A mediation on our place in the leviathan physics of the cosmos.

This is a concept that would provide living space of humans in space colonies, or at least in principle it could. In actuality, it is a bad idea. I don’t even see a place for it in science fiction, if the author is scientifically honest. There’s no plausible mechanism for getting material into the location where it would be needed, and even the most outer-fringes would be extremely impractical to reach, even by exotic rocketry technologies.

Nonetheless, it is very fun to talk about. Indeed, we should try to understand the engineering design environment.

There are companion calculations to this post in the juypter notebook here:

## The Concept — Tidal Gravity

Rotating space stations produce an undesirable side-effect, which is called the Coriolis effect. The effects on human health are not very well-understood, because the studies of continued exposure were very limited and undertaken a long time ago. Because this will very probably be a major problem for future inhabitants of space, we enter into a state of tradeoffs between requiring more material for larger gravity wheels and subjecting inhabitants to greater Coriolis forces, and the health impacts that brings.

Short of just living on the surface of a planet (as we are doing now), there are almost no ways out of this tradeoff. Linear acceleration isn’t useful, because it could only matter for extremely energy-inefficient spacecraft with major engineering constraints on propulsion thermal management and such, which may see tremendous advances in the future, but will still be problematic even assuming so.

Using tidal gravity is one of those few options we have to escape these tradeoffs. This has even been seriously suggested within Earth’s gravity well, although the tidal forces are so weak that you end up with a megastructure scale construction that delivers a very small fraction of Earth normal gravity:

However, we don’t have to limit our considerations to Earth. Clearly, the ideal candidate for tidal gravity would be one with tremendous tidal forces, which means tremendous mass plus density, which means black holes.

I tried to express the merits of this scheme in the following Stack Exchange question (comment actually):

What I wrote on this idea:

There could be several reasons that the structure might ultimately be a ring. It’s the largest construction that you can make for which the entire thing is uniformly co-orbiting. Let’s imagine that they wanted to maximize 1g habitability. It seems that they could have a dense cloud of rings, all of which provide a full 1g on the BH-facing and reverse-facing inner surfaces. I haven’t thought about this much, but it could provide astronomically greater habitat area than other designs, assuming you want 1g and minimal Coriolis forces.

After writing it, I realized that I’m talking about something so strange that there’s probably not much (if anything) already out there on it. So let’s hit the core of the argument now that goes beyond tidal gravity to the structural reasoning.

## Breaking Length and Mass

Building a space station, you are limited by materials. The essence of this reality can be expressed by several parameters, but many of them are very unwieldy to get an intuitive grasp. For the situation I describe here, the notion of breaking length is by far the most fruitful:

I like Zylon as a reference, because it’s not fictional (enough said about that). Note that breaking length in a tidal field is going to be 4 times the length in a uniform gravitational field (what is given in the article).

Assuming Zylon, breaking length is 384 km in an infinitely uniform gravitational field. The tidal gravitational field increases linearly as you move away from the central point, and if I recall the math correctly, this affords 2x the length of a uniform field. But you also have 2 sides (think of a barbell) on either side of the neutral point, so we can say 4x the length. But reality isn’t so forgiving, because this isn’t accounting for load from any actual payload that you attach to it, as well as engineering safety factors. The safety factor is often quoted to be 3. So we have 4 times increase from the field geometry, dock 3 for the safety factors, and then need to optimize economics to obtain the ideal length by balancing the mass of structural materials compared to habitat mass. Since this is still strictly sci-fi, and I don’t want to be a wet blanket on people’s imagination, I’ll be extremely generous and say the remaining factor is somewhere in the neighborhood of 1 to 2. We started out with 348 km breaking length from the material properties, and I’ll just round it out to 300 km total habitat size in the radial direction.

This is the maximum size we can make our habitat, while still generating 1g of gravity on the ends, and still being in the material constraints.

## Industrially Viable Zone

This constraint allows us to formulate the math for the range of radii that habitats could exist.

Here, I start out stating the obvious, what the gravitational and tidal field is around a star or a black hole.

