Now consider: because of the tidal force, the earth's water wants to become elongated in the direction of the Moon. However, the Earth is rotating underneath it, continually moving the water away from where it wants to be. In response, the water is continually sloshing back to its preferred position, moving against the rotation of the Earth. This causes friction, and, in fact, because of this drag, the Earth's spin is slowing down. Occasionally, near New Year, you'll hear a short news report about a fraction of a ``leap second'' being added at midnight. One reason for this is to compensate for the slowing of the Earth's rotation (which is about 3 milliseconds per century). In fact, the Earth has slowed so much that, in the days of the dinosaurs, an Earth day was only 22 hours, rather than 24.

If the Moon's tides are having an effect on the Earth, then it is reasonable to assume that the Earth's tides must be having an affect on the Moon. Specifically, since the Earth is 80 times more massive than the Moon, you would expect that the tides on the Moon would significantly greater. This is correct: long ago, the Moon was molten, and during that period, lava flowed with the tide. The friction caused by these lava flows was strong enough to stop the Moon's rotation completely. The Moon is now tidally locked with the Earth. That is, the time it takes the Moon to rotate on its axis is exactly the same time as it takes to go around the earth. As a result, the Moon keeps the same side facing the Earth at all times.

Another place where tides play a great role is in the Galilean Moons of Jupiter. The four biggest moons of Jupiter, in order of closest orbit to furthest orbit, are Io, Europa, Ganymede, and Callisto. Callisto's surface looks as though it was formed at the very beginning of the solar system; it has a very low density (about 1.8 times that of water), and has crater upon crater on its surface. Ganymede's has a slighly higher density (1.9) and its surface is not quite as old -- there has been geological activity on it in the past -- which has created a grooved surface and has covered up some of the craters. Europa's has yet a higher density (3 times that of water) and is geologically active, as evidenced by the paucity of craters on its surface. In fact, the surface of Europa is frozen ice, marked by cracks and ridges. Finally, Io, the highest density moon of Jupiter (density 3.5), has a surface that is brand new --- there are active volcanos on Io that continually resurface the moon.

Why the difference in these moons? The change in density as one gets further from the planet is reminscent of that seen in the inner planets in the solar system, so it is likely that these moons formed out a proto-Jovian nebula that worked in a similar fashion to the solar nebula. (At one point in the past, the energy radiated by Jupiter via its gravitational contraction was much greater than it is today.) Light elements could have therefore been evaporated out of Io, but not out of Callisto. But there's more.

The key is Jupiter's strong gravity, and the specific orbits of the moons. Callisto is far enough away so that the tidal force of Jupiter is moderately small. The moon formed from a 50-50 mix of water and rock, quickly froze, and its surface has been the same ever since (aside from the continuous addition of impact craters). Ganymede, being a bit closer in, was affected by Jupiter's tides in the past, and this tidal stress caused its ice to expand and contract. The result is a grooved terrain, produced when layers of ice buckled upon contact with each other. (This tidal stress could have also evaporated some of the lighter elements from its surface.) Today, Ganymede is tidally locked. Europa and especially Io are geologically active at present, due to continual stretching of their rocky interiors. Io is closest to Jupiter, so the tides in it are greatest, and the result is a completely molten interior, a very thin solid crust, and one volcano going off after another. Most of the light elements (water, etc.) from Io were evaporated long ago (and medium elements like sodium are being evaporated now). The tides on Europa aren't as bad, but there is plenty of heat in the moon's interior, which keeps the water in its interior liquid.

The strong tides of Jupiter cause Io's volcanos. But why hasn't Io become tidally locked, so that the rocks inside no longer have to stretch? Well, it has, almost. Unfortunately, Io's orbit is slightly elliptical, which (through Kepler's 2nd law) means the speed of the orbit around Jupiter changes. Since the moon must turn at a constant speed, this means that Io can't keep the same side exactly facing towards Jupiter all the time. That little jiggle forces all the tidal heating.

Contributing to this are Io's neighbors, Europa and Ganymede, which are in 1:2:4 orbital resonance with Io. In other words, it takes Io 1.77 days to go around Jupiter, it takes Europa exactly twice this time, and it takes Ganymede exactly four times this time. So, once every 4 x 1.77 = 7 days, Io, Europa, and Ganymede line up precisely on the same side of Jupiter. The combined gravitational pull of Europa and Ganymede (which is the largest moon in the solar system) tweaks the orbit of Io just enough so that Io cannot become tidally locked. The result is intense, continual, tidal heating.

Now consider what would happen if a moon were to be much closer to Jupiter than Io. The tidal strain, the difference in gravity from one side to the other on the moon, would be enormous. In fact, if the moon were inside the Roche limit, the moon would be completely torn apart. What would be left would just be rubble. An excellent example of this is Saturn's rings, which are inside the planet's Roche limit. These rings are made up of many, many small icy particles. Moons such as that seen around the outer planets cannot exist here.

Saturn's rings exhibit an amazing amount of structure. Some of it can't be explained, but alot of it can. Consider some of the gaps in the rings. Just through random collisions, etc., you might expect the distribution of particles to get spread out, smearing out the rings. However, consider what would occur if two moon-lets (called shepherd satellites) existed on either side of the ring. According to Kepler's and Newton's laws, the inner shepherd satellite would be moving around the planet faster than the particles in the ring; conversely, the outer shepherd satellite would be moving around more slowly. If a particle in the ring drifted out of the ring, say, to a slightly larger orbit, sooner or later, it would catch up to the moon-let and pass it. However, as it passes, the gravitational pull of the shepherd would slow it down; it would thus lose energy and fall back into the ring. By the same token, a particle that drifts out of the ring to a slightly lower orbit would eventually be passed by the shepherd, whose gravitational pull would whip it back up to a higher orbit and back into the ring. Thus the ring would not be able to smear itself out.

The above theory of shepherding satellites was tested when the Voyager probes flew past Saturn (and Uranus and Neptune). In theory, each separate ring should have a shepherd satellite on either side of it. Most times, these shepherds were found; in a few cases they were not. Whether this is a real problem, or just caused by an incomplete set of pictures (or a well disguised moon-let) is not known.