My Gravitational Pet Peeve That Ruins Most Sci-Fi
Modern sci-fi shows love to display astounding space vistas packed with multiple closely orbiting moons and planets all as giant disks in the sky.
In just about every single case, this would lead to massive catastrophe and total death, because of the 3-body problem.
The Three Body Problem
Gravitational orbits are fun things to model and simulate. And in our spatially three dimensional universe, we see very stable orbits between two close objects all the time. But if you have three objects that are anywhere near the same mass getting to within any sort of close distance to each other, it’s pretty much always chaos.
If you have three similarly-massed bodies in close proximity and they are connected by rubber bands, then the way they move is stable and predictable. But if they are “connected" by their own gravitational pull, then the resulting orbit is chaotic. No equations exist that can fully describe their orbits over time.
This is called the Three Body Problem, and Newton talked about it in 1687. But we can only predict how those orbits will change over time by doing simulations, where we just calculate the next tiny step that each of the three massive bodies take. As you can see below, the orbits are crazy. They don’t repeat, and they actually won’t ever repeat (even though this gif loops).
“But wait!” you might say. “I live on a planet from which I see two big disks in the sky all the time!” Yes, and that is the interesting part about the three body problem. It’s only a “problem” if all three masses are similar and close.
Here are some of the bounds that DO allow stable three-body orbits:
If one of the objects is a much larger mass than the other two.
If two of the objects are of much larger mass than the other one.
If two objects are in a stable orbit around each other and the third object is very distant.
Let’s evaluate the Sun-Earth-Moon system by these criteria.
Criteria 1: Is one of the objects much larger than the other two? The Earth is about 81 times heavier than the moon. That sounds like a lot, but in terms of gravitational attraction, the Earth and Moon masses are pretty close because the two bodies are pretty close. The moon is only about thirty Earth-widths from the surface of the Earth.
Because of this, some (a minority of) astronomers actually classify the Earth-Moon system as a double planet.1 But the mass difference between the Earth and Moon doesn’t meet Criteria #1 for allowed three body orbital systems because they are too similar and too close to each other. They are strongly self-interacting in both directions.
But the Sun is 333,000 times more massive than the Earth and also about that many times further away than the Moon. So the Sun-Earth mass discrepancy definitely meets Criteria #1 for stable three body orbits. The Earth simply doesn't strongly affect the Sun.
Criteria 2: Are two objects much larger mass than the other one? No, this is clearly not the case for the Sun-Earth-Moon system.
But our closest neighboring star system is like this! Alpha Centauri is a triple-star system. We call the three stars Alpha Centauri A, Alpha Centauri B, and Proxima Centauri. We call Proxuma that instead of Alpha Centauri C because it’s our closest star.
Alpha A and Alpha B are about the same size, being sun-like stars that are within 20% of the same mass of each other. They orbit in a pretty elliptical (but very stable) orbit, and so they get as close to each other as 3 billion miles and as far as 10 billion miles.2 Astronomers call them Alpha Centauri AB and classify them as a binary star system.
But Proxima Centauri is a much smaller star, about 1/8th the mass of each of the other two stars. That still is pretty close in mass to the other two, so it doesn’t meet Criteria 2. So why is that 3-body star system orbitally stable?
Criteria 3: Are two objects close and the third one far away? Alpha Centauri A & B are within 3 to 10 billion miles of each other. Alpha Proxima is currently 1,200 billion miles away from that pair. This is a huge difference, with Proxima being hundreds of times more distant than the binary pair is from each other. This is thus a stable 3-body system, because Proxuma is too distant to mess with the orbits of Alpha Centaur A&B.
The same is also true of the Sun-Earth-Moon system. The Earth and the Moon are very close to each other, but the Sun is hundreds of times further away. This closeness of the Earth and Moon means they lock together strongly enough so that the gravitational tugging of the Sun can’t disrupt them and make them fly apart. The Moon does wobble as it orbits the Earth, but that’s not a destabilizing wobble.
What Happens In Close and Similarly-Massed 3 Body Systems?
In 3 body systems that fail to meet the three stability criteria above, there is anarchy and rejection. The orbits become chaotic. And at some point, usually just thousands or a few million years into the interaction, a Fast Close Pass occurs. In a 3-star system, this would look like one of the larger stars orbiting very quickly and very closely past a somewhat smaller star. When this happens, the gravity of the larger star will strongly accelerate the smaller star not just toward it, but also along with it in the direction of the larger star’s fast movement.
