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Earlier today I came across this question, asking as to the effects of having a planet with a shell around it acting as a planet itself, so there was a planet within a planet with neither in contact with the other but held in place with gravity/atmospheric pressure or somesuch, which piqued my interest, however all the answers to that question seem to assume a thinner shell with the majority of the mass being the inner planet, I'm interested in the idea of the outer planet being far far thicker with a rather small inner planet and a smaller but still reasonably large atmosphere for the inner planet, perhaps along the lines of a large marble within a bowling ball.

Part of my idea behind this is that rather than the shell planet being affected by the inner planets gravity, the inner planet is affected by the shell planets gravity.

I also wondered about the possibility of three or more planets rather than just the two, though assumably this would require either the inner planets to be too small to be of any real use for life to survive, or for the outer planets to be far larger than would make sense for them to exist in a solar system similar to our own.

Edit: As for how this would have formed, I hadn't really made any decisions as to whether it was manufactured or naturally occurring, I suppose if I was going to, in the world I was pondering implementing this in, it would have to be naturally occurring, or manufactured in the sense that it was mined out, not built that way.

As for how it would be mined out I doubt it would be hugely feasible for it to just be mined by conventional means, but if a group had that as their specific intention and the required resources and ability to plan I assume they would be able to, or some form of magic, such as an explosion that wrapped around spherically and completely destroyed the area leaving no debris, or simply teleported the area somewhere else.

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  • $\begingroup$ Thank you for clearly highlighting the differences between this question and the older one. $\endgroup$ – a CVn Sep 30 '16 at 8:01
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    $\begingroup$ is the idea for this to be naturally occurring or manufactured to some extent? Unless the planet (by which I mean the whole system of inner/outer planets) is incredibly small, even if it could somehow naturally form like this, normally the whole mass would simply collapse in on itself and become a single spherical planet. Unless of course this is a manufactured planet and sufficient technology is in place to prevent this. $\endgroup$ – danl Sep 30 '16 at 8:18
  • $\begingroup$ I hadn't really made any decisions as to whether it was manufactured or naturally occurring, I suppose if I was going to, in the world I was pondering implementing this in, it would have to be naturally occurring, or manufactured in the sense that it was mined out, not built that way. $\endgroup$ – SlipperyPete Sep 30 '16 at 8:48
  • $\begingroup$ As for how it would be mined out I doubt it would be hugely feasible for it to just be mined by conventional means, but if a group had that as their specific intention and the required resources and ability to plan I assume they would be able to, or some form of magic, such as an explosion that wrapped around spherically and completely destroyed the area, or simply teleported the area somewhere else. $\endgroup$ – SlipperyPete Sep 30 '16 at 8:54
  • $\begingroup$ What's with the e/a? As a shortcut for both affected and effected it doesn't make sence since the latter would not be meaningful in that sentence. Maybe you want a word that imply a mutual two-way relationship? $\endgroup$ – JDługosz Sep 30 '16 at 10:00
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Hydrostatic Equilibrium

Planets are spherical because gravity makes them that way. The largest object to not be in hydrostatic equilibrium in the solar system is Iapetus, a moon of Saturn. Even a tiny planet the size of Mercury is more than 100 times the mass of Iapetus. Iapetus has no atmosphere and about 0.02g of surface gravity. If you want a habitable large planet, it will be crushed into a sphere.

But lets assume that this system was built by aliens with super-magic technology...

Surface Gravity

While there is no net gravitational force on the shell from the inner planet, there is still gravity on the surface of the inner planet; the entire mass of the system can be treated as a point source in the center. Let us assume a shell-core system with radius and diameter equal to earths (this is not really feasible, the mass would have to be incredibly dense to make up for the void in between, but roll with me I'm illustrating a point).

Surface gravity on the shell will be equal to earth's: $1g = 9.8 \text{m/s}$. Now lets consider the inner core. If it has a radius equal to the earth's core of 1220000m, then we get $$g_\text{core} = \frac{G\cdot m_{\text{system}}}{r_{\text{core}}^2} = \frac{6.67\times10^{-11}\frac{\text{N}\cdot\text{m}^2}{\text{kg}^2}\cdot5.97\times10^{24}\text{kg}}{\left(1.2\times10^{6}\text{m}\right)^2} = 277 \frac{\text{m}}{\text{s}^2} = 28.2\, g_\text{shell}.$$

So the surface gravity in the core is 28 times that on the surface. G and the mass of the system are the same for calculating the shell's gravity and the core's gravity, so the surface gravity ratio is the square of the ratio of radii. For example, the radius of earth is 6371km, so $$\left(\frac{6371\text{km}}{1200\text{km}}\right)^2 = 28.2.$$

Math is magic! No matter what your geological composition and mass, a tiny core inside a larger shell will result in wild surface gravity differences.

Conclusion

If you want enough gravity to walk around on, the shell will crush itself into a sphere. If you solve this problem with magi-tech, you will still get two objects with surface gravity so divergent they couldn't be inhabited by the same species.

