I try to plot a 2D gravity field or something similar in the form like $r/|r|^3$ with the standart builtin VectorPlot function:
VectorPlot[{-x/(x^2 + y^2)^(3/2), -y/(x^2 + y^2)^(3/2)}, {x, -5, 5}, {y, -5, 5}] It should look like: 
(source: euclideanspace.com)
I get something strange when I run my command:
Any suggestions?
Thanks Cx
You need VectorPoints to be adjusted, also, gravity explodes for point mass so it is good to adjust VectorScale and cut off the point mass with RegionFunction:
VectorPlot[-#/Norm[#]^3 &[{x, y}], {x, -1, 1}, {y, -1, 1}, VectorPoints -> 20, VectorScale -> .3, RegionFunction -> (Norm[{#, #2}] > .1 &), ImageSize -> 500, PlotRange -> 1] 
In order to reproduce your plot you need to play with VectorScale 3rd element:
VectorPlot[-#/Norm[#]^3 &[{x, y}], {x, -1, 2}, {y, -1, 1}, VectorPoints -> 30, VectorScale -> {.1, Automatic, (#5)^(1/3) &}, RegionFunction -> (Norm[{#, #2}] > .1 &), ImageSize -> 500, PlotRange -> {{-1, 2}, {-1, 1}}, VectorStyle -> "Pointer", GridLines -> ({#, #} &[Join[Range[-1, 2, .1], {{0, Directive[Thick, Blue]}}]]), Epilog -> {EdgeForm[{Thick, Blue}], Red, Disk[{0, 0}, .05]}, AspectRatio -> Automatic] 
VectorDensityPlot to the same function argument I get still strange results (no decay). $\endgroup$ ColorFunction the reason is the same. This field is exploding in the center and rescaled values are not different enough on the most of the area. $\endgroup$ RegionFunction -> (Norm[{#, #2}] > .1 &) works? I know # means slot, but what is it in this case? Replacing them with x and y doesn't work. $\endgroup$ RegionFunction should be a function that will be used like regF[ x, y ] internally, where x, y are coordinates of points. You can write Function[{x,y}, Norm[{x,y}... or you can use slots instead of named arguments: ` Norm[{#, #2}...&`. $\endgroup$