Real-life Sci-Fi World 17: the Verse from Firefly

Welcome to Real-life Sci-fi worlds.  In this series, I use science to explore life-bearing worlds that are the settings for science fiction stories. 

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Firefly.  A spectacular show, created by Joss Whedon.  One of the few science fiction shows that my wife likes. We’re re-watching it with our older son and he loves it too. The show was canceled in 2003 after just one season, but it won several awards that year, had a follow-up movie called Serenity, a series of comic books, and a role playing game also called Serenity. It remains a cult classic to this day (the Firefly subreddit has almost 150 thousand members).

The show is set in year 2517 in the “Verse”. The crew of the “Firefly-class” spaceship Serenity travels around to different worlds within the Verse, having all sorts of rowdy adventures. It feels like it’s set in the wild west, but in space and with a strong Chinese influence (in the language and culture).

Here is the intro to Firefly:
After the Earth was used up, we found a new solar system and hundreds of new Earths were terraformed and colonized. The central planets formed the Alliance and decided all the planets had to join under their rule. There was some disagreement on that point. After the War, many of the Independents who had fought and lost drifted to the edges of the system, far from Alliance control. Out here, people struggled to get by with the most basic technologies; a ship would bring you work, a gun would help you keep it. A captain’s goal was simple: find a crew, find a job, keep flying.

[This is one of two versions of the intro. The other one talks about a “galaxy of Earths” that were terraformed, which is interesting since ‘galaxy’ is an astronomical term but it’s being used like a gaggle of geese, or a murder of crows.]

Let’s dive into the Verse. First, let’s see how the story is set up, and then I’ll evaluate whether the system works from an astronomical point of view (spoiler: it doesn’t), and show how it could be fixed and seriously leveled up.

The Verse is said to be the star 34 Tauri, which is actually the designation given by British astronomer John Flamsteed in the year 1690 to a “star” in the constellation Taurus. It was only in 1781 that Sir William Herschel recognized it as the planet Uranus. (Cue the Uranus jokes).

The Verse is a complicated place. There are five main sequence (normal) stars, a plethora of rocky planets, both inhabited and not, a gaggle of gas giants, a myriad of moons, a few asteroid belts, and several brown dwarfs that have been “helioformed” into artificial stars (by shrinking them down to increase the pressure in their cores until fusion was ignited). A bunch of the planets were terraformed to make them habitable over the span of a few hundred years.

Here are the key features of the system, organized by central star, with properties taken from this impressive compilation.

• White Sun is the central star of the Core, the heart of the Verse, which has about 40 billion total inhabitants. White Sun is a 3.2 Solar-mass A star, with a luminosity of 80 times the Sun’s. It is orbited by 11 planets (no gas giants) and two artificial stars — one with one planet of its own and another with two. It also has an asteroid belt (the ‘Halo’) exterior to all of the planets’ orbits.
• Red Sun is 93% of the Sun’s mass and 79% of its brightness. It hosts 7 planets (no gas giants) and two artificial stars, each with four planets of their own. Its orbit is 68 astronomical units from White Sun (remember, 1 astronomical unit is the Earth-Sun distance). It has an asteroid belt (called ‘the Motherlode’) in the middle of the system, between the second and third planets from the star.
• Georgia, also called Huang Long, is 10% more massive than the Sun and 26% brighter. It hosts 13 planets (including two gas giants) and one artificial star (with three planets of its own). It also orbits at 68 astronomical units around the Sun. Red Sun and Georgia are in each other’s mutual L3 Lagrange points. (We’ll come back to this). No asteroid belt.
• Kalidasa is a 1.29 Solar-mass F star orbiting White Sun at a distance of 121 astronomical units. It has 12 planets (three gas giants) and one artificial star, with three planets of its own. It orbits White Sun at a distance of 121 astronomical units. No asteroid belt.
• Blue Sun, also known as Qing Long, is a 1.7 Solar-mass F star six times brighter than the Sun. Its orbit around White Sun is at 180 astronomical units. It hosts seven planets (two gas giants) and one artificial star with a single planet of its own. It has an asteroid belt (called ‘Uroborus’) just beyond the innermost gas giant, which is the fourth planet from the star.

