Welcome to what might very well be the culmination of the Building the Ultimate Solar System series. Teaser: the system built in this post could also be called the Ultimate Engineered Black Hole Eyeball Ringworld Solar System (if you’re really not into the whole brevity thing).
Our Solar System has one habitable planet. A few dozen known exoplanet systems (like Kepler-186) host a candidate habitable planet. The Trappist-1 system has three Earth-sized planets in the habitable zone (not too shabby — although we don’t know whether they have life, of course).
How many potentially habitable worlds could one system have? That question is at the heart of the Ultimate Solar System project I’ve been working on for the past several years. I first built Ultimate Solar Systems with 24 and 36 habitable planets. I upgraded in a big way with the Ultimate Engineered Solar System and packed 416 habitable planets in one star’s habitable zone. In the Black Hole Ultimate Solar System I used a supermassive black hole to cram planets 100 times closer together than I could around the Sun, and got up to 550 Earths orbiting in a single habitable zone.
Today I will build what I believe to be the Ultimate Ultimate System of this kind. I don’t think it’s possible to out-Ultimate this one.
Here we go.
Let’s start with a supermassive black hole, like in the Black Hole Ultimate Solar System. It’s 1 million times the Sun’s mass. A behemoth!
Now let’s see what rings of planets we can make. As we saw in the Ultimate Engineered Solar System, a ring of 42 Earths orbiting a Sun-like star is stable.
- The planets on a given ring must all have the same mass,
- There must be at least 7 of them, and
- They must be evenly spaced along a circular orbit and separated by at least 12 Hill radii. (The Hill radius is the distance inside which a planet’s gravity dominates over its star’s.)
Around a supermassive black hole (of 1 million Sun masses) the Hill radius shrinks to 1/100th of its value around the Sun. That means that 100 times more planets can fit on the same ring around a black hole! It looks like this:
See how the planets are so close the symbols are overlapping in the plot on the left? Well, that plot is still only showing one planet out of ever 50! (And their sizes are hugely exaggerated so you can see them). The zoom on the right shows just how close together the planets actually are (sizes still exaggerated, but by much less).
There is another big deal consequence of the shrunk-down Hill radius. Around the Sun 6 Earth-mass planets can fit on stable orbits within the habitable zone. Pack them any tighter and they’re unstable (more detail in this post).
Well, around a supermassive black hole a lot more planets can fit within any given region. Too many to easily visualize. Let’s just take a look at a small slice of the habitable zone:
The black lines are maximally-packed orbits of Earth-mass planets around the Sun. The green lines are around a supermassive black hole. In this little slice, two Earths can fit around the Sun. Or 145 can fit around the black hole!
Now we can use two tricks that we know and love (details here and here). First, each orbit can hold a whole ring of up to 4000+ planets. We’ll get to the numbers later, but you can already tell this is going to add up to a *lot* of planets (hence the title of this post). Second, if each neighboring ring of planets orbits in the opposite direction — such that rings 1, 3, 5, … orbit clockwise and rings 2, 4, 6, … orbit counterclockwise — then the rings can be more tightly-packed while remaining stable.
What should we do about illumination? We need sunlight to keep these planets habitable. I can’t choose, so I’m going to build three separate systems.
Let’s start simple. In the Black Hole Solar System I replaced the Sun with a Sun+black hole system. Let’s do the same thing again. Of course, in the Black Hole Solar System I used a Solar-mass black hole and here we will use a million Solar-mass black hole. But it doesn’t make all that much difference.
A supermassive black hole is not very big. Its event horizon (or Schwartzschild radius) — the distance inside which light can’t escape — is only 2% of the Earth-Sun distance (that is, 0.02 AU, or 3 million km). That’s about 4 times bigger than the Sun. The innermost stable circular orbit around the black hole is three times that distance, about 0.06 AU. To avoid anything too crazy, I’m going to put a single Sun three times farther out, at 0.2 AU.
In this system the central black hole+star weigh 1 million Suns (well, 1,000,001 to be annoyingly precise). But they produce the same amount of energy as one Sun. That means that the habitable zone is at the same place as for the Sun.
Let’s break out the planets. If we mega-pack rings, with alternating rings on retrograde orbits, we can fit up to 689 rings in the habitable zone. Each ring can hold up to 4154 planets. That makes for a maximum of 2.86 million planets! I’m going to be a cautious (I know, that is not my usual m.o.) and space things out more. Let’s use 400 rings with 2500 planets each. That’s a million Earths in the habitable zone!
