PLANETPLANET

Welcome to a new installment in the Building the Ultimate Solar System series. Be prepared: this is a far-reaching post with a big conclusion.

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Sometimes it feels good to find out you were wrong. I had one of those moments a few weeks ago.

I was thinking about how to pack the orbits of planets as tightly as possible (who doesn’t spend their free time thinking about that?). I was thinking about more than one planet sitting on the same orbit.  This is a co-orbital setup. I always thought that co-orbital planets were just a neat trick. The Trojan points 60 degrees in front and behind a planet can be stable — and that is awesome. But there’s nowhere else to go.

Then I had my mind blown.

Let’s start at the beginning.  Imagine two planets orbiting a star.  The planets’ orbits can’t be too close together because it’s not stable. The planets feel the star’s gravity but also each other’s gravity. If the two planets’ orbits are too close together, the repeated gravitational kicks cause their orbits to slowly stretch out. Eventually their orbits cross.  Then the two planets can be in the same place at the same time. Then boom, the planets might collide or one might get ejected into interstellar space.  In any case, the planets’ orbital setup changes completely.

There is a simple limit for how far apart two planets’ orbits must be to be stable. The key ingredient is the Hill radius, a measure of the strength of a planet’s gravity. Concentric planetary orbits need to be spaced by a minimum number of Hill radii for their orbits to be stable. Let’s call that closest stable spacing N Hill radii. There are lots of studies to determine N for different situations. N must be larger than 5-10 for systems with many planets for the system to remain stable.

For a star like the Sun, 6 concentric orbits can fit within the habitable zone, that Goldilocks region where a planet can have liquid water on its surface.  It looks like this:

This might make you think that a star can have at most 6 possibly life-bearing planets. You would be wrong. If you’ve read other installments of this series you know that we can do better than that.  Much much better.

As a first step, we can imagine more than one planet on each orbit.  At a minimum, each orbit can hold two planets.  If the planets are separated by about 60 degrees along the orbit, the setup is stable.

This is the part where I had my mind blown. I re-read a paper from 2010 by Smith and Lissauer (the same researchers behind the idea for the retrograde setup from the Ultimate Retrograde Solar System).

It turns out there is a stability limit for the number of planets that can be spread along the same orbit. The planets must be evenly spaced and there must be at least 7 on one orbit (not a typo: at least 7!). The limit is simple: the planets sharing the same orbit must be separated by at least 12 Hill radii in distance along the orbit.  This is different from before, where we were looking at the distance between orbits.

Smith and Lissauer ran simulations with not 2 or 3 but 42 Earth-mass planets sharing the same orbit!  That is the maximum number of Earths that can fit along Earth’s present-day orbit. And guess what? It’s perfectly stable for billions of years. Over the last couple weeks I ran my own N-body simulations and they match perfectly.  By the hammer of Thor, it really works!

Just this simple ring of planets eclipses our original Ultimate Solar Systems 1 and 2. They had 24 and 36 habitable worlds, and this one has 42.  And we’re not done yet.

Many rings of 42 planets can can be packed into the habitable zone.  The separation between rings depends on the individual planets’ masses, not the total mass on a given orbit.  That means that rings of planets can be packed pretty tightly.

Six rings of 42 Earths can fit within the Sun’s habitable zone and remain stable.

That is 252 possibly life-bearing worlds orbiting a single star!  That’s almost as many as in the 16-star Ultimate Solar System.

There are two factors that determine the number of planets that can be packed in the habitable zone.  The first is the planet mass.  Lower-mass planets have smaller Hill radii. Compared with more massive planets, this means that more low-mass planets can share the same orbit.  It also means that each ring of planets can be closer to its neighbors.

Here is what it looks like for packed systems containing planets of 1/10th Earth’s mass (roughly Mars’ mass), Earth’s mass, and 10 times Earth’s mass (close to the mass of Neptune and Uranus).

The Sun’s habitable zone can fit 57 mega-Earths (10 Earth-mass planets), 252 Earths, or a whopping 1157 Marses!  Holy banana pancakes Batman!

[Short note to skeptics. This may all just seem like too much. This is so far beyond what I thought was possible just a month ago. And as I’ve said, I was very skeptical. Luckily, this is physics that is easily testable. I ran a series of computer (N-body) simulations of a range of configurations (I run a lot of these for my day job after all).  I added some small random fluctuations into the system, and tested a bunch of different twists. And it works. I get the same answer as Smith and Lissauer. And extrapolating from there seems to work just fine.]

There is no need to stick with equal-mass planets. Within a given ring the planets must be evenly-spaced, so I believe the most stable setup is with equal-mass planets. However, there is no reason that all rings must have the same mass planets.  One could imagine a ring of Marses followed by a ring of Earths or super-Earths or whatever your heart desires (if your heart desires that sort of a thing…)

The second factor that influences how many planets can be packed into the habitable zone is the star, in particular its mass. For cooler the habitable zone is closer to the star than for the Sun.  And for hotter stars it is farther away. However, that turns out not to matter much in terms of how many planets can fit (see here). The star’s mass does affect the size of a planet’s Hill radius. Compared with an Earth orbiting the Sun, an Earth’s Hill sphere is twice as big around a star 1/8th as massive as the Sun. That means only half as many planets could fit on a given ring, and each ring would have to be twice as far apart. So only 1/4 as many planets would fit into the habitable zone.  This argues in favor of relatively massive stars. Let’s stick with a star like the Sun this time.