Put together, here is what the Verse looks like, according to Geoffrey Mandel via Quantum Mechanix:

There are a few key features that really tie the Verse together and make it a great setting for storytelling. There are different habitats around five different stars (and their six companion artificial stars). Planets in different parts of the system have different physical and orbital properties, different skies, as well as different cultures, languages, and geography. There is empty space between the stars, and travel in the wilds of space allows for stories involving ambushes (for instance, by the Reavers), unexpected technical problems, and downtime to get to know the characters better. The Verse also has wild cards like the asteroid belts, which can always provide some drama.

Overall, the Verse is a pretty awesome setting. There is material for a whole lot more than the single season of Firefly, and it’s a bummer that it was cancelled before its time.

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Let’s evaluate whether the Verse actually makes sense. I’m going to ask some pointed questions about the Verse. It’s going to get a little messy. But don’t worry, after knocking it down, I’ll pick it back up and build a new, better Verse (actually, four of them).

The big question is simply: is the Verse plausible from an astronomical point of view?

The answer is, sadly, no.

On the positive side, there are several pieces of the puzzle that are broadly pretty accurate. For example, the stars themselves have reasonable properties, astronomically-speaking (apart from the fact that, given its larger mass, White Sun would appear bluer than Blue Sun). In fan-created explanations of the Verse (like this one), there is a good amount of attention paid to the process of terraforming planets, explaining that only planets within a reasonable range of orbital distances could be terraformed. This is analogous to the circumstellar “habitable zone“, the Goldilocks-esque ring of orbits around a star inside of which a planet can plausibly have liquid water on its surface (closer-in is too hot, farther out is too cold).

The concept of “helioforming” is a little fishy. While compressing a brown dwarf to trigger fusion in its core is vaguely plausible (if such technology existed), the artificial stars in the Verse have masses that are as high as those of red dwarf stars. There would need to be another source of mass for this to make sense. But worrying about helioforming is a little nit-picky, and I think this concept is actually pretty cool.

The Verse’s Achilles heel is orbital stability. There is no getting around gravity, and the system of stars is completely unstable.

As I’ve discussed before, a significant fraction of stars are not alone but rather have companion stars.  The most common are binary systems (with two stars), but there are plenty of known triple, quadruple, quintuple, and even sextuple star systems.  Check out the Castor 6-star system:

Star systems follow a standard blueprint that keeps their orbits stable.  They are organized in a hierarchical setup.  Each set of orbits is on a different size scale.  The sizes of stars’ orbits do not go 1-2-3, they go 1-10-100. Any one star is really close to one other star.  All other stars are much farther away.

The Verse has two big problems. The first is that it doesn’t follow a hierarchical setup, and the second is that the orbits of Georgia and Red Sun are poorly-chosen (see technical note 1 at the end of the post).

To evaluate the stability of the Verse, I ran N-body simulations of the setup outlined in fan guides. I tested a few different configurations, and in all cases the Verse’s system of five stars (even without considering the artificial stars) was disrupted within a few hundred years. Within a hundred years there were close encounters between the stars, and one or more either collided with White Sun or was ejected into interstellar space within a thousand years.

In the context of the Firefly story, it took humanity a few hundred years to really make the Verse home by terraforming a bunch of planets (and helioforming some brown dwarfs). So the fact that the Verse itself is unstable on an even shorter time frame is a no go. It simply doesn’t work.

Naturally, I mean no disrespect toward Firefly, the fans, Joss Whedon, or the cast, especially Nathan Fillion (the actor who plays Malcolm Reynolds, captain of Serenity and one of the most charming actors out there), or anyone else associated with the show.

That’s just how physics works.

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But hope is not lost. Let’s build a better Verse.

I’m going to build four new Verses, starting from a nice simple one and ending up with a kind of crazy one. Each will be just as good as the original for storytelling, include just as much cool stuff and setups for adventure. And will actually be stable.

The first essential ingredient in any planetary system is the star. Or, in the case of the Verse, the (many) stars. There’s no problem having lots of stars in a system — I once built a system with 16 stars (and hundreds of habitable worlds). It looked like this:

Now let’s apply the same principles to the Verse.

Better Verse 1 is a classic, well-behaved, hierarchical system.

White Sun is a pretty massive star, with planets that are on relatively wide orbits. We don’t want any other stars so close that they disrupt the system’s orbits. The outermost orbit around White Sun is its asteroid belt, the Halo, which extends from 40 to 43 astronomical units. A binary star needs to be at least about 3 times as far to avoid overly perturbing the asteroids’ orbits. Let’s put the smallest orbit around White Sun at 200 astronomical units.

