[lightarrow (OP)]

Given a specific volum and a specific, uniform density (we could take them as unit), which shape should have a planet, so that the gravitational field in a point O (we can take it as the origin of the axis) of its surface is maximum?

Could this be the shape?
In the image I have drawn a polar plot (red, inner curve).

[RD]

Your diagram (red) is close to half nephroid ...

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http://en.wikipedia.org/wiki/Nephroid                                http://mathworld.wolfram.com/Nephroid.html

[lightarrow (OP)]

Your diagram (red) is close to half nephroid ...

Yes, it's very similar, I didn't know that curve, thank you RD.

The curve I drew is:

ρ(θ) = Sqrt(|cosθ|);  with ρ = x² + y²

while the Nefroid you drew is:

ρ(θ) = Sqrt(10 + 6|cosθ|).