Poisson's Equation - Newtonian Gravity

Newtonian Gravity

In the case of a gravitational field g due to an attracting massive object, of density ρ, Gauss' law for gravity in differential form can be used to obtain the corresponding Poisson equation for gravity. Gauss' law for gravity is:


and since the gravitational field is conservative, it can be expressed in terms of a scalar potential Φ:


substituting into Gauss' law

obtains Poisson's equation for gravity:

Read more about this topic:  Poisson's Equation

Other articles related to "newtonian gravity, gravity, newtonian":

Scalar Theories Of Gravitation - Newtonian Gravity
... The prototypical scalar theory of gravitation is Newtonian gravitation ... In this theory, the gravitational interaction is completely described by the potential, which is required to satisfy the Poisson equation (with the mass density acting as the source of the field) ...
Lagrangian - Selected Fields - Newtonian Gravity
... The Lagrangian (density) is in J·m−3 ... The interaction term mζ is replaced by a term involving a continuous mass density μ in kg·m−3 ...
Introduction To General Relativity - Experimental Tests
... Newton's law of gravity was accepted because it accounted for the motion of planets and moons in the solar system with considerable accuracy ... and Einstein himself devised three tests now known as the classical tests of the theory Newtonian gravity predicts that the orbit which a single planet ... In the diagram on the right, the ellipse predicted by Newtonian gravity is shown in red, and part of the orbit predicted by Einstein in blue ...
Theories Of Gravitation - History of Gravitational Theory - General Relativity
... Geodetic effect Event horizon · Singularity Black hole Equations Linearized gravity Post-Newtonian formalism Einstein field equations Geodesic equation Friedmann equations ADM formalism BSSN formalism ... In Newtonian physics, however, no such acceleration can occur unless at least one of the objects is being operated on by a force ... solution are practically identical to those predicted by Newton's theory of gravity ...
Jürgen Ehlers - Research - Frame Theory and Newtonian Gravity
... A basic derivation of the Newtonian limit of general relativity is as old as the theory itself ... and others showed more concretely how a geometrical generalization of Newton's theory of gravity known as Newton-Cartan theory could be understood as a (degenerate) limit of general relativity ... This allowed physicists to explore what the Newtonian limit meant in specific physical situations ...

Famous quotes containing the word gravity:

    Here I sit down to form characters. One I intend to be all goodness; All goodness he is. Another I intend to be all gravity; All gravity he is. Another Lady Gish; All Lady Gish she is. I am all the while absorbed in the character. It is not fair to say—I, identically I, am anywhere, while I keep within the character.
    Samuel Richardson (1689–1761)