We need to create a series of orbits to fit the four other stars. In Firefly, Red Sun and Georgia are both pretty close to White Sun, so let’s keep those close-by. We’ll put Red Sun and Georgia in orbit around each other, with an orbital size of 20 astronomical units. Both of those stars are close to the mass of the Sun, meaning that their habitable zones are at about 1 astronomical unit, so their mutual orbit at 20 astronomical units won’t cause any problems.

We’ll add in Blue Sun and Kalidasa as a binary on a wider orbit. We’ll maintain the same hierarchical setup: Blue Sun and Kalidasa’s mutual orbit is 200 astronomical units in size, whereas their orbit around the White Sun-Red Sun-Georgia triplet is 2000 astronomical units.

It looks like this (note: I didn’t draw the orbits of each planet, but there is space for all of them and the artificial stars too):

This system keeps all of the key characteristics of the Verse but makes it stable.

The only downside is that this new Verse is much bigger than the one envisioned in Firefly. So, the time for travel between stars would be a lot longer (unless, of course, you just want to appeal to faster space travel).

Nonetheless, I want to make a more compact Verse…

Better Verse 2 is a more compact hierarchical system that switches out the stars for lower-mass ones.

Which stars should we choose? Here is an H-R (Hertzsprung-Russell) diagram, which shows all the different types of stars out there. The diagram compares stars’ brightnesses and temperatures.

How could we swap out the stars in the Verse to allow the system to be more compact? We want stars that are not very bright, because those will have habitable zones that are much closer-in. With habitable zones close to their stars, other stars don’t need to be as far away to maintain stability.

The faintest stars come in two flavors: red dwarfs and white dwarfs. Red dwarfs are ‘normal’ stars in that they are on the stellar main sequence. They’re like the Sun, but a lot punier — the lowest-mass red dwarfs (like Trappist-1) are about 10% as massive as the Sun, more than 1000 times less luminous than the Sun, but live for trillions of years. The habitable zones of faint red dwarfs are typically located between 1% and 20% of an astronomical unit.

White dwarfs, on the other hand, are the skeletons of dead stars. After a star similar to the Sun evolves off the main sequence to become a red giant, then puffs off its outer layers, what is left behind is a white dwarf. White dwarfs are only about the size of Earth (which is about 1% the size of the Sun in radius). They don’t undergo nuclear fusion, but rather just sit and slowly cool off….for eternity. They start off hot and blue-ish, then evolve to become “white” and, in time will eventually become ultra-cold “black dwarfs” that don’t give off any light. The habitable zones of white dwarfs are located at about 1% of an astronomical unit.

Let’s swap out the stars in the verse for white dwarfs and red dwarfs. White Sun and Blue Sun will become white dwarfs — Blue Sun can be a little younger white dwarf to maintain its blue color, whereas White Sun can be a run-of-the-mill white dwarf. The three other stars will be red dwarfs.

Let’s make sure there is space for all of the planets (but I’m not going to pay attention to the artificial stars, although they could still fit in there as brown dwarfs for anyone who is worried about being extra-precise).

I’ll use the same orbital structure as in Better Verse 1, but with very different orbital sizes. The orbit that will set our minimum size scale is the Red Sun-Georgia binary. Let’s assume these are among the puniest of red dwarfs, with habitable zones at a few percent of an astronomical unit. With a binary orbit of 1 astronomical unit, the habitable zone (and well beyond) for both Red Sun and Georgia would remain nice and stable.

The next-biggest orbit — of White Sun around the Red Sun-Georgia binary — is then 10 astronomical units. This is the same size as the Blue Sun-Kalidasa binary. Finally, the widest orbit is 100 astronomical units.

Put together, Better Verse 2 looks like this:

It’s similar in architecture to Better Verse 1, but it’s 20 times smaller! That means that interstellar travel between the stars would be a whole lot easier.

Better Verses 1 and 2 are both physically plausible, stable, and fit the original setup of Firefly. But I still feel like they’re a little too…. normal. Let’s weird things up a little!

Better Verse 3 uses a supermassive black hole to make the Verse a horseshoe constellation system.

Two or more planets can share the same orbit around a star. In a “Trojan” setup, two planets remain 60 degrees apart along the same orbit. It’s completely stable (for example, a setup with three Jupiters at zero, 60 and 120 degrees orbiting the Sun is stable — details in this post).

