Can life exist on a moon orbiting binary planets?

Question

The situation i am trying to describe is a binary planet system where both planets are similarly sized, but without flora or fauna (basically an planet-sized moon). The planets are in the goldilocks zone and share a moon that with a bit of handwavium, hosts water and has a relatively livable atmosphere (no more than 1% variation from our atmosphere, generate your own values). Without going in too much detail, is this system able to support stable life (where life can last for at least several millenia at a time, with no maximum)

Answer 1

From the perspective of orbital stability, we would almost certainly need both planets to be much more massive than the moon. As the moon should be reasonably Earth-like for the sake of retaining an atmosphere, the planets would likely be gas giants. There are really several questions to answer, and none are necessarily obvious. Can two gas giants form a binary planet at all - binary rocky planets may form from collisions; is there a clear analog to this for gaseous planets? Can an Earth-like moon orbit these planets and remain dynamically stable for millions to billions of years? Can all above the above exist within a star's habitable zone?

The answer to the first question may be yes. I'm aware of at least two candidate systems with similar requisite properties: Kepler-1625b, which has an $\sim11.6M_J$ planet and another body (classified as a moon) of roughly the mass of Neptune; and 2MASS J11193254–1137466 AB, a free-floating system where both bodies are believed to weight in at a few Jupiter masses. There are suspicions of systematic errors and possible misinterpretations in the case of Kepler-1625b, but 2MASS J11193254 appears to be very real. Therefore, yes, it's possible to have two giant planets orbiting one another.

Next, can these planets host Earth-like moons? 2MASS J11193254 may have a moon a bit larger than Earth orbiting one component (Limbach et al. 2021). Unfortunately, it is not a circumplanetary orbit like you're looking for, but it indicates that there may be formation mechanisms to create the sort of moons you're looking for. Plus, it seems quite possible for said moon to find stability in a relatively wide circumbinary orbit.

Finally, can this apparatus orbit a star? That depends. It seems clear that a smaller body orbiting the Neptune-mass component of Kepler-1625b could orbit that component stably within the stellar habitable zone (Forgan 2018). This then begs the question of whether a circumbinary orbit would be stable. I would argue that it depends on the precise setup; we would need the binary planets to orbit each other tightly, which opens the possibility for tidal deceleration (as well as possibly perturbations from other bodies) to eventually induce a merger.

If you're content with the Earth-like moon just orbiting one component, then the answer is a definitive yes, based on the Kepler-1625b simulations. If you want it to orbit both, then things get dicey.

Answer 2

Here is some information about the possible masses and orbital distances of the three worlds in the question.

The OP asks:

The situation i am trying to describe is a binary planet system where both planets are similarly sized, but without flora or fauna (basically an planet-sized moon). The planets are in the goldilocks zone and share a moon that with a bit of handwavium, hosts water and has a relatively livable atmosphere (no more than 1% variation from our atmosphere, generate your own values). Without going in too much detail, is this system able to support stable life (where life can last for at least several millenia at a time, with no maximum)

Thats what i mean. Life has to evolve to around 1600s technology, but the system also has to support that life until 2600 at least.

Part One of Four: The Possible Mass Range of a Habitable Moon.

First let us find the minimum possible mass of a moon which has a natural atmosphere similar to Earth's.

So if the moon has intelligent beings with around 1600s technology, it has to have existed for billions of years since it took Earth billions of years to produce an oxygen rich atmosphere that multicelled land animals could breathe.

So if the atmosphere on the moon is produced and maintained naturally, the moon has to have had a high enough escape velocity that it could retain oxygen, nitrogen, and the minor atmospheric gases for billions of years.

There is a scientific study of what planets need to be habitable for humans, and since it is required that the atmosphere of the moon can't be more than 1 percent different from Earth's atmosphere the moon would definately be habitable for humans.

