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:

The orbits of planets packed into the habitable zone of our chosen star.  Each black circle around the star is the orbit of a single planet with a mass of 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 planets in a stable system that can be packed into the habitable zone for planets with 0.1, 1, or 10 times Earth's mass is 14, 7, and 3, respectively.

The orbits of planets packed into the habitable zone of our chosen star. Each black circle around the star is the orbit of a single planet with a mass of 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 planets in a stable system that can be packed into the habitable zone for planets with 0.1, 1, or 10 times Earth’s mass is 14, 7, and 3, respectively.  [Technical details: each pair of planets is spaced by 10 mutual Hill radii.  (see Smith & Lissauer 2009)]

What can destabilize a system of planets is the planets’ gravity.  The more massive (bigger) the planets, the stronger the gravity.  So we can pack low-mass (small) planets together more efficiently than high-mass (big) ones.  That means we can put a lot more small planets in the habitable zone than large ones. Systems can be packed most tightly if all the planets have the same mass.  If we mix planets with different masses in the same system, they need to be more widely-spaced (for the details, see this paper).

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 outer planet completes 3 orbits for every 2 orbits of the inner 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.

Orbital layout of Jupiter-mass planets in the habitable zone.  Each pair of adjacent planets is in 3:2 resonance, meaning the outer planet completes 3 orbits for every 2 orbits of the inner planet.

Orbital layout of Jupiter-mass planets in the habitable zone. Each pair of adjacent planets is in 3:2 resonance, meaning the outer planet completes 3 orbits for every 2 orbits of the inner planet.

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

 

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  1. Building the ultimate Solar System | planetplanet
  2. Building the ultimate Solar System part 2: choosing the right planets | planetplanet
  3. Building the ultimate Solar System part 4: two ninja moves — moons and co-orbital planets | planetplanet
  4. Building the ultimate Solar System part 5: putting the pieces together | planetplanet
  5. Les liens de la semaine – Édition #82 | French Coding
  6. Un hipotético sistema solar con 60 planetas habitables | Astronomía | Eureka

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