In a “horseshoe” setup, two planets share almost — but not quite — the same orbit. Since one planet is slightly closer to the star, it orbits a little faster, and eventually catches up to the other one. As the two approach each other, they have a gravitational flyby in which the planets swap orbital distances — the one that was closer to the Sun is now farther, and vice-versa. Then the pattern repeats until the next flyby. When viewed from above, in an “inertial” frame of reference, the planets just orbit the star, shifting their positions slowly. But when viewed from the point of view of a camera moving along at the planets’ average speed, the two planets trace out a horseshoe shape. That’s why they are called “horseshoe” orbits. It looks like this:

The horseshoe U-turns are slow — they only happen every 10-100 orbits (50 in this case). The planets don’t need to have the exact same masses like they do in this example — that is the case for Janus and Epimetheus are in a horseshoe configuration orbiting Saturn.

A horseshoe orbit can have more than two planets. I first noticed this phenomenon (which was previously unstudied) when writing a blog post called Cohorts of co-orbital planets, but I misunderstood exactly what was happening in my simulations. A little later, I performed a big set of N-body simulations and discovered how these horseshoe ‘constellations’ (systems of two or more planets undergoing horseshoe orbits) really work.

A horseshoe constellation can include up to 24 Earth-mass planets sharing the same orbit! I showed how the orbital dynamics works in this scientific paper that published in 2023 — for the gory details with many more animations, see Constellations of co-orbital planets.

In a horseshoe constellation, each planet moves relative to its neighbors simply because each is at a slightly different orbital distance. This next animation shows a 4-planet horseshoe constellation: when viewed from above (inertial frame) the planets are just zooming around the star. But when viewed from the co-moving frame of reference (moving at the average speed of the planets), then you can see that each planet is constantly moving relative to the others, and is performing horseshoe U-turns when it encounters its next-door neighbors.

Let’s re-imagine the Verse as a horseshoe constellation. It will be the stars of the Verse that are following horseshoe orbits, and to make it work we’ll need a supermassive black hole.

Let’s put a million-Solar mass supermassive black hole at the center of Better Verse 3. Black holes are convenient because they provide a lot of mass without any light (we’ll ignore their accretion disks made up of shredded stars). I’ve built several planetary systems around black holes in the past, like the Black Hole Solar System, the Black Hole Ultimate Solar System, the Million-Earth Solar System, and even a re-imagined version of Asimov’s Kalgash (from Nightfall).

The ratio between the mass of the Sun and a million-Solar mass black hole (1 in a million, of course) is comparable to the mass ratio between Earth and the Sun (which is only about 3 times higher). This means that the dynamics of stars orbiting the black hole are basically analogous to those in the animations above, although the distances and timescales will change.

How close should our ring of stars be to the black hole? We want the planets’ orbits to remain stable. To make things simple, let’s assume that all of the stars in the Verse are the same mass as the Sun. Now, since the stars are orbiting the black hole, and the planets will orbit the stars, our planets are the equivalent of moons. The stability limit for moons is well known to be about half of a planet’s Hill sphere; inside the Hill sphere, a planet’s gravity dominates over the star’s. So, in our case, a planet can remain stable around a star as long as its orbit is smaller than about half of its star’s Hill sphere (measured with respect to the black hole). Let’s say that we want orbits to be stable out to 10 astronomical units around each star — that will give enough orbital real estate to include all of the planets. After doing a little math, that means that we need the ring of star orbits to be at about 3000 astronomical units from the black hole (see technical note 2 at the bottom for details).

Let’s thrown in an asteroid belt around the black hole, just for fun (and because there’s a few asteroid belts in the Verse). I can imagine including all sorts of other things — like a more distant ring of mysterious other planets — but I’ll stop there to avoid over-complicating things.

And there you have it, with the stars following the same types of horseshoe constellation orbits that we saw in the animation:

Better Verse 3 is awesome, astrophysically speaking. It’s got all of the stars and planets the Verse needs. (If desired, you could even squeeze a lower-mass artificial star in between each of the normal stars along the co-orbital ring, as long as all of the artificial stars were the same mass).

One downside is that the orbital speeds are pretty gigantic, so interstellar space travel would be tricky. Each star is zooming around the black hole with an orbital speed of about 1000 kilometers per second, which is about 30 times higher than Earth’s orbital speed around the Sun of 30 kilometers per second. In order to move around among the planets orbiting a given star would not be a problem, but if a spaceship like Serenity wanted to travel between, say, White Sun and Georgia, it would need highly upgraded engines to provide the required acceleration and deceleration. Unless there were some clever orbital maneuvers to help out.