Stephen H. Dole, Habitable Planets for Man, 1964:

https://www.rand.org/content/dam/rand/pubs/commercial_books/2007/RAND_CB179-1.pdf

On page 35, table 5 shows the length of time a world can retain atmospheric gases in ratios of the escape velocity of the planet divided by the root-mean-square velocity of the atmospheric gases in the upper atmosphere.

Where the ratio is 1 or 2, the atmospheric lifetime is zero. Where the ratio is 3, the lifetime is a few weeks. Where the ratio is 4, the lifetime is several thousand years. Where the ratio is 5, the lifetime is about 100,000,000 years. And where the ratio is 6, the lifetime is about infinite.

Chapter 4, the Astronomical Parameters, begins with a discussion of planetary mass on page 53.

On page 54 Dole concludes that the minimum escape velocity necessary to retain an oxygenr rich atmosphere is 6.25 kilometers per second.

Going back to figure 9, this may be seen to correspond to a planet having a mass of 0.195 Earth mass, a radius of 0.63 Earth radius, and a surface gravity of .49 g.

The radius of Earth is about 6,378 kilometers or 3,963 miles, so such a small planet or large moon would have a radius of about 4,018 kilometers or 2,496 miles, and a diameter twice that.

But Dole didn't believe that such a small planet could form an oxygen rich atmosphere. Dole calculated two different minimum masses for a world that could produce an oxygen rich atmosphere, 0.25 Earth mass and 0.57 Earth mass, and decided that both were wrong on page 56. On pages 56 & 57 Dole guessed that the true lower limit would be between 0.25 and 0.57 Earth mass.

Since it is not possible to obtain a more precise determination of the minimum mass of a habitable planet, for our purpose the value of 0.4 Earth mass will be adopted as the lower limit of mass. This corresponds to a planet with a radius of 0.78 Earth radius and a surface gravity of 0.68 g.

The radius of Earth is about 6,378 kilometers or 3,963 miles, so such a small planet or large moon would have a radius of about 4,974 kilometers or 3,091 miles, and a diameter twice that.

Dole also calculated a maximum mass for a planet habitable for humans. He decided on page 12 that probably nobody would want to settle on a planet with a surface gravity higher than 1.25 or 1.5 g.

And on page 53 Dole wrote:

Now it will be recalled that, to be considered habitable, a planet must have a surface gravity of less than 1.5 g. From figure 9, it may be seen that this corresponds to a planet that has a mass of 2.25 Earth mass, a radius of 1.25 Earth radii, and an escape velocity of 15.3 kilometers per second.

Such a planet or moon would have a radius of about 7,972.5 kilometers or 4,953.75 miles, and a diameter twice that.

Dole did consider the possibility that other effects from a high mass planet could make it uninhabitable for humans even with a mass less than 2.25 Earth mass.

So if a writer wants to keep his human habitable planets or moons within the limits set by Dole, They should make their masses between 0.4 and 2.25 Earth mass, their radii between 0.78 and 1.25 Earth radii, and their surface gravity between 0.68 and 1.5 g.

Somewhat more adventurous writers might want to make the minimum masses of their habitable planets and moons to be 0.58 Earth mass, 0.25 Earth mass, or even as low as 0.195 Earth mass.

There are many other more recent discussions of the possible habitability of other worlds. But in most case the scientists would be statisfied if a world was habitable for any type of liquid water using life. Some, maybe most, worlds habitable for liquid water using life would not be habitable for humans. So worlds habitable for humans, or for intelligent beings with very similar environmental requirements, would be a minority subset of worlds habitable for liquid water using life in general.

There is a discussion "Exomoon Habitabiity Constrained by Illumination and Tidal Heating", Rene Heller and Roy Barnes, Astrobiology, volume 13, number 1, 2013, discussing the possibile habitability of giant planetary size exomoons orbiting giant exoplanets in the habitable zones of other stars.

https://faculty.washington.edu/rkb9/publications/hb13.pdf

And of course a planetary sized exomoon orbiting a giant exoplanet in the circumstellar habitable zone of a star is very similar to what the OP asks for, so that discussion should be relevant to this one. Of course the difference is that the OP asks about the comparatively rare case when a habitable moon orbits around the center of gravity of a double planet instead of orbiting around a single planet, and I don't know of any scientific discussions of a habitable moon orbiting a double planet.

