Gravitational field

Encyclopedia

The

to explain the existence of gravity

. In its original concept, gravity was a force

between point mass

es. Following Newton

, Laplace attempted to model gravity as some kind of radiation

field or fluid

, and since the 19th century explanations for gravity have usually been sought in terms of a field model, rather than a point attraction.

In a field model, rather than two particles attracting each other, the particles distort spacetime

via their mass, and this distortion is what is perceived and measured as a "force". In such a model one states that matter moves in certain ways in response to the curvature of spacetime, and that there is either

.

as in physics

, the field is not real, but merely a model

describing the effects of gravity. The field can be determined using Newton's law of universal gravitation

. Determined in this way, the gravitational field around a single particle is a vector field

consisting at every point of a vector pointing directly towards the particle. The magnitude of the field at every point is calculated applying the universal law, and represents the force per unit mass on any object at that point in space. The field around multiple particles is merely the vector sum of the fields around each individual particle. An object in such a field will experience a force that equals the vector sum of the forces it would feel in these individual fields.

Because the force field is conservative, there is a scalar potential energy per unit mass at each point in space associated with the force fields, this is called gravitational potential.

Gauss' law for gravity

is mathematically equivalent to Newton's law of universal gravitation, but is stated directly as vector calculus properties of the gravitational field.

the gravitational field is determined as the solution of Einstein's field equations

. These equations are dependent on the distribution of matter and energy in a region of space, unlike Newtonian gravity, which is dependent only on the distribution of matter. The fields themselves in general relativity represent the curvature of spacetime. General relativity states that being in a region of curved space is equivalent to accelerating

up the gradient

of the field. By Newton's second law, this will cause an object to experience a fictitious force

if it is held still with respect to the field. This is why a person will feel himself pulled down by the force of gravity while standing still on the Earth's surface. In general the gravitational fields predicted by general relativity differ in their effects only slightly from those predicted by classical mechanics, but there are a number of easily verifiable differences, one of the most well known being the bending of light in such fields.

of the California Institute of Technology

wrote:

Most scientists believe that the gravitational field and its gravitational waves are the physical interpretations of Einstein

's equations of general relativity

.

**gravitational field**is a model used in physicsPhysics

Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

to explain the existence of gravity

Gravitation

Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...

. In its original concept, gravity was a force

Force

In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

between point mass

Mass

Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

es. Following Newton

Isaac Newton

Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

, Laplace attempted to model gravity as some kind of radiation

Radiation

In physics, radiation is a process in which energetic particles or energetic waves travel through a medium or space. There are two distinct types of radiation; ionizing and non-ionizing...

field or fluid

Fluid

In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....

, and since the 19th century explanations for gravity have usually been sought in terms of a field model, rather than a point attraction.

In a field model, rather than two particles attracting each other, the particles distort spacetime

Spacetime

In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

via their mass, and this distortion is what is perceived and measured as a "force". In such a model one states that matter moves in certain ways in response to the curvature of spacetime, and that there is either

*no gravitational force*, or that gravity is a fictitious forceFictitious force

A fictitious force, also called a pseudo force, d'Alembert force or inertial force, is an apparent force that acts on all masses in a non-inertial frame of reference, such as a rotating reference frame....

.

## In classical mechanics

In classical mechanicsClassical mechanics

In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...

as in physics

Physics

Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, the field is not real, but merely a model

Scientific modelling

Scientific modelling is the process of generating abstract, conceptual, graphical and/or mathematical models. Science offers a growing collection of methods, techniques and theory about all kinds of specialized scientific modelling...

describing the effects of gravity. The field can be determined using Newton's law of universal gravitation

Newton's law of universal gravitation

Newton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them...

. Determined in this way, the gravitational field around a single particle is a vector field

Vector field

In vector calculus, a vector field is an assignmentof a vector to each point in a subset of Euclidean space. A vector field in the plane for instance can be visualized as an arrow, with a given magnitude and direction, attached to each point in the plane...

consisting at every point of a vector pointing directly towards the particle. The magnitude of the field at every point is calculated applying the universal law, and represents the force per unit mass on any object at that point in space. The field around multiple particles is merely the vector sum of the fields around each individual particle. An object in such a field will experience a force that equals the vector sum of the forces it would feel in these individual fields.

