Knowledge of some characteristics of the central planet can be gleaned from or enhanced by careful measurements of planetary ring systems. Such gleaning or knowledge enhancement requires a clear understanding of the precise nature of the interactions between the planet and its ring system. Furthermore, there must exist a means of determining the relevant ring system characteristics with sufficient precision to enable the extraction of the desired central planet information. Let's look at a couple of examples.
Early ring observers, including Christiaan Huygens (1629-1695), who correctly deduced on the basis of long-term observations that the Saturn ring circled the planet, nowhere touching it, incorrectly assumed first that the ring was a solid disk of material and then later that there were a number of solid concentric rings. Both theoretical considerations (by James Clerk Maxwell in 1859)  and observational data (by James Keeler in 1895)  eventually convinced scientists that the rings must consist of an innumerable array of discrete ring particles, which, like the tiny satellites they were, orbited according to the laws of motion described by Johannes Kepler (1571-1630). According to those laws, independent bodies orbiting closer to the planet complete an orbit of the planet in less time than those further from the planet. In addition, close orbiters must also move at higher velocities than their more distant siblings. The rate of motion is more or less independent of the size and mass of the individual rings particles, but, as implied above, the rate is highly dependent on the radial distance of each particle from the center of the planet. Additionally, that speed is dependent on the mass of the planet whose gravity holds the ring particles in their orbits. Theoretically, then, it should be possible to deduce the mass of the planet from measurements of the distance and orbital periods of a large number of ring particles.
In practice, however, it is very difficult to measure the orbital periods of individual ring particles, primarily because of their small size and the impracticality of uniquely identifying individual ring particles at all, let alone uniquely re-identifying the same particles on later circuits of the planet. Mass determination for the central planet is far more easily determined from the orbital motions of the larger natural satellites, or, still better, from radio tracking of properly equipped robotic spacecraft during swingbys or orbits of the respective planet.
Although ring observations contribute little toward improvement of the precision of mass determinations of the planet, they can, under certain circumstances, help us to better understand the distribution of mass within the central planet. At the same time, they can help define the planet's equatorial plane. The orbit of a ring that is eccentric (non-circular) will slowly precess (turn) at a rate that depends directly on the degree of flattening (oblateness) of the planet. Hence, a measurement of the precession rate of an eccentric ring orbit can lead to a determination of the planet's oblateness. Note, however, that the oblateness determined in this manner is not necessarily the same as the amount of flattening seen in images of the planet (i.e., the optical oblateness), but instead represents the degree to which mass has been shifted from the polar regions of the planet toward its equator. That quantity is known as the planet's dynamic oblateness and is generally designated as J2. A planet without polar flattening would have J2 = 0. With a J2 of 0.0163, Saturn is the most oblate planet in the solar system. The dynamic oblateness of Jupiter, Uranus, and Neptune are 0.0147, 0.0035, and 0.0034, respectively .
All four known planetary ring systems lie close to the equatorial planes of their respective planets, the largest departures of ring planes from planetary equatorial planes being less than a tenth of a degree—that is, less than 1/900th of a right angle. In that respect, rings provide a reasonably accurate visual marker for the planet's equator. But if the orientation of an inclined ring orbit can be tracked through a large part of a 360° precession, the actual orientation of the plane of the equator can often be determined to a small fraction of the ring's inclination—that is, to less than a hundredth of a degree.
Tiny dust particles in the rings also interact with the planetary magnetic field. Two specific examples of such interactions are radial spokes in Saturn's B ring and Jupiter's Halo ring. The B-ring spokes rotate, at least for a time, at the same rate as Saturn's magnetic field and therefore provide corroborating information on the rotation rate of Saturn's interior. The Halo ring has inner and outer boundaries near what are called Lorentz resonances, where electrically charged dust particles orbit Jupiter in periods that are rational multiples (like 3:2) of the rotational period of Jupiter's magnetic field (and the interior of the planet). At the radial distances of these resonances, the ring particles experience strong forces tending to remove them from the ring altogether, thus creating relatively sharp edges to these dust rings . Studies of these phenomena can help determine the rotation rate of the planet's magnetic field or serve as a verification of the rotation rate as determined from radio emissions.
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