All of the stars in Better Verse 3 are the same mass as the Sun, even though I’ve left them as different colors in the image. It would be possible to have two different masses of stars — for instance, half of them could be more massive, blue stars (like A or F stars), and half could be lower-mass, redder stars (like K or M stars). In that case, we would need to add one additional star to have an even number (important for stability), and alternate between the two types.

One thing that kind of bums me out about Better Verse 3 is that there would be a long long time between horseshoe U-turns of the stars. Out at 3000 astronomical units, it takes 164 Earth-years to complete an orbit around the black hole. Horseshoe U-turns don’t generally happen more frequently than about once every 10-100 orbits, so the time between events is measured in thousands of years.

Horseshoe U-turns would be pretty amazing — they would involve slowly seeing another star get closer and closer in the sky, before the close approach and orbital swap. It’s a shame they are so rare in Better Verse 3.

Let’s spice things up one last time and make horseshoe U-turns happen more frequently.

To make this happen, we’ll need to move the stars orbit closer to the black hole, which means we’ll need to shrink the stars’ masses so that planets can still orbit stably in the habitable zone. As we discussed above, we can either make the stars red dwarfs or white dwarfs. It doesn’t make much difference here. But I have a soft spot for red dwarfs (probably because of Trappist-1 and Kepler-186 f), so let’s go with those.

Let’s put the stars on an orbit around the black hole with a radius of 100 astronomical units. Now it takes only 1 year for each star to orbit the black hole. With this setup, horseshoe U-turns happen on a timescale of decades instead of millennia. They will be astronomical events of societal importance, happening at least once every generation.

And I’ll throw in another asteroid belt, this time exterior to the stars’ orbits. Here’s what we’ve got now:

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So there you have it, four better Verses! Boom!

Each Better Verse system has all the advantages of the original Verse from Firefly, with the benefit of actually being stable. Better Verses 1 and 2 are completely run-of-the-mill and reasonable, astronomically speaking. Better Verses 3 and 4 require putting together two exotic concepts — horseshoe constellations and planets orbiting black holes — and so, while plausible, are a little more of a stretch (kind of like the Ultimate Solar System).

(Of course, I didn’t go into excruciating detail by including each specific planet, artificial star and asteroid belt in these Better Verses. But don’t worry, there is plenty of space for all of them.)

Questions? Comments? Words of wisdom?

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Additional Resources

• The Real-life Sci-fi Worlds series
• The Firefly reddit fan page
• The Firefly intro song, You can’t take the sky from me
• Related blog posts: A 16-star Ultimate Solar System (about maintaining stability in multiple star systems), An Earth with five Suns in the sky (about including different types of stars in one big system), the Ultimate 2-star Trojan system (about Trojan orbits), A horseshoe planetary system and Constellations of co-orbital planets (about horseshoe orbits), the Black Hole Solar System, the Black Hole Ultimate Solar System, and the Million-Earth Solar System (about planets orbiting black holes), and, finally, Asimov’s Kalgash: a planet in permanent daytime (parts 1 and 2 — about re-imagining a specific planet from a sci-fi classic using planets orbiting a supermassive black hole).

[Technical note 1. For those of you who want to know why the Verse is unstable, the main glaring reason is the orbits of Georgia and Red Sun around White Sun. It is claimed that they orbit White Sun in each other’s L3 Lagrange points. However, the L3 point is locally unstable, meaning that two planets (or stars) would not remain in each other’s L3 points for long. And the concept of Lagrange points only applies when the primary (main star) is at least 27 times more massive than the secondary (largest planet, or other star) — as I discussed in creating the Ultimate 2-star Trojan system. So, it’s all bad.]

[Technical note 2. To calculate the Hill sphere, the equation is R_Hill = r * (m/3M)^1/3 — here, r is the orbital distance, m is the mass of the orbiting body and M is the mass of the central body. In our case, a star of the mass of the Sun is orbiting a black hole a million times more massive. So, m/M is 1 divided by a million. That means that (m/3M) is 1 divided by 3 million, and (m/3M)^1/3 is 0.00693. If we want the Hill radius R_Hill to be 20 astronomical units, then the orbital distance r must be 20/0.00693 = 2886 astronomical units. I rounded up to 3000 in Better Verse 3 to keep the numbers simple and to give a little extra wiggle room.]