# Maximum shell world planet size with earth-like conditions

I am trying to work out the theoretical limits on the size of a shell world (made with orbital rings constructed around a black hole). I have the following constraints:

1. The light to the planet must be provided by a sun/suns (can't use artificial lighting)
2. The day length should be about 24 hours, and there should be seasons with about the same time length as on earth.
3. The sun/suns have to last for at least a billion years (it can't be much more massive than it is)

One limiting factor I have identified is that if the days are going to be created by the rotation of the planet, then when the planet gets larger, the velocity at the equator counteracts the force of gravity. I think that if gravity varied from 1/2 earth's at the equator to 2x earth's at the poles that would be ok though. Using this as the only limiting factor, I get that the maximum size is approximately 1000x earth size.

What other issues will there be for such a planet? Can a shell world even rotate that fast and not rip itself apart? What will the weather on such a planet be like? Will the sun be able to provide enough heat for a super massive planet?

Are there any other formulations that allow for a bigger system (using multiple suns/any other kind of 'natural' lighting system)?

• it looks like natural sun and 24h is not easy to marry with a 6 million km diameter planet. so before u jump to so many questions about this, u need to build up understanding of what u have or propose. at the same time defining the system in better way, due the answers and improvements on your side, as as result it allows ask more focused narrow questions about your system. it looks like u have a difference in gravities at least 6 times not 4 as u calculated because 37m/ss is bh gravity which will be at full strength at the pole. also there will be difference in its vector orientation Feb 26, 2021 at 4:58
• Is your proposed planet a hollow sphere, or a circular ring?
– Sal
Feb 26, 2021 at 20:49
• @Sal the proposed planet is a hollow sphere May 4, 2021 at 4:43

Instead of planet orbiting the Sun, let the Sun(s) orbit the planet. According to Paul Birch's calculations (in his short story The Kernel), the maximum possible size of an Earth-like (dictated by surface gravity and the mass being just above the singularityphoton sphere) "planet" is about two light years in diameter. With this size, the illumination has to be provided by a network of synchronously rotating Suns, with day/night intervals caused by carefully setting the spacing between the Suns.

(needless to say, this requires some very advanced engineering and careful maintainance)

### Use a network of large reflective moons (or mirror) to reflect sunlight to give you your day/night cycle.

Rather than make the thing rotate at rediculous speeds to get a day/night cycle, use a network of mirrors to reflect sunlight to give day night. You can have multiple mirrors simultaneously directing sunlight, even focusing it, so you should be able to get it nearly as bright as current earth daylight.

That sun orbit should be about your year, plus or minus whatever rotation you want for your shell. If your shell is slowly rotating you can have the sun further away - which is useful for many reasons.

The mirrors in a tight, close, orbit, and arranged to reflect the sun onto the surface every 24 hours.

Summer is when the sun is facing you on the shell surface. Yes it's brighter at night in summer because there is a sun overhead, but its far away, depending on the rotation speed of the shell. If the shell is rotating at about 1 rotation every 2 years the sun can be quite far away ie 2-3AU, meaning this "night sun" is only marginally brighter than a full moon.

I think this takes "rotation speed for day night" out of your critical path for calculating the upper limit on the shell size. Make it out of carbon nanotubes and you're looking at least as large as the sun.

• it looks like with current assumptions is it a binary system 3:1 ratio of black hole mass and sun, does not make a huge difference for u answer but Feb 26, 2021 at 5:17
• As far as I understand it, a shell world would have no requirements for carbon nanotubes - because the rings that support the shell are orbiting, they don't need high tensile or compressive strength. Therefore under this kind of proposal I think that the maximum size would be more like 1 light year (the distance at which the surface gravity of the black hole is earth gravity). This could then be done with lots of mirrors and lots of suns. Feb 26, 2021 at 7:11
• Although this is a nice solution for producing a large world, i'm not sure it is exactly what I am looking for because the setup would only really work on the equator, leaving most of the planet uninhabitable. Feb 26, 2021 at 7:13