Gravitational field
It has dimension of acceleration (L/T2) and it is measured in units of newtons per kilogram (N/kg) or, equivalently, in meters per second squared (m/s2).
In its original concept, gravity was a force between point masses.
Following Isaac Newton, Pierre-Simon Laplace attempted to model gravity as some kind of radiation field or fluid,[citation needed] and since the 19th century, explanations for gravity in classical mechanics have usually been taught in terms of a field model, rather than a point attraction.
It results from the spatial gradient of the gravitational potential field.
[citation needed] In such a model one states that matter moves in certain ways in response to the curvature of spacetime,[2] and that there is either no gravitational force,[3] or that gravity is a fictitious force.
[4] Gravity is distinguished from other forces by its obedience to the equivalence principle.
In classical mechanics, a gravitational field is a physical quantity.
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.
Because the force field is conservative, there is a scalar potential energy per unit mass, Φ, at each point in space associated with the force fields; this is called gravitational potential.
where F is the gravitational force, m is the mass of the test particle, R is the radial vector of the test particle relative to the mass (or for Newton's second law of motion which is a time dependent function, a set of positions of test particles each occupying a particular point in space for the start of testing), t is time, G is the gravitational constant, and ∇ is the del operator.
The negative signs are inserted since the force acts antiparallel to the displacement.
In general relativity, the Christoffel symbols play the role of the gravitational force field and the metric tensor plays the role of the gravitational potential.
The latter is defined as κ = 8πG/c4, where G is the Newtonian constant of gravitation and c is the speed of light.
These equations are dependent on the distribution of matter, stress and momentum in a region of space, unlike Newtonian gravity, which is depends on only 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 deflection of light in such fields.
