Building the ultimate Solar System part 4: two ninja moves — moons and co-orbital planets

We are building the ultimate Solar System.    In Part 1 we chose the right star.  In Part 2 we chose the right planets. In Part 3 we chose the right orbits for the planets.


Today’s job: Discovering two ninja moves that will allow us to pack way more worlds in the habitable zone.

The last post (part 3: choosing the right orbits) was pretty simple stuff.  You can cram more small planets into the habitable zone than big ones.  Nothing too shocking.  Well, learning the basics always comes before the ninja moves.

What makes these moves ninja (to use ninja as an adjective) is that they put more than one world on the same orbit.  This means that we can pack a lot more worlds into our star’s habitable zone.  It’s like the 6-pack: a way to cram more awesomeness into a limited space.

Let’s meet the ninjas.

NINJA MOVE 1: MOONS.  A planet’s moons orbit the star just like the planet does.  I used this to my advantage this when I built a better Solar System.

Here are the large moons in the Solar System:

Large moons of the Solar System, with Earth for scale.  The moons are ordered by which planet they orbit.  From Wikipedia (https://en.wikipedia.org/wiki/File:Moons_of_solar_system_v7.jpg).

Large moons of the Solar System, with Earth for scale. The moons are ordered by which planet they orbit. From Wikipedia.

The biggest Solar System moons orbit the biggest planets (Jupiter and Saturn).  Systems of moons form like mini-Solar Systems, in disks of gas and dust around gas giant planets. [In fact, large Solar System moons have some properties in common with extra-solar planets].  The moons are located very close to the gas giants.  The orbits of the most distant large moons are only about 30 times larger than the radius of their host planet.  In comparison, Earth’s orbit is about 200 times larger than the radius of the Sun.

We want worlds in our ultimate Solar System that are a little bigger than these large moons.  We want worlds about half to twice Earth’s size. Although there is some debate, I’m going to allow any gas giant that is Saturn-sized or larger to have large moons.

In the Solar System, Jupiter has the most (four).  Given how close-in the Solar System moons are located, large moons are likely to stay close.  But how many big moons could a gas giant have?  Well, at least as many as Jupiter (four).  But probably not that many more.  The orbits of planets and moons tend to be spaced logarithmically.  Think, 1, 10, 100, 1000 rather than 10, 20, 30, 40.  The farther from the star/planet, the bigger the spaces between planets/moons.  If the zone with large moons extends from 5 to 50 times the planet’s radius, this only gives us room for 5 large moons spaced like Jupiter’s.  We’ll stick with a maximum of 5 large moons per gas giant planet.

Could a planet like Earth have a moon large enough for life?  The jury is still out on how to form such a moon (probably by a giant impact between two big growing planets).  But there is no reason not to consider this possibility.  However, an Earth-sized planet probably could not have more than one large moon remain stable.   [Note that Earth may have had a second large moon that crashed into the Moon!]  In fact, if an Earth-sized planet had an Earth-sized moon, this would essentially be a binary planet.  Each planet would orbit the other, as the pair orbited the star. Pretty awesome concept!  Pluto and Charon are basically a binary (minor) planet. Charon is about half as big as Pluto and about 10% as massive.

A binary Earth would behave mostly like the Earth-Moon system does today.  But tides would be much stronger.  The two Earths always show each other the same face as their orbit their common center of gravity.

A binary Earth.  An Earth-sized planet with a similar sized moon orbit their common center of gravity.  Each planet keeps the same side pointing to the other.  Credit: Wikipedia http://en.wikipedia.org/wiki/Double_planet

A binary Earth. An Earth-sized planet with a similar sized moon orbit their common center of gravity. Each planet keeps the same side pointing to the other. Credit: Wikipedia

The planets each make one full rotation for each orbit around each other.  This means that a day should be about a month in length.  This may have some impact on the planets’ climate, but probably in a good way.  Slowly-rotating planets may remain habitable closer to their stars than fast-rotating planets.

SUMMARY: A gas giant could have up to 5 moons large enough to be habitable.  Planets in our chosen size range can also have large moons but probably only one.

NINJA MOVE 2: CO-ORBITAL PLANETS.  When you hear the word “Trojan”, you probably don’t think of asteroids.  But they are real!  What is interesting about the Trojan asteroids is that they share the same orbit as Jupiter.  And so do the “Greek” asteroids.  This image shows where these asteroids are located.

The inner Solar System.  The planets are labeled and the blue lines show their orbits.  The small dots are asteroids.  The main asteroid belt is shown in white.  The green dots -- called "Greeks" and "Trojans" -- are co-orbitals with Jupiter.  From Wikipedia. http://en.wikipedia.org/wiki/File:InnerSolarSystem-en.png

The inner Solar System. The planets are labeled and the blue lines show their orbits. The small dots are asteroids. The main asteroid belt is shown in white. The green dots — called “Greeks” and “Trojans” — are co-orbitals with Jupiter. From Wikipedia.

The Trojan and Greek asteroids are about 60 degrees in front of and behind Jupiter.  Normally, when an asteroid comes close to Jupiter, the planet’s strong gravity deflects the asteroid.  Eventually the asteroid’s orbit takes it close to Jupiter.  Jupiter launches the asteroid out of the Solar System.

