Maximum shell world planet size with earth-like conditions

Question

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)?

Answer 1

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)

Answer 2

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.