The gas giant has a mass of about 2.13 Jupiter masses in the habitable zone of a Sun like star 0.981 Sol masses, all the moons will need at least >0.12 percent of Earth's mass and a Mars like density to support an atmosphere for billions of years. I assume the largest moons will be around 0.3 Earth masses as larger moons have larger hill spheres and will probably create orbital instabilities.
$\begingroup$ Not sure what you are asking here or how it could be answered. The number of moons would be determined by the initial conditions the planet formed in, and then the size distribution of the moons would probably be in a power law distribution $\endgroup$– ThucydidesJul 14, 2016 at 0:17
$\begingroup$ Maybe if I give the gas giant an actual mass it will be easier to determine? I guess 2-5 jovian mass is a huge difference. $\endgroup$– StephanieJul 14, 2016 at 0:20
$\begingroup$ Initial conditions include things like the planet's journey, clearing the local region of ice, dust, gas and small objects, how thick the protoplanetary disc actually was and so on. A Jovian world passing through dense clouds of matter will potentially pick up more material, but its gravity could also "slingshot" the mass out of the solar system. $\endgroup$– ThucydidesJul 14, 2016 at 3:57
I get 8 moons for a similar setup. Although you might be able to play some tricks to increase this...
The number of moons the giant planet could have simply depends on how tightly they could be packed while maintaining orbital stability. Assuming prograde orbits, moons are stable out to about 1/2 of a planet's Hill radius RH, defined as RH = a (Mp/3Mst)^(1/3), where a is the orbital distance of the planet around the star, Mp and Mst are the planet and star masses.
Jupiter's Hill radius is about 0.35 Astronomical Units on its current orbit of 5.2 AU, so if it took the place of Earth, its hill radius would simply shrink by a factor of 5.2, down to about 0.07 AU. The orbital distance of Jupiter's outermost large moon, Callisto, is about 0.013 AU, so all 4 of Jupiter's big moons would still be stable if Jupiter were on Earth's orbit.
Now, how many more moons could we pack in if Jupiter were at 1 AU? Io's orbital distance is about 0.003 AU. LEt's assume that is the closest a big moon can form. The farthest is 0.07 AU, because beyond that moons would not be stable.
To make things simple, let's assume that the moons will be in a chain of orbital resonances (like the 4:2:1 Laplace resonance between Io, Europa and Ganymede). The total size of orbital space we have to work with is between 0.003 and 0.07 AU. Kepler's 3rd law tells us that the orbital period scales as the orbital distance to the 1.5 power. In orbital period space, we have (0.07/0.003)^1.5 = a factor of 112 in orbital period. Actually, to make the numbers work better let's move our inner edge inward a little to get a factor of 128. Now, let's assume that each pair of adjacent planets is locked in 2:1 orbital resonance, where the outer planet's orbit takes twice as long to complete. This would give us 8 moons orbiting the planet. The moons would make a resonant chain of (inner to outer) 128:64:32:16:8:4:2:1. I've created similar resonant chains in computer simulations of planet formation and they are often stable. So, I think it's reasonable to assume this chain of 8 moons in resonance will be stable as well.
This is an analogous process to figuring out how many planets can be packed into a star's habitable zone. See here for more details on that: https://planetplanet.net/2014/05/21/building-the-ultimate-solar-system-part-3-choosing-the-planets-orbits/
And you may be able to sneak extra moons in on Trojan orbits. See here: https://planetplanet.net/2014/05/22/building-the-ultimate-solar-system-part-4-two-ninja-moves-moons-and-co-orbital-planets/
$\begingroup$ How many of those moons will be orbiting within the magnetic field of the gas giant? $\endgroup$ Jul 19, 2016 at 20:54
$\begingroup$ Also something interesting is how plants and animals would adapt to a very long day night cycle, if a moon has an orbital period of 31 days then it will be locked to the parent and have 15 days of night and day $\endgroup$ Jul 19, 2016 at 21:14
$\begingroup$ Is this a good example of 1:4:8:12 resonance? Moon one orbiting every 2.17 days, Moon two orbiting every 8.69 days, Moon three orbiting every 17.36 Days, Moon four orbiting every 34.72 days and Moon five orbiting every 69.44 days. $\endgroup$ Jul 25, 2016 at 6:29
Are you basing this on current technology? Because we probably could create sustainable colonies on existing planets using existing technology, but the costs are very high. Your theoretical planet could host a large number of orbiting bodies. The number of those which are habitable 'naturally' is going to vary based on 'we can live here, but it sucks to be so cold' to 'we can live here but it sucks to be so hot'. Throw in technology and the number goes up. I am going to guess you are counting technology into this answer. The reason is I take 'habitable' to mean for humans, and it would take technology to get onto multiple moons. If you mean, generally, 'life as we know it' then arguments abound to what ranges of temperature lifeforms would tolerate.
there will be a difficulty in retaining both atmospheres and the core temperature of these small planets, so even if they could support life when they formed, it would only be a matter of time before they could no longer support life, and this might not be enough time for life to, well, evolve
Jupiter radiates 1.5-2x the amount of energy it receives from the sun. When placed inside the Sun's 'habitable zone', Earth-like planets orbiting it would be baked constantly. A moon a third the size of Earth would only be barely holding onto an atmosphere, and it's unclear that between the Sun and Jupiter it wouldn't immediately bleed that atmosphere off to Jupiter itself. Certainly, any ecosystem would be wracked by a much larger body forcing tidal patterns both in liquid water and in the magma core (which is necessary to have an EM field capable of containing an atmosphere).
More Than Zero
Assuming you found the unlikely conditions to support even one planet, why would there be an upper limit on the number of planets?
$\begingroup$ What about smaller gas giants like Saturn? Or Neptune sized ones? $\endgroup$ Jul 14, 2016 at 2:49
4$\begingroup$ Actually, Jupiter would not radiate out so much more energy than it receives if it were close enough to receive much. Also, this energy is radiated away from Jupiter in all directions, so a moon would not necessarily receive 1.5-2x the energy even if that was still the case. $\endgroup$ Jul 14, 2016 at 2:50
$\begingroup$ @JarredAllen But it would be a lot closer to the Sun, and a lot of the radiation is due to surface albedo: acting as a giant mirror reflecting energy, in addition to being a space-heater. Earth is in a 'habitable zone' precisely because there isn't a little mini-sun in it's local volume. Consider the moon, where temperature varies wildly: the only time it would be on the 'low' side is when the face is pointed away from both Jupiter and the Sun. This does not suggest a stable weather system. $\endgroup$ Jul 14, 2016 at 2:53
1$\begingroup$ Only, Jupiter would now be receiving about 30 times as much radiation as it used to, so the 1.5-2x figure would now become about 1.016-1.033x (assuming that your figure includes re-radiated sunlight and that the energy Jupiter produces remains the same). $\endgroup$ Jul 14, 2016 at 3:09
1$\begingroup$ @Stephanie If a gas giant is supporting human-habitable moons, they are likely to be further out than what we consider to be the Sun's 'habitable zone', because of the additional energy considerations of the planet being orbited. But note that moons supporting life is dodgy at best. If you want to get a good number you have to narrow the constraints. $\endgroup$ Jul 14, 2016 at 3:20