General How big a moon for gas giants?

[Gray Lensman]

The questions are these: How big a moon could a large gas giant have? How many worlds of that size could a gas giant hold in different orbits? In the same orbit?

Thinking of setting up a game where it all takes place in one system (no FTL). I am NOT a science type. I would like realistic assumptions or hard science.

 

[aramis]

A world can, theoretically, capture another world of any size up to its own...

You need to know the hill sphere and the Roche limit; it will fall between those two values. Outside the hill sphere, gravity is below stable capture, below Roche, the tidal forces will exceed gravitationally bound soil's tensile strength. (in other words, nothing FORMS there; stuff can be captured there)

Hill Sphere:
H = Radius of Hill Sphere (in same units as A)
A = Semi-major axis (in same units as H)
E = Eccentricity
Ms = Mass of smaller body (in the same units as M)
Mp = Mass of larger (primary) body. (in same units as m)

For low ecentricity, use...
H = (1 - E) * A * (3*Ms/Mp)^(1/3)

For higher, as a simplification, just use the closest approach and ignore the eccentricity

For what can fit in there...

Given Star A, and GG's B & C...

Anything orbiting A at B's Orbit ±(B's hill sphere) is orbiting B. Anything orbiting a at C's orbit ± (C's hill sphere) is orbiting C, or is in a resonance with C (usually lagrange points) or in odd orbits (like Cruithne).

If you want to keep things stable, you just need to remember that if they're both inside the hill spheres of each other, both are likely tidelocked to each other, or eventually will be. (Earth is slowing thanks to tidal forces between Earth and the Moon.)

Nothing inside the Roche limit is stable; the roche limit calc below is for solid bodies as the secondary, and the roche limit is dependent upon the secondary object. (In simpler terms, you cannot generate a universal roche limit for the world, only check to see if a world is inside the roche limit for itself. A smaller moon has a smaller roche limit than a larger one, and a more dense world a smaller roche limit than a less dense one.

Given the densities and the radius of the secondary.
Ds =Density, secondary
Dp = Density, primary
Rs = radius of the secondary
Rrs = Radius of the Roche limit for s
Both radii need to be in the same unit. Both densities need to be in the same unit.

Rr = Rs * (2 * (Ds/Dp))^(1/3)

If an object s's orbit is lower from p than the Roche limit for s, you can launch from s by simply walking to the far side or the near side, and letting go. (Far side launches you into an elliptical orbit, as you're going too fast for the distance; near side pulls you to the p world, as you're going too slow.)

 

[shaunhilburn]

The questions are these: How big a moon could a large gas giant have?

How many worlds of that size could a gas giant hold in different orbits? In the same orbit?

The universe is a strange place and new discoveries continue to defy conventional thinking. Almost any moon system scenario is possible. The first exomoon discovery, Kelper 1652b, was found to be a gas giant itself.

For perspective on a typical system, consider the gas giants of our solar system, their principal moons, and the mass ratios for the gas giants to their moons, since they probably represent the norm:

JUPITER   317.8 Earth masses
-----------------
Io          0.015
Europa      0.008
Ganymede    0.025
Callisto    0.018
           -------
            0.066 earth masses
            mass ratio = 1:4,815.2



SATURN     95.159 Earth masses
-----------------
Mimas       6.27288E-06
Enceladus   0.000018
Tethys      0.000103
Dione       0.0001834
Rhea        0.00039
Titan       0.0225
Iapetus     0.00030234
            -----------
            0.023503013 earth masses
            mass ratio = 1:4,048.8


URANUS    14.536 Earth masses
-----------------
Miranda    0.00001103
Ariel      0.000226
Umbriel    0.0002
Titania    0.0005908
Oberon     0.0005046
           ---------
           0.00153243 earth masses
           mass ratio = 1:9,485.6



NEPTUNE  17.147 Earth masses
-----------------
Triton    0.00359 Earth masses
          mass ratio = 1:4,776.3

The lowest ratio among them belongs to the moons of Saturn, at around 1/4000th of the mass of Saturn.

The largest plausible non-luminous gas giant at the threshold of brown dwarfdom, weighs in at 13 Jupiter masses, or 4,131.4 Earth masses (again 1/4000th). Such a planet with a comparable Saturnian satellite mass ratio would host a retinue of moons totaling 1 earth mass. It could be a single Earth-sized moon, two smaller habitable moons of 0.5 earth masses, or four habitable moons of 0.25 earth masses each. This is not counting the swarm of small spherical moonlets of insignificant mass.

Keep in mind are that moons are almost always tidelocked to the parent body, which precludes the moon having rings or moons of its own.

For the *smallest* habitable moon, the tightest constraints represent the lowest possible masses of moon, gas giant, and host star. This is a Size 5 world (0.2 earth mass, 0.64 earth radius, 0.49 G) orbiting a large 2.5 MJup superjovian every two days. Given 50% of the gas giant's Hill radius, the smallest host star that will support this is M4V/3,000 K/0.25 Rsol/0.25 Msol/0.00454 Lsol, where the moon has 1/6 the orbital period of the gas giant. Larger habitable moons require bigger gas giants, more expansive orbits, and larger hotter stars.

 

[Timerover51]

The following is not at all meant to be facetious, but simply practical. I do not think that we know enough about planetary systems to set any hard and fast rules.

I would take a single D6 and roll it, and what comes up is the diameter of the Gas Giant satellite. If you think that would be a bit too big, then do a D6 - 2, giving you a range of 1 to 4. If the number ends up "0" or "-1", then take a D6, add 4 to the roll, and that is the satellite's size in hundreds of miles. That will give you a range in size from 500 miles to 6,000 miles for the size of the satellite.

 

[Gray Lensman]

Well, guess it's time to brush up on my math. I was a philosophy major ;D.

I suppose my first step will be to figure out how deep of a "habitable" zone I can get and see if I can squeeze three (Hopefully) orbits into it and go from there. Thanks folks.

 

[dalthor]

I've contemplated [and posted discussion about] this same issue.

I decided to simplify, such that when rolling satellites, they can be no more than 1/4 the size of the main body.

For the more detail-oriented folks around here, I use the following when I choose to go into excruciating detail when generating a complete system --

For me, it comes down to the center of mass of two or more non-stellar objects sharing a stellar orbit.

I decided a satellite is a body orbiting another, such that the center of mass (the barycenter) is within the body of the primary object being orbited. Our real-world moon is a satellite by that definition.

If the barycenter of the two lies between the two, and not within the diameter of either object, it is is a "wobbly" in my campaign, and each is a satellite of the other. Pluto and Charon would be a good example.

I use the remark WB to annotate each member of the wobbly.