Anyway, Heller and Barnes discuss the possible sizes of habitable exomoons and come to similar, though not identical, conclusions as Dole.

In section 2. Habitability of exomoons, they write:

A minimum mass of an exomoon is required to drive a magnetic shield on a billion-year timescale (MsT0.1M4; Tachinami et al., 2011); to sustain a substantial, long-lived atmosphere (MsT0.12M4; Williams et al., 1997; Kaltenegger, 2000); and to drive tectonic activity (MsT0.23M4; Williams et al., 1997), which is necessary to maintain plate tectonics and to support the carbon-silicate cycle. Weak internal dynamos have been detected in Mercury and Ganymede (Gurnett et al., 1996; Kivelson et al., 1996), suggesting that satellite masses > 0.25M4 will be adequate for considerations of exomoon habitability. This lower limit, however, is not a fixed number. Further sources of energy—such as radiogenic and tidal heating, and the effect of a moon’s composition and structure—can alter the limit in either direction. An upper mass limit is given by the fact that increasing mass leads to high pressures in the planet’s interior, which will increase the mantle viscosity and depress heat transfer throughout the mantle as well as in the core. Above a critical mass, the dynamo is strongly suppressed and becomes too weak to generate a magnetic field or sustain plate tectonics. This maximum mass can be placed around 2M4 (Gaidos et al., 2010; Noack and Breuer, 2011; Stamenkovic´ et al., 2011). Summing up these conditions, we expect approximately Earth-mass moons to be habitable, and these objects could be detectable with the newly started Hunt for Exomoons with Kepler (HEK) project (Kipping et al., 2012).

They give the minimum and Maximum masses in the form of M followed by the astronomical symbol for Earth, which comes out as M4 the quote. So where you see a number times M4 in that quote think of it as that number times the mass of Earth.

So they believe that the mass of a habitable exomoon would be somewhere between about 0.25 the mass of Earth and about 2.00 times the mass of Earth.

Combining that with Dole's mass range gives a conservative mass range of 0.4 to 2.0 times the mass of Earth, or a more optimistic mass range of 0.195 to 2.25 times the mass of Earth.

In order for your moon to be considered a moon orbiting a double planet instead of the smallest planet in a triple planet, each of the other 2 objects should be at least several times as massive as the moon.

With half the diameter and one eighth the mass of Pluto, Charon is a very large moon in comparison to its parent body. Its gravitational influence is such that the barycenter of the Plutonian system lies outside Pluto.

The center of mass (barycenter) of the Pluto–Charon system lies outside either body. Because neither object truly orbits the other, and Charon has 12.2% the mass of Pluto, it has been argued that Charon should be considered to be part of a binary system with Pluto. The International Astronomical Union (IAU) states that Charon is considered to be just a satellite of Pluto, but the idea that Charon might be classified a dwarf planet in its own right may be considered at a later date.[47]

Since some people think Pluto and Charon should be classed as a double planet, I suggest each of the two planets in the double planet be at least 10 times as massive as your moon, makign th total mass of the double planet 20 times that of the moon.

So making the moon a reasonable 0.4 to 2.0 times the mass of Earth, and assuming that each of the planets is at least 10 times as massive, each of those planets must be at least 4 to 20 times the mass of Earth, and the total mass of the double planet must be at least 8 to 40 times the mass of Earth.

Part Two: How Far Could the Moon Orbit From the Double Planet?

The habitable moon couldn't orbit very close to the double planet, because it would have to be several times as far from the center of the double planet as each of the planets is.

