Astronomy

Can smaller habitable planets (or moons) orbit a larger habitable planet?

Can smaller habitable planets (or moons) orbit a larger habitable planet?


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I am doing some research for my fantasy novel, but I'd like to really understand how my planet system would cause life to grow if at all possible.

My idea would be, there is a large core planet that is orbiting a sun. Two smaller planets (or moons) are in an orbit around it on polar opposite sides of the core planet. Is this even possible? Would the necessary means to spark life occur?


A planet and moon both habitable seems feasible to me, given the planet's orbit is in the stars 'goldilocks' orbital region. As an example, if an Earth/moon system were recreated except larger. So the Earth moon system was created early in our solar system by a large Mars sized collision with early Earth. We ended up with a rare larger than normal moon, compared to Earth, 1/6th the size. Looking at the other planets, no other moon comes close to being this big compared to the planet. Anyway, if instead of a collision creating two bodies the size of the Earth and moon you increased both masses by 2.5, you could end up with an Earth 2.5 times the size of ours, likely the edge of feasible, and a moon the size of Mars, also the edge of feasible. So yes both could sustain life, imo, assuming other conditions are met. (Water, organics, solar output, magnetic fields, etc.)

On the 1:1 resonant moons, I'd have to agree with the previous comment, very unlikely to be stable. Now if you want an advanced civilization to create an artificial one, that could work. Or use a very large Jupiter to have a couple of habitable planets in orbit and maybe even habitable planets at L3 and L4 (Lagrange points), though I am unsure of their stability too I don't think it's be too big a stretch. (Jupiter's Lagrange asteroids are called Trojans and appear stable but none are particularly big.)


First off, let me point out that if you have a central planet which is orbited by other bodies, those other bodies must necessarily be considered moons and cannot be planets. This is due to the official definition of a planet stating that it must orbit the central star. The objects orbiting your central planet are not primarily orbiting the central star and thus would be considered moons or satellites.

Orbital Dynamics

What you're proposing is that your central planet is orbited by two moons that are on opposite sides of the planet. This condition provides some strong constraints on your system as dictated by the laws of physics.

  1. If we are to consider that the moons are orbiting around the central planet, then the planet must be fairly massive. If all three of your bodies are of a similar or comparable mass, you'd have a much different (and not necessarily stable) type of orbit than what you're describing (see this link for example). The fact that you have two moons orbiting your planet, without your planet having a noticeable orbit about the moons, implies the planet has most of the mass of the system. This results in one of two scenarios, either

    • your central planet is very large (e.g, the size of Jupiter or Saturn) with moons the size of Mercury or Ganymede, or
    • your central planet is relatively small (e.g., the size of Earth or Venus) with moons the size of asteroids (e.g., Phobos and Deimos, the moons of Mars)

    Of course you could have any gradation between the two possibilities I just listed. The main point is, your planet must be much more massive than your moons in order to be the dominant gravitational player in its system.

  2. You also state your moons are orbiting such that they're on opposite sides of the planet. Such an orbital configuration is known as a 1:1 resonance. It necessarily implies that your moons are orbiting at the exact same distance from the planet and take the same amount of time to complete a single orbit. While such a system is technically stable, I can't say with certainty that it is stable for a long period of time. More than likely, small perturbations will occur that will build up over time and cause your moons to leave their 1:1 orbital resonance. This will result in unpredictable outcomes, but my best guess is that the moons may start gravitationally interacting if they get close enough after no longer being on the same side of the planet. Eventually this may result in them exchanging energy and one getting kicked to a closer orbit while another getting kicked to a further orbit. But that's just a guess.

So short answer, yes your system is possible but it comes with some constraints and is likely not going to be stable for a long time period.

Habitability

You also ask about the habitability of such a system. This is a bit tricky and there's no single answer. There are so many conditions that affect habitability. To make matters worse, we only have a single example of a habitable planet. However, there are general conditions we believe must be true for a planet to be habitable (for humans at least).

The big condition is that your system must be at a good temperature such that water can exist as a liquid. If your central planet is a Jupiter/Saturn analog, this is not going to happen since such planets have large, mostly hydrogen gaseous envelopes. There's not really any pools of water for humans. However, your moons could still host water. It really depends on how far out your planet is from the star. These types of planets form very far from the star, where water doesn't easily exist as a liquid so either your planet must migrate in to the inner stellar system early on (and stop at a respectable distance), or else some sort of tidal effect has to keep your moons much warmer than they would be other wise (see Enceladus, for example). The former means your chosen moon orbits are likely to be less stable and the latter means you're going to need other moons to help provide the heating, again making your orbits less stable. If your central planet is Earth-like, it can certainly host water and be as Earth-like as you want, but the moons are unlikely to be big enough to be habitable.

There are various other conditions for habitability such as nice atmospheres or magnetospheric protection from the star but one could write a whole book on this subject. I'll leave off by pointing you to this question on habitability.


2 Answers 2

I think that a planet that can hold an Earth like atmosphere can keep two spherical moons with no big issues.

Let's break down your question in sub-problems.

