On this page we try to show an intuitive understanding of what Divergence is for a Vector Field.
We use the idea of water, fluid, or a gas flowing thru a volume of space.
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Calculate the Divergence of a Gravitational field between two point masses: M0 and m1
Below is the Gravitational Field as Created by the Desmos On-Line Graph Application. 
Shown in the X-Y Plane. Not all of the Desmos calculations are shown. 
Compute the Divergence of the Gravitational Field.  
Notice, that it is critical that three dimensions added together result in a zero numerator.