão suficientemente distantes. Ele afirma que a força gravitacional líquida em um ...

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Education

JoVE Core

Physics

Física

Unit 1

Unidade 1

Gravitation

Gravitação

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

adding gravitational forces with superposition

Gravitational forces can be added using the principle of superposition. For objects that are sufficiently far apart, the net gravitational force on a point object is the vector sum of the forces from each mass. This means each force is found first, and then the forces are added as vectors.

Superposition is useful because gravity from more than one object can combine in ways that are not always easy to see. One force may be increased or reduced by another force, or the final effect may be a more complex combination of both. Even so, nature follows a simple rule for how these forces act together on a point object.

The same idea leads to the concept of the gravitational field. When the test object's mass is treated as a scalar quantity, it can be taken out of the force sum. The force per unit mass is then independent of the test mass. This quantity is called the gravitational field, and it is a vector that points in the same direction as the net gravitational force.

By definition, the gravitational field also follows superposition. Different objects create gravitational fields around themselves, and these fields add vectorially in space to make a net field. When a test mass is placed in that field, the net field produces a force on it equal to the field multiplied by the mass. This helps describe motion under gravity in a clear mathematical way.

Adding Gravitational Forces with Superposition

adding-gravitational-forces-with-superposition

gravitation

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gravitation between spherically symmetric masses

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reduced mass coordinates: isolated two-body problem

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acceleration due to gravity on other planets

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escape velocity

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circular orbits and critical velocity for satellites

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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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key terms and concepts

Learn how the principle of superposition adds gravitational forces as vectors and leads to the gravitational field, a key idea for describing motion under gravity.

Adding Gravitational Forces with Superposition | 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

Physical Science

Forces and Interactions

3.2.9-12.L

3.2.9-12.M

Louisiana Student Standards for Science

High School

Earth Science

Earth’s Place In The Universe

HS-ESS1-1

HS-ESS1-2

HS-ESS1-3

ohios-learning-standards-and-model-curriculum

Ohio’s Learning Standards and Model Curriculum

Forces And Motion

Forces

Forces, Momentum And Motion

Gravitational force and fields

Energy

Gravitational potential energy

Tennessee Academic Standards

motion-and-stability-forces-and-interactions

Motion and Stability: Forces and Interactions

PHYS.PS2.5

PHYS.PS2.7

Virginia  Standards of Learning

HIgh School

ES.2

ES.2.b

PH.3

PH.3.b

PH.7

PH.7.a

PH.7.b

Texas Essential Knowledge and Skills

Astronomy

112.48.c.11.

112.48.c.11.D.

Next Generation Science Standards

HS-PS2-4

HS-PS2-5

Florida Department of Education

SC.912.E.5

SC.912.E.5.6

SC.912.E.5.10

SC.912.P.10

SC.912.P.10.6

PHYS.5

PHYS.5.H

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Forces and Interactions

HS-PS2-4.

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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

In the early 17th century, German astronomer and mathematician Johannes Kepler postulated three laws for the motion of planets in the solar system. In ...

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Nuclear Power

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Nuclear Fission

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Nuclear Transmutation

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Atomic Structure

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Radioactivity and Nuclear Equations

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Nuclear Stability

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Students who demonstrate understanding can develop a model based on evidence to illustrate the life span of the sun and the role of nuclear fusion in the sun's core to release energy in the form of radiation.  Clarification Statement: Emphasis is on the energy transfer mechanisms that allow energy from nuclear fusion in the sun's core to reach Earth.  Examples of evidence for the model include observations of the masses and lifetimes of other stars, as well as the ways that the sun's radiation varies due to sudden solar flares ("space weather"), the 11-year sunspot cycle, and non-cyclic variations over centuries.  Assessment Boundary: Assessment does not include details of the atomic and sub-atomic processes involved with the sun's nuclear fusion.

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Detection of Black Holes

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Their ...

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Schwarzschild Radius and Event Horizon

No object with a finite mass can travel faster than the speed of light in a vacuum. This fact has an interesting consequence in the domain of extremely ...

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

Adding Gravitational Forces with Superposition

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