Which is the shape of a planet with the maximum gravity at one point?

  • 2 Replies
  • 2445 Views

0 Members and 1 Guest are viewing this topic.

*

Offline lightarrow

  • Neilep Level Member
  • ******
  • 4586
    • View Profile
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).
« Last Edit: 23/12/2009 18:10:06 by lightarrow »

*

Offline RD

  • Neilep Level Member
  • ******
  • 8169
    • View Profile
Your diagram (red) is close to half nephroid ...

[attachment=10922][attachment=10926]

http://en.wikipedia.org/wiki/Nephroid                                http://mathworld.wolfram.com/Nephroid.html
« Last Edit: 23/12/2009 18:45:34 by RD »

*

Offline lightarrow

  • Neilep Level Member
  • ******
  • 4586
    • View Profile
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|).