What Is a Gravitational Field, and How Can Its Strength Be Measured?

Model in physics

"Gravity field" redirects hither. For Earth'south gravity field, see Gravity of Earth.

In physics, a gravitational field is a model used to explicate the influences that a massive body extends into the space around itself, producing a force on some other massive body.^[1] Thus, a gravitational field is used to explain gravitational phenomena, and is measured in newtons per kilogram (N/kg). In its original concept, gravity was a force between point masses. Post-obit Isaac Newton, Pierre-Simon Laplace attempted to model gravity as some kind of radiation field or fluid, and since the 19th century, explanations for gravity have usually been taught in terms of a field model, rather than a betoken attraction.

In a field model, rather than ii particles attracting each other, the particles distort spacetime via their mass, and this baloney is what is perceived and measured as a "force".^{[ commendation needed ]} In such a model i states that matter moves in certain ways in response to the curvature of spacetime,^[2] and that there is either no gravitational force,^[3] or that gravity is a fictitious force.^[4]

Gravity is distinguished from other forces past its obedience to the equivalence principle.

Classical mechanics [edit]

In classical mechanics, a gravitational field is a physical quantity.^[5] A gravitational field tin can be divers using Newton's constabulary of universal gravitation. Determined in this manner, the gravitational field g around a unmarried particle of mass M 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 by applying the universal police force, and represents the force per unit of measurement mass on whatsoever object at that point in space. Because the forcefulness field is conservative, in that location is a scalar potential free energy per unit mass, Φ, at each indicate in infinite associated with the force fields; this is called gravitational potential.^{[half dozen]} The gravitational field equation is^[seven]

${\displaystyle \mathbf {g} ={\frac {\mathbf {F} }{m}}={\frac {\mathrm {d} ^{2}\mathbf {R} }{\mathrm {d} t^{2}}}=-GM{\frac {\mathbf {\lid {R}} }{\left|\mathbf {R} \correct|^{two}}}=-\nabla \Phi }$

where F is the gravitational force, m is the mass of the test particle, R is the position of the test particle (or for Newton's second law of motion which is a time dependent function, a set of positions of test particles each occupying a detail bespeak in space for the starting time of testing), R̂ is a unit vector in the radial direction of R , t is time, Thou is the gravitational constant, and ∇ is the del operator.

This includes Newton's constabulary of universal gravitation, and the relation between gravitational potential and field acceleration. Annotation that d² R / dt ^two and F / m are both equal to the gravitational acceleration g (equivalent to the inertial acceleration, and so same mathematical form, but also defined as gravitational force per unit mass^[eight]). The negative signs are inserted since the forcefulness acts antiparallel to the displacement. The equivalent field equation in terms of mass density ρ of the attracting mass is:

${\displaystyle \nabla \cdot \mathbf {grand} =-\nabla ^{2}\Phi =-4\pi 1000\rho }$

which contains Gauss's law for gravity, and Poisson's equation for gravity. Newton's law implies Gauss'southward law, but not vice-versa; run into Relation between Gauss'south and Newton's laws.

These classical equations are differential equations of motion for a test particle in the presence of a gravitational field, i.e. setting upwardly and solving these equations allows the motion of a examination mass to exist determined and described.

The field around multiple particles is just 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 private fields. This is mathematically^[nine]

${\displaystyle \mathbf {1000} _{j}^{\text{(net)}}=\sum _{i\neq j}\mathbf {yard} _{i}={\frac {1}{m_{j}}}\sum _{i\neq j}\mathbf {F} _{i}=-K\sum _{i\neq j}m_{i}{\frac {\mathbf {\hat {R}} _{ij}}{\left|\mathbf {R} _{i}-\mathbf {R} _{j}\right|^{ii}}}=-\sum _{i\neq j}\nabla \Phi _{i}}$

i.e. the gravitational field on mass m_j is the sum of all gravitational fields due to all other masses yard_i , except the mass chiliad_j itself. The unit vector R̂ _ij is in the management of R _i − R _j .

General relativity [edit]

In full general relativity, the Christoffel symbols play the role of the gravitational force field and the metric tensor plays the role of the gravitational potential.

In general relativity, the gravitational field is adamant by solving the Einstein field equations^[10]

${\displaystyle \mathbf {G} =\kappa \mathbf {T} ,}$

where T is the stress–energy tensor, Thou is the Einstein tensor, and κ is the Einstein gravitational constant. The latter is divers as κ = eightπG/c ⁴ , where Thou is the Newtonian constant of gravitation and c is the speed of lite.

These equations are dependent on the distribution of matter and energy in a region of space, unlike Newtonian gravity, which is dependent just 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 infinite is equivalent to accelerating up the gradient of the field. Past Newton's second law, this will cause an object to experience a fictitious strength if it is held still with respect to the field. This is why a person will experience himself pulled down by the force of gravity while standing all the same on the Earth'southward surface. In general the gravitational fields predicted by general relativity differ in their effects but slightly from those predicted by classical mechanics, but there are a number of easily verifiable differences, one of the well-nigh well known being the deflection of calorie-free in such fields.

See also [edit]

• Classical mechanics
• Gravitation
• Gravitational potential
• Gravitational wave
• Newton'south police force of universal gravitation
• Newton's laws of motility
• Potential free energy
• Speed of gravity
• Tests of general relativity
• Defining equation (physics)
• Entropic gravity

Notes [edit]

1. ^ Feynman, Richard (1970). The Feynman Lectures on Physics. Vol. I. Addison Wesley Longman. ISBN978-0-201-02115-8.
2. ^ Geroch, Robert (1981). General Relativity from A to B. Academy of Chicago Press. p. 181. ISBN978-0-226-28864-2.
3. ^ Grøn, Øyvind; Hervik, Sigbjørn (2007). Einstein's General Theory of Relativity: with Modern Applications in Cosmology. Springer Japan. p. 256. ISBN978-0-387-69199-2.
4. ^ Foster, J.; Nightingale, J. D. (2006). A Short Course in General Relativity (three ed.). Springer Science & Business. p. 55. ISBN978-0-387-26078-5.
5. ^ Feynman, Richard (1970). The Feynman Lectures on Physics. Vol. Two. Addison Wesley Longman. ISBN978-0-201-02115-8. A "field" is any physical quantity which takes on different values at different points in space.
6. ^ Forshaw, J. R.; Smith, A. M. (2009). Dynamics and Relativity. Wiley. ISBN978-0-470-01460-8. ^{[ page needed ]}
7. ^ Lerner, R. G.; Trigg, G. Fifty., eds. (1991). Encyclopaedia of Physics (second ed.). Wiley-VCH. ISBN978-0-89573-752-6. ^{[ page needed ]}
8. ^ Whelan, P. M.; Hodgeson, 1000. J. (1978). Essential Principles of Physics (2nd ed.). John Murray. ISBN978-0-7195-3382-2. ^{[ page needed ]}
9. ^ Kibble, T. W. B. (1973). Classical Mechanics. European Physics Series (second ed.). UK: McGraw Hill. ISBN978-0-07-084018-8. ^{[ folio needed ]}
10. ^ Wheeler, J. A.; Misner, C.; Thorne, One thousand. S. (1973). Gravitation. W. H. Freeman & Co. p. 404. ISBN978-0-7167-0344-0.

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Source: https://en.wikipedia.org/wiki/Gravitational_field

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