The larger star will slingshot the smaller star, vastly increasing its momentum. Because the smaller star has less mass, this momentum transfer also means an outsized speed transfer. The smaller star will be given a huge speed boost, enough so that it is going so fast that it leaves the system. It speed is so fast that the gravity of the other two stars can’t slow it down to bring it back into the chaotic orbit, and the smaller star goes rogue.
This happens to stars all the time. It can also happen to planets, creating cold wandering worlds floating alone through the galaxy. Jupiter might have kicked planets out of our solar system via a slingshot effect as Jupiter migrated to a further and further out orbit during the early solar system. This is a very bad thing for the planet:
And in stars in complex orbits around galactic black holes, stars can be slingshot so hard that they leave the galaxy, and are know as hypervelocity stars.
There are a few meta-stable orbits of close, similarly-sized 3-body systems, and more have been discovered just in the last 15 years or so. Here is one of them, by By MaxwellMolecule:
But if one of these is nudged by even a tiny bit, the whole system collapses and goes chaotic. This is true of all the found “stable” solutions of close gravitational 3 body systems. They exist on a knife-edge of stability, with no restoring force. They would last just a few years in real life (or a few thousand years at most), and could only exist even that long in a totally isolated region of space with not tidal forces from even distant other bodies.
But otherwise, close gravitational systems are simply not feasible.
Rolling My Eyes at Sci-Fi Vistas
Shows like Star Trek: The Next Generation and The Expanse handle this extremely well. You simply don’t see gravitationally ridiculous systems in those shows. But graphic artists cannot seem to help themselves in other shows.
Star Trek: Discovery
The planets above would crash together or eject one another from their solar system in a few dozen years. Or else they would simply pull each other apart, first siphoning off the atmosphere of the world the two people here are walking upon.
Marvel’s Guardians of the Galaxy
Morag simply cannot exist over any length of time in a real universe.
I give a partial pass to the Sovereign’s planetary “system", because it’s obviously an artificially-created situation:
Some crazy tech could perhaps bring those planets together, but then the stress of the combined gravity would make them basically smoosh and meld into each other. The rock of each planet is simply not strong enough to structurally withstand the close gravitational smushing. That said, if you can bring planets close to each other, maybe you also have some sort of internal inertial stabilizing system. Like I said, I give the Sovereign system a pass because they clearly have Clark Tech.3 Which is in-Universe consistent.
Star Trek 2009
If you see this, you have 14 minutes to live.
Star Wars
This is actually sort of fine, because Tatooine is clearly very far from its two very closely-self-orbiting suns. There is currently significant debate about whether planets can exist in close binary systems. I think Tatooine is impossible over millions of years in a habitable zone, but might be possible if the suns are very big and bright and the habitable zone is more than a billion miles from the two suns. It’s debatable, but probably fine.
Actually, I found that all three Star Wars trilogies were pretty good about this gravitational chicanery, with only one exception: Utapau in Episode III: Revenge of the Sith:
This one system, along with the fact that giant asteroid fields seems to stay super close to each other without gravitationally falling to make a planetesimal, are really the only gravitational beefs I have with the movie franchise. Though the extended universe unfortunately falls into this recent trend of graphic designer’s dream that are a physicist’s nightmare:
The Planet Nur from the video game Jedi: Fallen Order
Predators (2010)
GET TO THE CHOPPAH! Because if you ever see this, you will die very soon.
Night Sky (2022)
I hope J.K. Simmons still has really good Farmer’s Insurance.
So the next time you see such a vista in a movie, TV show, or video game, I hope you take a few second to pause it and simulate in your head what happens to the characters if everything suddenly were to become gravitationally accurate. Add your own sound effects.
I don’t personally accept this because the center of gravity of the Earth-Moon system is below the Earth’s surface. I think double planets should have their center of mass outside either’s surface.
Think the orbit of Saturn (3 billion miles) and a little past the orbit of Pluto (10 billion miles).
“Clark Tech” is a term in sci-fi that means unimaginable technology that looks like crazy magic to us, named after Arthur C. Clark based on his statement that “any sufficiently advanced technology will appear to be magic.” It’s usually reserved for tech advances that clearly break all known laws of physics, not just advanced technology. The Sovereign clearly are very technologically advanced, but they are also from a comic book.