Gravitational field
In
In its original concept,
In general relativity, 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".[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.
Classical mechanics
In classical mechanics, a gravitational field is a physical quantity.
This includes Newton's law of universal gravitation, and the relation between gravitational potential and field acceleration. 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[8]). 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:
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
General relativity
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.
In general relativity, the gravitational field is determined by solving the Einstein field equations[10]
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.
Embedding diagram
Embedding diagrams are three dimensional graphs commonly used to educationally illustrate gravitational potential by drawing gravitational potential fields as a gravitational topography, depicting the potentials as so-called gravitational wells, sphere of influence.
See also
References
- ISBN 978-0-201-02115-8.
- ISBN 978-0-226-28864-2.
- ISBN 978-0-387-69199-2.
- ISBN 978-0-387-26078-5.
- ISBN 978-0-201-02115-8.
A 'field' is any physical quantity which takes on different values at different points in space.
- ISBN 978-0-470-01460-8.[page needed]
- ISBN 978-0-89573-752-6. p. 451
- ISBN 978-0-7195-3382-2.[page needed]
- ISBN 978-0-07-084018-8.[page needed]
- ISBN 978-0-7167-0344-0.