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

Le champ gravitationnel subi par une particule d’une certaine masse en raison d’une autre particule est la force gravitationnelle agissant sur cette particule divisée par sa masse.
Le principe de superposition stipule que le champ gravitationnel net en tout point est la somme vectorielle des champs gravitationnels dus à des objets ponctuels individuels.
Un objet réel avec une forme définie peut être divisé en parties infinitésimales, chacune ayant une masse différentielle produisant un champ différentiel à une certaine distance. Le champ résultant dû à l’objet entier est obtenu selon le principe de superposition en s’intégrant sur une limite appropriée.
Considérons par exemple une sphère à densité constante. La masse différentielle de n’importe quelle couche constitutive peut être écrite comme la densité multipliée par le volume différentiel.
L’équation de champ d’une coquille est connue, dans laquelle la masse différentielle est substituée.
L’expression est ensuite intégrée de zéro au rayon de la sphère.
Comme la masse volumique multipliée par le volume donne la masse, le champ final obtenu est le même que celui d’une masse ponctuelle.

<ol>
	<li>Halliday, Resnick et Walker (2014), Fundamentals of Physics, 10e édition, Wiley and Sons Inc. : section 13.2 ; page 357.</li>
	<li>Verma, H.C. (2008). Concepts de physique. Volume 1, Bharati Bhawan Pub. & Dis. : section 11.6 ; page 210.</li>
</ol>

le principe de superposition et le champ gravitationnel

Le principe de la superposition s'applique aux forces gravitationnelles d'objets suffisamment éloignés. Il affirme que la force gravitationnelle nette exercée sur un objet ponctuel est la somme vectorielle des forces gravitationnelles qui lui sont dues par divers objets. Le principe permet de calculer la force en répertoriant les forces individuelles puis en les additionnant vectoriellement. Toutefois, il convient de noter que le principe de superposition n'est pas toujours apparent. En présence d'une deuxième force, la première force peut être amplifiée ou réduite, ou les deux forces peuvent avoir un effet combiné complexe. Heureusement, la nature est simple dans la manière dont les forces affectent un objet ponctuel ensemble.

Le principe de superposition aide à conceptualiser l'effet de la gravitation en termes d'un nouveau concept, le champ gravitationnel. Dans l'addition vectorielle des forces dues à de multiples masses, la masse d'un objet de test est une quantité scalaire qui se multiplie par l'accélération due à chaque force. Elle peut être retirée de la sommation et divisée. La force nette par unité de masse ne dépend alors pas de la masse de test. Cette quantité s'appelle le champ gravitationnel, une quantité vectorielle dont la direction est la même que celle de la force gravitationnelle nette. Par définition, le champ suit le principe de superposition.

Le champ gravitationnel nous aide à comprendre le problème mathématique de l'étude du mouvement des objets sous l'influence de la force gravitationnelle. Divers objets créent un champ gravitationnel autour d'eux ; ceux-ci s'ajoutent vectoriellement pour créer un champ gravitationnel net dans l'espace. Lorsqu'une masse de test est présente dans le champ, le champ net crée une force nette sur celle-ci, qui est le produit du champ et de sa masse.

Le principe de superposition et le champ gravitationnel

Le principe de superposition s’applique aux forces gravitationnelles des objets suffisamment éloignés les uns des autres. Il stipule que la force gravitationnelle nette sur un ...

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Education

Enseignement

JoVE Core

Physics

Physique

Unit 1

Unité 1

Gravitation

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

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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Measuring Gravity on Distant Planets

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the principle of superposition and the gravitational field

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escape velocity

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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 Physique présente plusieurs branches de la physique fondamentale grâce à des vidéos animées concises et faciles à comprendre ; cela inclut: la cinématique, la dynamique, la mécanique des fluides, la mécanique statique, les ondes et l'acoustique. En parallèle, les vidéos de scientifiques à l'action démontrent l'application de concepts associés à ces domaines dans des expériences de recherche classiques et originales réalisées dans des laboratoires modernes du monde entier.

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 Third Law of Planetary Motion

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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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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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