Shell World
The Shell World is essentially a supramundane planet with the underworld removed. Or, more accurately, broken up and spread over the interior surface. A normal spherical world contains mass all the way through, with most of it concentrated at a dense central core. A Shell World, however, reverses the usual distribution of mass, compressing most if it into a thin shell and leaving the interior hollow. A Shell World and a normal world of equal mass and radius will have equal surface gravity, but the material of the Shell World must be much denser. In order to keep average density down within a reasonable range, the Shell World must be made larger, thus moving the surface further from the center of mass and reducing gravity, thus requiring the addition of more mass and an adjustment to either shell thickness or density... until you have reached an acceptable compromise of gravity, shell thickness, and density, and hopefully haven't run out of materials.
Types of Shell Worlds
There are two types of Shell Worlds: Space Worlds, designed to provide a large microgravity environment in the interior, and Land Worlds, designed to provide a large surface area without uninhabitably high gravity or prohibitively large mass requirements.
Space Worlds
In order to provide a large internal volume, Space World shells are relatively thin. Thus, they must be either extremely large or extremely high density in order to produce sufficient gravity to hold an atmosphere. Additionally, increasing the radius of a Shell World while keeping the shell thickness constant produces an increase in surface gravity. Thus, in order to retain the same surface gravity, the shell must be made thinner at a slightly lower rate than the shell is made larger. That produces a better mass-to-volume ratio, so Space Worlds are likely to be very large, assuming a large amount of mass is available to construct them. Assuming you have 1 Jupiter Mass to play with, the average density of the shell is 4.5 grams per cubic centimeter, the average air density in/around the Shell World is .002458 g/cc*, and you wish to keep a surface gravity of 1G (9.8 m/s^2), a thickness/radius ratio of 2.327% is possible. Even better ratios can be produced if you reduce the acceptable gravity. The complete statistics for such a world are as follows:
Radius (km) 113630
Shell Thickness (km) 2644
Thickness/Radius 2.326850304%
Shell Density (g/cc) 4.5
Avrg. Air Density (g/cc) 0.002458
Internal Volume (km^3) 5.72655E+15 (5 quadrillion, 726 trillion, 550 billion)
Surface Area (km^2) 1.62254E+11 (317.3934193 Earths)
Mass (kg) 1.9E+27 (1 Jupiter Mass)
Surface Gravity (m/s^2) 9.81802889
*This is an essentially random number. I have no idea how to calculate how much the gasses of an Earth normal atmosphere would compress under their own gravity, so I have somewhat arbitrarily decided to simply double Earth sea level air density and use that for the average across the entire Shell World in all of my calculations. If you happen to have better data, please /msg me.
Land Worlds
When designing a Land World, internal volume is of secondary importance to providing the maximum livable surface area at the right level of gravity. By accepting a reduction in gravity of 1/2, a planet of ~1 Earth Mass can be expanded to nearly double 1 Earth of surface area. The small size, however, necessitates a very large Thickness/Radius ratio.
Radius (km) 8870
Shell Thickness (km) 1555
Thickness/Radius 17.53100338%
Shell Density (g/cc) 4.5
Avrg. Air Density (g/cc) 0.002458
Internal Volume (km^3) 1.63957E+12
Surface Area (km^2) 988683084.2 (1.934011911 Earths)
Mass (kg) 5.78036E+24 (Just under 1 Earth Mass)
Surface Gravity (m/s^2) 4.901892085 (~1/2 G)
One might think that if you double the mass, you could double the gravity. So, I tried it out. After much tinkering, I could not manage to get exactly 9.8 m/s^2, and so, although it is probably possible, I decided to settle with 9.74 rather than drive myself insane:
Radius (km) 8900
Shell Thickness (km) 4396.8
Thickness/Radius 49.40224719%
Shell Density (g/cc) 4.5
Avrg. Air Density (g/cc) 0.002458
Internal Volume (km^3) 3.82518E+11
Surface Area (km^2) 995382216.4 (1.947116415 Earths)
Mass (kg) 1.1568E+25 (2 Earth Masses)
Acceleration (m/s^2) 9.743891482
So, doubling the mass did
nearly double the surface gravity, but it shot the Thickness/Radius ratio straight to
Hades, leaving only a little over an eighth of the world's total volume hollow. Fortunately, that doesn't much matter in a Land World. I also managed to eke out a small increase in surface area, but it is still just below 2 Earths, so in this case you'd actually be better off (just barely) with two solid Earth-sized planets.
Living Arrangements
Living on a Land World with little or no access to the hollow space inside would be little different from living on a regular solid planet, with the exception that the large size would make the horizon farther away.
On a Space World, however, access to the interior is the whole point. With the core missing, a very uniformly strong superstructure would be required to keep a Shell World from collapsing in on itself. As with a Dyson Sphere, some of the load can be taken off of the equator by spinning it, but there will be a large load left at the poles. Possibly, two problems could be solved at once by cutting multi-hundred kilometer wide holes at the poles, removing a lot of excess mass and providing easy access to the interior, and allowing air to flow freely between the interior and exterior atmosphere. I have no idea how this would affect the weather, but I do not doubt it would be interesting.
Despite the fact that there is zero net gravitational force inside a uniform sphere, the interior of a Space World will actually be under microgravity, not null-gravity conditions, due to the small gravitational pull of the air inside (unless, of course, you have neglected to grant your world an atmosphere and left it with hard vacuum), but this effect would be so slight as to most likely go unnoticed except over extreme long time periods over which items would tend to drift into clumps near the center. People would be able to fly about the interior between floating buildings with little more than diving fins, a la The Smoke Ring, possibly making trips between the surface and the interior under their own power if large enough wings and low enough surface gravity were available. Interior lighting might be similar to a Bernal Sphere or O'Neill Cylinder, employing a statite over one or both poles to reflect light to a scattering mirror suspended at the center of the world, or the world might simply be tilted to allow a small amount of light to enter directly through holes at the poles to illuminate some of the interior surface. The latter method, however, would leave the interior in total darkness during spring and fall.
Diabolic writes: Is this far-flung theoretical astrophysics, or some thoroughly thought-out fan-fiction concerning a sci-fi novel? It isn't real and in the present tense, as it is presented... Could you please qualify this some so that those people who believe in nano-techonology and mind-control don't start bugging me with this too?
Certainly. Here goes the disclaimer: Shell Worlds are a thoroughly thought-out hard-science fiction, though they have not appeared in any novels, sci-fi or otherwise, that I know of. If you happen to know of any, please /msg me. The above w/u is a product entirely of my overactive imagination combined with far too much free time (although I have no doubt that someone else has probably thought of the idea before) for the purpose of providing reference material to the TJHSST Sci-fi Writers Club and similar groups. It is in no way an attempt to support the Hollow Earth Theory.
Zerotime writes: The closest thing I've read to this is a short story by Asimov called "Strikebreaker". It's set on a planet about the size of the Moon that's been hollowed out on multiple levels to provide a large amount of livable room below the surface, but even that's not very close.