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

地球を周回するスペースシャトルは、地球の重力に縛られて自由落下運動をしています。しかし、スペースシャトルの中にいる宇宙飛行士は、まるで力が自分に作用していないかのように、無重力を感じます。
スペースシャトルが9.8m/s2で上向きに加速し、スペースシャトルの部屋の床が浮かぶ宇宙飛行士に向かって移動すると仮定します。しかし、宇宙飛行士には、スペースシャトルの床に向かって9.8m/s2で加速しているように見えます。
彼にとって、加速はスペースシャトルに引力を生み出し、地球の表面の重力に似ています。宇宙飛行士は、密閉されたスペースシャトルの部屋の中に座っていると、自分が地球にいるのか、宇宙で加速しているのかを区別できません。
したがって、アインシュタインは、重力がない場合では、均一な重力場と均一な加速度との間に違いはないと述べました。これは等価性の原理として知られています。
彼は、重力は2つの質量間の力ではなく、物質と空間の相互作用から生じると結論付けました。

等価性の原理

アルバート アインシュタイン (1897-1955) によると、自由落下と無重力状態状態感は本質的に結びついています。 たとえば、飛行機から地球に向かって飛び込むなど、重力下で自由落下した場合、完全に無重力状態状態のように感じるでしょう。 同様に、リフトで下降している人は、部分的に無重力状態状態を感じることがあります。 大まかに言えば、一様な重力場にある物体と重力のない状態で一定の加速を受ける物体は同じ実験条件下にあると仮定されます（つまり、どの実験も 2 つのシナリオを区別できません）。 このステートメントは等価性の原則と呼ばれます。

この原理は、ニュートンの重力の法則の基本的な仮定に基づいています。2 つの物体間の引力を決定する質量は、ニュートン法を介して力に対する反応を決定する質量と同じであると想定されます。 の運動法則。 ただし、これら 2 つの質量は重力質量と慣性質量と呼ばれることもあり、実際には異なる場合があります。 それらが同じであると仮定した結果、つまりニュートンの重力の法則とニュートンの運動法則を組み合わせた結果は、実験と一致します。 言い換えれば、この仮定は実験的に有効であることがわかります。 ただし、この結果が生じる理由は理解されていません。

等価性の原則によれば、これは偶然ではありません。 基本的に、等加速度と重力は同じです。

アインシュタインは、一様加速度を重力と関連付けることにより、重力は 2 つの物体間の力ではないことを提案しました。 代わりに、それは 2 つの物体の周囲の時空に対する影響であり、それがそれらのダイナミクスを決定します。 彼は 1915 年に一般相対性理論の中でこれらのアイデアを数学的に表現しました。

このテキストは <a href="https://openstax.org/books/university-physics-volume-1/pages/13-7-einsteins- Theory-of-gravity"> から改変されたものです。 Openstax, University Physics Volume 1, Section 13.7: Einstein's Theory of Gravity.</a>

アルバート・アインシュタイン(1897-1955)によると、自由落下と無重力感は本質的に関連しています。もし人が重力下で自由落下していたら、...

Education

JoVE Core

物理学

Unit 1

ユニット1

Gravitation

万有引力

KEY TERMS AND CONCEPTS

主要用語と概念

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

gravitation-between-spherically-symmetric-masses

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

reduced-mass-coordinates-isolated-two-body-problem

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

Gravity on Earth: Mass, Direction, and Value

Gravity near Earth gives objects a downward acceleration called acceleration due to gravity. It comes from Earth’s gravitational pull and points toward the center of the Earth. Newton’s law of gravitation shows that the gravitational force depends on mass, while Newton’s second law shows that the acceleration produced by a force depends on how that force acts on the object. Because of this relationship, the acceleration due to gravity is independent of an object’s mass. An object and the Earth...

acceleration due to gravity on other planets

acceleration-due-to-gravity-on-other-planets

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

Earth’s spin changes how weight is measured on the surface. Because the Earth turns once every 24 hours, objects on the surface move in a circle. That motion requires a net centripetal force, which points toward the center of the circle. The north and south poles are the only exception. At the equator, the force that provides this inward pull comes from Earth’s gravity. It is the difference between an object’s true weight and the normal force from the ground. The normal force is the support...

