The show alludes to, but does not describe in detail, how unstable the planet is. A big part of the stability is having the planet rotate quickly. As in scary fast. I would have to look up the real science, but from what I recall it is fast enough that walking from the inside to the outside changes your weigh by a significant amount.
The problem is the tidal forces from the central star, and any moons, and any asteroid impacts that might slow the rotation might cause the whole thing to catastrophically revert to the more stable sphereoid shape.
high fractions of C small impactor into an already rapidly rotating disk punching through the center at near 90° inclination comes to mind as a potential creation scenario. As in, so fast that the vaporization is almost a linear path.
While not a donut world, this would be a world definitely different from the average. Basically the way Space: 1889 envisions Mercury. If you designed a world like this, you could use the Space: 1889 Mercury map for the inhabitable area.
http://www.space.com/20856-alien-planets-eyeball-earths.html
There are plenty of irregularly-shaped planetoids and plantesimals.
Maybe they are the "apple fritters" of the doughnut planet genre...
Shalom,
Maksim-Smelchak.
While not a donut world, this would be a world definitely different from the average. Basically the way Space: 1889 envisions Mercury. If you designed a world like this, you could use the Space: 1889 Mercury map for the inhabitable area.
http://www.space.com/20856-alien-planets-eyeball-earths.html
I saw a doc last year and this year about odd worlds, and "Deadliest Space Weather" hosted by the Weather Channel, and they had a world very much like that one. Though it had a different geography.
It was a Goldilocks planet tilted on its side. I can't remember all of the commentary ... I'll have to track down the doc.
But to get back on topic; I'm close to getting my office set up, and I have an artificial world for an adventure module that has a very loose resemblance to mister "doughnut world". But it's an artifice. It's not a naturally occurring body.
There may be (or have been, and will be) a few doughnut worlds, but I can't imagine them retaining their shape, or otherwise lasting for any length of time.
Thoughts?
Once you get it stable, it's likely to remain stable until it gets hit.
It would need to be hit by something massive enough to break the surface tension, and/or fast enough to alter the spin, the orbit, or the axis.
Essentially, it's just a many-many-many world version of a rosette, all orbiting the central point of the mass. In other words, it's a torroid because it's spinning at orbital velocity around its own center of mass.
Depending upon the tilt of the world relative to the sun and if it has any significant moons, the tidal forces from either or both will eventually slow the rotation enough to have the world collapse. On an world in the habitable zone around a G class star with no moons you might be talking a few hundred million years. Around smaller stars it would be less. In the outer zone and assuming no gas giants or binary stars, it may half a billion years.
You could colonize the world, and it would be safe for a while. But sooner or later it will collapse.
You could colonize the world, and it would be safe for a while. But sooner or later it will collapse.