For a body to become a sphere, it has to have sufficient self-gravity to pull it into a spherical shape. This depends on what the body is made of, for two reasons. The first reason is because the strength of self-gravity depends on the mass of the object rather than its size, implying that bodies made of denser materials become spherical at smaller radii.

The second reason is that some materials are easier to mould into a sphere than others, implying that less strong gravity is needed to push some materials into a spherical shape. The second reason tends to win out. Therefore, for bodies made mainly of rock, the minimum size to become a self-gravitating sphere is about 600km diameter but, for bodies mainly made of ice, the minimum size is about 400km diameter.

I will take this as a planet capable of trapping water and oxygen in its atmosphere, while being at a distance from the star such that liquid water can exist.

Using the (probably) most quoted worldbuilding image ever, we get that it can be slightly bigger than Mars, or better with an escape velocity slightly higher than Mars, around 7 km/s.

It depends on how far they orbit the planet and if their Hill spheres avoid reciprocal gravitational interference between the two moons.

For a body the mass of Ceres (diameter 900 km) orbiting at 100 thousands km from a body the mass of Venus, the Hill sphere would be 3900 km. If you place the second moon with same mass at 400 thousands km from the main body, its Hill sphere would be 15600 km.

The Hill spheres of the two moons seems therefore to be far enough to not interfere with each other. If you play with the distances so that you have some orbital resonance between the moons you can be rather sure of their long term stability.

What do you mean by "half the size of Earth" when you describe that as a desired goal?

The Planet Earth has a radius of 6,371 Kilometers and a diameter of 12,742 Kilometers. A planet with half the diameter of the Earth, or 6,371 kilometers, would have one eighth the volume. If that planet had the same average density as Earth it would have one eighth (0.125) the mass of Earth.

For a planet to have one half the mass of Earth and the same average density as the Earth, it would have to have half the volume of the Earth. Thus it would need to have approximately 0.7937 times the diameter of Earth, about 10,113.3254 Kilometers, to have a volume of about 0.499999006 that of Earth.

Compare those figures with the minimum masses for a planet to keep and/or to produce a breathable oxygen rich atmosphere which are given below.

Long, long ago, back in 1964, a book was published with a scientific discussion of what is necessary for a planet (or other world) to be habitable for humans.

Habitable Planets for Man, Stephen H. Dole, 1964, 2007. I don't know if the 2007 edition was updated with more recent scientific information.

There have been many more recent discussions of the habitability of other worlds using more recent and advanced science. But as far as I know most or all of those discussions are about habitability for life in general, not habitabilty for the more specific case of humans and life forms with similar requirements. On Earth, for example, many or maybe even most lifeforms flourish where humans would swiftly die.

On pages 53 to 58, Dole discusses how massive a world would have to be to retain a dense enough atmosphere of oxygen. On page 54 Dole concludes that a planet would have to have an escape velocity of 6.25 kilometers per second to retain an oxygen atmosphere for geological time periods. That corresponds to a planet with:

a mass of 0.195 Earth mass, a radius of 0.63 Earth, and a surface gravity of 0.49 g.

A radius of 0.63 Earth is a radius of 4,013.73 kilometers or a diameter of 8,027.46 kilometers.

Dole believed that a planet of that size could retain an oxygen rich atmosphere, but could not produce one. If Dole was correct, a planet of that size could only have an oxygen rich atmosphere if it was terraformed to have such an atmosphere by a highly advanced society.

Dole made two different calculations of the minimum mass that might be necessary for a world to not only retain an oxygen rich atmosphere but also to produce one. One was a mass of 0.25 Earth mass, and the other was a mass of 0.57 Earth mass. Dole considered those masses to be inaccurate, and settled on a mass of 0.4 Earth mass as the minimum mass required to produce an oxygen rich atmosphere.

This corresponds to a planet having a radius of 0.78 Earth radius and a surface gravity of 0.68 g.

A radius of 0.78 Earth radius is a radius of 4,969.38 kilometers and a diameter of 9,938.76 kilometers.

Mars has a mass of 0.107 Earth mass, a radius of 3,389.5 kilometers, and a diameter of 6,779 kilometers, so any world massive enough to retain and/or to produce an oxygen rich atmosphere should be significantly more massive and large than Mars.

Until and unless a science fiction writer finds a later and better set of calculations than Dole's they should not write about a planet with an oxygen rich atmosphere breathable for being similar to humans unless it has mass of at least 0.195 Earth and a diameter of at least 8,027.46 kilometers. And if they don't want the planet to have an artificial oxygen rich atmosphere created by a highly advanced civilization but have a naturally formed oxygen rich atmosphere instead, they should make their world have a mass of at least 0.4 Earth mass and a diameter of at least 9,938.76 kilometers.

And of course either minimum mass would be significantly greater than the mass of Mars, 1.822 or 3.738 times the mass of Mars. And also significantly less than the mass of Venus, 0.239 or 0.490 that of Venus. L Dutch - Reinstate Monica used a planet with the mass of Venus, 0.815 that of Earth, to calculate the Hill sphere of the planet in his answer.

I note that the size of your planet's Hill Sphere, will depend on the planet's mass, the distance to its star, and the mass of the star. I also note that a moon can have a stable orbit only within about 0.5 to 0.666 of the outer edge of the Hill Sphere.