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

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

How Earth’s Shape Affects Apparent Weight

Apparent weight changes slightly on Earth because of rotation and the planet’s shape. Apparent weight is the weight measured by a spring balance at a location. It is different from true weight, which is the force Earth pulls on an object with. Earth’s rotation reduces apparent weight by adding a centripetal force. Centripetal force is the inward force that keeps an object moving in a circle. The apparent weight equals the true weight minus this force. The difference depends on the square of...

potential energy due to gravitation

Gravitational Binding and Potential Energy

Gravitational potential energy describes how gravity stores energy between two masses. Because gravity is a conservative force, the work needed to move an object between two points depends on the starting and ending positions, not on the path taken. That is why a gravitational potential energy function can be written in terms of spatial coordinates. For a mass bound by gravity to another object, the potential energy is negative near the attracting body and rises toward zero as the distance...

the principle of superposition and the gravitational field

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

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...

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escape velocity

Launching a Satellite Beyond Gravity

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circular orbits and critical velocity for satellites

circular-orbits-and-critical-velocity-for-satellites

Orbital Speed and Period in Circular Paths

Orbital speed and period in circular paths explain how the Moon, planets, and satellites stay in motion around larger bodies. The Moon orbits Earth. Earth and the other planets orbit the Sun. The space above our atmosphere also contains many artificial satellites. A circular orbit is the simplest orbit to study. It helps show how an object’s speed and its period, or the time for one full orbit, depend on where it is and what it circles. Nicolaus Copernicus first suggested that Earth and the...

energy of a satellite in a circular orbit

energy-of-a-satellite-in-a-circular-orbit

Satellite Orbits and Energy in Space

Satellite orbits and energy in space depend on altitude, orbit shape, and gravity. Thousands of artificial satellites circle Earth every day at many different distances. Satellites below 1,600 km are in low-Earth orbit, or LEO. Research satellites and Earth observation satellites are usually placed in LEO. They mostly move in elliptical orbits, which are oval-shaped paths. Navigation satellites are placed in medium-Earth orbit, or MEO, which ranges from 2,000 km to 36,000 km above Earth’s...

kepler's first law of planetary motion

Planet Orbits as Ellipses

Planet orbits are not perfect circles. Johannes Kepler used planet data from Tycho Brahe to show that each planet follows an ellipse, with the Sun at one focus. This idea came from studying Mars, which did not fit the circular path expected in the Copernican heliocentric model. Copernicus had proposed that the solar system is heliocentric, meaning the Sun is at the center and the planets, including Earth, move around it. His model treated those paths as circles. Brahe later recorded the...

kepler's second law of planetary motion

Kepler's Equal-Area Planet Motion

Kepler's second law explains how a planet moves faster and slower in its orbit around the Sun. Johannes Kepler, a German astronomer and mathematician in the early 17th century, developed three laws for planetary motion. His first law says that planets travel in elliptical orbits, with the Sun at one focus of the ellipse. Because the planet-Sun distance changes during the orbit, the planet does not move at the same speed all the time. In an elliptical orbit, the total energy of the planet is...

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

How the Moon Shapes Earth’s Tides

Earth’s ocean tides are driven by gravitational tidal forces. Scientists have studied the origin of tides for more than 2000 years, and Newton’s work marked the start of a proper understanding. These same tidal forces also act on other astronomical bodies. They can produce internal heat that leads to volcanic activity on Io, one of Jupiter’s moons, and they can tear apart stars that pass too close to black holes. Newton’s law of gravitation says that gravitational force is inversely...

schwarzschild radius and event horizon

Escape Velocity Limits and Black Holes

Escape velocity helps explain how black holes and event horizons form. It is the minimum speed a projectile needs to leave the surface of an object and eventually escape its gravitational field. In this context, escape velocity does not depend on the mass of the object being launched. The key idea is that no object with finite mass can move faster than the speed of light in a vacuum. When escape velocity is compared with that speed limit, the Schwarzschild radius becomes important. If an...

detection of black holes

How Astronomers Find Black Holes

Black holes are found through indirect astronomical evidence. They were first proposed in the 1920s, but they stayed outside observational astronomy until the 1970s. Their closest known cousins are neutron stars, which are made mostly of packed neutrons and are extremely dense. A neutron star can have the mass of the Sun while its diameter is only a few kilometers. Because of that, the escape velocity from its surface is close to the speed of light. Interest in black holes rose again in the...

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

space-time-curvature-and-the-general-theory-of-relativity

Einstein’s Gravity and Mercury’s Orbit

Einstein’s theory of gravity explains how space-time affects motion. In 1905, Einstein published his special theory of relativity. It says that no object can travel faster than the speed of light in a vacuum, which is the speed limit of the universe. Special relativity also changed the way scientists think about space and time. Two observers moving relative to each other do not agree on object length or on how time passes. Newton’s laws still work well for many cases, even for objects moving...

