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

Si consideri un oggetto di massa m a una distanza r1 dal centro della Terra. Poiché questo oggetto si trova nel campo gravitazionale terrestre, possiede un'energia potenziale gravitazionale U1.
Supponiamo che l'oggetto si allontani a una distanza r2 tale che la sua energia potenziale cambi in U2.
Seguendo la legge di conservazione dell'energia, la somma dell'energia cinetica e dell'energia potenziale in r1 è uguale alla somma dell'energia cinetica e dell'energia potenziale in r2.
Considerando la distanza r2 come infinito, dove il campo gravitazionale terrestre è trascurabile, l'energia potenziale U2 è zero.
Teoricamente, K2 è uguale a zero, poiché l'oggetto diventa stazionario all'infinito. Sostituendo l'energia cinetica e l'energia potenziale in r1, la velocità dell'oggetto in r1 è uguale alla radice quadrata di due volte il prodotto della costante gravitazionale e della massa terrestre, diviso per r1.
Approssimando r1 uguale al raggio della Terra, si ottiene un'espressione per la velocità di fuga dell'oggetto. È la velocità iniziale minima che un oggetto richiede per sfuggire al campo gravitazionale terrestre.

velocità di fuga

La velocità di fuga di un oggetto è definita come la velocità minima iniziale richiesta per fuggire dalla superficie di un altro oggetto al quale è gravitazionalmente legato e non fare ritorno. Per esempio, quale sarebbe la velocità minima alla quale un satellite dovrebbe essere lanciato dalla superficie terrestre così che fugga dal campo gravitazionale della Terra?

Per calcolare la velocità di fuga, si presume che non venga persa energia per le forze d'attrito. In pratica, un satellite lanciato dalla superficie terrestre non solo deve fuggire dal campo gravitazionale della Terra, ma anche l'atmosfera della Terra lo rallenta. Perciò, la velocità di fuga è calcolata esclusivamente dalle considerazioni sull'energia gravitazionale è più piccola rispetto alla velocità di fuga effettiva.

Si presume anche che il satellite abbia zero velocità all'infinito, dove la forza gravitazionale terrestre è zero. Dato che la velocità di fuga non dipende dalla massa del satellite, essa dovrebbe essere la stessa per ogni oggetto, che sia un satellite o una palla.

Se un oggetto è ad una grande distanza dalla superficie terrestre, per esempio, la Luna, necessiterebbe di una velocità minore per fuggire dal campo gravitazionale della Terra. Questo a meno che la massa non si diriga direttamente verso la Terra e collida con essa, dando origine a forze che non sono solo gravitazionali.

In alternativa, la velocità di fuga può essere calcolata equiparando l'energia totale di un sistema, ad esempio la Terra e un satellite, a zero. L'energia potenziale gravitazionale a grandi distanze è convenzionalmente ritenuta essere zero. Visto che l'energia di fuga è definita come la velocità minima alla quale un satellite dovrebbe essere lanciato dalla superficie, anche la sua energia cinetica dovrebbe essere ritenuta zero. Ovviamente, se è positiva, andrà molto lontano e non farà più ritorno. Pertanto, la velocità di interesse è quando l'energia cinetica all'infinito è zero; cioè, il corpo appena fuggito dal campo gravitazionale.

I calcoli rivelano che la velocità di fuga dalla superficie terrestre, ipotizzando che non ci sia l'atmosfera, è di circa 11 km/s. In confronto, la velocità di fuga dal campo gravitazionale del Sole è di circa 42 km/s alla distanza della terra. La sonda che viene lanciata dalla Terra per fuggire al sistema solare dovrebbe considerare entrambi i fattori.

Questo testo è adattato da <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>

Velocità di fuga

La velocità di fuga di un oggetto è definita come la velocità iniziale minima che richiede per sfuggire alla superficie di un altro oggetto a cui è ...

Education

Didattica

JoVE Core

Physics

Fisica

Unit 1

Unità 1

Gravitation

Gravitazione

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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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gravitation between spherically symmetric masses

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Center of Mass in the Two-Body Problem

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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

Gravity near Earth’s surface is measured as acceleration due to gravity. On Earth, students can test it with simple experiments. On other planets, that kind of direct experiment is not possible. Instead, astronomers use observations to find a planet’s gravity. They study how the planet affects nearby objects, especially its satellite. The key idea is that the acceleration depends on the planet’s gravity, not on the object’s mass. To make the calculation, scientists track a satellite’s path...

apparent weight and the earth's rotation

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variation in acceleration due to gravity near the earth's surface

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potential energy due to gravitation

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escape velocity

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...

circular orbits and critical velocity for satellites

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kepler's second 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

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 Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

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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Schwarzschild Radius and Event Horizon

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Nuclear Binding Energy

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Metal Flame Emission

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Atomic Absorption Spectroscopy: Radiation and Light Sources

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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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