I am not certain that two moons could have stable orbits around the least massive possible habitable planet at the distances indicated in L Dutch - Reinstate Monica's answer.

The Hill Sphere of Earth extends to about 1,500,000 kilometers, so the zone where moons can have stable orbits should extend to about 500,000 to 750,000 kilometers.

The example in L Dutch - Reinstate Monica's answer has two moons orbiting at about 100,000 and 400,000 kilometers, and both would be within the stable orbital zone of Earth. However, the question asks for a planet as small as possible, and L Dutch - Reinstate Monica mentioned a planet slightly larger than Mars earlier in his answer.

A planet significantly smaller than Earth would have a smaller Hill Sphere than Earth, and the moons would have to orbit closer. But if the planet is less massive, moons of a specific mass will have larger Hill spheres, perhaps interfering with one another.

Perhaps L Dutch - Reinstate Monica should recalculate his orbits for a planet massive enough to have an oxygen rich atmosphere orbiting a more massive and brighter star than the Sun at a greater distance than Earth orbits the Sun, to find a stable orbital configuration.


Habitable Moons Instead of Habitable Planets?

One of the primary goals of exoplanet-hunting missions like Kepler is to discover Earth-like planets in their hosts’ habitable zones. But could there be other relevant worlds to look for? A new study has explored the possibility of habitable moons around giant planets.

Seeking Rocky Worlds

Since its launch, the Kepler mission has found hundreds of planet candidates within their hosts’ habitable zones — the regions where liquid water can exist on a planet surface. In the search for livable worlds beyond our solar system, it stands to reason that terrestrial, Earth-like planets are the best targets. But stand-alone planets aren’t the only type of rocky world out there!

Many of the Kepler planet candidates found to lie in their hosts’ habitable zones are larger than three Earth radii. These giant planets, while unlikely to be good targets themselves in the search for habitable worlds, are potential hosts to large terrestrial satellites that would also exist in the habitable zone. In a new study led by Michelle Hill (University of Southern Queensland and University of New England, Australia San Francisco State University), a team of scientists explores the occurrence rate of such moons.

Kepler has found more than 70 gas giants in their hosts’ habitable zones. These are shown in the plot above (green), binned according to the temperature distribution of their hosts and compared to the broader sample of Kepler planet candidates (grey). [Hill et al. 2018]

A Giant-Planet Tally

Hill and collaborators combine the known Kepler detections of giant planets located within their hosts’ optimistic habitable zones with calculated detection efficiencies that measure the likelihood that there are additional, similar planets that we’re missing. From this, the authors estimate the frequency with which we expect giant planets to occur in the habitable zones of different types of stars.

The result: a frequency of 6.5 ± 1.9%, 11.5 ± 3.1%, and 6 ± 6% for giant planets lying in the habitable zones of G, K, and M stars, respectively. This is lower than the equivalent occurrence rate of habitable-zone terrestrial planets — which means that if the giant planets all host an average of one moon, habitable-zone rocky moons are less likely to exist than habitable-zone rocky planets. However, if each giant planet hosts more than one moon, the occurrence rates of moons in the habitable zone could quickly become larger than the rates of habitable-zone planets.

Lessons from Our Solar System

Distribution of the estimated planet–moon angular separation for known Kepler habitable-zone giant planets. Future missions would need to be able to resolve a separation between 1 and 90 microarcsec to detect potential moons. [Hill et al. 2018]

185 moons known to orbit planets within our solar system, all but a few are in orbit around the gas giants. Jupiter, in particular, recently upped its tally to a whopping 79 moons! Gas giants therefore seem quite capable of hosting many moons.

Could habitable-zone moons reasonably support life? Jupiter’s moon Io provides a good example of how radiative and tidal heating by the giant planet can warm a moon above the temperature of its surroundings. And Jupiter’s satellite Ganymede demonstrates that large moons can even have their own magnetic fields, potentially shielding the moons’ atmospheres from their host planets.

Overall, it seems that the terrestrial satellites of habitable-zone gas giants are a valuable target to consider in the ongoing search for habitable worlds. Hill and collaborators’ work goes on to discuss observational strategies for detecting such objects, providing hope that future observations will bring us closer to detecting habitable moons beyond our solar system.

Citation

“Exploring Kepler Giant Planets in the Habitable Zone,” Michelle L. Hill et al 2018 ApJ 860 67. doi:10.3847/1538-4357/aac384


PLANETPLANET

Can moons orbit moons? — the poem

Note: here is a video of me reciting this poem.

Can moons orbit moons? wondered Juna and I.
Some planets have moons, you know, up in the sky
But none of those moons has its own moon around it.
When Juna’s son learned this he just was astounded!
We wanted to figure it out, solve the mystery:
Where did those moons of moons go? What’s their history?

And one thing that gave this another dimension
The exomoon candidate got our attention.
When Teachey and Kipping found evidence for it
Those submoons called up and we couldn’t ignore it.

“Submoons” or “moonmoons” — now what’s in a name?
A name tends to stick so it shouldn’t be lame.
What should we call them? There’s oodles of choices
And plus, thanks to Twitter, there’s millions of voices.
There’s lots of opinions, there’s: moonmoons, mooncitos,
There’s moonlets and lunettes and planet burritos.

