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Given ideal circumstances and a type 4 or 5 Kardashev scale level of technology to set the system in motion (but not to maintain the motion over time):

How many planets 1/4 of the Earth's mass could share an orbit while remaining stable assuming there is an equal spacing between the worlds?

If at least 4 of these objects could share an orbit, how many stable orbits could coexist within/bordering the goldilocks zone?

Vincent
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Tyson of the Northwest
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  • "1/4 Earths" = planets 1/4 the mass of Earth? – HDE 226868 Dec 06 '14 at 00:28
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    Yes. Rocky bodies with gas/liquid atmosphere approx 1/4 the mass of earth. – Tyson of the Northwest Dec 06 '14 at 00:29
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    I'm not sure any planet that size can hold an atmosphere in the habitable zone. Mars is .4g and it has its problems. – Oldcat Dec 06 '14 at 00:51
  • hmm, good point. So smaller planet (less surface area) higher density to get approx 1g? – Tyson of the Northwest Dec 06 '14 at 00:52
  • If that would have no effect (since comparable gravity undermines any gains you would get for less volume but more complexity) than earthlike would be fine. Basicly sufficient to support human life. – Tyson of the Northwest Dec 06 '14 at 00:54
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    I wonder if you could make this work by switching from planets to moons. Consider a Jupiter or Saturn sized planet with Earth gravity moons. The planet would make much larger moons stable. If the moons orbit perpendicular to the star but rotate on a parallel axis, that might make them Earth-like. – Brythan Dec 06 '14 at 01:32
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    The question lacks a key parameter: How long does the system need to be stable? Three is probably the only one that could be "forever" without outside disturbance, but a civilization might be satisfied by a few million years of stability. Especially if they assumed being able to retune the system later on. Given how small the effect of the planets on each other would be over any kind of distance, you could probably get away with a relatively high number. Especially if you use a hotter star that would not live long enough to generate habitable planets naturally, but has a large habitable zone. – Ville Niemi Dec 06 '14 at 11:19
  • By share an orbit do you just mean orbit the same star or do you mean a ring of them orbiting one behind the other? – Tim B Dec 06 '14 at 17:27
  • Yep Tim B, multiple bodies tracing each other paths. – Tyson of the Northwest Dec 11 '14 at 22:29
  • Since you specify that the system was "created" you'd have the ability to stabilize them so why limit yourself to 4 planets in an orbit? You could probably have a more or less continuous line of them streaming around the sun--I assume that would equate to hundreds or thousands. At some point you'd end up with https://en.wikipedia.org/wiki/Ringworld – Bill K Mar 09 '17 at 01:52

3 Answers3

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This problem was solved by Sean Raymond. (Also here, here, here and here.) He calculated that you can fit four gas giants into a habitable zone. Each of them could have 5 planet-sized moons and a double-planet in both its stable Langrange points. Like this, you will get to 4*(5+2+2) = 36 planets. The gas giant planets are there to stabilize the whole system. You could still double the number by adding a second star in sufficient distance (100 AU) from the first one. So you would have two copies of this system, one for each star.

We can ask how plausible is the stability of such system. The terrestrial planets orbiting the gas giants will be stable, since they are in the Hill sphere of much heavier body. Similar system is Jupiter with his Galilean moons. Double planets look also stable - double-planet is in a good approximation two-body problem, which is stable, and it is in the Lagrange point, which is stable place to be. (But we cannot rule out there would be some destabilizing iteraction between the gas giants and the terrestrial double-planets.) The most questionable factor is, if all four gas giants will fit into the Habitable zone.

