Captured Earth-Like Moons around Gas Giants

Question

Is there a limit (and if so, what is it) to the size (mass) of terrestrial planet that could be "captured" as a moon by a migrating gas giant?

I'm writing a novel where a colony ship crashes on such a moon. My research tells me that a moon around a gas-giant is not likely to be larger than 1:10,000th of the mass of its parent. If this is true, an Earth-like moon is unlikely to form around anything with less than 30 Jupiter masses, which puts the parent planet in the brown dwarf range. Not what I want.

So, can I get round this by having the gas giant migrate into the inner system, snaring a rocky world approximately the size of Earth, as it goes?

I'm not too concerned about other issues - I'm happy to fudge tidal locking, and have the gas giant only have a couple of other moons to avoid tidal heating, and stick the Earth-like moon 10ish million kms out to avoid the worst of the radiation. But I feel like I can't fudge the mass of the related bodies.

Any help, or related thoughts, would be greatly appreciated.

SOURCES:

http://phl.upr.edu/library/notes/themassandradiusofpotentialexomoons

https://www.reddit.com/r/askscience/comments/32ixle/is_there_a_clear_maximum_gas_giant_moon_size/

This is indicative of similar sites and forums where I got the figures. I've struggled to find anything concrete anywhere else; language is vague, but supports the notion that there is a mass limit for moons forming around gas giants, and that an Earth-mass moon would require a gas giant of several multiples of Jupiter. One site I read suggested that Earth-sized ice moons might form past 10 Jupiter masses, but that any terrestrial moon would be considerably smaller. Obviously, I'm looking for an Earth-mass, terrestrial planet, not a slushie world, and I want to avoid small terrestrial worlds because of the low-gravity.

I'm grateful for the response re the Roche Limit. I did wonder about two planets orbiting a mutual gravitational center, but I don't know how to figure out what kind of effects that might have on the Earth-like planet, and whether I could keep it far enough outside the gas giant's radiation belts.

Thanks for all the replies so far.

Answer 1

I'm not sure where you are looking, but first look here: https://www.reddit.com/r/askscience/comments/23a96x/could_an_earth_sized_object_orbit_jupiter/

The answer is Yes; any two objects can orbit each other, include Earth and Jupiter.

You need to be concerned about the Roche Limit, which tells you how far apart they must be in order to do so.

And be aware that gravity works both ways, even for smaller objects: The Earth is pulled into a rotation by our Moon just as much as our Moon is pulled into a rotation by Earth: It isn't just the tides moved by the Moon, but the center of Earth is moving in small circles due to the moon.

So planets of equal mass would circle each other. But Jupiter is 318 x the mass of Earth, and the most massive known planet in the Universe is about 30 x the mass of Jupiter. (FWIW our Earth is 81 x our Moon).

Look up the Roche Limit; that should also tell you what your minimum orbit should be around your big planet (but actual orbit can be thousands of times bigger).

Roche Limit says Earth cannot be any closer than about 67,000 miles to Jupiter without breaking up. However, your planet can be quite a bit further, our Moon is about 40x its rigid body Roche Limit from Earth. But what this means is you can put it about where you like; it does not have to be extremely far from the gas giant. If you want tidal heating of your planet (and lots of earthquakes) put it close; if your planet is warmed otherwise and you want it calmer; I'd keep it at least twenty Roche units away, say 1.4 million miles from Jupiter.

Answer 2

You are better off with a habitable moon than a captured terra. One scenario would be a massive moon which migrated in towards its planet, while the planet migrated in towards its sun. The migration is explained by universal "shrinkage" so it's consistent, and there are no improbable catcher's mitt or billiard physics necessary.

The problem is your gas giant and terra planet were not formed in the same part of the solar system. The current thinking is there's a defining frost line created when the solar nebula formed into planets. Within the frost line you get the rocky terrestrial planets, beyond it are the gas and ice giants.

A migrating terra planet is possible – knocked from its orbit by a brush with another planet, but to later be gently plucked by a gas giant into a stable orbit is improbable – like knocking a baseball 10,000 miles to gently land a catcher's glove. You probably don't want your planet to be in the outer solar system, even if it could hold its atmosphere during cosmic billiards.

A migrating gas giant is believable because it could easily migrate in towards the sun, but then what made it stop migrating – assuming your terra planet isn't being dragged into a death spiral? The answer would be another even bigger gas giant in a resonance orbit, but again this set of circumstances seems like improbably cosmic billiards, now involving three planets.

Resonance orbits are unstable, they don't "settle" an object into a stable groove so much as fling the other bodies away. The definitions of a planet is how they clear their own orbit of all other objects (the 1:1 resonance ratio), and Jupiter is theorized to have been the big baby that threw all the toys out of the pram. As your gas giant approaches the inner system, it would send your terra planet flying out of the solar system long before it got close enough to be captured.

Getting captured by a rogue planet also seems impossible, the rogue would tear through the solar system at escape velocity. That's not going to gently snag a planet either.

A habitable moon is the only reasonable way you could end up with something stable.

Answer 3

My research tells me that a moon around a gas-giant is not likely to be larger than 1:10,000th of the mass of its parent.