It’s only a name, there’s no science or glory
I’m sticking with submoons. Now, back to our story…

Around every planet there’s sort of a zone
In which a moon’s stable if left all alone
It orbits in peace ’round the planet in charge
And up in its sky, well, that planet looms large.
And ’round every moon there’s a similar space,
A submoon in there should just orbit in place.

A moon orbiting a planet orbiting a star. The thin lines show stable orbits and the five Lagrange points are labeled (only L4 and L5 are stable. The “camera” is orbiting along with the planet or moon. Adapted from Domingos & Winter (2005).

Where things can get messy and fall off the table:
It’s tides, it turns out, that can make things unstable
The planet’s large gravity tugs on the moon
And stretches it out like a poodle balloon

When stretched out, its gravity changes a nick
The submoon can feel this and gets a small kick
The kicks push the submoon first to and then fro
Its orbit can either get smaller or grow.
The submoon can crash down upon the moon’s lawn
Or else can be pushed out until it’s just gone

Lines of force showing the tidal stretching of a moon by a giant planet. Adapted from Wikipedia.

The very best spot for a submoon to thrive
Is ’round a big moon. And to help it survive
The moon also needs to be far from its planet
And that applies whether it’s icy or granite.

There’s three or four moons in our system that work
Around which a nice stable submoon could lurk
There’s our Moon, Callisto and also Iapetus
(a weird moon of Saturn’s — now let’s check my abacus).

If submoons are stable, then where could they be?
Those moons don’t have submoons. No, none of the three.

For Earth’s Moon, we think at the time of its birth
Its orbit was much much much closer to Earth
So even though submoons are stable there now
They never could form. They just didn’t know how.

Artist’s impression of the Moon’s submoon. From Science & Vie.

Callisto is one of the moons Galilean,
There’s four around Jupiter with room to play in.
The gravity kicks from the moons all add up
The safe zone for submoons just shrivels right up.

Iapetus is kinda weird. Just a smidge.
Along its equator it’s got a long ridge
We think that a submoon did form up around.
The ridge was produced when the submoon crashed down.

The exomoon candidate’s really quite big
With plenty of space for a sweet submoon rig.
The bad thing is submoons are real hard to find
And, to exo-submoons we’re totally blind.

Moons might be friendly to life, up in space.
So what about submoons? Are they a good place?

To have a big submoon that might have tectonics
And don’t forget water (and, yes, gin and tonics)
The host moon must be pretty big and quite far.
It also should orbit a pretty big star.

For big stars the hab zone is farther away
And planets out there give moons more space to play
Tides are much weaker, so submoons can thrive
Even a submoon like Earth might survive!

Let’s not hold back. Let’s see this thing through.
Subsubmoons: could they exist out there too?
The answer is yes but they’d have to be wimpy
‘Cuz tides get so strong that the stable zone’s shrimpy.

And now a last thought: tell me, what should humanity
Do just in case we succumb to insanity?
Where can we stash all the best things we’ve done:
Inventions, discoveries, art by the ton?

A human-made submoon that orbits the Moon
Could hold all that stuff in a giant cocoon.
For billions of years it could tell our last fable
(Although we should make sure its orbit is stable).

And now we are done. So I’ll head off to bed
With visions of submoons afloat in my head….

My favorite post on Twitter about submoons/moonmoons. Based on the classic bedtime story that my parents read to me about five thousand times (and I read to my kids too…).


Research redefines lower limit for planet size habitability

In this artist’s concept, the moon Ganymede orbits the giant planet Jupiter. A saline ocean under the moon’s icy crust best explains shifting in the auroral belts measured by the Hubble telescope. Astronomers have long wondered whether Jupiter’s moons would be habitable if radiation from the sun increased. Credit: NASA/ESA

In The Little Prince, the classic novella by Antoine de Saint-Exupéry, the titular prince lives on a house-sized asteroid so small that he can watch the sunset any time of day by moving his chair a few steps.

Of course, in real life, celestial objects that small can't support life because they don't have enough gravity to maintain an atmosphere. But how small is too small for habitability?

In a recent paper, Harvard University researchers described a new, lower size limit for planets to maintain surface liquid water for long periods of time, extending the so-called habitable zone or "Goldilocks zone" for small, low-gravity planets. This research expands the search area for life in the universe and sheds light on the important process of atmospheric evolution on small planets.

The research was published in the Astrophysical Journal.

"When people think about the inner and outer edges of the habitable zone, they tend to only think about it spatially, meaning how close the planet is to the star," said Constantin Arnscheidt '18, first author of the paper. "But actually, there are many other variables to habitability, including mass. Setting a lower bound for habitability in terms of planet size gives us an important constraint in our ongoing hunt for habitable exoplanets and exomoons."

Generally, planets are considered habitable if they can maintain surface liquid water (as opposed to frozen water) long enough to allow for the evolution of life, conservatively about 1 billion years. Astronomers hunt for these habitable planets within specific distances of certain types of stars—stars that are smaller, cooler and lower mass than our sun have a habitable zone much closer than larger, hotter stars.

