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

Il campo gravitazionale sperimentato da una particella di una certa massa a causa di un'altra particella è la forza gravitazionale che agisce su quella particella divisa per la sua massa.
Il principio di sovrapposizione afferma che il campo gravitazionale netto in qualsiasi punto è la somma vettoriale dei campi gravitazionali dovuti ai singoli oggetti puntiformi.
Un oggetto reale con una forma definita può essere diviso in parti infinitesimali, ciascuna con una massa differenziale che produce un campo differenziale a una certa distanza. Il campo risultante dovuto all'intero oggetto si ottiene secondo il principio di sovrapposizione integrando su un limite opportuno.
Si consideri, ad esempio, una sfera con densità costante. La massa differenziale per ogni guscio costituente può essere scritta come densità moltiplicata per il volume differenziale.
L'equazione di campo per un guscio è nota, in cui la massa differenziale è sostituita.
L'espressione viene quindi integrata da zero al raggio della sfera.
Poiché la densità moltiplicata per il volume dà la massa, il campo finale ottenuto è lo stesso di quello di una massa puntiforme.

<ol>
	<li>Halliday, Resnick e Walker (2014), Fondamenti di fisica, 10a edizione, Wiley and Sons Inc.: sezione 13.2; pagina 357.</li>
	<li>Verma, HC (2008). Concetti di fisica. Volume 1, Bharati Bhawan Pub. & Dis.: sezione 11.6; pagina 210.</li>
</ol>

il principio di sovrapposizione e il campo gravitazionale

Il principio di sovrapposizione si applica alle forze gravitazionali di oggetti che sono sufficientemente distanti tra loro. Esso stabilisce che la forza gravitazionale netta su un oggetto puntiforme è la somma vettoriale delle forze gravitazionali su di esso dovute a vari oggetti. Il principio aiuta a calcolare la forza elencando le singole forze e poi sommandole vettorialmente. Tuttavia, va notato che il principio di sovrapposizione non è sempre evidente. In presenza di una seconda forza, la prima forza potrebbe essere amplificata o ridotta, oppure le due forze potrebbero avere un effetto combinato che è una combinazione complessa delle due. Fortunatamente, la natura è semplice nel modo in cui le forze influenzano un oggetto puntiforme insieme.

Il principio di sovrapposizione aiuta a concettualizzare l'effetto della gravitazione in termini di un nuovo concetto, il campo gravitazionale. Nell'addizione vettoriale delle forze dovute a masse multiple, la massa di un oggetto di prova è una quantità scalare che moltiplica l'accelerazione dovuta a ciascuna forza. Può essere estratto dalla sommatoria e diviso. La forza netta per unità di massa quindi non dipende dalla massa di prova. Questa quantità è chiamata campo gravitazionale, una quantità vettoriale la cui direzione è la stessa della direzione della forza gravitazionale netta. Per definizione, il campo segue il principio di sovrapposizione.

Il campo gravitazionale ci aiuta a comprendere il problema matematico dello studio del moto degli oggetti sotto l'influenza della forza gravitazionale. Vari oggetti creano un campo gravitazionale intorno a sé stessi; questi si sommano vettorialmente per creare un campo gravitazionale netto nello spazio. Quando è presente una massa di prova nel campo, il campo netto crea una forza netta su di essa, che è il prodotto del campo e della sua massa.

Il principio di sovrapposizione e il campo gravitazionale

Il principio di sovrapposizione si applica alle forze gravitazionali di oggetti sufficientemente distanti tra loro. Afferma che la forza gravitazionale netta su un ...

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Education

Didattica

JoVE Core

Physics

Fisica

Unit 1

Unità 1

Gravitation

Gravitazione

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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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Measuring Gravity on Distant Planets

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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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space-time curvature and the general theory of relativity

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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

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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 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

Although black holes were theoretically postulated in the 1920s, they remained outside the domain of observational astronomy until the 1970s.
Their ...

Space-Time Curvature and the General Theory of Relativity

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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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