The theoretical mass limit between a planet and a brown dwarf is about 13 Jupiter masses, or about 4,131.4 times the mass of Earth. Thus if a moon can be no more than 0.0001 times as massive as a gas giant, it can have no more than 0.41314 times the mass of Earth.

Jupiter has a mass 317.8 of Earth. Its most massive moon, Ganymede, has a mass of 0.025 of Earth. Thus the mass of Jupiter is 12,712 times the mass of its most massive moon.

Saturn has a mass 95.159 of Earth. Its most massive moon, Titan, has amass of 0.0225 Earth. Thus the mass of Saturn is 4,229.28 times the mass of its most massive moon.

Uranus has a mass 14.536 of Earth. Its most massive moon, Titania, has mass 0.0005908 of Earth. Thus the mass of Uranus is 44,603.926 times the mass of its most massive moon.

Neptune has mass of 17.147 of Earth. Its most massive moon, Triton, has mass 0.00359 of Earth. Thus the mass of Neptune is 4,776.3231 times the mass of its most massive moon.

So according to the examples of gas giant planets in our solar system, a moon with the mass of the Earth could orbit around a gas giant planet with a mass of 4,229.28 or 4,776.3231 times the mass of Earth, which would be 13.307992 or 15.029336 times the mass of Jupiter. That would be a little bit above the theoretical lower mass limit for a brown dwarf.

The largest and most massive moon in the Solar System, Ganymede, has a radius of only≈0.4R⊕ (R⊕ being the radius of Earth) and a mass of≈0.025M⊕. The question as to whether much more massive moons could have formed around extrasolar planets is an active area of research. Canup and Ward (2006) showed that moons formed in the circumplanetary disk of giant planets have masses ≲10−4 times that of the planet's mass.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3549631/1

Canup R.M. Ward W.R. A common mass scaling for satellite systems of gaseous planets. Nature. 2006;441:834–839. [PubMed]

Mass-constrained in situ formation becomes critical for exomoons around planets in the IHZ of low-mass stars because of the observational lack of such giant planets. An excellent study on the formation of the Jupiter and the Saturn satellite systems is given by Sasaki et al. (2010), who showed that moons of sizes similar to Io, Europa, Ganymede, Callisto, and Titan should build up around most gas giants. What is more, according to their Fig. 5 and private communication with Takanori Sasaki, formation of Mars- or even Earth-mass moons around giant planets is possible. Depending on whether or not a planet accretes enough mass to open up a gap in the protostellar disk, these satellite systems will likely be multiple and resonant (as in the case of Jupiter) or contain only one major moon (see Saturn). Ogihara and Ida (2012) extended these studies to explain the compositional gradient of the jovian satellites. Their results explain why moons rich in water are farther away from their giant host planet and imply that capture in 2:1 orbital resonances should be common. Ways to circumvent the impasse of insufficient satellite mass are the gravitational capture of massive moons (Debes and Sigurdsson, 2007; Porter and Grundy, 2011; Quarles et al., 2012), which seems to have worked for Triton around Neptune (Goldreich et al., 1989; Agnor and Hamilton, 2006); the capture of Trojans (Eberle et al., 2011); gas drag in primordial circumplanetary envelopes (Pollack et al., 1979); pull-down capture trapping temporary satellites or bodies near the Lagrangian points into stable orbits (Heppenheimer and Porco, 1977; Jewitt and Haghighipour, 2007); the coalescence of moons (Mosqueira and Estrada, 2003); and impacts on terrestrial planets (Canup, 2004; Withers and Barnes, 2010; Elser et al., 2011). Such moons would correspond to the irregular satellites in the Solar System, as opposed to regular satellites that form in situ. Irregular satellites often follow distant, inclined, and often eccentric or even retrograde orbits about their planet (Carruba et al., 2002). For now, we assume that Earth-mass extrasolar moons—be they regular or irregular—exist.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3549631/1

Sasaki T. Stewart G.R. Ida S. Origin of the different architectures of the jovian saturnian satellite systems. Astrophys J. 2010;714:1052–1064.

Ogihara M. Ida S. N-body simulations of satellite formation around giant planets: origin of orbital configuration of the Galilean moons. Astrophys J. 2012;753 doi: 10.1088/0004-637X/753/1/60.

Triton has a mass 2.0936 times as great as a moon formed in the circumplanetary disc of Neptune should have according to Canup and Ward. Triton is believed to have been captured by Neptune.

Titan has a mass 2.3644 times as great as a moon formed in the circumplanetary disc of Saturn should have according to Canup and Ward. Thus Titan should have acquired its mass by one or more of the processes suggested to enable moons to exceed the mass limit postulated by Canup and Ward.

But why are gas giants and their moons the only models for the satellite systems of gas giants?

The Earth is 81.300813 times the mass of the Moon. Using the Earth-Moon system as a model, a moon with the mass of Earth could orbit a gas giant planet with a mass 81.300813 times the mass of the Earth, less massive than Saturn.

The dwarf planet Pluto has a mass of 8.1967 times its largest moon, Charon. Using the Pluto-Charon system as a model, a moon with the mass of Earth could orbit a gas giant planet with a mass 8.1967 times the mass of the Earth, less massive than Uranus.