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

El campo gravitatorio que experimenta una partícula de cierta masa debido a otra partícula es la fuerza gravitacional que actúa sobre esa partícula dividida por su masa.
El principio de superposición establece que el campo gravitatorio neto en cualquier punto es la suma vectorial de los campos gravitatorios debidos a objetos puntuales individuales.
Un objeto real con una forma definida se puede dividir en partes infinitesimales, cada una de las cuales tiene una masa diferencial que produce un campo diferencial a una cierta distancia. El campo resultante debido a todo el objeto se obtiene de acuerdo con el principio de superposición integrando sobre un límite adecuado.
Por ejemplo, considere una esfera con densidad constante. La masa diferencial de cualquier capa constituyente se puede escribir como densidad multiplicada por el volumen diferencial.
Se conoce la ecuación de campo para una capa, en la que se sustituye la masa diferencial.
A continuación, la expresión se integra desde cero hasta el radio de la esfera.
Dado que la densidad por el volumen da la masa, el campo final obtenido es el mismo que el de una masa puntual.

<ol>
	<li>Halliday, Resnick y Walker (2014), Fundamentos de Física, 10ª Edición, Wiley and Sons Inc.: sección 13.2; página 357.</li>
	<li>Verma, H.C. (2008). Conceptos de Física. Volumen 1, Bharati Bhawan Pub. & Dis.: sección 11.6; Página 210.</li>
</ol>

el principio de superposición y el campo gravitacional

El principio de superposición se aplica a las fuerzas gravitacionales de objetos que están suficientemente separados. Afirma que la fuerza gravitacional neta en un objeto puntual es la suma vectorial de las fuerzas gravitacionales sobre él debido a varios objetos. El principio ayuda a calcular la fuerza al enumerar las fuerzas individuales y luego sumarlas vectorialmente. Sin embargo, cabe mencionar que el principio de superposición no siempre es evidente. En presencia de una segunda fuerza, la primera fuerza podría haber sido amplificada o reducida, o las dos fuerzas podrían tener un efecto combinado que es una combinación compleja de ambas. Afortunadamente, la naturaleza es simple en cómo las fuerzas afectan a un objeto puntual juntas. El principio de superposición ayuda a conceptualizar el efecto de la gravitación en términos de un nuevo concepto, el campo gravitacional. En la suma vectorial de fuerzas debido a múltiples masas, la masa de un objeto de prueba es una magnitud escalar que se multiplica con la aceleración debido a cada fuerza. Se puede sacar de la suma y dividir. La fuerza neta por unidad de masa entonces no depende de la masa de prueba. Esta magnitud se llama campo gravitacional, una magnitud vectorial cuya dirección es la misma que la dirección de la fuerza gravitacional neta. Según la definición, el campo sigue el principio de superposición. El campo gravitacional nos ayuda a comprender el problema matemático de estudiar el movimiento de objetos bajo la influencia de la fuerza gravitacional. Varios objetos crean un campo gravitacional a su alrededor; estos se suman vectorialmente para crear un campo gravitacional neto en el espacio. Cuando hay una masa de prueba presente en el campo, el campo neto crea una fuerza neta sobre ella, que es el producto del campo y su masa.

El principio de superposición y el campo gravitacional

El principio de superposición se aplica a las fuerzas gravitacionales de los objetos que están suficientemente separados. Afirma que la fuerza gravitacional neta sobre un ...

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Education

Educación

JoVE Core

Physics

Física

Unit 1

Unidad 1

Gravitation

Gravitación

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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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reduced mass coordinates: isolated two-body problem

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acceleration due to gravity on other planets

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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 Física presenta la teoría y la aplicación de conceptos físicos fundamentales, como la cinemática, dinámica, mecánica de fluidos, estática, ondas y acústica, mediante animaciones audiovisuales concisas y fáciles de entender. Además, los vídeos de científicos en acción muestran la aplicación de los conceptos relacionados en experimentos de investigación clásicos y originales, realizados en laboratorios de todo el mundo.

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

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Nuclear Fission

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Nuclear Transmutation

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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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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

Adding Gravitational Forces with Superposition

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