Because the force field is conservative, there is a scalar potential energy per unit mass at each point in space associated with the force fields, this is called gravitational potential.

Gauss' law for gravity

Gauss' law for gravity

In physics, Gauss's law for gravity, also known as Gauss's flux theorem for gravity, is a law of physics which is essentially equivalent to Newton's law of universal gravitation...

is mathematically equivalent to Newton's law of universal gravitation, but is stated directly as vector calculus properties of the gravitational field.

## In general relativity

In general relativityGeneral relativity

General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

the gravitational field is determined as the solution of Einstein's field equations

Einstein field equations

The Einstein field equations or Einstein's equations are a set of ten equations in Albert Einstein's general theory of relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy...

. These equations are dependent on the distribution of matter and energy in a region of space, unlike Newtonian gravity, which is dependent only on the distribution of matter. The fields themselves in general relativity represent the curvature of spacetime. General relativity states that being in a region of curved space is equivalent to accelerating

Acceleration

In physics, acceleration is the rate of change of velocity with time. In one dimension, acceleration is the rate at which something speeds up or slows down. However, since velocity is a vector, acceleration describes the rate of change of both the magnitude and the direction of velocity. ...

up the gradient

Gradient

In vector calculus, the gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change....

of the field. By Newton's second law, this will cause an object to experience a fictitious force

Fictitious force

A fictitious force, also called a pseudo force, d'Alembert force or inertial force, is an apparent force that acts on all masses in a non-inertial frame of reference, such as a rotating reference frame....

if it is held still with respect to the field. This is why a person will feel himself pulled down by the force of gravity while standing still on the Earth's surface. In general the gravitational fields predicted by general relativity differ in their effects only slightly from those predicted by classical mechanics, but there are a number of easily verifiable differences, one of the most well known being the bending of light in such fields.

## Generally accepted fundamental hypothesis

Dr. Jesse L. GreensteinJesse L. Greenstein

Jesse Leonard Greenstein was an American astronomer. His parents were Maurice G. and Leah Feingold....

of the California Institute of Technology

California Institute of Technology

The California Institute of Technology is a private research university located in Pasadena, California, United States. Caltech has six academic divisions with strong emphases on science and engineering...

wrote:

The detection of gravitational waves bears directly on the question of whether there is any such thing as a "gravitational field," which can act as an independent entity. … this fundamental field hypothesis has been generally accepted without observational support. Such credulity among scientists occurs only in relation to the deepest and most fundamental hypotheses for which they lack the facility to think differently in a comparably detailed and consistent way. In the nineteenth century a similar attitude led to a general acceptance of the ether ….

Most scientists believe that the gravitational field and its gravitational waves are the physical interpretations of Einstein

Albert Einstein

Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

's equations of general relativity

General relativity

General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

.

## See also

- Classical mechanicsClassical mechanicsIn physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...
- GravitationGravitationGravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...
- Gravitational potential
- Gravitational induction
- Newton's law of universal gravitationNewton's law of universal gravitationNewton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them...
- Newton's laws of motionNewton's laws of motionNewton's laws of motion are three physical laws that form the basis for classical mechanics. They describe the relationship between the forces acting on a body and its motion due to those forces...
- Potential energyPotential energyIn physics, potential energy is the energy stored in a body or in a system due to its position in a force field or due to its configuration. The SI unit of measure for energy and work is the Joule...
- Speed of gravitySpeed of gravityIn the context of classical theories of gravitation, the speed of gravity is the speed at which changes in a gravitational field propagate. This is the speed at which a change in the distribution of energy and momentum of matter results in subsequent alteration, at a distance, of the gravitational...
- Tests of general relativityTests of general relativityAt its introduction in 1915, the general theory of relativity did not have a solid empirical foundation. It was known that it correctly accounted for the "anomalous" precession of the perihelion of Mercury and on philosophical grounds it was considered satisfying that it was able to unify Newton's...