Fantasy Astrophysics and Hard Fiction

Some of you have probably already observed that it's my nature to try and find ways to reconcile fantasy worlds' physics, such as Felarya's, with plausible (-ish) science. This thread isn't exactly about Felarya but about similarly fantastic worlds: here we can discuss how unusual worlds such as Felarya could or couldn't exist in a universe without a wizard having to have done it - or if a wizard did have to do it, how he might have done so. I put it here because, well, at least at present the people around here seem amenable to discussing preposterous physics and actually providing useful information (so no "magic, therefore none of this matters" please ).

My first question for discussion:
I thought of a seemingly awesome sci-fi idea a few years back: the largest planet in the universe. It would be larger than a star (at least, a smallish star... maybe a little smaller than the Sun), but still have reasonable gravity and not collapse into a star itself because... it's a bubble. The planet would be hollow, possibly as the result of an explosion or whatever during its formation that inflated the magma to an orbital radius, where it cooled. Consequently it would have too little mass to form a star, and due to the thickness of the shell vs. the diameter of the whole planet, its surface gravity could perhaps be near that of Earth.
But could that actually exist? AFAIK, geostationary orbits can only exist very close to the equator, so only the equator of this planet should be able to sustain its shape, while the poles would inevitably collapse inward. Could the planet's shell be strong enough to hold a significant portion of the sphere in place, at least for a few million years? Am I doomed to have just a ring world at best? I'd really like to make this idea work, but I'm no longer sure how it could.

it's not necessarily the size of the planet, it is the mass, meaning how much space it takes, including the inside of the planet shell itself, the more mass, the stronger the gravitational pull

For the most part, yes, because the radius of any given planet is normally far smaller than the effective radius of its gravitational field. But at extreme scales the size becomes significant: an object the mass of Earth that's the size of a marble would have gravity so strong its escape velocity would exceed the speed of light (yes, it would be a black hole ;P ). On the other hand, a diffuse nebula could have the mass of a million Suns but negligible gravity at the edge due to the low density.
So if the thickness of the shell were in the ballpark of Earth's radius, and the planet were infinitely large, its surface gravity would match Earth's (barring infinity coming and messing up our calculations as it likes to do). So for a very large planet, a relatively thin shell somewhat smaller than Earth's radius should roughly yield Earth-like gravity, because the other side of the planet would be very far away, so its gravity would be weak on this side... right?

parameciumkid wrote:

For the most part, yes, because the radius of any given planet is normally far smaller than the effective radius of its gravitational field. But at extreme scales the size becomes significant: an object the mass of Earth that's the size of a marble would have gravity so strong its escape velocity would exceed the speed of light (yes, it would be a black hole ;P ). On the other hand, a diffuse nebula could have the mass of a million Suns but negligible gravity at the edge due to the low density.
So if the thickness of the shell were in the ballpark of Earth's radius, and the planet were infinitely large, its surface gravity would match Earth's (barring infinity coming and messing up our calculations as it likes to do). So for a very large planet, a relatively thin shell somewhat smaller than Earth's radius should roughly yield Earth-like gravity, because the other side of the planet would be very far away, so its gravity would be weak on this side... right?

it's not just the shell, you have the mantle and then the cores to add, the less mass overall the less gravitational pull you have

aside from that you're goood

We were taught how to calculate gravity, actually. A good simplification for it is that you can assume it concentrated in a point right at the center of the object involved. If you take, for instance, a hollow world like you say, it shouldn't be too hard.

However, it does seem, materials-wise, impossible. Say we go with a world the size of Jupiter- 71492 km equatorial radius. 11.2 earths. We'd need a mass of square that, or 125.6 earths, spread over a crust, to keep the gravity at Earthlike levels- on the Equator, at least. Now, say we divide the mass of Earth... 5.9736 x 10^24 kg, by the area of Earth, 5.1 x 10^8 square metres. Pressure is 1.17 x 10^16 kg/square metre. Assuming uniform Earthlike gravity, take 1.17x10^16 kgf/m^2.

1 Pa = 1 N/m^2. 1 kgf = 9.81 N/m^2. We're talking, thus, 1.15 x 10^17 pascals pressure per area unit. Suppose we take a round shell slice- differentially thin. Each surface unit will be withstanding 115 terapascals pointing downward, compensated by the sides of the slice, each of which carries a shear stress compensating that. However, shear and compression modes would have even carbon nanotubes buckling, even if you could devise a thick enough shell to put said stress below the 200 gigapascals they can [theoretically] stand.

^ That's at the poles, right? At the equator the downward pressure would be zero due to the centrifugal force effected by the planet's rotation, so there would be a gradient of pressure between zero at the equator and maximum at the poles.
And would some shape other than a sphere be more stable? Perhaps an oblate spheroid where the poles are closer to the center and the equator farther would be more stable... or the opposite shape? Would it be more stable with the poles at a higher altitude than the equator (however improbable that shape is to occur)?