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 and is:
where and 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:
In the case where one of the masses is much larger than the other, 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. By defining the gravitational field as
with 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.
Read more about this topic: Test Particle
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