Name: weightlessness and einstein’s equivalence
Uploaded: 2023-04-30T11:07:46.000Z
Duration: 1 min 18 s
Channel: JoVE

K12 Standards

Virginia  Standards of Learning

HIgh School

Physics

PH.9

PH.9.c

Principle of Equivalence

Ein Space Shuttle, das die Erde umkreist, befindet sich in einer freien Fallbewegung, die durch die Schwerkraft der Erde gebunden ist. Ein Astronaut im Inneren des Space Shuttles fühlt sich jedoch schwerelos, als würde keine Kraft auf ihn wirken.
Angenommen, das Space Shuttle beschleunigt mit 9,8 m/s2 nach oben; der Boden des Space-Shuttle-Raums bewegt sich nach oben in Richtung des schwebenden Astronauten. Für den Astronauten sieht es jedoch so aus, als würde er mit 9,8 m/s2 nach unten in Richtung des Space-Shuttle-Bodens beschleunigen.
Für ihn erzeugt die Beschleunigung einen Sog in der Raumfähre, ähnlich wie die Schwerkraft auf der Erdoberfläche. Der Astronaut sitzt in dem geschlossenen Space-Shuttle-Raum und kann nicht unterscheiden, ob er sich auf der Erde befindet oder im Weltraum beschleunigt.
Einstein stellte daher fest, dass es keinen Unterschied zwischen einem gleichmäßigen Gravitationsfeld und einer einheitlichen Beschleunigung in Abwesenheit von Gravitation gibt. Dies ist als Äquivalenzprinzip bekannt.
Er kam zu dem Schluss, dass die Gravitation keine Kraft zwischen zwei Massen ist, sondern aus der Wechselwirkung von Materie und Raum entsteht.

prinzip der Äquivalenz

Laut Albert Einstein (1897-1955) sind freier Fall und das Gefühl der Schwerelosigkeit intrinsisch miteinander verbunden. Befände sich eine Person im freien Fall unter der Schwerkraft, zum Beispiel bei einem Sturz aus einem Flugzeug auf die Erde, würde sie sich völlig schwerelos fühlen. Ebenso kann sich eine Person, die in einem Aufzug abwärts fährt, teilweise schwerelos fühlen. Im Allgemeinen wird angenommen, dass ein Objekt in einem gleichmäßigen Gravitationsfeld und ein Objekt, das in Abwesenheit von Gravitation einer konstanten Beschleunigung ausgesetzt ist, unter denselben experimentellen Bedingungen stehen (d. h. kein Experiment kann zwischen den beiden Szenarien unterscheiden). Diese Aussage wird als Prinzip der Äquivalenz bezeichnet.

Das Prinzip behandelt eine grundlegende Annahme von Newtons Gravitationsgesetz: Man geht davon aus, dass die Massen, die Anziehungskraft zwischen zwei Objekten bestimmen, dieselben sind, die über die Newtonschen Bewegungsgesetze ihre Reaktion auf die Kräfte bestimmen. Diese beiden Massen, manchmal als gravitative Masse und trägheitsbedingte Masse bezeichnet, können in der Praxis jedoch unterschiedlich sein. Die Konsequenzen der Annahme, dass sie gleich sind, und daher die Ergebnisse der Kombination von Newtons Gravitationsgesetz mit Newtons Bewegungsgesetzen, stimmen mit den Experimenten überein. Mit anderen Worten, die Annahme erweist sich als experimentell gültig. Dennoch ist der Grund für diese Konsequenz nicht verstanden.

Gemäß dem Prinzip der Äquivalenz ist dies keine Zufälligkeit. Im Grunde genommen sind gleichmäßige Beschleunigung und Gravitation dasselbe.

Indem er gleichmäßige Beschleunigung mit Gravitation in Beziehung setzte, schlug Einstein vor, dass Gravitation keine Kraft zwischen zwei Objekten ist. Stattdessen ist sie eine Wirkung der beiden Objekte auf den Raumzeit um sie herum, die wiederum ihre Dynamik bestimmt. Diese Ideen hat er 1915 in seiner allgemeinen Relativitätstheorie mathematisch dargestellt.

