By this time, its orbit will have been tilted all the way back into Saturn's equatorial plane, so that it is once again looking at the rings edge-on.

Moreover, its periapsis will have been lowered so that it's also making the closest approaches to Saturn that it has made since its first very low swoop over the planet while it was braking into orbit around Saturn (albeit these new periapses will be on the planet's nightside).

After its "Titan-32" flyby on June 13, 2007, it will swoop down at the end of its next orbit to a periapsis of only 87,000 km above Saturn's clouds - the closest approach to the planet it will make during its orbital tour.

And on the way down to that periapsis, it will skim past the edge of Saturn's visible rings at the closest distance it has yet made to them since its arrival at Saturn - only 17,000 km beyond the skinny "F" ring.

(This is as close as it dares to come to them during the 4-year tour, since there is likely to be a faint zone of much less dense ring material beyond that visible ring edge, with just enough small particles in it to constitute a slight risk to Cassini.)

During Phase III, Cassini won't make any more close flybys of Saturn's other moons - it has other things to do - but its long series of low-altitude passes over Titan's north polar region (usually at the minimum permissible altitude of 950 kg or so) will have allowed it to do good radar mapping of much of that region on Titan, and it will also be able to make two more radio occultations of Saturn's rings during this phase.

And then, after the end of Phase III, Cassini will go on to the fourth and final phase of its primary orbital tour, in which (starting on Aug. 31, 2007) it will once again tilt its orbit, this time all the way to a tilt of fully 75 degrees to the equator, which will allow it to fly within only 15 degrees of Saturn's north and south poles - and to resume getting those spectacular sweeping views of Saturn's rings.

As most readers know, Saturn's rings were thought to be simple in structure before the Voyager flybys - a matter of three rings of different particle densities and opacities with (perhaps) a couple more extremely faint rings inside and outside them, one big gap (the Cassini Division between the bright "A" and "B" rings), and a few smaller gaps.

Instead, the Voyager's TV cameras revealed an astounding spectacle of thousands of visible separate ringlets making up those major rings.

And Voyager 2's "stellar occultation" of the rings - in which it spent over two hours making high-speed measurements of a star's light as it twinkled through a cross-section of the rings - revealed that even those visible ringlets were subdivided into hundreds of thousands of finer ringlets as narrow as a few dozen meters, with the "gaps" between them being mostly just areas where the number of ring particles was less.

(For instance, the Cassini Division actually turned out to have quite a lot of material orbiting within it, and even four fairly large individual ringlets there.) Moreover, some of these ringlets turned out to be very oddly shaped - even, in a few cases, lopsided.

We still have only a very small degree of understanding of the processes that create this staggeringly fine detail.

Much of it is due to the weak gravitational tuggings of Saturn's small inner moons.

For instance, the F Ring turns out to be "herded" into its narrow shape by two tiny moons, Prometheus and Pandora, that orbit just inside and outside it - the particles near the ring's outside are braked by the tuggings of the slower-moving moon Pandora as they pass it and so tend to fall back down into a lower orbit around Saturn, while those near the inner edge are dragged along in the wake of the faster-moving inner moon Prometheus and thus catapulted back out to a wider orbit around Saturn.

(Their tuggings also produce a series of wavelike structures in different strands of the F Ring, which gives the strands the false appearance of being "braided" around each other.)

Other sharp boundaries between different parts of the rings are due to the fact that any ring particles at those distances from Saturn have orbital periods that are some fairly even fraction of the periods over which some other inner moon of Saturn orbits around the planet - and so the ring particles keep making their closest passes to that moon at the same few points spaced around their orbit, causing repeated "resonant" gravitational tugs that stretch the ring particles' orbits out of circular, and thus making them cross the paths of and crash into other ring particles so that they soon get deflected away from their original orbits in the resonant zone.

For instance, it's been known for over a century that the ring particles at the outermost edge of the B Ring - Saturn's brightest and thickest ring - are just at the point where their orbital period is exactly half that of Saturn's moon Mimas, so that it thus jockeys them away from wandering into that area.

