Test particle

test chargetest particlestest masscharged test particle theoretical point particleinfinitesimal masstest body
In physical theories, a test particle, or test charge, is an idealized model of an object whose physical properties (usually mass, charge, or size) are assumed to be negligible except for the property being studied, which is considered to be insufficient to alter the behavior of the rest of the system.wikipedia
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Classical field theory

field equationsclassical field theoriesfield theory
:.In the case where one of the masses is much larger than the other (m_1\gg m_2), one can assume that the smaller mass moves as a test particle in a gravitational field generated by the larger mass, which does not accelerate.
The gravitational field of M at a point r in space is found by determining the force F that M exerts on a small test mass m located at r, and then dividing by m:

Electric field

electricelectrostatic fieldelectrical field
In simulations with electric fields the most important characteristics of a test particle is its electric charge and its mass.
The electric field is defined mathematically as a vector field that associates to each point in space the (electrostatic or Coulomb) force per unit of charge exerted on an infinitesimal positive test charge at rest at that point.

General relativity

general theory of relativitygeneral relativity theoryrelativity
In metric theories of gravitation, particularly general relativity, a test particle is an idealized model of a small object whose mass is so small that it does not appreciably disturb the ambient gravitational field.
According to Newton's law of gravity, and independently verified by experiments such as that of Eötvös and its successors (see Eötvös experiment), there is a universality of free fall (also known as the weak equivalence principle, or the universal equality of inertial and passive-gravitational mass): the trajectory of a test body in free fall depends only on its position and initial speed, but not on any of its material properties.

Gravitational field

gravity fieldgravitationalgravitational fields
In metric theories of gravitation, particularly general relativity, a test particle is an idealized model of a small object whose mass is so small that it does not appreciably disturb the ambient gravitational field.
is the mass of the test particle,

Coulomb's law

Coulomb forceelectrostatic forceCoulomb interaction
Multiplying this field by a test charge gives an electric force (Coulomb's law) exerted by the field on a test charge.
An electric field is a vector field that associates to each point in space the Coulomb force experienced by a test charge.

Electrovacuum solution

electrovacuum
In the case of test particles in a vacuum solution or electrovacuum solution, this turns out to imply that in addition to the tidal acceleration experienced by small clouds of test particles (spinning or not), spinning test particles may experience additional accelerations due to spin-spin forces.
In this case, the electromagnetic field is often called a test field, in analogy with the term test particle (denoting a small object whose mass is too small to contribute appreciably to the ambient gravitational field).

Theoretical physics

theoretical physicisttheoreticaltheoretical physicists
In physical theories, a test particle, or test charge, is an idealized model of an object whose physical properties (usually mass, charge, or size) are assumed to be negligible except for the property being studied, which is considered to be insufficient to alter the behavior of the rest of the system.

Mass

inertial massgravitational massweight
In simulations with electric fields the most important characteristics of a test particle is its electric charge and its mass. In physical theories, a test particle, or test charge, is an idealized model of an object whose physical properties (usually mass, charge, or size) are assumed to be negligible except for the property being studied, which is considered to be insufficient to alter the behavior of the rest of the system.

Charge (physics)

chargechargescharged
In physical theories, a test particle, or test charge, is an idealized model of an object whose physical properties (usually mass, charge, or size) are assumed to be negligible except for the property being studied, which is considered to be insufficient to alter the behavior of the rest of the system.

Volume

volumetriccapacityOrders of magnitude (volume)
In physical theories, a test particle, or test charge, is an idealized model of an object whose physical properties (usually mass, charge, or size) are assumed to be negligible except for the property being studied, which is considered to be insufficient to alter the behavior of the rest of the system.

Computer simulation

computer modelsimulationcomputer modeling
In addition to its uses in the simplification of the dynamics of a system in particular limits, it is also used as a diagnostic in computer simulations of physical processes.

Newton's law of universal gravitation

law of universal gravitationuniversal gravitationNewtonian gravity
The easiest case for the application of a test particle arises in Newtonian gravity.

Center of mass

center of gravitycentre of gravitycentre of mass
In the general solution for this equation, both masses rotate around their center of mass R, in this specific case:

Newton's laws of motion

Newton's second lawNewton's third lawNewton's second law of motion
with r as the distance between the massive object and the test particle, and \hat{r} is the unit vector in the direction going from the massive object to the test mass. Newton's second law of motion of the smaller mass reduces to

Satellite

satellitesartificial satelliteartificial satellites
This approach gives very good approximations for many practical problems, e.g. the orbits of satellites, whose mass is relatively small compared to that of the Earth.

Earth

Earth's surfaceterrestrialworld
This approach gives very good approximations for many practical problems, e.g. the orbits of satellites, whose mass is relatively small compared to that of the Earth.

Electric charge

chargeelectrical chargecharged
In simulations with electric fields the most important characteristics of a test particle is its electric charge and its mass.

Coulomb constant

Coulomb's constantCoulomb force constantelectrostatic constant
where k is Coulomb constant.

Einstein field equations

Einstein field equationEinstein's field equationsEinstein's field equation
According to the Einstein field equations, the gravitational field is locally coupled not only to the distribution of non-gravitational mass-energy, but also to the distribution of momentum and stress (e.g. pressure, viscous stresses in a perfect fluid).

Mass–energy equivalence

mass-energy equivalencemass-energyE=mc²
According to the Einstein field equations, the gravitational field is locally coupled not only to the distribution of non-gravitational mass-energy, but also to the distribution of momentum and stress (e.g. pressure, viscous stresses in a perfect fluid).

Momentum

conservation of momentumlinear momentummomenta
According to the Einstein field equations, the gravitational field is locally coupled not only to the distribution of non-gravitational mass-energy, but also to the distribution of momentum and stress (e.g. pressure, viscous stresses in a perfect fluid).

Stress (mechanics)

stressstressestensile stress
According to the Einstein field equations, the gravitational field is locally coupled not only to the distribution of non-gravitational mass-energy, but also to the distribution of momentum and stress (e.g. pressure, viscous stresses in a perfect fluid).

Fluid solution

perfect fluidfluiddust
According to the Einstein field equations, the gravitational field is locally coupled not only to the distribution of non-gravitational mass-energy, but also to the distribution of momentum and stress (e.g. pressure, viscous stresses in a perfect fluid).

Vacuum solution (general relativity)

vacuum solutionvacuum solutionsVacuum
In the case of test particles in a vacuum solution or electrovacuum solution, this turns out to imply that in addition to the tidal acceleration experienced by small clouds of test particles (spinning or not), spinning test particles may experience additional accelerations due to spin-spin forces.