Dieser Text wurde angepasst von <a href="https://openstax.org/books/university-physics-volume-1/pages/13-7-einsteins-theory-of-gravity">Openstax, University Physics Volume 1, Section 13.7: Einstein's Theory of Gravity.</a>

Prinzip der Äquivalenz

Nach Albert Einstein (1897-1955) sind der freie Fall und das Gefühl der Schwerelosigkeit untrennbar miteinander verbunden. Wenn sich eine Person im freien Fall unter der Schwerkraft befände, ...

Education

Lehre

JoVE Core

Physik

Unit 1

Einheit 1

Gravitation

KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

weightlessness and einstein’s equivalence

Weightlessness and Einstein’s equivalence principle are closely connected in gravity. A person in free fall under gravity, such as someone diving toward Earth from an airplane, would feel completely weightless. A person descending in a lift may feel partially weightless.

The principle of equivalence says that an object in a uniform gravitational field and an object accelerating at a constant rate with no gravity are under the same experimental conditions. In other words, no experiment can tell the two situations apart. This idea links gravity with uniform acceleration.

The principle also addresses a key assumption in Newton’s law of gravitation. It assumes that the mass that creates gravitational attraction is the same as the mass that responds to force in Newton’s laws of motion. These are sometimes called gravitational mass and inertial mass. They can be different in practice, but the results from combining Newton’s law of gravitation with Newton’s laws of motion still match experiments.

Einstein argued that this agreement is not a coincidence. He proposed that gravitation is not simply a force between two objects. Instead, it is an effect of those objects on the space-time around them, which then shapes their motion. He turned these ideas into mathematics in his general theory of relativity in 1915.

Weightlessness and Einstein’s Equivalence

gravitation

Newton’s Law Behind Planet Motion

Newton’s law of gravitation links falling objects, the Moon’s orbit, and planetary motion. Before Newton, many people thought the sky and Earth followed different laws. Kepler later described the three laws of planetary motion, but their connection to a deeper force was still unclear. Isaac Newton made that connection in 1665 to 1666. He showed that the same phenomenon explains why objects fall to Earth and why the Moon moves around Earth. He also found that the Moon’s centripetal acceleration...

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newton's law of gravitation

Newton's Gravity and the Motion of Bodies

Newton's gravity links the fall of objects on Earth with the motion of the Moon and planets. People once thought the downward pull seen near Earth was unique to our planet. Later, Nicolaus Copernicus proposed the heliocentric theory, which placed Earth and the other planets around the Sun, with the Moon orbiting Earth. Isaac Newton connected these motions in the 17th century. He reasoned that the same attraction that keeps the Moon on its path around Earth also makes an apple fall from a tree.

gravitation between spherically symmetric masses

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Gravitational Potential Inside a Shell

Gravitational potential energy for spherically symmetric bodies depends on their masses and the distance between them. The idea is to treat each body as if its mass were concentrated at its center of mass. This makes the calculation easier for high school physics. A spherically symmetric mass can be thought of as many concentric spherical shells. Now place a point mass at a distance r from the center of one shell. Every particle on a given spherical ring is the same distance from that point...

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gravity between spherical bodies

Point-Mass Approximation in Spherical Gravity

Newton’s law of gravitation gives the force between two point masses. For large spherical objects, such as the Earth, the Moon, and other planets, the same law can be used by treating each body as if its mass were concentrated at its center. This idea can be proven by comparing gravitational potential energy. The transcript shows that a hollow sphere of mass M and a point mass m give the same energy result as two extended solid spherical objects. To set up the proof, a tiny ring on the shell...

reduced mass coordinates: isolated two-body problem

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Center of Mass in the Two-Body Problem

Reduced mass coordinates help simplify the classical two-body problem. In classical mechanics, this problem describes the motion of two interacting bodies under gravity or another central force. The key idea is that the system can be treated like a single-body problem when reduced mass is used. For this description, one body is imagined to move with the reduced mass while the other body is fixed in place with infinite mass. The reduced mass is a property of the two-body system and is defined...

