Creating a stable, liveable ringworld orbiting a binary black hole/stellar pair

Question

I'm creating a setting for a sci-fi RPG. I would like to check whether the concept is physically possible. The main action happens on a giant ringworld which centrifugally orbits a paired black hole and star. Here is a diagram of what I mean:

I am hoping that this setup would provide a day-night cycle. When the star is visible from a point on the ringworld, it is "day". When the star goes "behind" the black hole, it becomes "night".

Constraints:

1. The ringworld orbit should be stable.
2. The star orbit around the black hole should be stable - ie the star is not feeding the black hole (due to radiation issues) and therefore there is no accretion disk.
3. The radius of the ringworld should be reasonable - between 0.1 - 2 AU.
4. The mass of the star should be reasonable, erring on the smaller side
5. The mass of the black hole should be reasonable, erring on the smaller side
6. The irradiance (watts of radiation per square meter) on the ringworld should be comparable to that of Earth.
7. The wavelength profile of the irradiance on the ringworld should either: be comparable to that of Earth (preferable) or if the black hole generates insanely dangerous gamma rays (reduced due to no accretion disk?), it should be at least plausible that the ringworld has some sort of magnetic field generation technology powerful enough to deflect them.
8. The orbital period of the star around the back hole should be comparable to that of a day. Anywhere between 12-48 hours would work though.
9. Something also to consider: the day/night cycle will break down if the black hole Schwartzchild radius is smaller than the radius of the star. So the radius of the black hole has to be greater than the radius of the star. I imagine this will require a black hole of considerable mass. This can be scifi'd away with "inertial dampeners" in the ring or something if required.

Is such an orbital setup mathematically possible without leading to an absurdly large ring?

Thanks!

Answer 1

There are several problems with this type of ringworld. I think they are solvable, but require changes to your setup.

The first problem is that the central black hole will be much smaller than the star, so it will never eclipse the star. All you'll get is a wobbly star, as the star and the black hole orbit their common barycenter. No night. To have night, you'll need to have a smaller ringworld, made up of opaque sheets, orbiting at a higher orbital speed. Since it'll need to be close to the ringworld to avoid being too close to the star-black hole system, this means the speed difference won't be too great, so you'll require a ringworld made up of sheets connected with cables - the area with the cables will supply the day, the opaque sheets will supply the nights.

Then, the star needs to be sufficiently far away from the black hole, so the ringworld must be farther still. Which requires a somewhat larger star to achieve the same irradiance on the ringworld surface.

Finally, gravity. A 1AU ringworld rotating around a G0 star like the Sun will have a "neutral" orbital speed of one rotation per year. No apparent gravity inside then. To have gravity, the ringworld must rotate faster than that. We need the square of the peripheral velocity, divided by the radius in meters, to equal 9.81 m/s^2. Since the peripheral velocity is 2*PI*R/T, this gives 9.81*T*T=4*PI*PI*R, or T=2*PI*SQRT(R/9.81) with R=150 billion meters (1AU); T turns out to be a little less than nine days.

But this equals tension in the ring - imagine 1G of force over almost one billion kilometers of ringworld. The tension of a ring rotating to develop one G of "gravity" turns out to be that 1G multiplied by the mass and divided by 2*PI; even using the lighter material possible, the mass of the ringworld will be too much. This is a similar problem to that of the space elevator: a cable that must be able to hold its own weight. But this cable is one billion kilometers long. Whatever you do to reinforce the cable, it will increase its mass, increasing the force on the ring. Long story short, no known material is strong enough (the record for theoretical breaking length is specially crafted carbon nanotubes, around 6200 km breaking length; so we can build a space elevator. What we can't do is build a 980,000,000 km ringworld).

Usually this is handwaved using materials made of (so far purely hypothetical) anomalous matter, whose tensile strength is not derived from the electromagnetic force between atomic orbitals as it happens in ordinary matter, but by the nuclear strong force. You need to be able to construct ring-shaped atomic nuclei, then link them like chain rings without the nuclei fusing together (somewhat the nuclear equivalent of rotaxanes). The resulting "chain" has a tensile strength suitable for weaving the foundation of a rotating ringworld.