Black holes and planets, part 2. In Part 1 we talked about black holes and built the Black Hole Solar System.

In this post I’ll build a planetary system with lots of possibly life-bearing worlds — an Ultimate Solar System — with a black hole.

Let’s go big. The center of our system will be a black hole 1 million times as massive as the Sun. That’s almost as massive as the one in the center of the Milky Way. Boom!

I’ll use the awesome image from the movie Interstellar to represent the black hole. It’s not exactly the setup we’re going for (our black hole isn’t spinning and doesn’t have a disk around it), but it looks awesome, and it was created by Kip Thorne using some heavy-duty computer simulations (on that note, I highly recommend his book the Science of Interstellar).

A supermassive black hole buys us something important. It shrinks the Hill radius.

The Hill radius is the ball around a planet in which its gravity dominates over the star’s. Planets are naturally spaced in units of Hill radii. For our purposes Hill radii are like kilometers or liters or slices of pizza – a unit of measure.

A planet’s Hill radius depends on the mass of whatever it’s orbiting. Around a million-sun black hole, a planet’s Hill radius is 100 times smaller than around the Sun. That means a given region of space can stably fit 100 times more orbits around a black hole than around the Sun.

Planets can be super close to each other because the black hole’s gravity is so strong! If planets are little toy Hot wheels cars, most planetary systems are laid out like normal highways (side note: I love Hot wheels). Each car stays in its own lane, but the cars are much much smaller than the distance between them. Around a black hole, planetary systems can be shrunk way down to Hot wheels-sized tracks. The Hot wheels cars — our planets — don’t change at all, but they can remain stable while being much closer together. They don’t touch (that would not be stable), they are just closer together.

Let’s put things in perspective. About six Earth-mass planets can fit on stable orbits within the Sun’s habitable zone. Simply replace the Sun with a million-Sun black hole, and 550 Earths can fit in the same region!

Take a look at this tiny slice of orbital space, from Earth’s orbital distance at 1 AU out to 1.2 AU. Around the Sun 2 Earths can fit. Around a black hole 145 Earths can fit!

For scale, Earth’s nearest neighbors – Venus and Mars – are 0.3 and 0.5 Astronomical Units (AU) away. In a maximally-packed system, another Earth could sit on an orbit just 0.1 AU away. But around a black hole the closest neighbor could be just 1/1000th (0.001) of an AU away!

Now we can’t just keep making our supermassive black hole more and more massive, shrinking the Hill radius down smaller and smaller. Because if the Hill radius gets down to Earth’s actual size, the black hole would start to tear the planet apart, and we don’t want that. With our million-Sun black hole the Earth’s Hill radius (on its current orbit) would already be down to the limit, just a bit more than twice Earth’s actual radius.

How are we going to illuminate our planets? We have three choices:

Put the Sun in a close orbit around the black hole. This should work fine, as long as the Sun doesn’t get torn to pieces, which it wouldn’t as long as it’s outside about 0.1 AU.

Use a disk of material glowing as it falls onto the black hole to provide light. This was the setup in Interstellar.

Put a ring of stars around the black hole, as in the Kalgash 5 system we built (based on the Ultimate Engineered Solar System).

I just love rings of orbiting planets and stars. They are like glittering space necklaces! (Note from my younger self: where did that space necklaces thing come from?)

Given how massive the black hole is, one ring could hold up to 75 Suns! But that would move the habitable zone outward pretty far and I don’t want the system to get too spread out. So I’ll use 9 Suns in the ring, which moves everything out by a factor of 3. Let’s put the ring at 0.5 AU, well outside the innermost stable circular orbit (at about 0.02 AU) but well inside the habitable zone (from about 2.7 to 5.4 AU).

And Boom! Here is the Ultimate Black Hole Solar System:

This system has ten times more planets than the original Ultimate Solar Systems 1 and 2, and it’s more packed than the Ultimate Engineered Solar System. We could go nuts and toss in some co-orbital (Trojan) planets to up the number of planets in the habitable zone to about 1000. However, this is already getting really hard to draw so let’s stick with the 550 planet system.

It would be pretty interesting to live on a planet in this system. Despite the larger orbit compared with Earth, the length of the year would be insanely short. It would take just a few days to complete an orbit around the black hole – about 1.6 days at the inner edge of the habitable zone and 4.6 days at the outer edge.

From the surface of a planet in the Ultimate Black Hole Solar System, the sky would not be boring. Even though it looks like planets are on the verge of crashing into one another, they are on stable, concentric orbits. However, they do pass very close to one another. At closest approach (conjunction) the distance between planets is about twice the Earth-Moon distance. These planets are all Earth-sized, about 4 times larger than the Moon. This means that at conjunction each planet’s closest neighbor appears about twice the size of the full Moon in the sky. And there are two nearest neighbors, the inner and outer one. Plus, the next-nearest neighbors are twice as far away so they are still as big as the full Moon during conjunction. And four more planets that would be at least half the full Moon in size during conjunction. Conjunctions happen a little less than once per orbit, so every few days there is a gaggle of giant objects passing across the sky!

The Suns themselves would also be a sight to behold (but don’t look straight at them of course). The ring of nine Suns would complete an orbit around the black hole every 3 hours. That means that every twenty minutes one of the Suns would pass behind the black hole. The black hole itself is small. Its event horizon (or Schwartzchild radius) is only the size of the Sun despite being a million times more massive. But since each Sun is moving really fast, it passes behind the black hole in less than one minute (49 seconds).

When a Sun passes behind the black hole, the black hole’s gravity bends its light and can act like a lens. It focuses the Sun’s light toward the planet. This distorts the shape of the Sun into a ring with a size of 2.5 degrees (the size of the Einstein radius). Here is an animation of what this would look like, done by @GregroxMun using Space Engine:

As you can see, at any given time at least one of the stars is being lensed into an arc shape as viewed from the planets. A pretty sweet light show!

So that’s the Black Hole Ultimate Solar System! Boom! Be prepared: in my next post I will “Engineer” this system even further…

Questions? Comments? Words of wisdom?

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