The Trojan and Greek asteroids live on islands of stability.  It turns out that the positions 60 degrees ahead and behind Jupiter are protected from its strong gravity.  These are called the L4 and L5 points (the L is for Lagrange, who discovered that they are stable).  Since they share the same orbit, they are also called co-orbitals.

Lagrange points of a planet (blue) orbiting a star.  L4 and L5 are the place where co-orbital planets are most likely to be.  From Wikipedia  http://en.wikipedia.org/wiki/Co-orbital_configuration

Lagrange points of a planet (blue) orbiting a star. L4 and L5 are the place where co-orbital planets can survive.  The other points (L1, L2 and L3) and not stable.  Credit: Wikipedia

Asteroids that orbit at L4 or L5 are stable.  They can orbit happily at those points forever.  They don’t stay exactly at L4 or L5; rather, they trace little circles about those points.  That is why the Trojans and Greeks are clouds instead of all being found at a single point.

Co-orbital (aka Trojan) planets are like a person walking with a man-eating tiger but always staying behind it, just in its blind spot.  Perfectly safe, it turns out, but with mortal (gravitational) danger right nearby.

L4 or L5 would be stable islands for an Earth-sized planet.  Even one with a large moon.  In fact, two Earth-sized planets — one at L4 and one at L5 — could be stable. In some circumstances L4 or L5 could even be stable for another gas giant (but just one).

Now switch out Jupiter for Earth.  Earth also has L4 and L5 points.  Earth even has a Trojan asteroid.  Two Earth-sized planets can share an orbit in their mutual L4/L5 points.  Separated by 60 degrees, the two planets’ orbits are stable.

Systems of planets that include co-orbitals have to be a bit more widely-spaced.  Otherwise they become unstable.  That means that we can’t cram quite as many orbits into the habitable zone.

The orbits of planets packed into the habitable zone of our chosen star, with co-orbitals (Trojan planets).  Each orbit is occupied by two planets separated by 60 degrees.  The planets are either 0.1, 1 or 10 times Earth's mass.  The shaded area represents the habitable zone, which extends from about 0.2 to 0.4 Astronomical Units (AU; 1 AU is the Earth-Sun distance).  The number of pairs of co-orbital planets that can be packed into the habitable zone is 9, 6, and 2 for planets with 0.1, 1, or 10 times Earth's mass, respectively.

The orbits of planets packed into the habitable zone of our chosen star, with co-orbitals (Trojan planets). Each orbit is occupied by two planets separated by 60 degrees. The planets are either 0.1, 1 or 10 times Earth’s mass. The shaded area represents the habitable zone, which extends from about 0.2 to 0.4 Astronomical Units (AU; 1 AU is the Earth-Sun distance) for our chosen star. The number of pairs of co-orbital planets that can be packed into the habitable zone is 9, 6, and 2 for planets with 0.1, 1, or 10 times Earth’s mass, respectively.

Even though there are fewer orbits in the habitable zone, there are more planets.  With just one planet per orbit we were able to fit 14, 7, and 3 orbits of planets of 0.1, 1 or 10 times Earth’s mass.  Including co-orbitals we can only fit 9, 5 and 2 orbits.  But two planets per orbit makes it 18, 10 and 4 planets in the habitable zone.  Give them each a large moon and the numbers are doubled.  Boom!

As we saw previously, a system of gas giant planets tends to have different orbital spacing (in resonances).  The gravitational effects of Earth-sized Trojan planets don’t change anything in that case.  So we could still fit four gas giant planets in the habitable zone of our chosen star.  Of course, we can add in some ninja moves there too…

SUMMARY: Given one planet orbiting a star, stable islands exist on the same orbit: 60 degrees in front and 60 degrees behind the planet.  A gas giant planet can have an Earth-sized planet in each of these points with no effect on orbital stability.  Two (but not three) Earth-sized planets can share the same orbit, separated by 60 degrees.  These are called co-orbital or Trojan planets.  Wider orbital spacing is needed for a system of co-orbital planets.

OVERALL SUMMARY: We are becoming ninjas!  With moons and co-orbitals, many worlds can share the same orbit. This means we can pack more Earth-sized worlds into the habitable zone.


Up next: putting the pieces together to build our ultimate Solar System.

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  1. #1 by Jim Baerg on June 15, 2014 - 10:14 pm

    Will co-orbital planets tend to stay about 60° from each other or will they play catch up like Janus & Epimetheus in the Saturn system

    ISTR reading that the the trojan configurations gets unstable when the smallest of the 3 bodies gets a mass that is a significant fraction of the 2nd largest body. Is that correct?

    • #2 by Sean Raymond on June 16, 2014 - 10:36 am

      Co-orbitals will indeed stay at about 60 degrees separation. There are other types of co-orbital configurations such as horseshoe orbits (like Janus and Epimetheus) or even eccentric 1:1 resonances that are extremely weird.

      In terms of the mass ratios, the planets need to be less than about 1/30th of the stellar mass. This is no problem, since Jupiter is about 1/1000th of the mass of the Sun, so anything up to about 30 Jupiter masses can participate in a co-orbital configuration. The two planets can have the same mass.

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