2
$\begingroup$

I have some questions regarding the feasibility of this planetary shell-based construction. I have read other questions about shell worlds, but this case has some unique elements, so I thought I would ask anyways (I apologize if it comes off as redundant, this is my first post).

The system is comprised of three almost concentric shells. Each shell isn't a solid surface, but rather a loose collection of floating islands and floating continents, roughly at the same elevation. Their relative position may change over time.

Immediately above each shell there would be a magical source of light and heat called “lantern”, and the three lanterns would be aligned in the same axis, called “luminous axis”. All shells rotate at the same angular speed with respect to the lanterns, along an axis roughly perpendicular to the luminous axis, called “rotation axis”. In order to have different seasons, I thought that the luminous axis could spin in a cone-like motion, with the vertex centered in the center of the system.

I am pretty sure everything I am describing is gravitationally impossible, so let’s say that there is magically-induced gravity towards the center of the system, and that due to magic the landmasses don’t just collapse into a ball (if there is another plausible way for them to maintain their structure, please let me know!)

• What I wanted to know is if it could be somehow possible to tweak the distance between each shell and lantern, and the energy output of each lantern so that the middle shell, with 2 lanterns above and 1 below, could have some semblance of an habitable temperature. The thickness of the landmasses is also up for tweaking. What would happen in the other shells? Note that I don't require precise numbers, only rough estimates, as this isn’t a hard sci-fi universe.

It also would be nice if the distances between shells weren’t super large, with travel between each shell being relatively simple, not something akin to space travel, more similar to travel by plane. My current intuition dictates that it would make sense for the radius of the outermost shell to be something like 10,000 km

Finally, it would be great if all three shells could share an atmosphere. However, this would mean that the lanterns would be on direct contact with the atmosphere too, and I suspect that it would make everything way too hot. If there is magically-induced gravity towards the center of the system, due to pressure I believe that the atmosphere around the innermost shell would possibly be much denser. A google search reveals that on Earth we have only 50km of atmosphere, and given that it already exerts considerable pressure, just think what 2000km of atmosphere would do, both to density, temperature and any humans trying to survive there. I am not sure if earthlike gasses are compressible enough while remaining in a gaseous state though. In this case, perhaps the stability of the system can be justified due to the buoyancy of the materials that each shell is made out of.

Finally-finally, I would be willing to accept a solid core (preferably fully surrounded by water) inside the innermost shell, and separate atmospheres too, if it would help with gravitational stability. In this case, the structure would resemble a larger planet orbited by continent-shaped asteroids, I suppose.

Simple diagram of the structure. This is a 2d cross section, that intersects the segment where the lanterns (in red) are located. Not up to scale.

$\endgroup$
6
  • $\begingroup$ Are you saying that the shells and lanterns rotate together, and therefore have a permanently light side and a permanently dark side? $\endgroup$
    – Monty Wild
    Aug 14, 2023 at 1:55
  • $\begingroup$ Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. $\endgroup$
    – Community Bot
    Aug 14, 2023 at 2:03
  • $\begingroup$ @Monty Wild. No, the shells rotate with respect to the lanterns, so that a day-night cycle is experienced. From a different perspective, the same movement can also be thought of as the shells staying still and the lanterns rotating. $\endgroup$ Aug 14, 2023 at 5:20
  • $\begingroup$ Would you please add a diagram of the structure you are visualising. Saying that a lantern is "above" a shell is unclear, especially as the lantern seems to be a (large) point-source of light and heat but the shell is a sphere... if I'm understanding any of it correctly. $\endgroup$ Aug 15, 2023 at 10:52
  • $\begingroup$ @KerrAvon2055. I've added a simple diagram of a cross-section of the shells. This cross-section intersects the segment where the three lanterns (in red) are located. Definitely not up-to-scale. Hope it helps! $\endgroup$ Aug 15, 2023 at 16:42

1 Answer 1

1
$\begingroup$

you wrote,

I am pretty sure everything I am describing is gravitationally impossible, so let’s say that there is magically-induced gravity towards the center of the system, and that due to magic the landmasses don’t just collapse into a ball (if there is another plausible way for them to maintain their structure, please let me know!)

