Building the ultimate Solar System part 3: choosing the planets’ orbits
We are building the ultimate Solar System. In Part 1 we chose the right star. In Part 2 we chose the right planets.
Today’s job: choosing the right orbits for the planets.
Let’s get started. Our goal is simple. We want to pack as many planets into our star’s habitable zone as possible. We have one key constraint: our system must remain stable for billions of years. We don’t want any planets falling into the star. Or crashing into each other. Or getting thrown out into interstellar space. No, we want their orbits to remain relatively constant and definitely not do those terrible things.
Orbits. Gravity. That should be pretty simple, shouldn’t it? [Short answer: No. Long answer: keep reading.]
How close together can we cram planets’ orbits without making the system unstable? The habitable zone is only so wide. The closer we can pack the planets, the more we can fit into the habitable zone. And the awesomer our ultimate Solar System becomes.
This image shows systems of planets in our preferred size/mass range packed as tightly as possible:
When planets become big enough, their orbital spacing changes. Big planets are pushed around by the gas disks in which they form. This pushing — called “orbital migration” — puts planets in special configurations called resonances. In resonance, the time for nearby planets to complete an orbit becomes a simple fraction, like 3/2. Meaning, the inner planet completes 3 orbits for every 2 orbits of the outer planet. It can be any simple fraction but the most common ones are simple, like 3/2 or 2/1 or 4/3. Planets, even massive ones, are usually stable in these resonances. So as planets get more massive they don’t need to be spaced farther and farther apart. For example, in this image, four Jupiter-mass planets fit comfortably within the habitable zone of our chosen star.
Why do we care about Jupiter-sized planets? They are way too big and don’t have solid surfaces. Well, wink wink, we’ll talk about this tomorrow.
There you have it. Gravity and orbits show us how to squish as many planets as possible into a given area. And the area we care about is, of course, the habitable zone! Of course, it’s possible that different-sized planets could have different habitable zones. But that’s a story for another day.
SUMMARY: The right orbits is the configuration that can squeeze the most planets into the habitable zone. Small planets can be squished tighter than large ones. We can fit 14 of our smallest planets in the habitable zone of our chosen star, or 7 Earth-sized planets, but only 3-4 of our largest (10 Earth mass) planets.
But not to fear: tomorrow’s ninja moves will add two big twists to this story. And blow your mind.
Up next: Two ninja moves — moons and co-orbitals
Very cool blog!
I wonder if the habitable zone could be extended for exotic planets. Perhaps low density planets with a radius of twice that of Earth’s but with the same surface gravity would have more surface to collect sunlight and could be outside the “standard” habitable zone? Particularity if they only showed one side to their star? Conversely could a very dense (tungsten?), small planet orbit inside the habitable zone and yet support life? Perhaps a dense ring of orbiting bodies could block some starlight for the planet?
You are right that the “habitable zone” is a pretty vague concept. What counts is not whether a planet is in what we consider to be the habitable zone but whether it has life! There are plenty of possible life-bearing planets outside the habitable zone (e.g., Jupiter’s moon Europa, Saturn’s moon Titan, hypothetical free-floating Earths — see here: https://aeon.co/essays/could-we-make-our-home-on-a-rogue-planet-without-a-sun).
Whether a planet can host life surely depends on the planet: how big it is, what kind of atmosphere it has, etc. But there is also feedback: life can make a planet more habitable! This is called the “Gaia” hypothesis. There are several real feedbacks on planets that do tend to make planets more liveable when they have life.
The question then becomes: how do you get life on a planet in the first place?
I just did some spreadsheeting and, using 10 hill radius spacing the higher-mass stars were able to hold more orbits in their habitable zones. The number of orbits within the habitable zone which are in 3/2 resonance is of course invariant as long as the defined habitable zone varies only with stellar luminosity, though I would be concerned about gas giants 2 orbits away trying to force each other from 9/4 to 2/1 resonance.
I also found more orbits than you did, which I assume is due to difference in where we placed the limits of habitable zones.
“the outer planet completes 3 orbits for every 2 orbits of the inner planet.”
Isn’t this backwards?
You’re right — that is exactly backwards! I will fix that.