And the double planets should have formed at a distance of several times their diameters, and thus several tens of thousands of kilometers. And as they orbited each other their tidal interactions should have slowed down the lengths of their days and pushed them farther apart.

While gravitation causes acceleration and movement of the Earth's fluid oceans, gravitational coupling between the Moon and Earth's solid body is mostly elastic and plastic. The result is a further tidal effect of the Moon on the Earth that causes a bulge of the solid portion of the Earth nearest the Moon. Delays in the tidal peaks of both ocean and solid-body tides cause torque in opposition to the Earth's rotation. This "drains" angular momentum and rotational kinetic energy from Earth's rotation, slowing the Earth's rotation.[175][182] That angular momentum, lost from the Earth, is transferred to the Moon in a process (confusingly known as tidal acceleration), which lifts the Moon into a higher orbit and results in its lower orbital speed about the Earth. Thus the distance between Earth and Moon is increasing, and the Earth's rotation is slowing in reaction.[182] Measurements from laser reflectors left during the Apollo missions (lunar ranging experiments) have found that the Moon's distance increases by 38 mm (1.5 in) per year (roughly the rate at which human fingernails grow).[183][184][185] Atomic clocks also show that Earth's day lengthens by about 17 microseconds every year,[186][187][188] slowly increasing the rate at which UTC is adjusted by leap seconds. This tidal drag would continue until the rotation of Earth and the orbital period of the Moon matched, creating mutual tidal locking between the two and suspending the Moon over one meridian (this is currently the case with Pluto and its moon Charon). However, the Sun will become a red giant engulfing the Earth-Moon system long before this occurrence.[189][190]

https://en.wikipedia.org/wiki/Moon#Lunar_distance

The two planets should have rapidly tidally locked to each other, and then their outward acceleration would stop. So they might possibly stop moving apart when still only tens of thousands of kilometers apart, or possibly when they are over a hundred thousand kilometers.

And the third object, the habitable moon, should also be gradually accelerating away from the double planet, and had to have several times their original separation to begin with. So by the time of the story it should be several hundred thousand kilometers, or maybe a few million kilometers, from the center of gravity of the two planets.

For the moon to have a long term stable orbit around the center of mass of the double planet, it would have to be within the Hill radius or Hill sphere of the double planet.

The Hill sphere of an astronomical body is the region in which it dominates the attraction of satellites. The outer shell of that region constitutes a zero-velocity surface. To be retained by a planet, a moon must have an orbit that lies within the planet's Hill sphere. That moon would, in turn, have a Hill sphere of its own. Any object within that distance would tend to become a satellite of the moon, rather than of the planet itself. One simple view of the extent of the Solar System is the Hill sphere of the Sun with respect to local stars and the galactic nucleus.1

https://en.wikipedia.org/wiki/Hill_sphere

The Hill sphere is calculated from the mass of the planet, the mass of the star, and the distance between them.

The article lists the sizes of the Hill spheres of various solar ystem objects.

https://en.wikipedia.org/wiki/Hill_sphere#Solar_System

The radius of the Hill sphere of Earth is about 1,471,400 kilometers. But:

The Hill sphere is only an approximation, and other forces (such as radiation pressure or the Yarkovsky effect) can eventually perturb an object out of the sphere. This third object should also be of small enough mass that it introduces no additional complications through its own gravity. Detailed numerical calculations show that orbits at or just within the Hill sphere are not stable in the long term; it appears that stable satellite orbits exist only inside 1/2 to 1/3 of the Hill radius.

https://en.wikipedia.org/wiki/Hill_sphere#True_region_of_stability

So the actual outer radius of stable orbits around the Earth would extend to about 490,466 or 735,700 kilometers from Earth. Since the semi-major axis of the orbit of the Moon around the the Earth is 384,399 kilometers, the moon is within the region of true stability.

