Is a moon inside a hollow Earth possible?
The Hollow Earth theory is/was a pseudoscientific idea that our world is actually on the inside of a large sphere. The "sky" points inward towards the center, where the "Sun" (a light source) is, while the "ground" points outward.
Let's assume that we have a planet the size of Earth, except that it is a hollow Earth. In reality, it's simply an Earth-sized cavity inside a larger body, notably, some sort of artificial megastructure. I had assumed that said megastructure was spherical, but clearly I should have stated it explicitly, so I'll do so now. The structure will have spherical symmetry and be as uniform as possible.
Is it possible to put a moon inside the sphere - somewhere between the central light source and the "ground" - and have it move in an "orbit" around the center? Would the moon crash into the ground, or would it be stable?
I'm almost positive that the moon can't be as big as Earth's moon, but I don't know a reasonable size. I'm fine with anything bigger than, say, Janus or Epimetheus.
Bonus question (not necessary to answer): Is the setup possible if the hollow Earth is non-spherical, i.e. ellipsoidal?
1 answer
Not without artificial gravity or some other outside source.
Your mega structure large enough to have an earth sized pocket is going to have a lot of mass. Something that big is going to need futuristic materials and technologies to keep from collapsing.
Anything on the inside of the sphere is going to be drawn toward the center of the structure. If the sphere is off center then everything will be pulled toward one side. If it's in the center of the structure then things would just fall off the surface toward the "sky", unless...
To get gravity on the inside surface of a sphere without artificial gravity it needs to be spinning, meaning the structure needs to be spinning around the sphere, or a mechanism needs to be spinning the earth size sphere independently of the structure.
Spinning the whole structure is not a good idea, since if you have 1g at the surface of the sphere, you'll have even more the further out you go.
Angular Velocity: 0.0118 rotations/minute
Earth Radius: 3959 miles
Gravities: 1g
Radius: 5000 miles
Gravities: 1.26g
Radius: 8000 miles
Gravities: 2g
Stress on the structure would be increased exponentially the further out from the center of gravity you get.
If you just spin the sphere independently you still need super materials like ringworld scrith and you better hope it's really well balanced.
So you'll have to pick your magic: Artificial gravity or impossible building materials.
Edit:
Without artificial gravity you'd need a gravity point source in the center to orbit a moon around, since centripetal force wouldn't work to orbit inside a sphere.
Any variations in mass in the outside structure would tend to destablize the system, similar to the three body problem, requiring constant corrections to keep the moon from crashing.
With artificial gravity, getting a moon to do anything you want is easy.
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