Consider a piece of a deformable material with mass m and constant density [itex] \rho [/itex]. To what shape should we deform it so that its gravitational field is maximum in a given point?
This looks a bit like homework, so I'll start with a hint: for the best shape, every point on the surface will contribute the same to the gravitational field strength (I guess field strength is meant, not potential).
This isn't a homework, because I have no idea what to do about it!!! I should say that just naming a shape isn't enough, the equation of the shape should be derived somehow!