Name: gravity on earth: mass, direction, and value
Uploaded: 2023-04-30T11:05:59.000Z
Duration: 1 min 21 s
Channel: JoVE

K12 Standards

Tennessee Academic Standards

High School

Physics

motion-and-stability-forces-and-interactions

Motion and Stability: Forces and Interactions

PHYS.PS2.5

Acceleration due to Gravity on Earth

物体に作用する唯一の力が地球の重力である場合、物体は自由落下していると見なされます。このような自由落下物体の加速度は、重力による加速度と呼ばれ、gで表されます。
ニュートンの運動の第二法則によれば、物体に作用する力の大きさは、その質量に加速度を掛けたものに等しくなります。これは、オブジェクトの重量とも呼ばれます。
mgを重力方程式と同一視すると、物体の重力による加速度は、重力定数と地球の質量の積を地球の中心からの距離の2乗で割ったものとして表すことができます。
地表付近のgの平均測定値は9.8m/s2です。g は物体の質量に依存しないため、地球の表面付近のすべての質量は同じ加速度で自由落下します。
したがって、重力による加速度、重力定数、距離の値を地球の半径に置き換えると、地球の質量は5.97×1024キログラムと推定されます。

地球上の重力加速度

ニュートンの重力の法則によれば、物体にかかる重力はその質量に比例します。 ニュートンの運動の第 2 法則によれば、外力によって生じる加速度は力に反比例します。 したがって、重力の外力を受けた物体の加速度は、その質量とは無関係です。

地球の重力による、地球に近い物体の加速度は、重力加速度と呼ばれます。 それは常に地球の中心に向かっています。

もちろん、どんな物体も地球に対して同じ逆向きの引力を加えます。 ただし、地球の質量はそれに近い通常の物体よりもはるかに大きいため、その加速は無視できます。 したがって、地球は、その上に置かれた物体のダイナミクスを研究するのに適した慣性座標系として機能します。

地球の表面に近い物体が感じる重力加速度は、約 9.80 m/s であると測定されています。 物体が地球の表面に比較的近い限り、その値は一定であると想定できます。 たとえば、地球の表面で最も高い山であるエベレストの重力加速度は、実際のあらゆる目的において大きな違いはありません。 ただし、地表から数百キロメートル離れた場所では、その値は大きく異なります。 さらに、地球は地軸を中心に回転しているため、重力加速度は赤道から極まで変化します。

地球の質量と平均半径は地球上の重力定数と重力加速度に関係しているため、一方が分かればもう一方も推定できます。 たとえば、幾何学的測定によって地球の半径がわかれば、その質量を測定できます。

このテキストは <a href="https://openstax.org/books/university-physics-volume-1/pages/13-2-gravitation-near-earth-surface"> から編集されたものです。 Openstax, University Physics Volume 1, Section 13.2: Gravitation Near Earth's Surface.</a>

ニュートンの重力の法則によれば、物体にかかる重力はその質量に比例します。ニュートンの第二法則によると...

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

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 pull on each other with equal force in opposite directions. But Earth’s mass is so large compared with ordinary objects that Earth’s acceleration is negligible.

For problems on or near Earth’s surface, Earth can be treated as an inertial frame of reference. That makes it a useful frame for studying motion. The acceleration due to gravity near the surface is about 9.80 m/s², and it can usually be taken as constant when the object stays close to the ground.

This approximation works even for tall places like Mount Everest. It does not hold as well far above Earth, where gravity changes at distances hundreds of kilometers from the surface. Gravity also varies from the equator to the poles because Earth rotates about its axis.

The value of g is linked to Earth’s mass and average radius through the gravitational constant. If one of these quantities is known, the other can be estimated. For example, if Earth’s radius is measured geometrically, Earth’s mass can also be found.

Gravity on Earth: Mass, Direction, and Value

gravity-on-earth-mass-direction-and-value

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 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

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

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

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 why gravity near Earth is about 9.80 m/s², why it points toward Earth’s center, and why an object’s mass does not change its acceleration.

Gravity on Earth: Mass, Direction, and Value | 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。

PHYS.PS2.7

Virginia  Standards of Learning

HIgh School

Earth Science

ES.3

ES.3.b

PH.3

PH.3.b

Arizona Science Standards

Physical Science

HS.P2

HS.P2U1.5

Alabama Course of Study Science

9-12

9-12.P.1.5.b

Florida Department of Education

Earth and Space Science

SC.912.E.5

SC.912.E.5.10

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.

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Forces and Interactions

HS-PS2-4.

Georgia Standards of Excellence

SPS8.

Falling Objects

Kinematic Equations - II

The second kinematic equation expresses the final position of an object in terms of its initial position, the distance traveled with the initial constant ...

Kinematic Equations - III

The first two kinematic equations have time as a variable, but the third kinematic equation is independent of time. This equation expresses final velocity ...

Kinematic Equations: Problem Solving

When analyzing one-dimensional motion with constant acceleration, the problem-solving strategy involves identifying the known quantities and choosing the ...

Acceleration Vectors

In everyday conversation, accelerating means speeding up. Acceleration is a vector in the same direction as the change in velocity, &#916;v, therefore the ...

Solving Problems in Physics

Problem-solving is the ability to apply general physical principles to specific situations, usually expressed by equations. It is an essential skill in ...

