How Can We Deform a Material to Maximize Its Gravitational Field at a Point?

[ShayanJ]

Consider a piece of a deformable material with mass m and constant density $\rho$. To what shape should we deform it so that its gravitational field is maximum in a given point?

 

[mfb]

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).

 

[ShayanJ]

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!

 

[A.T.]

https://www.physicsforums.com/showthread.php?t=543287