As per the research article published on Science, there is an implication that Saturn, a planet discovered in the 1600s, might have its rings made recently-perhaps, in the era of the dinosaurs.
Some facts about Saturn’s Rings:
*The Pioneer Saturn flyby in 1979 made several new discoveries about the rings:
* The rings consist largely of particles several centimeters in diameter. They are extremely cold and possibly composed of frozen water and other ices.
* An extensive cloud of hydrogen was discovered around the rings.
* Two new rings (called F and G) were discovered, and a gap between rings was confirmed.
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* Voyager 1 provided much more detail on the beauty, complexity, and sometimes baffling nature of the rings. Among the discoveries were
* The six known rings are actually composed of hundreds of tiny, thin ringlets with intervening spaces, so that the whole ring system looks something like the grooves in a phonograph record. Even the Cassini division, once thought to be empty space between the A and B rings, contains several dozen ringlets. There are far too many rings to be explained by our present theories of how planetary rings form and remain stable.
* Elongated radial features that last from hours to days were observed in the Bring. These “spokes” may be clouds of electrified dust rotating around Saturn above the plane of the rings.
* The thin outer F-ring, discovered by Pioneer Saturn, was resolved into three distinct but intertwined ringlets. This braided ring structure is very difficult to explain; it seems likely that both electrical and gravitational forces are at work.
* Two small moons, one on each side of the F-ring, may act as “shepherds,” their gravitational attraction keeping the ring particles on track between the orbits of the two moons.
On Oct. 9, 2008, just after coming within 25 kilometers (15.6 miles) of the surface of Enceladus, NASA’s Cassini captured this stunning mosaic as the spacecraft sped away from this geologically active moon of Saturn. Image Credit: NASA/JPL/Space Science Institute 
This stunning false-color view of Saturn’s moon Hyperion reveals crisp details across the strange, tumbling moon’s surface. Differences in color could represent differences in the composition of surface materials. The view was obtained during Cassini’s close flyby on Sept. 26, 2005. Image Credit: NASA/JPL-Caltech/Space Science Institute 
Saturn’s moon Dione is captured in this view from NASA’s Cassini spacecraft, half in shadow and half in light. Image Credit: NASA/JPL-Caltech/Space Science Institute 
NASA/JPL-Caltech/Space Science Institute
How old are the rings?
The abstract of the article states that:
“The interior structure of Saturn, the depth of its winds and the mass and age of its rings constrain its formation and evolution. In the final phase of the Cassini mission, the spacecraft dived between the planet and the innermost ring, at altitudes 2600-3900 km above the cloud tops. During six of these crossings, a radio link with Earth was monitored to determine the gravitational field of the planet and the mass of its rings. We find that Saturn’s gravity deviates from theoretical expectations and requires differential rotation of the atmosphere extending to a depth of at least 9000 km. The total mass of the rings is (1.54 ± 0.49)×10^19 kg (0.41 ± 0.13 times that of the moon Mimas), indicating that the rings may have formed 10^7-10^8 years ago.
Cassini gravity measurements
The researchers made use of the Cassini probe, and here’s what they had to say in their own words:
“We determined Saturn’s gravitational field by reconstruction of Cassini’s trajectory during the Grand Finale, using a coherent microwave link between Earth tracking stations and the spacecraft. Range-rate measurements were obtained from the Doppler shift of a carrier signal sent from the ground at 7.2 GHz (X-band) and retransmitted back to Earth by Cassini’s onboard transponder at 8.4 GHz. An auxiliary downlink at Ka-band (32.5 GHz) was also recorded.”
Dynamical model
“ Our orbital fitting is based on the dynamical model previously adopted and tested in the determination of the gravity fields of Titan and Enceladus , implemented in the Jet Propulsion Laboratory navigation code MONTE . The model was extended to include Saturn’s gravitational parameter GM, the zonal harmonic coefficients J2–J20, the tesseral (longitude-dependent) field of degree 2 (to account for possible non-principal axis rotation), and the mass of the rings. “
Gravity determination
“ Our deterministic model, based on the geophysical expectations for the gravity field of a gas giant like Saturn, can adequately fit the Doppler data if each arc is analyzed separately. However, the same model cannot jointly fit all passes in a combined, multi-arc, gravity and orbital solution. The signatures in range-rate residuals are as large as 0.2 mm·s−1 over time scales of 20-60 min, corresponding to radial accelerations of the order of 10−7 m·s−2. This value is an underestimate of the real unmodeled accelerations, as a large fraction of them are aliased in those associated with estimated parameters. The unmodeled accelerations acting on Cassini must be compensated for, to avoid biases in the estimates of the gravity harmonics and ring mass. “
Saturn interior models with uniform rotation
“ Although gravity measurements provide constraints on the interior of gas giants, every model using gravity data unavoidably suffers from uncertainties. We tested whether interior models based on uniform rotation can explain the measured gravity harmonics. We developed a suite of interior models based on the common assumption that the fluid in Saturn’s interior rotates uniformly like a solid body. “
The consequent methods are purely mathematical, we won’t see them here. Rather, let us only take a look at the titles:*Differential rotation on cylinders with the CMS method*Differential rotation with finite depth flows*Mass and age of Saturn’s rings
