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In physical theories, a test particle is an idealised 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 set to some convenient unit value. The concept of a test particle simplifies some problems, and often provides a good approximation for physical phenomena in a specified domain of applicability.

In computer simulations, a test particle is a particle whose movement according to potentials and the particles respective charge is traced (also called traced particles) but which does not otherwise interact with the system as other types of simulation particles usually would. The test particle method can be almost synonymous with a Monte Carlo method, though as a term it does not necessary involve any randomness, for example with respect to its initial location or velocity.

Contents 1 Classical Gravity 2 Test particles in general relativity 3 Test particles in plasma physics or electrodynamics 4 See also 5 References

The easiest case for the application of a test particle arises in Newtonian gravity. The general expression for the gravitational force between two masses m₁ and m₂ is:

where r₁ and r₂ represent the position of each particle in space. In the general solution for this equation, both masses rotate around their center of mass, in this specific case:

^[1]

In the case where one of the masses is much larger than the other (m₁ > > m₂), one can assume than the smaller mass moves as a test particle in a gravitational field generated by the larger mass, which remains immobile. By defining the gravitational field as

with r as the distance between the two objects, the equation for the motion of the smaller mass reduces to

and thus only contains one variable, for which the solution can be calculated more easily. 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.

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 the Einstein field equation, 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).

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.^[2]

In simulations with electromagnetic fields the most important characteristics of a test particle is its electric charge and its mass. In such simulations the particles are moved with the Lorentz force

,

where q is the particle's electric charge, v its velocity and E and B the electric and magnetic fields, respectively.

• Papapetrou-Dixon equations
• Magnetogravitic tensor and the Bel decomposition of the Riemann tensor
• test charge
• point mass

1. ^ Herbert Goldstein (1980). Classical Mechanics, 2nd Ed.. Addison-Wesley, p.5. 
2. ^ Poisson, Eric. The Motion of Point Particles in Curved Spacetime. Living Reviews in Relativity. Retrieved on March 26, 2004.