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

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