The Ultimate Retrograde Solar System

Welcome to the Building the Ultimate Solar System series about building planetary systems with as many life-bearing worlds as possible. This post presents a new “ninja move” to compactify planetary system and build systems with more planets in the habitable zone.

Tell the truth. When you saw the word retrograde in the title of this post, did you think I would be writing about “retro” planets with funny hairstyles or wearing disco clothes?  That would be awesome, wouldn’t it?  Maybe next time…

I stumbled upon a simple way to tighten up the Ultimate Solar System And by stumbled upon, I mean I discovered that someone else had figured it out.  And I took it.

It is a little technical, so let’s get to the basics.  Two planets orbit the same star.  If the orbits are far apart, the setup is stable because the planets don’t feel each other’s gravity too strongly. If the orbits are too close together, the planets give each other little gravitational kicks that add up. Over time, these kicks change the shapes of the planets’ orbits. Eventually the planets’ orbits cross and the two planets either collide or at least cause major re-arrangement of the system’s orbits. Not stable.

There is a stability limit. Two orbits closer than the stability limit are unstable.  A central goal of Building the Ultimate Solar System is to create planetary systems that are just a little bit wider than the stability limit. This maximizes the number of planets that can fit into a given area.  The area we care about is the habitable zone, where planets can have liquid water on their surfaces.

But there’s a twist. It turns out that the stability limit only applies to normal planetary systems. Systems in which all the planets orbit the star in the same direction.

In a great paper from 2009, Smith and Lissauer show that there is a different stability limit for systems in which half of the planets orbit the star in the opposite direction.  In that case, the stability limit is closer, so planetary systems can be more compact.

It makes a big difference.  You can fit about twice as many planets into a given stretch of orbital real estate. The requirement is simply that every other planet must orbit in the opposite direction.  So, planets 1, 3, 5, and 7 orbit the star in a clockwise direction, and planets 2, 4, 6, and 8 orbit counter-clockwise.

Take Earth-mass planets orbiting a star like the Sun. On prograde orbits, 4 Earths fit within the habitable zone.  For alternating prograde and retrograde orbits, 8 Earths fit.

Orbits of Earth-mass planets packed into the habitable zone (shaded) of a star like the Sun.  In the system on the left, all four planets orbit in the same direction.  In the system on the right, eight planets can fit within the habitable zone by alternating the direction that they orbit the star (planets on blue orbits go counter-clockwise and those on red orbits go clockwise).

Let’s use this to beef up Ultimate Solar System 1.  That’s the one with planets a little smaller than Earth and no giant planets with moons.   Here is what it looks like:

Our first ultimate Solar System. Each orbit around the star (thick gray line) contains two pairs of binary Earths in a co-orbital (Trojan) configuration. See here for details of its construction.

The planets are all half an Earth-mass, and there are 6 orbits packed into the habitable zone.  Each orbit has two sets of binary Earths, separated by 60 degrees on the same orbit.  This setup is stable for billions of years, and puts 24 habitable worlds in the habitable zone of a single star.  Not too shabby.

[We’re not going to mess with Ultimate Solar System 2 because the orbital spacing of that one is built on resonances (different story).]

Let’s tweak Ultimate Solar System 1 based on what we learned about retrograde orbits.

It’s simple.  In between each set of orbits from Ultimate Solar System 1 we can insert another orbit as long as it goes around the star in the opposite direction.  And there’s no reason we can’t put the same pair of binary Earths on each retrograde orbit.  Our Ultimate Retrograde Solar System looks like this:

The Ultimate Retrograde Solar System. Planets are half an Earth-mass. There are 12 sets of orbits in the habitable zone: 6 on prograde (gray) orbits and 6 on retrograde (brown) orbits going around the star in opposite directions. Each orbit holds four planets: two pairs of binary Earths separated by 60 degrees along the orbit (in the stable Lagrange L4/L5 points)

We basically just took two copies of Ultimate Solar System 1, flipped one of them onto retrograde orbits, and enmeshed the two together.  Now there are 48 planets in the habitable zone instead of just 24! Boom!

The only downside of our retrograde setup is philosophical.  Up to this point, everything in the Ultimate Solar System happens on its own naturally. Tightly-packed planetary systems exist. Gas giant planets really have large moons, as well as Trojan  companions (well, asteroids although we think that Trojan planets must exist).  And we know of complicated groups of many stars bound together. Of course, it’s unlikely for all of these things to happen at the same time in an optimal way, but not impossible.

With the Retrograde Ultimate Solar System we are now swimming in impossible waters. Two planets can end up orbiting the same star in opposite directions, but only if their orbits are widely separated. I don’t know of any way that nature could produce a system of tightly-packed planets with each set of planets orbiting in the exact opposite direction of its immediate neighbors.

This means that the Ultimate Retrograde Solar System would have to be engineered.  Created on purpose by some very intelligent and powerful beings.

And if these beings were engineering a Solar System, they might take things even further. The next Ultimate Solar System post will show just how deep this rabbit hole goes….   (it’s way way deeper)


14 thoughts on “The Ultimate Retrograde Solar System

  1. Awesome! Place this system in your 16 star system and you get 768 habitable worlds! Looks like you could have a densely populated system like the Firefly ‘Verse.

  2. I wonder if two colliding stars with planets in opposite motion have at least a chance of producing a system with alternating motion orbits…

    1. I don’t think that would work. The planets would have to each jump through a maze of unstable configurations to find a retrograde configuration…

  3. In case anyone wants to see a test of how effective retrograde orbits can be on such systems, here is a video of a guy managing to put Jupiter between the Earth and Venus.

    Sean, did you ever considered using universe sandbox²?

  4. I’m still unsure about the stability of binary planets in the tide-locking region of a star (which, for red dwarves iirc, includes all of the goldilocks zone). My problem is that, even with the binary planets tide-locked to each other, they still feel tidal forces from the star. These tidal forces generate heat, but all energy in a closed system remains constant, so the orbits of each binary planet around their barycenter decay to compensate. This effect, over time, would cause the two planets to merge into one tide-locked planet.

    Earth-like worlds orbiting gas giants would have the same problem, experiencing tighter and tighter orbits until they’ve all collided with the planet.

    How big of an impact is the tidal forces, really? It doesn’t help us for a star to shine for 10 trillion years if our worlds die before then.

  5. Beyond the philosophical problem, I would think that getting from a prograde planet to a retrograde planet would be extraordinarily expensive in terms of delta-v. Wouldn’t it be something like 5x the delta-v required to escape the sun from Earth’s solar orbit (not counting the escape velocity of Earth itself, counting that it’s something like 3.5x total delta-v).
    So, the retrograde system is something like two different planetary empires that can only communicate through a SETI program.

    1. On further thought, the maximum cost would be something like twice solar escape from the planet’s orbit. Since you could do an exact escape, asymptotically reach a point where you were stationary and _just_ unbound, then an infinitesimal push could send you back down on the mirror retrograde orbit, at which point you have to recapture at the retrograde planet.
      Of course, that particular transfer would take literally forever. 🙂

      I would assume that there’s some way to slingshot around another planet to get there cheaper. But without doing any maths, it feels like slingshotting around another prograde planet would leave you going too slow, and slingshotting around a retrograde planet would leave you going scary fast.
      But hey, if you’re talking stories, having your battle fleet slingshotting through low orbit of of a neutral planet at twice orbital velocity with the local authorities screaming at the protagonists in order to attack some system-ending threat on another retrograde planet would certainly add drama to events.

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