![]() The amount of energy that is radiated away over time.The total amount of tidal work that is done on a moon.They also cool down much faster though I don't think this is relevant in this case. The inner moons are much to small (and too stiff) to experience significant tidal work. They don't flex as much as do those larger moons, and hence there is significantly less heat production in those small moons. Small bodies such as those innermost moons of Jupiter are solid throughout. This makes the interiors of larger bodies such as Io partially liquid. Heating induced by those negligible tidal forces and negligible self-gravitation forces dissipates quickly in small bodies, not so quickly in larger bodies. This means cooling per unit mass is inversely proportional to radius. Cooling is proportional to surface area and hence the radius squared while mass is proportional to radius cubed. This makes the tension between self-gravitation and tidal forces negligible for those small bodies.Īnother factor that comes into play is the square-cube law. (Tidal forces are proportional to body radius). The tidal forces on those small bodies are also smallish. The fuzzy boundary between small bodies such as those innermost moons and dwarf planetary bodies such as Pluto is the potato radius, somewhere between 200 and 300 km.Īll of those four innermost moons of Jupiter are well below the potato radius, too small to pull themselves into a roundish shape via self-gravitation. Small bodies such as those four innermost moons of Jupiter are too small to pull themselves into a roundish shape. Tidal heating results in part from a tension between the tidal forces exerted by the planet that tends to pull a moon out of round and the moon's self-gravitational force that tends to pull a moon into a roundish shape. Compare that with Io's mean radius of 1821.6 km. The largest of the four, Amalthea, has a mean radius of 83.5 km. The reason they don't exhibit volcanism is because they are too small. The other three have lower eccentricities. Only one of those innermost moons (Thebe) has an eccentricity higher than that of Io. There are four moons that are closer to Jupiter than Io with higher eccentricities, yet they don't seem to have any volcanism at their surface. But they survive because most small bodies aren’t held together primarily by gravity (just as your own body isn’t) - the internal electromagnetic forces between atoms (which manifests macroscopically as the rigidity of the rock) is the main source of the bodies’ structural strength. On a related note, the inner three of those four satellites are inside Jupiter’s Roche limit, the orbital distance at which a purely self-gravitating body should be pulled apart by tidal forces. The small mass plays a role, too, but the dependence on radius is stronger.įor this same reason, small objects on Earth don’t feel tidal stretching from our Moon, yet the Earth as a whole does. The strength of the tidal heating scales as the body’s radius to the 5th power, quite a strong dependence. When an object is small, the difference in distance to the two sides of it is necessarily small as well.Īccording to Wikipedia, Amalthea, the largest of those four innermost moons has a long axis that is only 250 km, and the others are smaller yet. Tidal forces are differential forces, that is, they result from the difference in gravitational pull on one side of a body compared to the other. It’s because they are much smaller than Io.
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