Bu what about your fictional moon which is probably hundreds of thousands or even millions of kilometers from the double planet? It could easily be outside the true region of stability of the Earth. Fortunately it is orbiting a double planet with a total mass of at least 8 to 40 times the mass of Earth, and so the true region of stability of the double planet should be several times as far as that of Earth.

If the double planet is moved closer to its star, it's Hill sphere and true region of stabiity will shrink. If the double planet is moved farther to its star, it's Hill sphere and true region of stabiity will expand.

If the double planet and its moon are moved to the habitable zone of a dimmer and less massive star, the region of stable orbits around the double planet will shrink. If the double planet and its moon are moved to the habitable zone of a brighter and more massive star, the region of stable orbits around the double planet will expand.

Part Three: The Masses of the Double Planet and the Orbital Radius of the Moon.

I suggested that each of the two planets in the double palnet should be at least 10 times as massive as your habitable moon with 0.4 to 2.0 times the mass of Earth, and thus should have 4 to 20 times the mass of Earth.

A planet with 4 times the mass of Earth would be uninhabitable for humans and most large Earth animals because of the increased gravity. Of course native animals adjusted to the increased gravity could evolve and flourish there.

A super-Earth is an extrasolar planet with a mass higher than Earth's, but substantially below those of the Solar System's ice giants, Uranus and Neptune, which are 14.5 and 17 times Earth's, respectively.1 The term "super-Earth" refers only to the mass of the planet, and so does not imply anything about the surface conditions or habitability. The alternative term "gas dwarfs" may be more accurate for those at the higher end of the mass scale, although "mini-Neptunes" is a more common term.

According to one hypothesis,[92] super-Earths of about two Earth masses may be conducive to life. The higher surface gravity would lead to a thicker atmosphere, increased surface erosion and hence a flatter topography. The end result could be an "archipelago planet" of shallow oceans dotted with island chains ideally suited for biodiversity. A more massive planet of two Earth masses would also retain more heat within its interior from its initial formation much longer, sustaining plate tectonics (which is vital for regulating the carbon cycle and hence the climate) for longer. The thicker atmosphere and stronger magnetic field would also shield life on the surface against harmful cosmic rays.[93]

https://en.wikipedia.org/wiki/Super-Earth

This says:

The mass of a potentially habitable exoplanet is between 0.1 and 5.0 Earth masses.[21] However is possible for a habitable world to have a mass as low as 0.0268 Earth Masses [57]

https://en.wikipedia.org/wiki/Planetary_habitability#Mass

So it sets an upper mass limit of 5 times the mass of Earth for a habitable planet.

On the other hand Heller and Barnes cite sources which claim that about 2 times the mass of Earth is the upper limit for a habitable planet.

In any case, it is possible to make the two parts of the double planet much more massive than any planet habitable for Earth type life, let alone for humans.

Let's jump to planets with the mass of JUpiter, 317.8 times the mass of Earth. Jupiter has an equatorial radius of 71,492 kilometers, and thus an equatorial diameter of 142,984 kilometers.

Suppose that two Jupiter sized planets orbit their barycenter at distances of 2.5 times their diameters, with a total separation of 5 times the diameter, or 749,920 kilometers. If the habitable moon has to orbit them at at least 5 or 10 times the separation it would have to orbit at least about 3,749,600 to 7,499,200 kilometers.

Suppose that two Jupiter sized planets orbit their barycenter at distances of 25 times their diameters, with a total separation of 50 times the diameter, or 749,920 kilometers. If the habitable moon has to orbit them at at least 5 or 10 times the separation it would have to orbit at least about 37,496,000 to 74,992,000 kilometers.

The Hill sphere of Jupiter has a radius of 50,573,600 kilometers, and the true region of stabilty should have a radius of about about 16,857,866 to 25,286,800 kilometers.

Of course in this case the double planet would have twice the mass of Jupiter, increasing the radius of the region of stability. On the other hand, the double planet would have to be closer to its star in order to have temperatures suitable for life on the habitable moon, and that would shrink the region of stabiity.