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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

Earth's Spin and Apparent Weight

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

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How Earth’s Shape Affects Apparent Weight

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potential energy due to gravitation

Gravitational Binding and Potential Energy

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the principle of superposition and the gravitational field

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

Adding Gravitational Forces with Superposition

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escape velocity

Launching a Satellite Beyond Gravity

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circular orbits and critical velocity for satellites

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Orbital Speed and Period in Circular Paths

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energy of a satellite in a circular orbit

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Satellite Orbits and Energy in Space

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kepler's first law of planetary motion

Planet Orbits as Ellipses

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kepler's second law of planetary motion

Kepler's Equal-Area Planet Motion

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kepler's third law of planetary motion

Kepler’s Planet Distance Law

Kepler’s third law links a planet’s average distance from the Sun to the time it takes to orbit the Sun. This rule gives a clear mathematical relationship between orbital distance and orbital period, which is the time for one full revolution. Johannes Kepler developed this law in the early 17th century after building on the observations of Nicolaus Copernicus and Tycho Brahe. Kepler first formed his first two laws from those earlier observations. He later published the third law of planetary...

tidal forces

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schwarzschild radius and event horizon

Escape Velocity Limits and Black Holes

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detection of black holes

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principle of equivalence

Weightlessness and Einstein’s equivalence principle are closely connected in gravity. A person in free fall under gravity, such as someone diving toward Earth from an airplane, would feel completely weightless. A person descending in a lift may feel partially weightless. The principle of equivalence says that an object in a uniform gravitational field and an object accelerating at a constant rate with no gravity are under the same experimental conditions. In other words, no experiment can tell...

space-time curvature and the general theory of relativity

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Einstein’s Gravity and Mercury’s Orbit

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key terms and concepts

Learn how free fall, weightlessness, and constant acceleration connect in Einstein’s equivalence principle and why it led to general relativity.

Weightlessness and Einstein’s Equivalence | 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.

Alabama Course of Study Science

9-12

Earth and Space Science

Earth's Place in the Universe

9-12.ESS.1.3

Florida Department of Education

High School

SC.912.E.5

SC.912.E.5.5

SC.912.E.5.10

Georgia Standards of Excellence

Astronomy

SAST4

SAST4.1

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PH.9.a

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PH.9.b

According to Albert Einstein (1897-1955), free-falling and feeling weightless are intrinsically linked. If a person were in free-fall under gravity, for ...

Space-Time Curvature and the General Theory of Relativity

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Radioactive Decay and Radiometric Dating

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Nuclear Fission

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Nuclear Power

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Nuclear Fusion

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The student will investigate and understand that extremely large and extremely small quantities are not necessarily described by the same laws as those studied in Newtonian physics. Topics, such as these listed, may be included. nuclear physics;

PH.9.d

Molecular and Ionic 
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Network Covalent Solids

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States of Matter

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Physical and Chemical Properties of Matter

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Physical Properties of Matter

A physical property is ...

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Molecular Comparison of Gases, Liquids, and Solids

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Ionic Crystal Structures

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Chemical Bonds


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Covalent Bonds

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Ionic Bonds

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Hydrogen Bonds

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Van der Waals Interactions

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The Born-Haber Cycle

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Bond Polarity, Dipole Moment, and Percent Ionic Character

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The student will investigate and understand that extremely large and extremely small quantities are not necessarily described by the same laws as those studied in Newtonian physics. Topics, such as these listed, may be included. solid state physics;

PH.9.e

The student will investigate and understand that extremely large and extremely small quantities are not necessarily described by the same laws as those studied in Newtonian physics. Topics, such as these listed, may be included.

Weightlessness and Einstein’s Equivalence

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