Irigi
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  • Nice. I hadn't thought someone had actually attacked this thing. Do you know if Raymond has done any calculations regarding a specific star's habitable zone? – HDE 226868 Dec 06 '14 at 19:12
  • Would the double planet scenario perturb the moons at all? – HDE 226868 Dec 06 '14 at 23:48
  • I updated the links when I found his blog. He chose low mass star (0.5 suns). He writes: The habitable zone is narrower for low-mass stars. It’s almost a full AU wide for the Sun but only a few tenths or hundredths of an AU wide for low-mass stars. Does this mean there is less space for planets? No! The orbits of a system of planets tend to be spaced in a logarithmic way (for example, at 1, 2, 4, 8, 16 rather than at 1, 2, 3, 4, 5) . There is about the same amount of “dynamical space” for planets in orbit around cool stars and Sun-like stars. – Irigi Dec 07 '14 at 08:32
  • Tighter orbits from cooler stars would increase the chances of the double planets being perturbed by the other gas giants though? Probably not important for created systems and since this would have to be a created system and question is specifically about created systems... – Ville Niemi Dec 07 '14 at 09:00
  • @HDE226868 I am no expert in this, but Raymond's Ultimate Solar System (USS) 2 seems quite stable to me. I don't think even terrestrial planets in L4, L5 would destabilize the gas giant moons if they are close enough. On the other hand, his USS 1 seems at least suspicious, there seems to be too many planets packed together without any obvious stabilizing mechanism. – Irigi Dec 07 '14 at 09:01
  • @VilleNiemi True, it can be estimated from calculation of Hill spehere, but I haven't checked when it becomes a problem. Once, I calculated that for very light red dwarf, Earth-Moon system couldn't fit into the habitable zone and remain stable. – Irigi Dec 07 '14 at 09:15
  • @Irigi What would be unstable? The Earth and Moon remaining together, or be tossed out of the habitable zone? – HDE 226868 Dec 07 '14 at 14:46
  • @HDE226868 Earth and Moon couldn't remain together, the gravity of the close star would disrupt them. – Irigi Dec 08 '14 at 13:52
  • @Irigi Okay, thanks. I had though that wouldn't be possible because red dwarfs can be really low-mass. – HDE 226868 Dec 08 '14 at 16:00
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    @HDE226868 I think it is the inhomogeneity of the gravitational field that hurts, not the mass of the star. Smaller star means bigger inhomogeneity. – Irigi Dec 08 '14 at 17:30
  • Although this answers the question about Goldilocks zone, I wonder if moons that spend a significant proportion of their time with their star eclipsed by a gas giant they orbit, might be cooler than you'd expect simply from their being in the zone. Are the moons far enough out from their gas giants that this isn't an issue? – Steve Jessop Jan 15 '15 at 16:59
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It depends on the size of the habitable zone.

Whether or not a planet's orbit is within the (circumstellar) habitable zone (aka the Goldilocks zone) depends on a wide variety of factors determined primarily by the star. Here's the Solar System's habitable zone compared to the habitable zone around the star Kepler-186:

Habitable zone comparison
Image courtesy of Wikipedia user Bhpsngum under the Creative Commons Attribution-Share Alike 4.0 International license.

Here are some of the factors that determine whether or not a planet is habitable:

  • Luminosity of the star
  • Eccentricity of the planet's orbit (highly eccentric orbits, such as the one displayed here, may venture outside the star's habitable zone)
  • Temperature of the planet (yes, the planet's characteristics impact habitability)
  • Distance from the star (well, of course)
  • Whether or not other objects exist nearby which may destabilize the planet

These are really just factors that impact habitability of a planet, but they show that just being in the habitable zone isn't enough. If your planet's atmosphere is such that it's too hot (like Venus), you're in trouble. If the orbit isn't stable because of other objects, or there is lots of debris in the area (e.g. asteroids), you're also in trouble. However, stellar luminosity is probably the biggest factor.

In general, the habitable zones of stars follow the pattern shown here:

Habitable zone pattern
Image courtesy of Wikipedia user Henrykus under the Creative Commons Attribution-Share Alike 3.0 International license.

However, there's a lot of error. We're not too sure of how far our own habitable zone extends, as can be seen here.

So it depends on a lot of factors. Next, I'll discuss our habitable zone.