The inner edge of the habitable zone is defined by how close a planet can be to a star before a runaway greenhouse effect leads to the evaporation of all surface water. But, as Arnscheidt and his colleagues demonstrated, this definition doesn't hold for small, low-gravity planets.

This illustration shows the lower bound for habitability in terms of planet mass. If an object is smaller than 2.7 percent the mass of Earth, its atmosphere will escape before it ever has the chance to develop surface liquid water. Credit: Harvard SEAS

The runaway greenhouse effect occurs when the atmosphere absorbs more heat that it can radiate back out into space, preventing the planet from cooling and eventually leading to unstoppable warming that finally turns its oceans turn to steam.

However, something important happens when planets decrease in size: As they warm, their atmospheres expand outward, becoming larger and larger relative to the size of the planet. These large atmospheres increase both the absorption and radiation of heat, allowing the planet to better maintain a stable temperature. The researchers found that atmospheric expansion prevents low-gravity planets from experiencing a runaway greenhouse effect, allowing them to maintain surface liquid water while orbiting in closer proximity to their stars.

When planets get too small, however, they lose their atmospheres altogether and the liquid surface water either freezes or vaporizes. The researchers demonstrated that there is a critical size below which a planet can never be habitable, meaning the habitable zone is bounded not only in space, but also in planet size.

The researchers found that the critical size is about 2.7 percent the mass of Earth. If an object is smaller than 2.7 percent the mass of Earth, its atmosphere will escape before it ever has the chance to develop surface liquid water, similar to what happens to comets today. To put that into context, the moon is 1.2 percent of Earth mass and Mercury is 5.53 percent.

The researchers were also able to estimate the habitable zones of these small planets around certain stars. Two scenarios were modeled for two different types of stars: a G-type star like our own sun and an M-type star modeled after a red dwarf in the constellation Leo.

The researchers solved another long-standing mystery in our own solar system. Astronomers have long wondered whether Jupiter's icy moons Europa, Ganymede, and Callisto would be habitable if radiation from the sun increased. Based on this research, these moons are too small to maintain surface liquid water, even if they were closer to the sun.

"Low-mass water worlds are a fascinating possibility in the search for life, and this paper shows just how different their behavior is likely to be compared to that of Earth-like planets," said Robin Wordsworth, associate professor of environmental science and engineering at SEAS and senior author of the study. "Once observations for this class of objects become possible, it's going to be exciting to try to test these predictions directly."


Weird orbits of neighbors can make ‘habitable’ planets not so habitable

Astronomers hunting for planets orbiting nearby stars similar to the sun are looking for signs of rocky, Earth-like planets in a “habitable” zone, where conditions such as temperature and liquid water remain stable enough to support life.

New findings from computer modeling indicate that some of those exoplanets might fluctuate between being habitable and being inhospitable to life because of the forces exerted by giant neighbors with eccentric orbits.

A lone Earth-like, or terrestrial, planet with a generally circular orbit toward the inner edge of its sun’s habitable zone could be expected to remain within that zone, said Rory Barnes, a University of Washington postdoctoral researcher in astronomy. Adding a planet comparable to Jupiter to the system, however, and giving it a highly elliptical orbit — similar to most exoplanets discovered so far — can cause strange things to happen to the smaller planet, possibly causing it to cycle between habitable and uninhabitable conditions.

The smaller planet’s orbit will elongate and then become more circular again, all in as little as 1,000 years, and could do so repeatedly. That raises the possibility, for example, that its average yearly temperature could change significantly during each millennium.

“For part of the time liquid water could exist on the surface, but at others it would boil off,” said Barnes, who will present the findings Wednesday at a meeting of the American Astronomical Society in Miami.

The effect would be similar for an Earth-like planet at the outer edge of its habitable zone, except that its altered orbit likely would, at times, take it too far from its star, possibly resulting in planetary glaciation.

“The bigger issue here is that the habitable zone is very complicated,” Barnes said. “Earth’s climate is affected slightly over tens of thousands of years by the orbits of other planets in the solar system, but it is possible that in many exoplanetary systems the layout of the planets is very important to habitability.”

The problem becomes even more complex for what could be habitable planets orbiting low-mass stars, perhaps one-third the mass of the sun. In such systems, the habitable zone is much closer to the smaller star, and tidal forces from the star’s gravity are critical in determining whether the planet is habitable. Adding an eccentric orbit of a Jupiter-like planet could greatly alter conditions on the smaller planet as its orbit changes.

“There could be planets out there that have their geological properties change over very long timescales,” Barnes said. “You can imagine planets that cycle in and out of intense volcanism and earthquake stages.”

Tidal forces also fix the planet’s rotation period, and as the orbit becomes more elongated the length of day can change significantly, Barnes said.

“The length of the day changes almost day to day,” he said. “It’s fascinating to think about how evolution occurs on such a world.”

The work, funded by NASA’s Virtual Planetary Laboratory, was conducted with Brian Jackson of NASA’s Goddard Space Flight Center, Richard Greenberg of the University of Arizona and Sean Raymond of the Laboratoire d’Astrophysique de Bordeaux in France.