OK, now that we have a handle on things let’s get building.

Here are the ingredients for our mega-system. Our star: the Sun (or its twin).  Our planets: half of Earth’s mass (a lot of upside and little downside — see here). Our setup: a series of maximally-packed rings of planets in the habitable zone. Moons? No (I suspect they would mess up the system’s stability).

The smaller mass gives us 52 planets per orbital ring.

Let’s use the retrograde upgrade.  We can pack planets’ orbits more tightly if the neighboring planets orbit the star in the opposite direction.  For our purposes,  odd-numbered rings of planets (1, 3, 5, 7) will orbit in a prograde direction and even-numbered rings (2, 4, 6, 8) in a retrograde direction.  In case you are wondering, prograde is counter-clockwise when viewed from above the North pole.

Putting the pieces together, here is what we’ve got:

The early Solar System may have had three habitable planets, before Venus and Mars went bad. The TRAPPIST-1 system has three Earth-sized planets in the habitable zone (four if you’re feeling generous). In our first two ultimate Solar Systems we fit 24 and 36 habitable worlds into the habitable zone. That was already pretty awesome.

Now we’ve got 416 planets in the habitable zone of a single star!  This is getting ridiculous!  That’s as many as the 16-star Ultimate Solar System!

I can only think of one way our 416-planet system could form. It must have been purposely engineered by a super-intelligent advanced civilization.  I’m calling it the Ultimate Engineered Solar System.

You might ask, if a civilization were advanced enough to create such a complicated planetary system, couldn’t they just give any planet the right conditions for life?  Well, I guess that makes sense (even though you are kind of raining on my parade here).

Let’s go with that and take it a step further. Assuming that this super-advanced civilization only inhabits one star, what is the most grandiose planetary system it could create?

I can think of one constraint that is hard to overcome. It’s the same one that sunk the Ultimate 16-star Solar System. No star exists in isolation. The region past about 1000 Astronomical Units (remember, 1 AU = the Earth-Sun distance) is affected by other parts of the Galaxy. Passing stars, spiral arms, and clouds of gas all give little gravitational kicks that add up and can destabilize things.  So, even advanced civilizations will want to keep their fancy system within 1000 AU.

This means many more rings of planets, so the spacing between rings will need to be a little wider to keep everything stable.  If we use Earth-sized planets (instead of half Earth-mass ones), here is what we’ve got.

There are 57 rings of 42 planets each. That’s 2394 planets!  Ridiculous!  Most are colder than the habitable zone but hey, this advanced civilization might just throw a Dyson sphere up to warm them up!

I actually built this ridiculous system in a pretty conservative way.  I didn’t include any planets on orbits hotter than the inner edge of the habitable zone, and used larger planets that in our chosen system.

What if this civilization was able to maintain habitable conditions on slightly-smaller planets than Earth?  Let’s say, planets one-tenth as massive as Earth (about the size of Mars).  Well, in that case things get even crazier.

With the smaller planet mass, 89 Marses can fit on each ring (instead of 42 for Earths). And 121 rings of Marses fit out to 1000 AU (instead of 57 for Earths). That makes a whopping total of 10769 planets in one system!

Here’s one final, completely bonkers system.  Imagine that 1) these aliens could maintain livable conditions on Moon-sized planets (~1% as massive as Earth), and 2) they could handle orbits as close to the star as 0.1 AU. [Maybe these advanced creatures could transfer energy from the too-hot planets out to the too-cold ones.]  In that case the numbers skyrocket to 341 rings with 193 planets each. It adds up to more than 65,000 planets orbiting a single star! It would be a titanic job to maintain habitable conditions on all of those planets, but hey, the engineers that built this thing must have been pretty smart already (right, Slartibartfast?).

This type of planetary system — with rings of co-orbital planets — would be an amazing setting for science fiction. The night sky would be dominated by arcs of bright stars, the different rings of co-orbital planets lining up on the sky because of their nearly coplanar orbits.  It would be a constant reminder of the existence and proximity of other worlds. Imagine the competition between species to develop interplanetary travel. Widespread colonization by the fastest-developing species. Only to ultimately discover that their whole Universe was created by a civilization so advanced they seemed like gods. And imagine a disillusioned terrorist who tries to take the whole system down. Any perturbation to one ring of planets would cause a cascade that would trickle down and destroy the whole system (like what happened to the 16-star Ultimate Solar System).  The good guys stop the terrorists at the last minute, only to meet the Creators, who had it under control the whole time….

So there you have it: the Ultimate Engineered Solar System.  Kind of nuts, isn’t it?

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NEW: check out the visualizations of what it would be like to stand on a planet in the Ultimate Engineered Solar System by Lucas Bourneuf using the Space Engine software.