Unknown Moons and Planetary Flybys

Question

I’ve a question for any trajectory experts out there:

The Pioneer and Voyager probes discovered new moons during their flybys of our four giant planets (and indeed rings). These didn’t come as much of a surprise, as they had been theorised to be there. But they must have had an effect on the crafts' trajectories. So, besides the known bodies, how did the flight dynamics teams factor in the gravitational influence of possible “unknown unknowns”, as it were?

I’m thinking of Voyager 1’s Titan flyby in particular. The target window was incredibly narrow and new moons were being discovered even as it approached Saturn. Did the FiDos just leave a large enough margin in their calculations to cover unknowns, knowing they’d be pretty small; or did they detect the influence of these new bodies by changes to the craft’s trajectory, and update accordingly?

Any links to scholarly articles etc much appreciated.

Answer 1

But they must have had an effect on the crafts' trajectories.

Not really. The known unknowns included the masses of Saturn and Titan. To this day, the uncertainty in Saturn's gravitational parameter outweighs that of all of the moons of Saturn discovered since Voyager, and by many orders of magnitude. The uncertainty at the time of the Voyager mission was orders of magnitude larger.

Another way to look at it: The largest outer Saturnian moon discovered since the Voyager missions has a mass of $43\times10^{15}$ kg. A near miss of 10000 km of this unknown moon would have bent Voyager 1's trajectory by half of an arcsecond and changed it's velocity by 0.04 meters/second. That's tiny, and it would have been a one in a million kind of encounter. (Actually, the odds would have been zero since that moon's orbit is inclined by 46° and Voyager 1 came in on a trajectory inclined by 66°.)

The wikipedia article on Voyager 1 mentions that the "Titan flyby occurred as the spacecraft entered the system to avoid any possibility of damage closer to Saturn compromising observations." I suspect this is not the case. The Titan flyby occurred first because if it had happened the other way around, a massive trajectory correction maneuver would have been needed to put the vehicle back on track for a Titan flyby given the large uncertainty in Saturn's mass (better: gravitational parameter). As mentioned above, that uncertainty remains somewhat large to this day, and that's with two additional flybys and a vehicle (Cassini) that orbited Saturn for over 13 years.