Timeline for answer to Exact analytical solution for the surface gravity of an oblate spheroid by Ghoster
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| when toggle format | what | by | license | comment | |
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| Sep 20, 2024 at 22:36 | vote | accept | KDP | ||
| Mar 16, 2024 at 7:05 | comment | added | KDP | "At first I was surprised by the fact that such a complicated external potential gives rise to simple linear relations for the surface force components." I was too until I realised that the oblate is the equilibrium shape when centrifugal force matches gravitational force and the centrifugal has a linear relationship with r ($F_{centrifugal} = m \omega^2 r$) so the surface gravity must too. | |
| Mar 15, 2024 at 22:11 | history | edited | Ghoster | CC BY-SA 4.0 |
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| Mar 15, 2024 at 21:55 | comment | added | Ghoster | $\vec F= -\vec\nabla U$. The gradient of a potential function is always orthogonal to the equipotential surfaces. | |
| Mar 15, 2024 at 21:52 | comment | added | KDP | Nice idea to find a simpler solution for the surface gravity by using the interior potential. Wish I had thought of that! So the force is orthogonal to the equi-potential surface ($(a'e')^2 = (3/5) (ae)^2$) (Eq26) and not to the equi-force surface ($(a'e')^2 = (9/10) (ae)^2$) (Eq27)? | |
| Mar 15, 2024 at 21:21 | history | edited | Ghoster | CC BY-SA 4.0 |
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| Mar 15, 2024 at 21:11 | history | edited | Ghoster | CC BY-SA 4.0 |
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| Mar 15, 2024 at 8:15 | comment | added | KDP | Nice work @Ghoster +1 I checked your simplified equations and they are spot on. I think together, we are the first to come up with an exact solution for the surface gravity of a homogenous density oblate spheroid of arbitrary ellipticity. | |
| Mar 15, 2024 at 7:08 | history | edited | Ghoster | CC BY-SA 4.0 |
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| Mar 15, 2024 at 6:26 | history | edited | Ghoster | CC BY-SA 4.0 |
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| Mar 15, 2024 at 6:19 | history | edited | Ghoster | CC BY-SA 4.0 |
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| Mar 15, 2024 at 6:04 | history | edited | Ghoster | CC BY-SA 4.0 |
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| Mar 15, 2024 at 5:58 | history | edited | Ghoster | CC BY-SA 4.0 |
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| Mar 15, 2024 at 5:46 | history | edited | Ghoster | CC BY-SA 4.0 |
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| Mar 15, 2024 at 5:35 | history | answered | Ghoster | CC BY-SA 4.0 |