Jupiter happens to be almost as large as a giant planet can be - except for giant planets very close to their stars which are super hot and have expanded atmospheres.

As more and more mass is added to a giant planet, its gravity tends to compress its matter and make it more dense, slowing the expansion of the planets. Planets a little more massive than Jupiter are as large as they can be. Planets more massive than that stay the same siz eor even shrink their size.

So I think that it is impossible for giant planets in the habitable zones of stars to have more than say, 1.2 times th diameter of Jupiter. But they can have up to about 13 times the mass of jupiter, which is the approximate transition mass between the least massive planets and the least massive brown dwarfs.

So imagine that the two giant planets each have 1.2 times the diameter of Jupiter, or 171,580.8 kilometers.

Suppose that two planets with 1.2 times the diameter of Jupiter orbit their barycenter at distances of 2.5 times their diameters, with a total separation of 5 times the diameter, or 857,904 kilometers. If the habitable moon has to orbit them at at least 5 or 10 times the separation it would have to orbit at least about 4,289,520 to 8,579,70 kilometers.

Suppose that two planets with 1.2 times the diameter of Jupiter orbit their barycenter at distances of 25 times their diameters, with a total separation of 50 times the diameter, or 8,579,040 kilometers. If the habitable moon has to orbit them at at least 5 or 10 times the separation it would have to orbit at least about 42,895,200 to 85,790,400 kilometers.

So the largest possible planets would not require orbits much more distant but they could have up to 13 times the mass of Jupiter and thus have significantly larger Hill spheres than Jupiter mass planets.

Part Four: The Length of Day of the Moon and its Orbit.

There is also the question of the length of day of the habitable moon. The closer the habitable moon is to the double planet it orbits, the more likely it would be to be within the Hill sphere of the double planet - but it would also be more likely to be tidally locked to the planet.

If the habitable moon is tidally locked to its double planet, it will have a rotation period the same length as its orbital period areound the double planet. So one side will always face the double planet, and the other side will always face away from the double planet.

And every part of the habitable moon will have a cycle of day and night as that part alternately faces toward the star and away from the star.

But if the day night cycle lasts a long as an orbital period around the double planet, how long will that be?

Stephen Dole, in Habitable Planets for Man believed that if the day night cycle got too long, the days would get too hot and the nights would get too cold for habitability. And plants which produced oxygen by photosynthisis might die from lack of light during long nights.

On page 60 Dole wrote:

Just what extremes of rotation rate are compatable with habitability is difficult to say. Theese extremes, however, might be estimated at, say, 96 hours (4 Earth days) per revolution at the lower end of the scale and 2 to 3 hours per revolution at he upper end, or at angular velocities where the shape becomes unstable because of the high rotation rate.

I found an orbital period calculator and entered some figures.

https://www.calctool.org/CALC/phys/astronomy/planet_orbit

If the double planet has a mass of 8 times the mass of Earth, a moon with 0.4 times the mass of Earth at a distance of 213,000 kilometers would have an orbital period of 4.00286 days.

If the double planet has a mass of 40 times the mass of Earth, a moon with 2 times the mass of Earth at a distance of 213,000 kilometers would have an orbital period of 3.99967 days.

If the double planet has a mass of 635.6 times the mass of Earth (2 times the mass of Jupiter), a moon with 1 times the mass of Earth at a distance of 916,000 kilometers would have an orbital period of 4.00180 days.

If the double planet has a mass of 8,262.8 times the mass of Earth (26 times the mass of Jupiter), a moon with 1 times the mass of Earth at a distance of 2,152,000 kilometers would have an orbital period of 3.99963 days.

So if the limit of 4 Earth days for the length of the moon's day and thus for its orbital period is valid, the two planets should be close to each other to give room for the moon to orbit relatively close to them.

Or possibly the moon might orbit far enough from the double planet that it is not tidally locked to them, and so has a day much shorter than its orbital period.