Great article, and the answer seems to be “in theory yes, but it’s never been found”.
(nm)
Well then the Moon should be Selene. So there!
In addition to what the article talks about, one of Saturn’s moons, Rhea, is thought by some to have a ring (which is* like *a moon, except it’s tiny little pieces instead of one big rock). No one has found definitive evidence, though.
Is there not a sense in which Pluto and Charon are each other’s moons, since their barycenter lies between outside of Pluto?
I wonder what it would be like if the barycenter was on the surface of Pluto. If we postulate this happens by Charon moving closer, it might put it inside the Roche Limit. But what if Charon were just less massive?
Would you feel Charon lift you off the surface when it passed overhead?
The moon of a moon would be a “lunette.”
Two moons of a moon would be a “dinette”.
You’d feel less gravity, and someone could do the math to show how much less, but you’d still be a lot closer to the main mass of the system, Pluto, and be firmly stuck to that body.
You wouldn’t even be lifted off the surface of Charon let alone off Pluto. Think of it this way, the barycenter of the Earth-moon system is inside the Earth (well outside the moon), but the loose rocks on the surface of the moon are not lifted off towards Earth.
Jonathan Coulton has a song about Pluto and Charon called “I’m Your Moon, You’re My Moon”.
Probably not much different than the gravity we feel from the moon. It’s nothing a human can detect without equipment, but we do see the effect on the ocean.
So knowing the masses of the planet and the moon and their distance from each other, could we calculate how far a moonlet could be from the moon to have a stable orbit? For the purposes of this post, assume stable orbit implies higher than a lunarsync orbit (i.e. not spiraling down to the planet) and will not be eventually captured by the planet. The first part is easy since the lower bound is
[(G x M x t[sup]2[/sup])/(4pi[sup]2[/sup])][sup]1/3[/sup] where M is the mass of the moon and t is its sideral rotation period.
People already noted that the gravity difference wouldn’t be enough to notice, and in any case you’d have to travel around rather than wait for Charon to “pass overhead” – the two bodies are tidally locked to each other.
I’m surprised I haven’t seen the word “planetesimal” in this thread yet.
There have been several asteroids that have been discovered to have satellites. 
Is the Barycenter the same thing as the L1 Lagarange Point? (sp?)
No, the Barycenter is the center of Mass. In the Eart-Moon system it is inside the Earth. The L1 Lagrange point is on the line connecting the Earth and Moon but much closer to the moon. It is the point where the gravitational forces from the two are equal making it an equilibrium point (though unstable).
No because the Lagrange Points also take centripetal force into account.
Does this mean that artificial Lunar satellites, like LM ascent stages or Lunar Orbiter spacecraft, will eventually either crash into the Moon itself, or be dragged into their own Earth orbits? I’m assuming that the LM ascent stage for each Apollo mission, in transporting the two moonwalkers up to the CSM, had to achieve the latter’s same basically circular orbit. Give the absence of a lunar atmosphere, there’s no friction to drag leftover spacecraft down to the surface.
As I understand it, yes…and nearly always the former. I don’t believe perturbations from the Earth’s mass could add enough energy to a Lunar orbiter to allow it to achieve escape velocity. (I may very well be wrong. I think I actually can do the math…but it would take a lot of time, and I’d probably flub it anyway.)
Also, as noted above, the Moon’s mass is not smooth, but has mass concentrations, and these also perturb orbits. (Just as the earth’s masses, such as the Himalayan chain, affect the orbits of our artificial satellites.)
Perturbation isn’t necessarily fatal. Mars gets nudged a bit by Jupiter, but not enough to destabilize it. It is theoretically possible to have a planet orbiting a double star – thus the sunset scene in Star Wars – but the planet has to be far enough away that the two stars are effectively only a point-mass.
(This is also the kind of math that showed that Larry Niven’s Ringworld could not be stable. There, the perturbations would be additive, whereas the metastable Lagrangian points, such as L-5, experience self-cancelling perturbations. Much of this goes back to Maclaurin – looky that hair! – who also showed that Saturn’s rings could not be solid objects, but had to be made up of grains or granules.)