Algebraically solve problems including constant velocity and constant acceleration in onedimension. Algebraically solve problems including constant velocity and constant acceleration in onedimension. EXPLANATION:  Students can use the models they have developed in PHYS.PS2.1 to evaluate systems. For a system to undergo constant acceleration, the net force on the object must be constant throughout the problem. Algebraic problem solving should be extended to include proportional reasoning, beyond simple manipulation of variables.

PHYS.PS2.2

Angular Velocity and Displacement

Uniform circular motion is motion in a circle at a constant speed. Although this is the simplest case of rotational motion, it is very useful for many ...

Angular Velocity and Acceleration

We previously discussed angular velocity for uniform circular motion, however not all motion is uniform. Envision an ice skater spinning with their arms ...

rotation-with-constant-angular-acceleration-i

Rotation with Constant Angular Acceleration - I

If angular acceleration is constant, then we can simplify equations of rotational kinematics, similar to the equations of linear kinematics. This ...

rotation-with-constant-angular-acceleration-ii

Rotation with Constant Angular Acceleration - II

Kinematics is the description of motion. The kinematics of rotational motion discusses the relationships between rotation angle, angular velocity, angular ...

Equation of Rotational Dynamics

Angular variables are introduced in rotational dynamics. Comparing the definitions of angular variables with the definitions of linear kinematic ...

/files/media/science-education/science-education-thumbs/14705.jpg

Relating Angular And Linear Quantities - I

If the rotational definitions are compared with the definitions of linear kinematic variables from motion along a straight line and motion in two and ...

relating-angular-and-linear-quantities-ii

Relating Angular And Linear Quantities - II

In the case of circular motion, the linear tangential speed of a particle at a radius from the axis of rotation is related to the angular velocity by the ...

Moment of Inertia

The comparability between linear and angular velocities, linear and angular accelerations, and the kinematic equations of translational and rotational ...

moment-of-inertia-and-rotational-kinetic-energy

Moment of Inertia and Rotational Kinetic Energy

The rotational kinetic energy of a body is equal to half the square of its angular speed and the moment of inertia.
This relationship between the ...

Algebraically solve problems involving arc length, angular velocity, and angular acceleration. Algebraically solve problems involving arc length, angular velocity, and angular acceleration. EXPLANATION: Though not explicitly stated, it is beneficial to develop this standard in the same manner which PHYS.PS2.1 is used to develop PHYS.PS2.2. In doing so, students can parallel rotational properties to translational properties, e.g., arc length can be seen as the rotational equivalent to displacement in the translational world. In doing so, radians becomes a logical unit of measure for rotational displacement. Since neither torque, nor moment of inertia are addressed in this course, discussions can be limited to considering only kinematics and not venturing into the realm of rotational dynamics.

PHYS.PS2.3

Force

Forces affect every moment of our life. Our bodies are held to the Earth by force, and they are held together by the forces of charged particles. When we ...

Types of Forces

In most situations, forces can be grouped into two categories: contact forces and field forces.&#160; Contact forces occur as a result of direct physical ...

Newton's First Law: Introduction

Motion draws our attention. Motion itself can be beautiful, causing us to marvel at the forces needed to create spectacular sights, such as that of a ...

Newton's First Law: Application

Experience suggests that an object at rest remains at rest if left alone, and that an object in motion tends to slow down and stop unless some effort is ...

Newton's Second Law

Newton&#39;s second law is closely related to his first law of motion. It mathematically gives the cause-and-effect relationship between force and changes ...

Newton's Third Law: Introduction

Whenever one body exerts a force on a second body, the first body experiences a force equal in magnitude and opposite in direction, to the force that it ...

Newton's Third Law: Examples

Newton&#39;s third law states that every action has an equal and opposite reaction. Consider a swimmer pushing off the side of a pool. They push against ...

Drawing Free-body Diagrams: Rules

The first step in describing and analyzing most phenomena in physics involves the careful drawing of a free-body diagram. Free-body diagrams are useful in ...

Free Body Diagrams: Examples

Solving problems that involve forces is easy using free-body diagrams. A free-body diagram is a sketch showing all the external forces that are acting on ...

vector-components-in-the-cartesian-coordinate-system

Vector Components in the Cartesian Coordinate System

Vectors are usually described in terms of their components in a coordinate system. Even in everyday life, we naturally invoke the concept of orthogonal ...

Polar and Cylindrical Coordinates

The Cartesian coordinate system is a very convenient tool to use when describing the displacements and velocities of objects and the forces acting on ...

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Use free-body diagrams to illustrate the contact and noncontact forces acting on an object. Use the diagrams in combination with graphic or component based analysis with Newton’s first and second laws to predict position of the object on which the forces act in a constant net force scenario. Use free-body diagrams to illustrate the contact and noncontact forces acting on an object. Use the diagrams in combination with graphic or component based analysis with Newton’s first and second laws to predict position of the object on which the forces act in a constant net force scenario. EXPLANATION: The concept of net force and Newton’s laws have been introduced in 8.PS2.3 and 8.PS2.4. At that time, free-body diagrams are introduced as a tool to represent the forces acting on an object. In further developing the use of free-body diagrams, it is now appropriate to include vectors that must be evaluated to parallel and perpendicular components. This includes objects on inclined planes as well as projectile motion as addressed in PHYS.PS2.13.

PHYS.PS2.4

Gravity on Earth: Mass, Direction, and Value

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