Next, we require that the length of the habitat (l) be the exact length that will obtain 1g on the edges (I incorrectly wrote “r” in the equation where I should have used “g”, sorry).

This gives us our constraint in terms of mass of the black hole, and distance from its center (r) that we need to be at in order for materials to be sufficiently strong to keep 1 Earth-normal gravity in the habitat. In more palpable inequality terms, it looks like:

You’ll notice that I added an additional constraint. This is because the mathematics are not actually fully valid for an orbiting body. Nonetheless, at sufficient distances from the object you’re orbiting, the rotational accelerations can be neglected, and this is what I did. I’m not interested in analyzing cases where the assumption would hold invalid, because that would defeat the value proposition (low Coriolis forces) anyway.

Here are some graphs, first, starting with a zoomed-in view of the low mass options, with lines representing the constraints. Here, the values of M (the x-axis) and r (the y-axis) need to be above the red line but below the green line.

Here is a much larger view, showing the eventual intersection of the lines at high masses.

One result of these calculations is that almost every black hole in the universe has sufficient tidal forces for us to use to make a habitat that provides Earth-normal gravity with acceptable materials.

## The Problem — Escape Velocity

I did a bit of a case-study with a stellar-mass black hole of 5 times the mass of our sun. This yields a radius range that is extremely tight compared to the distance that Earth orbits the sun from. The outer edge of this range (where the habitat would be exactly 300 km in length) would have an escape velocity of 76 km/s. For reference, it takes a little less than 10 km/s to get into orbit from the surface of Earth. Any Delta V of this value would be outright impossible with chemical propulsion, and would require some kind of ion drive.

I will stop a moment here and note that this is still entirely acceptable hard-sci-fi fodder. Stellar mass black holes are very common, and 76 km/s is attainable (though not easy), and even small compared to values that might otherwise be involved in interstellar journeys in the first place. An advanced civilization could come up on such a common object, and then create orbital habitats that get gravity from tidal forces.

However, this is right about where the viability stops. A “smaller” habitat closer in to the black hole would require around 2,000 km/s, to get to, which is very exotic. It’s not just getting there that’s the problem either. It’s not entirely clear if any usable natural satellites would exist in this area, although they could. The tidal forces would rule out planet-like things, but a ring (like Saturn’s) would still be possible, and could provide the material to make the habitats out of. Maybe.

Next, I looked into a black hole of the size of the one at the center of the Milky Way. The industrially usable range around that would be about 1 full Astronomical Unit (the distance between the Earth and the sun) from the center of the black hole. This would provide an enormous amount of space — similar to the conventionally envisioned Dyson sphere. The problem then becomes the downright absurd values of Delta V that would be necessary in order to access this.

## Habitat Geometry

The habits could be a ring fully encircling the black hole, sure. To me, though, this seems like an irrelevant point. Since the different parts of the ring are self-contained pressurized habitats, and since they are all independently orbiting in a stable orbit, any given section of a ring could be considered its own independently functioning space habitat. Connecting the atmospheres between multiple sections of the ring is possible, physics just doesn’t impose any additional constraints, and this would all be up to the prerogative of the inhabitants.

Let me return to the source material, and a reply to the comment I left about habitat rings around black holes:

dangerous, expensive, pointless. I was trying to say, sure it’s all those things if it’s your 2nd circumstellar ring — probably not if it’s your 1000th.

Granted, I would afford full validity to this claim. After interstellar society becomes a thing, then one day, presumably, black holes will become a frontier. After all, stellar-mass black holes are not uncommon.

I do want to conclude by pointing out that the potential for gravity from tidal forces is genuinely unique. If you had a habitat ring around another star, then it would seem assumed that gravity was obtained by rotating habitats. It’s possible (although unlikely due to transhumanism, etc.) that black hole gravitational environments could provide relief to human-like people who otherwise would have spent their entire lives in high Coriolis force environments because the scale of their society was beyond what could be sustained on planetary surfaces along, and black holes opened up the possible of a mega-habitat with gravity that would have felt normal to their ancestors back when they used to live on Earth.