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.

  • $\begingroup$ The mass of Saturn is 5.6834×10^26 kg, its largest moon Titan is 1.35×10° 23 kg, that is 180 % of our Moon but only less than 1/1000 of its planet. There is a small effect on trajectory of a space probe, but only measurable when the probe passes very close to the moon. But I think the mass of Titan was not precisely known before the flyby of Voyager. $\endgroup$ – Uwe Oct 17 '18 at 16:00
  • $\begingroup$ 14 moons of Saturn were known before the Voyager flyby, 3 more were discovered in the years 1980 to 1981 on Voyager images. But another moon Pan was found by its gravitaional wake and later on archived images from Voyager in 1986. $\endgroup$ – Uwe Oct 17 '18 at 16:28
  • $\begingroup$ This is a great question!! I don't mean to diminish it in any way by nitpicking on the use of Rumsfeld's There are known knowns... but I think that this would fall squarely into the "known unknowns." Nobody at NASA would have been surprised that there could have been moons not previously seen from way back on Earth. If you told the scientists planning these missions "There might be moons you don't already know about, and they will have gravity" they would have likely replied "Yes, why do you think we're doing this in the first place?" $\endgroup$ – uhoh Oct 18 '18 at 11:32
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    $\begingroup$ Haha, you’re quite right. Politics aside, his phrase pretty much sums up how I bimble through life! $\endgroup$ – Gavin Dobson Oct 18 '18 at 19:41
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    $\begingroup$ This phrase "unknown unknowns" predates Rumsfeld by a lot. It's just that that's the first time lay people heard that term. $\endgroup$ – David Hammen Oct 20 '18 at 21:04

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.

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    $\begingroup$ Just curious; what is "..the uncertainty in Saturn's gravitational parameter..." today? $\endgroup$ – uhoh Oct 21 '18 at 10:34
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    $\begingroup$ @uhoh - A 2006 paper cites three preceding values and adds one more. The first, based on Pioneer 11 only, has an uncertainty of 2400 km^3/s^2. The second, based on Pioneer 11 and the two Voyager probes, has an uncertainty of 200 km^3/s^2. The third is a reproduction of the trajectories of those three probes, but using an improved ephemeris, yielding an uncertainty of 57 km^3/s^2. The final value, based on about a year's worth of data from Cassini, has an uncertainty of 1.1 km^3/s^2. $\endgroup$ – David Hammen Oct 21 '18 at 12:06
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    $\begingroup$ I just started to read it now, that looks like quite a lot of fun! Such a mixed set of data to work with, observation types, spacecrafts, bodies... The final uncertainty is like 0.3 ppm roughly, incredible. $\endgroup$ – uhoh Oct 21 '18 at 12:18

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