“There is this crazy zoo of planets out there that probably are habitable,” Barnes said, “but their properties are very different from Earth and they’re different from Earth because of their eccentric neighbors.”


How many habitable planets can one star have? Turns out, about 6.

How many habitable planets can you have orbiting a single star?

In our solar system, only one planet is actually habitable in a narrow sense of the word: Earth. Mars is too cold with air too thin, and Venus just the opposite.

More Bad Astronomy

But… that’s happenstance. If you swapped the positions of Mars and Venus, and maybe swapped a significant fraction of Venus’ atmosphere, their temperatures would be a lot more suited for us * . That’s because both are in our Sun’s habitable zone, the range of distance from our star where liquid water could exist on a planet’s surface.

The idea of a habitable zone is a bit squishy, because having liquid water depends on a laundry list of other things, including the existence of an atmosphere, what’s in it, and more. But it’s a useful concept as long as you don’t look at it too closely † .

So technically, three planets orbit the Sun in its habitable zone. But how many could you fit in there?

Artwork showing the TRAPPIST-1 planetary system, seven Earth-sized planets orbiting a cool red dwarf. Credit: NASA/JPL-Caltech

At some number you’d hit a limit. The finite region of space means planets would get too close together. They’d interact gravitationally, and celestial hijinks would ensue: They’d create chaos, and some planet or planets would have their orbit messed up, dropping them into the Sun or ejecting them from the system entirely.

Also, a star’s habitable zone depends on how hot it is. When you do the math, you find a cool red dwarf has a small, narrow one, while a massive blue star has a huge habitable zone that extends out a long way.

So when we look to other stars, should we expect to see systems like ours, with few planets in the habitable zone, or can there be more stuffed in there?

A team of astronomers took a look at this, using software that calculates the gravity and motion of a system of planets over time to check for stability. For a given star mass, they calculated the size of the habitable zone, then placed one Earth-mass planet on the inside edge of the zone, another at the outside edge, and then added more evenly-spaced between the two. For every kind of star they ran the simulation for a total of 5, 6, and 7 planets, letting the simulation go for 100 million orbits of the inner planet to give things a good long time to play out.

What they found is pretty cool. For very low mass stars, say 0.1 times the Sun’s mass, no system is stable. The habitable zone is too narrow, so the planets always interacted. However, once you get up to stars with 0.2 times the Sun’s mass (still pretty low, so we’re talking red dwarfs here) the zone widened enough that every 5-planet system was stable. For stars with 0.7 or so times the Sun’s mass, 6-planet systems do pretty well, too.

Artwork depicting a star with several planets orbiting it. Credit: NASA/JPL-Caltech/R. Hurt (IPAC)

For some narrow mass ranges of stars, 7-planet systems wind up being stable as well. You’d think that a more massive star means a bigger habitable zone, so more planets would fit in, but there’s a monkey in that wrench: Resonances. If one or more planets have orbital periods that are simple fractions of each other, like 2:1, or 5:4, they periodically tug on each other, adding or removing orbital energy. It’s like kicking your legs at the right time on a swing, amplifying your motion.

In this case though, resonances can spell doom for a system. For certain size habitable zones and stellar masses the planets find themselves in a resonance, and the orbits become unstable. That’s why a lower mass star might be able to hold on to more planets than a higher mass one. There might be no resonances in the habitable zone for the smaller star, whereas there are for the bigger one.

There’s another problem, too, and it’s literally a big one: Giant planets orbiting outside the habitable zone. They influence inner planets, and can create even more instabilities, making it harder to pack a star’s habitable zone with Earth-sized planets. If a star lacks those giant planets then it’s all good, but if it has one or more — as ours does — that can seriously drop the number of stable planetary habitable zone orbits.

There are more subtle things to look out for, too. As a star ages it gets hotter, so its habitable zone moves outward. A planet that orbits on the inside edge of a star’s habitable zone might find itself getting uncomfortably warm after a few billion years.

Also, they didn’t look at lower mass planets (like, say, Mars) or planets on elliptical orbits. Tilting the orbits a bit can prevent resonances from making a mess of things, too. Clearly, there’s room here for running lots more simulations on this.

The TRAPPIST-1 planetary system (middle) can fit entirely inside Mercury’s orbit (bottom), yet three planets are in their cool star’s habitable zone. Jupiter’s four big moons are also shown to scale (top) for comparison. Credit: NASA/JPL-Caltech

It’ll be a while before this prediction can be checked in the real Universe, though. Finding that many planets around a star is rare (TRAPPIST-1 being one of a few exceptions so far) and it gets harder for more massive stars, where the planets are farther out from the star our best detection methods work well for closer-in planets.

But what a thing to learn! Will we find systems with 5 planets in their habitable zone? And if so, how many will actually be habitable?

The Universe is a pretty cool place, and loves diversity. If I had to bet, I’d say such systems exist. Rare, but out there. How long will it be before we find one?

* We’d still need to give them both oxygen and probably replace the CO2 with nitrogen, but go with me here.

Also, it’s possible to have undersurface oceans in icy moons around gas giants, so again the habitable zone concept is a bit limited. It’s more of a good place to start then the be-all of looking for clement places in the Universe.