Our habitable zone looks like this:

Our habitable zone
Image courtesy of Wikipedia user EvenGreenerFish under the Creative Commons Attribution-Share Alike 3.0 International license.

The dark green part is the range of conservative estimates; the light part is the range of liberal estimates. Look at the difference!

I'll deal with the more liberal estimates, because they lead to more interesting scenarios. These mean that Earth, Mars, Ceres (a dwarf planet/asteroid) and the asteroid belt may all be inside it. Most models include Venus as well, as you can see in the second graphic in this answer. So three major bodies (Venus through Mars) and a dwarf planet can easily co-exist.

Scale them down a little, and things are looking good. Venus is about the same size as Earth, and Mars is half as big. Ceres, though, is much smaller. However, I'm willing to bet that scaling it up wouldn't impact the others, although its proximity to the asteroids in the asteroid belt is worrisome. But for now, let's leave it in.

So we can comfortably fit in four bodies. What about five? Well, if you move Mars in a bit, perhaps you could squeeze in a fifth. After that, though, things get dicey. You need to further decrease the distance between the planets. Six would probably be fine; seven is a stretch. Why? Because you have to account for orbital evolution. It's nearly impossible for eight (don't forget about Mercury!) terrestrial planets to form so close to one another, because the early chaos of the Solar System surely would have thrown some of their orbits out of whack. However, this Type IV or V civilization can easily do that. The trouble lies in maintaining long-term orbital stability, although perhaps they could adjust that. Still, perhaps you could put seven in the habitable zone, even if you let them be for a while.

One last thing. As I'm typing this, Oldcat mentioned in a comment something I had planned to get to:

I'm not sure any planet that size can hold an atmosphere in the habitable zone. Mars is .4g and it has its problems.

I don't know about Mars' problems with holding an atmosphere (although that by no means means that they don't exist). Wikipedia claims that the lack of a magnetosphere means that the solar wind can play an issue; whether or not that's true is up for debate, unless anyone reading this wants to go to Mars. Anyway, there is at least one example that shows that even a moon can hold an atmosphere: Titan, a moon of Saturn.

Titan is really large - larger than Mercury, although not nearly as massive. Its atmosphere is more massive than that of Earth, although it's clearly not the same! So small bodies clearly can hold atmospheres. Admittedly, Titan is farther from the Sun than anything in the habitable zone, so it may not be subjected to strong solar effects. But it's something. I don't think it's likely that these small planets can hold atmospheres, but it's certainly possible.

As for how many bodies could share an orbit - well, that's a bit complicated. I've been able to find a question on Physics that talks about it, and it doesn't seem as if even two planets could share the same orbit. Here's something from Carson Myer's answer:

I don't think the situation you mentioned is possible. You're describing two planets, each of which being in each others L3 points (a lagrangian point is a point in an orbit with special gravitational properties, where an object will remain somewhat stationary relative to the body whose orbit it's in). Even our comparatively tiny spacecraft which sit in Earth's L1 point (between the Earth and Sun) require periodic corrections.

Planetary orbits are somewhat unstable: they change by little bits over time, as the sun loses mass and as other planets and solar-system junk push and pull on the planets. If one of these planets' orbit changed just a tiny bit it would fall out of the lagrange point and into another orbit. The planets would begin moving at different speeds and would either collide or move into independent orbits in an astronomically short period of time.

So it doesn't look like four small planets could share the same orbit.

