How will the Cassini spacecraft help constrain the mass of Saturn's rings?

Question

In the BBC news article To see finally the face of Peggy (Peggy is a very small moonlet interacting with a ring) there is an audio interview with Carl Murray of Queen Mary University of London. After about 08:45 he discusses the masses of the rings, including this (approximately transcribed) sentence:

And that’s what you get with Cassini, in the final orbits, the Grand Finale orbits, we will get the mass of not only the rings, but the mass of the B ring, which is the most massive of the ring system.

Will this be enough of a constraint to interpret "get the mass" as an approximate mass measurement? How is this done - by sampling and characterization, or through actual gravitational interaction? If so, actually how?

The article also links to Linda Joyce Spilker's talk abstract P33B-2136: Cassini’s Grand Finale at the American Geophysical Union's 2016 fall meeting.

Answer 1

From New Scientist:

At such close quarters, Cassini’s instruments can gather unprecedented information about the composition of the planet’s ionosphere and atmosphere. The craft will also collect data on radiation belts girding the planet, and will be in a position to use gravity measurements to give the best estimate yet of the mass of the rings.

Cassini has already contributed to a better understanding of the B ring's mass, but with this information there's still a ± 50% uncertainty (link to the original paper):

The scientists found that, while the opacity of the B ring varied by a large amount across its width, the mass – or amount of material – did not vary much from place to place. They "weighed" the nearly opaque center of the B ring for the first time -- technically, they determined its mass density in several places -- by analyzing spiral density waves. These are fine-scale ring features created by gravity tugging on ring particles from Saturn's moons, and the planet's own gravity. The structure of each wave depends directly on the amount of mass in the part of the rings where the wave is located.