TWO/3 Lunar Objects
STEP ONE: Check for presence and number of lunar objects on chart 2.3.1.
STEP TWO: Determine lunar orbits on 2.3.2.
STEP THREE: Determine size and density on 2.3.3. Check for rings.
STEP FOUR: Calculate mass, gravity and lunar year from 2.3.4.
Moons can be considered much the same as normal chunks and planets - they have the same basic properties and the sections on atmospheric and geophysical data applies to them too. The main difference is of course that they orbit a larger planet to which they typically are tidally locked. Thus, the "day" of a moon is really the lunar "year", the orbital period around the main planet. Moons normally don't have axial tilt (as long as they are tidally locked), but the main planet has one that will carry onto the moon as well as moons tend to orbit in a rough plane around the equator of the planet. Similarly, moons are affected by the eccentricity of the main planet's orbit. Very large moons within the stellar life zone could well be habitable.
The moon (not applicable to rings) has a odd orbit. Some such cases could be (roll 1d10):
Lunar objects of gas giants and superjovians are typically formed along with the planet. Lunar objects of terrestrial planets are typically either captured bodies (chunks) or formed by collision between planetesimals in the early system. Moons formed by collision will have lower density than the parent planet, because lighter material will form the moon. Captured moons may have any density. For average-sized gas giants, the moons have no significantly different density depending on distance from the world. Larger moons may be slightly denser, as they are compressed by gravity and the formation process might have ejected some of the lighter materials. But for large gas giants and superjovians (about 200 Earth Masses and up) in the outer system, the gas giant radiated enough heat during formation to leave more dense moons close to the planet and less dense further away, much as in the star system itself. If you wish to simulate this, consider multiplying the density of moons within 8 planetary radii by 2, and those within 8-12 radii by 1.5. For superjovians, use 7 + (Mass in Earths / 300) to determine the x 2 limit, and 1.5 times that distance as the x 1.5 limit.
UNLOCKED LUNAR OBJECTS:
If a moon orbits so far from the planet as to bring the tidal force down below 7-8, the moon may rotate around its axis. Note that this typically is a very big distance most applicable to moons in the outer system. Also, irregular moons slightly closer may be in chaotic orbit due to influences from other (big) moons. Stable orbits are also possible haveing 2:3 orbital periods, etc.
If a moon orbits a world faster than the world rotates, tidal forces will eventually cause the moon to crash onto the planet. It could get especially fast for worlds with large extensive atmospheres. Large moons tend to break up first as the Roche limit tear them apart, but smaller (<100km) moons or remnant pieces of a big moon may survive to impact in almost one piece.
There are many types of rings, and some amount of imagination is recommended. What the chart generates as one ring may well be half a dozen rings. Rings can consist mainly of very fine dust (these rings are almost undetectable), of ice particles of larger size (like the famous rings of Saturn) or by darker, ribbon-like rings of meter-size and larger material, or incomplete ring "arcs". In the inner system rings are stony or perhaps metallic (though stony is far more likely), while in the outer system ices (dark, reddish, gray or whitish) form the bands and ribbons. Ring material may range in size from dust and grain to blocks 10, even 100 meters across. Rings are formed either by breakup of satellites (collision etc), remnants from the old lunar creation or by dust and grain blown off moons, typically by volcanic activity.
A moon has seasons based upon the eccentricity of the planet, and the combined axial tilt of the planet and the inclination of the moon's orbit to the planet's rotational plane. Moons are seldom much inclined towards the plane, so usually it is the axial tilt of the planet which counts. But there are of course exceptions, some moons may be inclined 20° or 30°, or even more.
Moons that are affected by the strong tidal forces of the central planet (being fairly close to the planet) and other sizable moons get a significant deal of heating from tidal deformation. (Io and Europa are two such moons.) In extreme cases this powerful tectonic activity may turn an otherwise promising moon into an inferno. In other cases it may be enough to melt water and allow oceanic life on an otherwise frozen world. Tidal stress of this kind requires a central planetary mass of at least 30 to be really effective as a heat source.
Many gas giants radiate more heat than they receive, but only superjovians radiate enough heat to make them possible heat sources for lunar life zones. Superjovians, like brown dwarves, contract and cool with age. The big problem with superjovians as a source of heat is that they cool off fairly rapidly and start with lower temperatures than brown dwarves. A superjovian 10 times the size of Jupiter and about 1Gy old would have a surface temperature of 700°K, and the life zone would be within the tidal instability region (the "Roche" limit). Smaller and older superjovians would have even lower temperatures, dropping down to 300°K or less in a few Gy, and have no tenable life zones either. Superjovians cooler than 750°K (any superjovian older than a few hundred milion years) do not generate any visible light, only heat.
Habitable moons of superjovians are outside the life zone and must get the majority of heat from a stellar primary. Superjovians contract in size too, but not much compared to the loss of temperature. All superjovians are roughly of Jupiter size (70-80000 km in radius).
You can use this chart to see the evolution of a superjovian. For every 1 Gy after the first, move up one row on surface temperature and luminosity, but keep the original tidal stability limit. This roughly simulates the cooling of the superjovian.