UPDATE: It was pointed out to me by Phil Armitage, astrophysicist (and photographer) extraordinaire, that the Sun would tidally disrupt anywhere within about half an AU of the black hole. (I should have realized this since he and I had recently worked together on tidal disruption of ‘Oumuamua.) Million-Earth system 1 would not survive with the Sun on a 0.2 AU-wide orbit. Instead, the Sun would be torn to shreds and spiral onto the black hole in an accretion disk. Let’s transform the Sun into that disk, and for now regulate its rate of infall to make it give off the same amount of light as the normal Sun. Now it looks like this:
In Million Solar System 2 we’ll just change things up a tiny bit. As in the Black Hole Ultimate Solar System, we’ll add a stable ring with 9 Sun-like stars evenly spaced along the same orbit at 0.5 AU. Since the central “star” is 9 times brighter than the Sun, the habitable zone is three times farther away than the Sun’s. Apart from that we have the same setup of planets as before. It looks like this:
Let’s switch up the illumination again. This time I’ll put a ring of stars on an exterior orbit. I’ll put 36 Suns on a 6 Astronomical Unit-wide orbit. That means that a planet on a 1 AU-wide orbit will still receive the same amount of total illumination as Earth. Now it looks like this:
With an outer ring of Suns, the source of illumination is separate from the central object around which planets are orbiting. Each planet is bathed in sunlight from all sides. The planets have no night side! It’s like Asimov’s permanent-daytime planet Kalgash!
The most magnificent view in this system would come from the North (or South) pole. All 36 stars would be at the horizon in permanent sunrise/sunset. You could only see the stars from the poles if you could block out all the stars.
You would never feel alone in these systems. The other planets would loom huge in the sky! Neighboring planets are about ten times closer than the Moon (on an Earth-like orbit in systems 1 and 3). Earth is about 4 times larger than the Moon, so neighboring planets would be about 40 times larger in the sky than the full Moon. That’s 20 degrees in the sky. That’s about the size of a laptop computer held at arm’s reach, only up in the sky!
Meanwhile, planets on adjacent rings of orbits would zip across the sky, growing larger than the full Moon before shrinking and fading in a matter of minutes, only to make room for the next planet. I explained what this would look like for the Black Hole Ultimate Solar System — now it would be amplified by rings of planets.
There are some big differences between these million-Earth systems and the Solar System.
Everything moves ridiculously fast. Instead of taking 365 days to orbit the Sun, a planet on Earth’s orbit would take just 9 hours to complete an orbit around the supermassive black hole! The planet is orbiting at about 10% the speed of light. At these super-high speeds, relativity starts to matter. Starlight would also be stretched by the black hole’s gravity. Stars closer to the black hole would appear redder and those farther from the black hole would appear bluer. Time would move more slowly for planets on different rings around the black hole. Two babies born at the same instant on different rings would age at slightly different rates. The baby on the inner ring would age slightly more slowly. This effect is small in this system, but it is huge in the super-extreme environment of Miller’s planet in the (awesome) movie Interstellar.
There would also be a gravitational lensing effect every time a star passed behind the black hole. As seen from the planets, stars are distorted into arcs and then into rings when the star is aligned just behind the black hole. Here is an animation of what this would look like specifically for the 9-star ring setup of the Black Hole Ultimate Solar System (done by @GregroxMun using Space Engine):
In all these systems, the planets are tidally-locked to the central black hole.
In Million-Earth systems 1 and 2, all planets may be Eyeball planets. The illumination comes from the same direction as the black hole, so one side of each planet is in permanent daytime while the opposite side is in permanent darkness. A perfect setup for Eyeball worlds! (Of course, whether or not they become Eyeball-like depends on details like their atmospheric thickness and total water contents).
In Million-Earth system 3 the planets will not be Eyeball worlds because their source of illumination is separate from the strong gravity they feel. Since the ring of Suns is external these planets are in permanent daylight. There is no hot/cold side of the planet.
The planets in all three systems would not be spheres. The black hole’s gravity would squish them. The side closer to the star would be pulled on more strongly than the side opposite the black hole. This is the tidal force, and it would stretch the planets out. (It’s the same kind of force that makes planets always show the black hole the same face).
Time for a twist.
Imagine living in million-Earth Solar System 1 or 3. The size of your planet’s orbit is the same as Earth’s around the Sun. There are a ton of other planets in the sky. But the relative speeds of different planets is enormous. You cannot travel to another planet because the speeds involved are beyond the capabilities of any current (or even yet envisioned) technology.
But thousands of planets share your orbital ring. The closest ones huge in the sky, 40 times as big as the full Moon. Given that all planets are locked to the black hole, these giant neighboring worlds never move in the sky.