Contents

Lehmer et al. found if the moon of Europa were to end up near to Earth orbit it would only be able to hold onto its atmosphere for a few million years. However, for any larger, Ganymede-sized moons venturing into its solar system's habitable zone, an atmosphere and surface water could be retained pretty much indefinitely. Models for moon formation suggest the formation of even more massive moons than Ganymede is common around many of the super-Jovian exoplanets. [3]

Martínez-Rodríguez et al. found exomoons with the mass of Mars around IL Aquarii b and c could be stable on timescales above the Hubble time. Like an exoplanet, an exomoon can potentially become tidally locked to its primary. However, since the exomoon's primary is an exoplanet, it would continue to rotate relative to its star after becoming tidally locked, and thus would still experience a day/night cycle indefinitely. The CHEOPS mission could detect exomoons around the brightest M-dwarfs or ESPRESSO could detect the Rossiter–McLaughlin effect caused by the exomoons. [4]

Given the general planet-to-satellite mass ratio of 10000, [5] large Saturn or Jupiter-sized gas planets in the habitable zone are believed to be the best candidates to harbour Earth-like moons, with more than 120 such planets by 2018. [6]

Massive exoplanets known to be located within a habitable zone (such as Gliese 876 b, 55 Cancri f, Upsilon Andromedae d, 47 Ursae Majoris b, HD 28185 b and HD 37124 c) are of particular interest as they may potentially possess natural satellites with liquid water on the surface. It was also found that moons at distances between about 5 and 20 planetary radii from a giant planet could be habitable from an illumination and tidal heating point of view.

There is a minimum mass of roughly 0.20 solar masses for stars to host habitable moons within the stellar habitable zone. René Heller & Rory Barnes found that, depending on a moon's orbital eccentricity, there is a minimum mass for stars to host habitable moons at around 0.2 solar masses. [7]

Earth-sized exoplanets in the habitable zone around M-dwarfs are often tidally locked to the host star. This has the effect that one hemisphere always faces the star, while the other remains in darkness. An exomoon in an M-dwarf system does not face this challenge, as it is tidally locked to the planet and it would receive light for both hemispheres.


Are trojan planets possible? Are habitable trojan planets possible?

A Trojan relationship is when an astronomical object A is orbited by astronomical object B, and a third object, C, orbits A at the same distance as B and 60 degrees ahead of or behind B, in the L4 or L5 position.

In our solar system, hundreds of asteroids (C) have Trojan orbits relative to Jupiter (B) and the Sun (A), and there are 17 known Neptunian Trojans, 4 known Martian Trojans, 2 known Uranian Trojans, 1 Known Earth Trojan, and 1 temporary Venusian Trojan.

Thetys, a moon of Saturn, has two Trojan moons, Telesto and Calypso, and Dione, another moon of Saturn, has two Trojan moons, Helene and Polydeuces.

It is obvious that in these cases object A is many times more massive than object B, which in turn is many times more massive than object C.

For example, Mars, the smallest planet with Trojan asteroids, has a mass 0.3227 X 10 to the minus 6th power, or 0.0000003277 the mass of the Sun, while Jupiter, the most massive planet with Trojan asteroids, has a mass of 0.0009547919 the mass of the Sun.

Tethys and Dione, moons of Saturn, are thousands and tens of thousands of times as massive as their Trojan moons.

The largest Trojan asteroid, 624 Hektor has a diameter of 225 kilometers. Earth should be over 100,000 times as massive as 624 Hektor and Jupiter is 317.7 times as massive as Earth.

So in our solar system the object A (the Sun or Saturn) ranges from thousands to millions of times as massive as object B (a planet or a large Saturnian moon) and object B ranges from thousands to millions (and possibly billions) of times as massive as object C (an asteroid or a tiny, asteroid-size moon of Saturn).

Obviously, a Trojan orbit can be stable for millions and even billions of years if there are such vast differences in mass between objects A, B, & C.

But in science fiction there are many examples were object C is much larger than an asteroid, and in fact is a planet, often one habitable for Humans.

The common types are systems where A and B are both stars and C is a planet, and systems where A is a star and B and C are both planets.

And for a long time, I believed that it was impossible for object C in a Trojan orbit to be as massive as a planet, regardless of whether object B was a star or a planet.

It is said that as a rule of thumb, a Trojan orbit can be stable if the mass of object A is greater than 100 times the mass of object B and greater than 10,000 times the mass of object C.

In our solar system the least massive planet, Mercury, is 0.00017 the mass of the most massive planet. Thus Jupiter is 5,882.35 times as massive as Mercury.

Of the five official dwarf planets in our solar system, Ceres has the smallest known mass, 0.0015 the mass of Earth, meaning Earth has 66,666.66 times the mass of Ceres. Since Jupiter has 317.7 times the mass of Earth, it has 2,117,999.9 times the mass of Ceres.

An object has planetary mass if it is massive enough to pull itself into a regular, more or less spherical shape, and is less massive than a star.

An object more massive than about 13 times the mass of Jupiter will have great enough core pressure and temperature to fuse hydrogen, and thus be a star. But the least massive stars can only fuse the rare hydrogen isotope deuterium and thus are very, very dim. They are called brown dwarfs and can be classified as planets, stars, or neither.