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 物理学は、運動学、力学、流体力学、静力学、波動、音響などの基礎的な物理学の理論と応用を、簡潔でわかりやすいアニメーション ビデオで紹介します。さらに、科学者の実際のビデオでは、世界中の今日の研究所で行われている古典的および独自の研究実験における関連概念の適用を示しています。

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

The de Broglie Wavelength

In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a ...

dual-nature-of-electromagnetic-em-radiation

Dual Nature of Electromagnetic (EM) Radiation

Electromagnetic (EM) radiation consists of electric and magnetic field components oscillating in planes perpendicular to each other and mutually ...

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. wave/particle duality;

PH.9.a

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that ...

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of ...

Quantum Numbers

It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy ...

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. quantum mechanics and uncertainty;

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

In 1905, Albert Einstein published his special theory of relativity. According to this theory, no matter in the universe can attain a speed greater than ...

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. relativity;

Nuclear Stability

Protons and neutrons, collectively called nucleons, are packed together tightly in a nucleus. With a radius of about 10&#8722;15 meters, a nucleus is ...

Nuclear Binding Energy

The difference between the calculated and experimentally measured masses is known as the mass defect of the atom. In the case of helium-4, the mass defect ...

Radioactive Decay and Radiometric Dating

Radioactivity is a spontaneous disintegration of an unstable nuclide and is a random process, as all the nuclei in the sample do not decay simultaneously. ...

Nuclear Fission

Many heavier elements with smaller binding energies per nucleon can decompose into more stable elements that have intermediate mass numbers and larger ...

Nuclear Power

Controlled nuclear fission reactions are used to generate electricity. Any nuclear reactor that produces power via the fission of uranium or plutonium by ...

Nuclear Fusion

The process of converting very light nuclei into heavier nuclei is also accompanied by the conversion of mass into large amounts of energy, a process ...

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 
Solids

Crystalline solids are divided into four types: molecular, ionic, metallic, and covalent network based on the type of constituent units and their ...

Metallic Solids

Metallic solids such as crystals of copper, aluminum, and iron are formed by metal atoms. The structure of metallic crystals is often described as a ...

Network Covalent Solids

Network covalent solids contain a three-dimensional network of covalently bonded atoms as found in the crystal structures of nonmetals like diamond, ...

States of Matter

Solids, liquids, and gases are the three states of matter commonly found on Earth. A solid is rigid and possesses a definite shape. A liquid flows and ...

physical-and-chemical-properties-of-matter

Physical and Chemical Properties of Matter

The characteristics that enable us to distinguish one substance from another are called properties.

Physical Properties of Matter

A physical property is ...

molecular-comparison-of-gases-liquids-and-solids

Molecular Comparison of Gases, Liquids, and Solids

Particles in a solid are tightly packed together (fixed shape) and often arranged in a regular pattern; in a liquid, they are close together with no ...

comparing-intermolecular-forces-melting-point-boiling-point

Comparing Intermolecular Forces: Melting Point, Boiling Point, and Miscibility

Intermolecular forces are attractive forces that exist between molecules. They dictate several bulk properties, such as melting points, boiling points, ...

Structures of Solids

Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds ...

lattice-centering-and-coordination-number

Lattice Centering and Coordination Number

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Ionic Crystal Structures

Ionic crystals consist of two or more different kinds of ions that usually have different sizes. The packing of these ions into a crystal structure is ...

Chemical Bonds


Atoms participate in a chemical bond formation&#160;to acquire a completed valence-shell electron configuration similar to that of the noble gas nearest ...

Covalent Bonds

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Ionic Bonds

When atoms gain or lose electrons to achieve a more stable electron configuration they form ions. Ionic bonds are electrostatic attractions between ions ...

Hydrogen Bonds

Hydrogen BondsHydrogen bonds are weak attractions between atoms that have formed other chemical bonds. One of these atoms is electronegative, like oxygen, ...

Van der Waals Interactions

Atoms and molecules interact with each other through intermolecular forces. These electrostatic forces arise from attractive or repulsive interactions ...

Lewis Symbols and the Octet Rule

Chemical bonds are complex interactions between two or more atoms or ions, which reduce the potential energy of the molecule. Gilbert N. Lewis developed a ...

Ionic Bonding and Electron Transfer

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The Born-Haber Cycle

Lattice Energy&#xA0;

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trends-in-lattice-energy-ion-size-and-charge

Trends in Lattice Energy: Ion Size and Charge

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Covalent Bonding and Lewis Structures

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Electronegativity

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Electronegativity values of ...

bond-polarity-dipole-moment-and-percent-ionic-character

Bond Polarity, Dipole Moment, and Percent Ionic Character

Bond Polarity

The absolute value of the difference in electronegativity (&Delta;EN) of two bonded atoms provides a rough measure of the polarity to be ...

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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