Gravitational field
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A gravitational field is the force field that describes the acceleration of gravity in a region of space. If one knows the gravitational field in a region of space, one can calculate the the force of gravity on any object in that space. The meaning and form of the field differs whether one is operating in classical mechanics or general relativity.
[edit] Gravitational Fields in Classical Mechanics
In classical mechanics, the field is not an actual entity, but merely a model used to describe the effects of gravity. The field can be determined using Newton's universal law of gravitation. Determined in this way, the gravitational field around a single particle is a vector field consisting at every point of a vector pointing directly towards the particle. The magnitude of the field at every point is calculated with the universal law, and represents the force per unit mass of any object at that point in space. The field around multiple particles is merely the vector sum of the fields around each individual particle. An object in such a field will experience a force that equals vector sum of the forces it would feel in these individual fields.
[edit] Gravitational Fields in General Relativity
In general relativity the gravitational field is determined as the solution of Einstein's field equations. These equations are dependent on the distribution of matter and energy in a region of space, unlike Newtonian gravity, which is dependent only on the distribution of matter. The fields themselves in general relativity represent the curvature of spacetime. General relativity states that being in a region of curved space is equivalent to accelerating up the gradient of the field. By Newton's second law, this will cause an object to experience a fictitious force if it is held still with respect to the field. This is why a person will feel himself pulled down by the force of gravity while standing still on the Earth's surface. In general the gravitational fields predicted by general relativity differ in their effects only slightly from those predicted by classical mechanics, but there are a number of easily verifiable differences, one of the most well known being the bending of light in such fields.