This presents an opportunity. The sides of each planet could be joined. Despite the huge orbital speeds relative to the black hole and to neighboring rings of planets, the relative speeds between neighbors is almost zero. If they could be joined you could travel between the planets. A space elevator could connect planets at the bull’s eye points, where the worlds are closest to each other. It’s kind of like the setup in the book Hothouse by Brian Aldiss, in which the Moon and the (tidally-locked) Earth are connected, although in that case it it by a planet’s spider-web like branches.
Imagine that each pair of neighboring planets along a given ring was connected. It would almost make a Ringworld:
The difference between this setup and the Ringworld from Larry Niven‘s book is that in this case there is no livable surface area in between the planets. The space elevators only serve to connect the different worlds.
People living on all the planets on a given ring can intermix. But the huge relative speeds between rings means that all other rings of planets are off-limits. It would be prohibitively expensive (in terms of energy) to land on a planet from a separate ring. Then again, it wouldn’t be hard to communicate with them (or, for that matter, to launch pretty devastating bombs at them).
This could make a great setting for science fiction stories, a blend between the Ultimate Engineered Solar System, Hothouse and Ringworld (and featuring Eyeball planets!). That’s why I’m also putting this post in the Real-life Sci-Fi worlds series.
A final big question: where would such a system come from?
In the Ultimate Engineered Solar System, I argued that systems with rings of planets are not likely to form naturally. There are way too “just-so”. Instead, they must be engineered by super-advanced civilizations that can make their own planets and systems (like Slartibartfast from the Hitchhiker’s Guide to the Galaxy).
Of course, you might ask: if super-intelligent aliens can make their own Solar Systems, couldn’t they just make any planet they want habitable? To which I reply once again (very loudly): sheesh, stop raining on my parade!
I can imagine super-advanced aliens creating a system like the million-Earth Solar System as a cosmic work of art. Kind of like the art of skyscrapers or painted icebergs. A way to say “look how fancy we are” on the grandest scale.
Or maybe aliens would create this kind of system as a zoo. They could have a gradient in climates from the hottest to coldest, and stock the planets with all sorts of creatures they collect across the Universe. Of course, they’d have to be careful not to put the wrong combinations of space-creatures on the same ring of planets, because that wouldn’t end well!
There you have it: the million-Earth Solar System(s). BOOM!
Questions? Comments? Words of wisdom?
Technical issues. I don’t want to hide anything under the rug, so I’ll mention that there are a couple of small potential issues with this system. The first is related to stability of compact planetary systems in the face of strong tides. The planets are simultaneously stretched by the black hole’s gravity (which is super strong) as well as their closest neighboring planets (which are super close-by). This can make the planets want to point their bulges in two places at once, and repeated tidal flexing can cause energy losses that translate into orbital shifts that on long timescales can sometimes destabilize planetary systems (details here). In such an extreme environment I’m not convinced this is a real problem, as it’s possible that the planets will actually get stretched not into cigar-shapes but instead into ninja star-shapes, with longer parts pointing both toward their neighbors toward and away from the black hole.
Of course, there is an easy way to circumvent this issue. Tides are strongest for planets super close to their stars (or the largest mass, here the black hole). As in million-Earth system 2, we could just put a ring containing as many bright stars as possible to move the habitable zone outward. For example, with a ring of 64 stars, each with twice the Sun’s mass (and 16 times its brightness), the habitable zone would be moved out past Neptune’s orbit. A million Earths would still fit in the habitable zone, they would just be somewhat farther apart. For instance, neighbors on the same ring would now be a little farther than the Earth and Moon.
It’s also worth mentioning that the concept of stable rings of planets was developed in Newtonian gravity, without accounting for the extra effects that arise from general relativity. While those should not in principle have a strong effect on circular orbits, this environment is so extreme that it’s possible that additional effects could make a difference.
- Building the Ultimate Solar System page
- Real-life Sci-Fi Worlds page: testing ideas from science fiction (and coming up with new ones)
- The Ultimate Engineered Solar System: introduction to stable rings of planets
- The Black Hole Solar System: an introduction to black holes
- The Black Hole Ultimate Solar System: first crazy system with a supermassive black hole
- Real-life Sci-Fi World 2: the Hot Eyeball planet
- The movie Interstellar (with supermassive black hole Gargantua)
- Hothouse by Brian Aldiss
- Ringworld by Larry Niven
- Kalgash by Isaac Asimov. Related posts here and here.
- The Hitchhiker’s Guide to the Galaxy by Douglas Adams.
- Thanks again to @GregroxMun for making that sweet animation of the stars passing behind the black hole (and also to Space Engine)