Timeline for Could an underground civilisation deduce the size and shape of their planet?
Current License: CC BY-SA 4.0
9 events
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| Oct 9, 2021 at 4:42 | comment | added | Nuclear Hoagie | You've defined the equation as a function of depth below the surface, which is the very quantity you're trying to solve for. Those equations don't help unless you can express a depth difference in radius-relative units. Agree with the Shell Theorem POV - gravitationally, the mass above you is indistinguishable from no mass being there at all, so it can have no effect on measurements inside the shell. | |
| Oct 9, 2021 at 0:17 | comment | added | Dewi Morgan | Exactly. The claim "Gravity at a depth below the surface varies due to less mass below you and the pull of the mass above you." is incorrect because there is no net "pull of the mass above you.". Even the answers at your link say this: "All the mass farther away from the center cancels out". | |
| Oct 8, 2021 at 19:57 | comment | added | John Doty | By the Shell Theorem (en.wikipedia.org/wiki/Shell_theorem), the gravity of a uniform spherical shell is zero in its interior. You thus cannot measure the thickness of a spherical shell by measuring its gravity from the inside. | |
| Oct 8, 2021 at 19:50 | comment | added | Josh King | It's all systems of equations algebra, take a third measurement of gravity at another known relative elevation and you would get a third equation to solve for the third unknown (planetary mass) It all depends on accurately measuring gravity | |
| Oct 8, 2021 at 19:16 | comment | added | Nuclear Hoagie | But how do you find the mass of the planet (M) without knowing how big it is? | |
| Oct 8, 2021 at 19:09 | comment | added | Josh King | Edited the answer to explain more in depth how it would work. | |
| Oct 8, 2021 at 19:08 | history | edited | Josh King | CC BY-SA 4.0 |
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| Oct 8, 2021 at 18:58 | comment | added | Nuclear Hoagie | It's not clear to me how this method lets you know if you're near or far from the surface. Suppose you find some relationship of gravity vs depth - I don't see how you can extrapolate that to find the location of the surface unless you know either the strength of gravity on the surface (which you wouldn't), or the thickness of the different density layers above you (in which case you already know the size of the planet). | |
| Oct 8, 2021 at 14:53 | history | answered | Josh King | CC BY-SA 4.0 |