Test particle

From Wikipedia, the free encyclopedia

This article or section is in need of attention from an expert on the subject.
Please help recruit one or improve this article yourself. See the talk page for details.
Please consider using {{Expert-subject}} to associate this request with a WikiProject

In physical theories, a test particle is an idealised model of a small object some of whose physical properties (usually mass and size) are assumed to be negligible. The concept of a test particle simplifies some problems, and often provides a good approximation for physical phenomena in a specified domain of applicability.

1 Classical Gravity
2 Test particles in general relativity
3 See also
4 References

[edit] Classical Gravity

The easiest case for the application of a test particle arises in Newtonian gravity. The general expression for the gravitational force between two masses $m 1$ and $m 2$ is:

$F(r) = -G \frac{m_1 m_2}{(r_1-r_2)^2}$

where $r 1$ and $r 2$ 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:

$R = \frac{m_1r_1+m_2r_2}{m_1+m_2}$ ^[1]

In the case where one of the masses is much larger than the other ( $m 1 > > m 2$ ), 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

$g(r) = \frac{Gm_1}{r^2}$

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

$a(r) = \frac{F(r)}{m_2} = -g(r)$

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.

[edit] Test particles in general relativity

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 graviational 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]

[edit] See also

Papapetrou-Dixon equations
Magnetogravitic tensor and the Bel decomposition of the Riemann tensor

[edit] References

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