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HDE 226868
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  • So that is the how many orbits can fit within a habitable zone. But how many bodies can coexist spaced across a similar orbit without interfering with each other and decaying the orbit. – Tyson of the Northwest Dec 06 '14 at 01:00
  • Ah, I see. Hold on a bit. – HDE 226868 Dec 06 '14 at 01:01
  • You might get six in two orbits in the habitable zone - L4 and L5, although this might not work if the planet size is 1:1 with the real planet. – Oldcat Dec 06 '14 at 01:07
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    The cold at Titan's orbit is a big factor. Earth can't hold onto Methane at its distance, despite the larger size. – Oldcat Dec 06 '14 at 01:08
  • Re L4 and L5: Wikipedia does indicate that this would not be possible for planets nearly the same size - or anywhere close to that. I didn't know about the cold on Titan, though. – HDE 226868 Dec 06 '14 at 01:10
  • I don't know the exact equation, but it does involve T and Mass of the planet/moon. Also the mass of the gas - light gasses escape easier. – Oldcat Dec 06 '14 at 01:13
  • @Oldcat Hmm. Might this be related? Ah, never mind; you meant the atmosphere. – HDE 226868 Dec 06 '14 at 01:15
  • Two bodies might share a Janus-like orbit pairing...done twice? – Oldcat Dec 06 '14 at 01:18
  • @Oldcat Damn. Got me. Not sure about 4, but only because natural formation would be unlikely. But a Type IV civilization could probably iron it out like that. Still, I'm worried, because the switches might have to happen at the exact same time - and over the years, they might disalign, and so it would become unbalanced, and perhaps unstable. But that's a big if, I suppose. – HDE 226868 Dec 06 '14 at 01:21
  • Each switch is an interaction of the 2 bodies in the one orbit, from the little I have read. It has the best chance of working above 2. – Oldcat Dec 06 '14 at 01:24
  • You're right; it does have the best chance. The orbits would have to be close together to be something like co-orbital, but I suppose it could be done. – HDE 226868 Dec 06 '14 at 01:26
  • I'm saying a Janus pair in Earth orbit, and one in Mars orbit. Not all 4 in one orbit. – Oldcat Dec 06 '14 at 01:26
  • @Oldcat Oh, well, definitely. Definitely. – HDE 226868 Dec 06 '14 at 01:26
  • Regarding lagrange points, the logic in the first paragraph your quote is wrong, the L1 is an unstable point, the potential energies are equivalent because it is a maximum point. L3 is a minimum point and thus vastly more stable. Objects actually get trapped in L3 points naturally. So you can't really deduce anything about L3 planets from spacecraft in L1. So three planets might be possible, if created artificially. (requires roughly equal mass and lack of other bodies in nearby orbits) – Ville Niemi Dec 06 '14 at 11:03
  • @VilleNiemi You'll have to take that up with Carson Myer. I don't think s/he ever implied total stability, though. – HDE 226868 Dec 06 '14 at 19:04
  • I have no issue with what Carson Myer said. In general, the lagrange points are not stable enough for planets, period. It is only when talking about "created systems" that the difference between the two different types of points is relevant. This is because the time scales are much shorter and natural planet formation is not needed. My previous comment might have minima and maxima confused, I haven't checked since I trust you to get the idea regardless. Apologies, if that bothered you. – Ville Niemi Dec 06 '14 at 19:18
  • @VilleNiemi No, you might be right. I'm a bit busy at the moment, but I can get back to you (and some other people) in a few hours, if that's okay. – HDE 226868 Dec 06 '14 at 19:21
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    Try here: Is there a ceiling for stable L4 or L5 masses? – Mazura Jul 26 '15 at 20:32
  • So we're going with the assumption that a race can create a system of planets to fit it's need but can't find a way to stabilize them, or is there a requirement that this is fire-and-forget (No active corrections over enormous periods of time)? – Bill K Mar 09 '17 at 01:55
  • @BillK I assumed it was the second. Otherwise, the answer to the question is a trivial yes, – HDE 226868 Mar 09 '17 at 18:38
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There was an earlier post about the moons of Saturn Janus and Epimetheus, that share virtually the same orbit. When they get close, the two swap orbits until the next encounter. This seems to be stable for them.

So a 4 body solution for our Solar System would be 4 earthlike planets, 2 in Earth orbit and 2 in Mars' orbit. All should hold oxygen like Earth does and be suitable for life.

Oldcat
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