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Imagine you are an space entrepreneur with infinite resources who has an incompressible substance of constant density and you want to make a body with the same gravity as earth at a point with the least material. What shape do you make it?

I was posed this question and my intuition says an oblong shape but I'm unsure if/how to back it up, this post seems relevant but it isn't rigorous.

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  • $\begingroup$ Welcome belkarx. I think you need to be more specific and describe what exactly you mean when you write "the same gravity as earth".. in the current accepted model of gravity which is GR the shape of the gravitating object also determines the gravitational field (or more precisely, the spacetime curvature) in its vicinity. Since the earth is very nearly a sphere (it's in fact an oblate spheroid) for example, the gravitational field is almost completely symmetric with respect to angular movement around it, so if you want to keep that feature too, you'll also need something similar. $\endgroup$
    – Amit
    Commented Jun 24, 2023 at 18:26
  • $\begingroup$ @Amit: The OP says "the same gravity as Earth at a point", which I would interpret as "create a shape for which the gravitational acceleration has a magnitude of 9.8 m/s^2 at at least one point on its surface." $\endgroup$
    – Michael Seifert
    Commented Jun 24, 2023 at 18:44
  • $\begingroup$ @MichaelSeifert It's a very good guess and there's a high probability you're correct, but I would still prefer that be made as explicit as you made it ;) $\endgroup$
    – Amit
    Commented Jun 24, 2023 at 18:46
  • $\begingroup$ Hey @Amit, I do mean "at at least one point" :) $\endgroup$
    – belkarx
    Commented Jun 24, 2023 at 19:01
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    $\begingroup$ @belkarx You may be interested to take a look at this question (it isn't quite the same, but closely related): Maximal Gravity $\endgroup$
    – Amit
    Commented Jun 24, 2023 at 20:12

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