I think you would like to know the following (which can be verified with not-super-difficult math (technically it's called "complex analysis" but it's not really all that complex):

  1. Assume the total mass of all the shells equals the mass of the earth and
  2. Somehow the mass distribution within each shell is symmetric and not too lumpy (in other words not necessarily perfectly symmetrical but not extremely different from symmetrical)
  3. The size of teh outershell is equal to the size of the earth

Then

  1. The gravity on the surface of the outshell will be more or less exactly what we experience on earth.
  2. The gravity on the surface of the middle shell will be much less... it will be reduced by a proportion that is equal to the proportion of mass in the outer shsell (yes! the mass in the outershell has no effect in the interior of the outershell -- again assuming approximate symmetry of the mass distribution in the outer shell)
  3. the gravity on the surface of the innermost shell... that will itself be proportional to the proporion of mass of the inner shell to the total mass of all 3 shells...again, the gravity exerted by the middle and outer shells has no effect in the space that interior to the middle shell. Hence you can think of the innermost shell as a very small planet / moon and for the purposes of thinkinga bout the gravity there... it's as if the other two shells don't exist.... again, assuming relatively symmetrical mass distribution in the middle and outer shells.

Cool, right?! So I don't hink you need any magical gravity to support all this... you just need (for example) a "normal" (ie solid) inner "shell"... and then the other two shells just need some super strong structural element/material to keep them from collapsing. ... they can simply have indpendent orbits around the sun (is there a sun that they are obiting??) .... so the orbits are independent, but, yes, they are nested one inside the other... not ery stable, I guess, but not impossible in principle. Maybe there are (many!) "ropes"/tethers that keep them stabilized relative to each other.

If the mass of the inner shell is low enough... eg maybe it's only 5% of the total mass... then you might be able to "jump" from the inner shell to the middle shell... you would feel no significant gravity contribution from the middle and outer shells until you got pretty close to the middle shell.... then, once very close to it, you would drift toward the middle shell instead of falling back to the inner shell... if you happen to "land" near a hole in the middle shell you should just pop up though the hole and ... if you grab on to something you could avoid sinking back into the hole and simply step onto the surface of the middle shell and suddenly "feel" the -- very suddenly -- increased gravity there... this assumes that the mass distribution near the hole is symmetric around the hole and you manage to launch yourself right through the centre of the hole.

Same thing when "jumping" from the middle shell to the outer shell... but... I presume the gravity of the 2nd shell would be too much for a human to simply "jump"... then again.. if the outer shell is close enough to the middle shell and if it has a significant proportion of the total mass of all the shells... maybe 70 % of it??? and if the outer shell isn't too far away from the middle shell... maybe you could just jump with a little help from a trampoline :)

I'm ignoring the lantern idea. Sorry! I'm not clear on that part.

$\endgroup$
5
  • $\begingroup$ Complex analysis is called like not because it's difficult, but because it uses function of complex numbers (aka numbers like $i=\sqrt{-1}$. That apart, gravity also scales with distance squared, not only with mass. I think your conclusion should take it into account. $\endgroup$
    – L.Dutch
    Mar 7 at 5:58
  • $\begingroup$ Correct: "complex" refers to the complex plane. And gravity does indeed vary with distance squared... but that's what inspired my answer: In the interior of each shell, you can ignore gravity due to the shell (complex analysis proves it) again, provided the mass distribution of the shell is relatively uniform and symmetric... hence, in the interior of each shell the distance to the shell (to the "roof") has no influence whatsoever. It's a simplifying fact of nature. $\endgroup$
    – two
    Mar 7 at 14:51
  • $\begingroup$ You state "gravity will be reduced by a proportion that is equal to the proportion of mass in the outer shsell". That's incorrect. If the inner shell has half the mass, its gravity won't be half: half the mass will be at lower radius, so it won't be just half. $\endgroup$
    – L.Dutch
    Mar 7 at 15:03
  • $\begingroup$ Quite right! I see what you are getting at. Thanks. I was assuming the same radius for each of the shells! oops. But inner shells haver reduce radius, of course ;) ... A reduction in g due to reduced mass of each shell is offset by a reduction in the radius of the shell. However, if the radius is not significantly reduced (eg if the interior shells have radius that exceeds 80% of the total outer shell... then the R-related-"offset" in the reduction of g (ie reduction from the g of the outer shell) is not significant; reduction in g would be dominated by reduction in mass. $\endgroup$
    – two
    Mar 7 at 16:04
  • $\begingroup$ the same mass at 0.8 times the radius would exert $1/(0.8)^2=1.56$ times the gravity. That's significant. $\endgroup$
    – L.Dutch
    Mar 7 at 16:21

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .