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My question is the following:

How could I design and/or justify a habitable planet that is 80,000 km in circumference?

The planet should:

  • Be habitable
  • Have a gravity similar to earth's
  • Have active plate tectonics
  • Have a sidereal rotation of 24 hour

The use of internal god-made mega structures is allowed, or even entire layers of the planet can be made of devine-ium.

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    $\begingroup$ Of course if you basically are saying "you can use magic", the answer is "because magic". I think this is even the best possible approach. Instead of using physics you don't understand to build your world - a bit of magic here and there will do more good than harm. $\endgroup$ – Raditz_35 Jan 30 '18 at 11:07
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    $\begingroup$ Related: What's the biggest reasonable natural planet or moon with Earth-like surface gravity? $\endgroup$ – Mołot Jan 30 '18 at 11:36
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    $\begingroup$ Check out the Majipoor series by Robert Silverberg fo an exmaple of habitable mega-planet. I can't remember the "explanation" but there might be a good one. $\endgroup$ – Pierre Henry Jan 30 '18 at 16:11
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    $\begingroup$ You are going to need a VERY large turtle, and possibly more than 4 elephants... $\endgroup$ – ivanivan Jan 30 '18 at 19:08
  • $\begingroup$ Specifying "sidereal" rotation is a bit odd. Earth has a sidereal day of 23.9 hours. Instead of having a planet twice as large, can you have characters half as big? $\endgroup$ – Acccumulation Jan 30 '18 at 20:03
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Circumference and volume of a sphere have a cubic relation. So 2 times the circumference means 8 times the volume. Surface gravity is relative to the mass divided by the radius squared, so in order for your planet to have the same gravity with 8 times the volume it would need to have just half the density. Possible options to achieve this are:

  • Make the core of the planet of a material which is much less dense than silicate rocks and iron, yet uncompressible enough to not get crushed by its own gravity. You said you want active plate tectonics, so that material would likely be available in abundant quantities at the surface. Keep possible economic applications for it in mind.
  • Make the core of the planet hollow. Hollow planets would be impossible to form under current theories of astrophysics and impossible to be stable under current theories of geophysics. So you will have to explain how that shell-planet was created and why it doesn't collapse. A possible model could be an unobtanium shell of an implausibly rigid yet light material surrounded by a rock layer (the lower part of it molten so you have plate tectonics).
  • When you don't want one huge cave in the center of the planet, have many, many small caves. Its inner structure would then be more like a sponge. Again, this is very unlikely to occur naturally with normal planetary formation. It would also be hard to make this work with a geologically active planet. If it does work and the caves are accessible from the surface, then the vast cave systems would likely affect the culture of your planet a lot. They would make mining a lot easier and might be big enough to host whole ecosystems and even subterranean civilizations.
  • If you are willing to literally create a separate universe with its own laws of physics, reduce the gravitational constant. That way the planet would not just have a lower surface gravity in relation to its surface area, it would also have a lower density because it gets less compressed under its own gravity. But this would affect a lot of other things, too. For example, stars would need to be larger in order to generate enough gravitational pressure to keep nuclear fusion going.
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    $\begingroup$ Make the core of the planet of a material which is much less dense than silicate rocks and iron It's not just enough to make the core less dense, you need to make the whole planet less dense. If the core is less dense than the rest of the planet then you have a massive density instability and everything will want to invert over time. $\endgroup$ – bon Jan 30 '18 at 15:02
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    $\begingroup$ @bon Hence the continuation of that sentence: yet uncompressible enough to not get crushed by its own gravity, to specifically address that concern. Given a rigid enough structure, nothing will invert. $\endgroup$ – Flater Jan 30 '18 at 16:46
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    $\begingroup$ @Flater incompressible will not help. Empty, closed glass bottle is relatively incompressible in bathtub full of water, but it just won't stay at the bottom. Same thing with light core. It just won't stay at the bottom of gravity well unless it's a densest part of the planet. $\endgroup$ – Mołot Jan 30 '18 at 18:04
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    $\begingroup$ @Flater at planetary scale, and in geological timescales, rocks behave just like liquid. That's why we talk about hydrostatic equilibrium. $\endgroup$ – Mołot Jan 30 '18 at 18:10
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    $\begingroup$ @Flater OP specified active plate tectonics. If you're stirring those rocks around then the bottle will indeed end up at the surface. $\endgroup$ – Geoffrey Brent Jan 30 '18 at 20:43
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A priori you don't need magic for any of the points you mentioned, though you do need some explanation for having a gravity similar to Earth's in a planet that it is twice the size.

A planet with the same average density as Earth and double its radius, as you propose (Earth has a 40000 km circumpherence), will have eight times the Earth's mass, but since the surface will be twice the distance from the center of mass and gravity decreases by the square of the distance, surface gravity in your planet will be twice that of Earth. That's "similar", for some values of "similar", though rather uncomfortable for actual Earth-born humans.

If you want your planet to have less surface gravity then it should be less dense. The problem is that the elements (iron, nickel) needed for a massive core that can generate a magnetic field (which is somewhat of a requisite for surface habitability of complex organisms) are heavy.

The planet can rotate at any rate you want, within reason. In general we have found that larger planets rotate faster, but that's not a hard-and-fast rule.

If you're willing to work with twice Earth's gravity, then you don't need any magic. Even in that gravity normal humans will be able to live, if not very comfortably. Natively evolved beings should have no problem at all.

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  • $\begingroup$ everyone would have to be buffed up like a soldier (whose loadout is sometimes 100lb but not twice body weight). The transition would not be easy. $\endgroup$ – Harper Jan 30 '18 at 17:23
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    $\begingroup$ @Harper Not easy, but not impossible either: If you look at us modern humans today, we seem to be sitting, or lying flat most of the time. There is only a relatively small portion of our lives that would get significantly harder (albeit that may be the most fun portion of the average's person's lives). Just look at overweight people today, there is quite a number of them that weights more than twice what other people weigh, and they still get by. Speaking of weight, double gravity would imply that people would be very fussed about not putting on too much weight, though. $\endgroup$ – cmaster Jan 30 '18 at 20:49
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Your planet has a limited supply of devine-ium, it's slightly more rare than gold in the crust but closer to the core of the planet is a bit more plentiful. It interacts with the magnetic field of your planet in such a way as to produce a para-magnetic affect see here. counteracting gravity enough so that it feels like earth, but not enough to make people float.

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If you really want plate tectonics plus earth-standard gravity and you don't mind having some really massive internal mega-structures, you could have a world built like a Rubik's Cube - the surface is composed of massive ultralight Divinium platforms, each resting on a 12,000 KM stalk reaching down to the planet's core.

The core of the planet is a superdense divine widget upon which the stalks slide and rotate, giving you plate tectonics.

In order to keep the internal mechanisms from clogging up with junk, the widget at the center sucks up all normal matter that falls between the gaps of the plates and attempts to eject it from the planet by pumping it up through the stalks.

Several million years of bombardment by comets and asteroids, combined with a slight miscalculation as to what the escape velocity of the planet actually is, has led to crud building up on top of the Divinium platforms. This crud forms familiar-looking oceans and continents. Whenever earth and water falls through the cracks, it's spat back out through volcanoes that form over the stalk exhausts.

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