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In classical mechanics, a gravitational field is a physical quantity. [5] A gravitational field can be defined using Newton's law of universal gravitation.Determined in this way, the gravitational field g around a single particle of mass M is a vector field consisting at every point of a vector pointing directly towards the particle.
This section follows the analysis of Fritz Rohrlich (1965), [6] who shows that a charged particle and a neutral particle fall equally fast in a gravitational field. Likewise, a charged particle at rest in a gravitational field does not radiate in its rest frame, but it does so in the frame of a free-falling observer.
In theories of quantum gravity, the graviton is the hypothetical elementary particle that mediates the force of gravitational interaction. There is no complete quantum field theory of gravitons due to an outstanding mathematical problem with renormalization in general relativity.
This formulation is dependent on the objects causing the field. The field has units of acceleration; in SI, this is m/s 2. Gravitational fields are also conservative; that is, the work done by gravity from one position to another is path-independent. This has the consequence that there exists a gravitational potential field V(r) such that
The magnitude of the gravitational field that would pull a particle at point in the x-direction is the gravitational field multiplied by where is the angle adjacent to the x-axis. In this case, cos ( θ ) = p p 2 + R 2 {\displaystyle \cos(\theta )={\frac {p}{\sqrt {p^{2}+R^{2}}}}} .
The gravitational field g (also called gravitational acceleration) is a vector field – a vector at each point of space (and time).It is defined so that the gravitational force experienced by a particle is equal to the mass of the particle multiplied by the gravitational field at that point.
In Newtonian gravity, a particle of mass M creates a gravitational field = ^, where the radial unit vector ^ points away from the particle. The gravitational force experienced by a particle of light mass m , close to the surface of Earth is given by F = m g {\displaystyle \mathbf {F} =m\mathbf {g} } , where g is Earth's gravity .
The method is iterative; an initial solution for particle motions is used to calculate the gravitational fields; from these derived fields, new particle motions can be calculated, from which even more accurate estimates of the fields can be computed, and so on.