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Which is the shape of a planet with the maximum gravity at one point?
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Which is the shape of a planet with the maximum gravity at one point?
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lightarrow
Neilep Level Member
4586
Which is the shape of a planet with the maximum gravity at one point?
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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).
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Last Edit: 23/12/2009 18:10:06 by lightarrow
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RD
Neilep Level Member
8185
Which is the shape of a planet with the maximum gravity at one point?
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Reply #1 on:
23/12/2009 18:37:36 »
Your diagram (red) is close to half nephroid ...
[attachment=10922][attachment=10926]
http://en.wikipedia.org/wiki/Nephroid
http://mathworld.wolfram.com/Nephroid.html
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Last Edit: 23/12/2009 18:45:34 by RD
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lightarrow
Neilep Level Member
4586
Which is the shape of a planet with the maximum gravity at one point?
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Reply #2 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 = x
^{2}
+ y
^{2}
while the Nefroid you drew is:
ρ(θ) = Sqrt(10 + 6|cosθ|).
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