The minimum mass of a brown dwarf might be between 11 and 25 times the mass of Jupiter, which is enough to make the largest possible planet tens of millions of times as massive as the least massive possible planet.

The maximum mass for a brown dwarf, and the minimum mass for a full-fledged star is believed to be about 75 to 80 times the mass of Jupiter, and thus about 0.0716 to 0.076 times the mass of the Sun. The least massive known normal star, VB10, or Van Biesbroeck's Star, has a mass of about 0.075 that of the Sun, or the Sun is 13.333 times as massive as VB10.

It has been calculated that a star above about 150 times the mass of the Sun, would have fusion reactions so strong they would blow the star apart. But there a few stars which might have masses higher than 150 times the mass of the Sun, listed here:

RMC 136a1 is both the most luminous known star and the most massive, allegedly having 315 times the mass of the Sun - or between 265 to 375 times the mass of the Sun.

Thus the most massive stars should be 1,999.99 times as massive as the least massive stars, or possibly even as much as 4,999.99 times as massive.

So the possible mass range of stars, and the possible mass range of planets is such that as a rule of thumb, there could be a stable Trojan system with a star as object A, a planet as object c, and either a star or a planet as object B.

We already know there can be a Trojan system were object B is a habitable planet and object C is a tiny asteroid. But there is nothing glamorous or interesting about tiny asteroids in Trojan orbits relative to a habitable planet, except for the possible advantages of mining those asteroids.

There can be a plausible story involving mining operations or scientific research of some kind on a lifeless and uninhabitable planet in a Trojan orbit, with object B being either a star or another lifeless and uninhabitable planet.

But what about a system in which object C is a habitable planet?

If we arbitrarily assume that a planet habitable for Humans should have a mass between 0.5 and 2.0 that of Earth (planets outside that range might be habitable for other forms of life, including some from Earth), then a giant planet might be as much as 11,913.75 to 50,832 times as massive as an Earth-like and habitable planet.

So a Trojan system with a star as A, a giant planet as B, and an Earth-like and habitable planet as C, seems to fit within the 1:0.01:0.0001 rule of thumb.

And yesterday, March 5, 2018, I found some online scientific papers discussing hypothetical Trojan planets.

And those articles consider Earth-mass and potentially habitable Trojan planets possible.

So it appears that a system with a star, a giant planet, and an Earth-mass planet can have a stable Trojan orbital configuration, despite what I believed for a long time.

What about a system with two stars and an Earth mass and a habitable planet in a stable Trojan orbital configuration?

That is a bit more complicated. The Earth is about 4,550,000,000 years old. The first microscopic life appeared about 4,100,000,000 to 3,500,000,000 years ago, but Earth was not yet habitable for Humans.

Lifeforms began to produce oxygen about 2,000,000,000 years ago and oxygen levels in the atmosphere rose to breathable levels by about 500,000,000 years ago when Earth was about 4,000,000,000 years old.

Complex multicellular life appeared about 580,000,000 years ago and the first land organisms appeared about 480,000,000 years ago.

If one assumes that the evolution of life could be much faster or slower on different planets, one might assume that the minimum possible age for a planet to have a breathable oxygen-rich atmosphere and multicellular lifeforms on land, and thus be habitable for Humans, might be 3,000,000 years.

A F5V class main sequence star would have a lifetime on the main sequence of 3,440,000,000 years before becoming a red giant star. Thus some F5V stars can have planets over 3,000,000,000 years old with advanced life and breathable air, planets suitable for being colonized by Humans or having native intelligent beings. Such a star would have a mass of 1.4 times the Sun or 18.666 times the mass of the least massive stars.

This blog post says that in a Trojan system with two stars and a planet the larger star has to be at least 25 times as massive as the least massive star, a ratio of 1:04.

This is a much smaller mass difference that the 1:01 rule of thumb ratio.

In this system, the smaller star has 0.08 the Mass of the Sun and the larger star thus must have at least 2 times the mass of the Sun.

For my Trojan star-star systems I’m choosing a puny star at the border between brown dwarfs and stars, at 8% the mass of the Sun. This keeps the mass of the high-mass star as low as possible. This, in turn, will allow for a long-lived high-mass star. The high-mass star is an A star twice as massive as the Sun and about 12 times as bright (see here). This star has a lifetime of about 2 billion years as a “normal” main sequence star.

With a lifetime of about 2,000,000,000 years, the brighter star will not remain on the main sequence long enough for the planet(s) in the Trojan positions to develop advanced life and become habitable for Humans, unless life on those planets develops more than twice as fast as life on Earth for some reason. That is why spectral type A stars are not considered suitable for having habitable planets.

So, from what I have learned today, I would say that a Trojan system with a suitable type star as object A, a habitable planet as object C, and either a giant planet or a brown dwarf as object B may be mathematically possible.

But it still seems that a Trojan system with a suitable type star as object A, a habitable planet as object C, and a smaller star as object B is mathematically impossible, because the two stars could not have the proper mass ratio for a stable Trojan system.

So can anyone clarify whether the two types of Trojan systems with habitable planets are stable or not?