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  • $\begingroup$ Thankyou for mentioning the differences between surface gravity, I had completely not thought of that though at the mention of it I'm not sure how I forgot that would be an issue. As for the Hydrostatic Equilibrium, I have a few questions, firstly, is there anyway you could have a rough estimate of how long something like this would last before there were noticeable signs it would collapse in on itself? I'm assuming this process would take a very long time, atleast a couple of centuries, perhaps millennia? Secondly how would an extremely dense atmosphere for the inner core (e/a)ffect [...] $\endgroup$ – SlipperyPete Sep 30 '16 at 23:50
  • $\begingroup$ (I hate those words) the shells ability to crush inwards? and thirdly, would it be possible to, under the right conditions, probably also requiring magic and handwaving to be plausible, for there to be a situation where the inner sections of the shells (if we're calling the inner planet the core, this would be the mantle I suppose) is too compressed for the gravity (e/a)ffecting it to have enough force to compress it any further? $\endgroup$ – SlipperyPete Sep 30 '16 at 23:50
  • $\begingroup$ A lot of questions here: First, the force of gravity is constant based on distance and mass; it starts acting immediately. If the planet is not made of alien super-materials, it will collapse immediately, and continue collapsing until it is a sphere. Second, even the densest atmosphere is trivial compared to the density of rock or iron, so that won't (A)ffect that rate of collapse. Third, iron is already too compressed for the planet earth to compress its iron core any more, no magic needed. $\endgroup$ – kingledion Oct 1 '16 at 12:51
  • $\begingroup$ I understand that gravity is constant, but if I drop a brick from the Eiffel Tower, it doesn't immediately appear on the ground, it has to fall first, or an example more related, if I'm building a card tower, by leaning the first two against each other, they would each slow the other falling, from friction and such, and if i did the same thing next to that then put another card flat across the top, gravity would be affecting all the cards, but that top card would not be noticeably falling, as the two sides are held up by the other cards. so while gravity would immediately be [...] $\endgroup$ – SlipperyPete Oct 2 '16 at 0:08
  • $\begingroup$ acting on each and every particle, each particle would be compressed together well enough that it would take some time before they actually fell. as for the atmosphere, I'm not saying it would stop gravity by itself, but alongside other factors slowing it such as the mantle being as compressed as it is, it would help to make the process take longer. as for your third point, I'm not sure you've understood me at all, obviously on actual earth the core is as compressed as it can be, that's how gravity works and all, hydrostatic equilibrium and all that, but as you move further out from the [...] $\endgroup$ – SlipperyPete Oct 2 '16 at 0:09
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The relative size/weight of the shell and the core have no impact at all, as long as the shell is a perfect sphere, the sum of the gravitational forces from the shell to the core is 0.

That said, it answer (in a way) the second part of the question, the 2/3 inner planetoïds would interact exactly as 2/3 planetoïds in the void of space.

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    $\begingroup$ "No impact" also assumes the shells are of uniform density. $\endgroup$ – WhatRoughBeast Sep 30 '16 at 15:14
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Sefa's answer is correct. Due to Newton's shell theorem, the force on any object inside (and due to) a spherically symmetric object of uniform mass density of exactly zero. The exact integration (see e.g. Wikipedia or these notes) is messy, but it indeed relies on the density of the shell, $\rho$.

Now, if we give the shell non-uniform density, then there will indeed be a net gravitational pull on the "planet" inside it. We can compute the force on this planet by computing the potential in any location inside the shell. Basically, if we assume that $\rho=\rho(r,\theta,\phi)$ (in spherical coordinates), we can solve the equation using spherical harmonics (where the factor of $\epsilon_0^{-1}$, used in electrostatics problems, is replaced with the appropriate set of gravitational constants).

This is not easy to solve analytically; numerical solutions are often better. Also - and I don't normally say this - there's a point at which you have to consider if this much effort is worth it to solve a worldbuilding problem. Odds are good that the mass density will be roughly spherically symmetric, as will the shell, and so the "planet" inside will feel very little force.

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  • $\begingroup$ So, I'm having some issues wrapping my head around what exactly you mean by this, from looking at your answer with Sefa's and doing some quick research of my own, are you saying that if there is a uniform mass density for the shell, then the inner planet will be perfectly in the center, but if there is a non-uniform mass density the inner [...] $\endgroup$ – SlipperyPete Sep 30 '16 at 23:27
  • $\begingroup$ planet will be pulled towards the section of the shell with the highest mass density? if so that is pretty much what I had thought initially with my limited knowledge of gravity for own own planet (it's strongest at the center so everything is pulled towards the center and the closer it is the faster it's pulled) $\endgroup$ – SlipperyPete Sep 30 '16 at 23:27
  • $\begingroup$ @SlipperyPete If there's a uniform density, the planet inside the shell won't be influenced at all by the shell; it will keep moving in its original trajectory unless it crashes into the shell. If there's non-uniform mass density in the shell, then the planet could move anywhere, depending on the mass distribution. $\endgroup$ – HDE 226868 Sep 30 '16 at 23:30
  • $\begingroup$ I thought that might be what you mean, but that doesn't quite seem right to me, nonetheless, if the inner planet would be completely uninfluenced, then if it had been part of the shell originally, and therefore orbiting the same star, would it continue to do so in the same fashion, or would the two planets orbits eventually begin to differ causing them to impact? or if it were a rogue planet, not orbiting a star, would the two planets rates of movement begin to differ? I assume because space is a void there would be very little to cause an issue in the rogue planets case, but I feel like [...] $\endgroup$ – SlipperyPete Oct 1 '16 at 0:11
  • $\begingroup$ there would be issues in the orbiting case, though would the atmospheric pressure inside keep the inner planet fairly balanced in the center? and if the shell was to be non uniform, but fairly close to spherically symmetric as you have proposed would be likely in your last paragraph, would the small amount of force, depending on the rotation, A) pull the inner core forwards if the shell rotated slowly enough that the point the inner planet was pulled towards was always "forwards" along the orbits trajectory, or perhaps be just enough force to adjust the inner planets orbit if it were to [...] $\endgroup$ – SlipperyPete Oct 1 '16 at 0:12

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