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":
... 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) ...
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—Samuel Richardson (16891761)