Naked Science Forum

Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: lightarrow on 23/12/2009 18:03:51

Title: Which is the shape of a planet with the maximum gravity at one point?
Post by: lightarrow on 23/12/2009 18:03:51
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).
Title: Which is the shape of a planet with the maximum gravity at one point?
Post by: RD on 23/12/2009 18:37:36
Your diagram (red) is close to half nephroid ...

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http://en.wikipedia.org/wiki/Nephroid                                http://mathworld.wolfram.com/Nephroid.html
Title: Which is the shape of a planet with the maximum gravity at one point?
Post by: lightarrow on 23/12/2009 19:33:34
Quote from: RD on 23/12/2009 18:37:36
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|).