Gravitational field

In physics, a gravitational field is a model used to explain the influence that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational phenomena, and is measured in newtons per kilogram (N/kg). 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, and since the 19th century explanations for gravity have usually been taught in terms of a field model, rather than a point attraction. In physics, a gravitational field is a model used to explain the influence that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational phenomena, and is measured in newtons per kilogram (N/kg). 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, and since the 19th century explanations for gravity have usually been taught in terms of a field model, rather than a point attraction. In a field model, rather than two particles attracting each other, the particles distort spacetime via their mass, and this distortion is what is perceived and measured as a 'force'. In such a model one states that matter moves in certain ways in response to the curvature of spacetime, and that there is either no gravitational force, or that gravity is a fictitious force. In classical mechanics, a gravitational field is a physical quantity. 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. The magnitude of the field at every point is calculated applying the universal law, and represents the force per unit mass on any object at that point in space. 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. The gravitational field equation is where F is the gravitational force, m is the mass of the test particle, R is the position of the test particle (or for the second Newton's 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), R̂ is a unit vector in the direction of R, t is time, G is the gravitational constant, and ∇ is the del operator. This includes Newton's law of universal gravitation, and the relation between gravitational potential and field acceleration. Note that d2R/dt2 and F/m are both equal to the gravitational acceleration g (equivalent to the inertial acceleration, so same mathematical form, but also defined as gravitational force per unit mass). The negative signs are inserted since the force acts antiparallel to the displacement. The equivalent field equation in terms of mass density ρ of the attracting mass is: which contains Gauss's law for gravity, and Poisson's equation for gravity. Newton's and Gauss's law are mathematically equivalent, and are related by the divergence theorem. Poisson's equation is obtained by taking the divergence of both sides of the previous equation. These classical equations are differential equations of motion for a test particle in the presence of a gravitational field, i.e. setting up and solving these equations allows the motion of a test mass to be determined and described. The field around multiple particles is simply the vector sum of the fields around each individual particle. An object in such a field will experience a force that equals the vector sum of the forces it would experience in these individual fields. This is mathematically i.e. the gravitational field on mass mj is the sum of all gravitational fields due to all other masses mi, except the mass mj itself. The unit vector R̂ij is in the direction of Ri − Rj. 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.