And the outermost edge of Saturn's bright outer A Ring turns out to have particles whose orbital period is exactly 6/7 that of Saturn's little "co-orbital" moons Janus and Epimetheus, which keep most of them from straying out any further from Saturn.

The tuggings of Saturn's moons have other effects, too - such as setting up tightly spiraling "density waves" in some parts of the A Ring, like a far more tightly wound version of a galaxy's spiral arms, so that what looks like dozens of separate ringlets is actually a single ringlet that spirals in toward the planet like the groove in a phonograph record.

But, embarassingly, we simply do not know the exact cause of most of the vast detail in Saturn's rings, much of which may be caused by the complex ways in which the flocks of particles in different parts of the rings themselves tug at each other.

We don't even know what creates the sharp inner edge of the A Ring, or the sharp division between the B Ring and the much fainter, translucent C Ring closer in.

Nor do we know why the chunks of ice making up the C Ring are distinctly smaller and darker in color than the chunks of light-colored water ice making up the outer rings.

In order to try to answer these questions, Cassini will spend a great deal of time observing the fine ring detail and the way it changes with time. For instance, there's suspicion that a lot of otherwise inexplicable fairly large ring gaps are caused by the fact that such a gap has an as-yet undiscovered tiny moon, a few km or less wide (or, if you prefer, an unusually big chunk of ring material), whose gravitational tugs on ring particles within and outside its orbit "shepherd" them away from the moonlet's orbit in the same way that Prometheus and Pandora shpherd the F Ring's particles between them.

So far, only one such gap - the "Encke Division" in the A Ring - has been proven to be due to such a "ring-embedded moonlet", and to finally see that tiny moon, Pan, took a decade of squinting at thousands of Voyager photos.

But there are probably many others - for instance, there are a few ringlets in the C Ring and the Cassini Disivion that are actually slightly elliptical in shape, and these are very hard to explain any other way - and the Cassini spacecraft will have the time to look for them.

It will also look at the strangest ring feature of all, discovered by the Voyagers - the "ring spokes", huge dark radial stripes which repeatedly form in the rings and rotate around the planet while keeping their straight shapes for amazing periods of time, despite the fact that the laws of elementary orbital mechanics say that they should swiftly smear out of shape as the inner spoke particles whirl around the planet faster than the outer ones.

Apparently these are caused when clouds of extremely fine dust particles are actually yanked straight toward and away from the planet by electrical currents flowing through its magnetosphere (with the dust clouds drifting to the north and south of the normally flat ring plane); but, again, we badly need to know more.

And Cassini will repeatedly use a high-speed photometer that's part of its UV spectrometer experiment to make more "stellar occultation" observations, like the one made by Voyager 2, and thus get a whole parade of cross-section surveys of Saturn's super-fine ring structure and the way it changes with time.

To tilt itself back into that near-polar 75-degree inclined orbit to make these round-the-clock ring studies (and to resume observing the weather, auroras and magnetospheric phenomena of Saturn's polar regions), Cassini, during Phase IV, will make still another series of 10 low-altitude Titan flybys from August 31, 2007 to May 28, 2008, this time usually flying over Titan's southern hemisphere and thus getting the chance to map that part of Titan better.

These flybys will also steadily shorten its orbit.

Its periapsis will stay close to Saturn, on the planet's nightside - indeed, after its "Titan-37" flyby in November 2007 it will make another brush within only 17,000 km of Saturn's visible ring edge.

But the distant dayside apoapsis it had during phase III will be steadily shortened, until it is finally only just beyond Titan's orbit (1.2 million km) - and so, for the first time in Cassini's tour, its orbital period will actually become less than Titan's 16-day period.

These close-in polar orbits will allow it to continue making sweeping observations of the rings and of Saturn's weather patterns, but with sharper resolution than the orbits of Phase III - and they will also allow it to study Saturn's inner magnetosphere better.

Moreover, during Phase IV, it will make two final close targeted flybys of Saturn's other moons.