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Say you have a planet and the planet has a moon: could the moon have visible satellites as well? I don't mean a gas giant planet, I mean something habitable by humanoids or humans.
Will the moon's satellite get pulled into orbiting the planet?
If you are going to use detailed scientific terminology, please also try to provide a 'layman's terms' summary. My physics skills are rudimentary.
Sattelites of the moon are unstable: too close and it notices the lumpiness and does not make a nice ellipse, so after a while will crash. If too far, it will fall out and orbit the Earth instead.
Look at the “Hill Sphere” represented as a topological map, and you get the feeling for how the gravity of the Earth interferes, leaving only a small region where orbits look like they would go around in a normal manner.
But you can’t orbit that close, since the moon is not just lumpy but off ballance. As it turns out, certain high-inclination orbits work out better, on paper anyway.
So first, you need to find out what makes the hill sphere bigger. I don’t know off hand, but I suppose the moon can be larger and farther away. But if the moon is far from the primary, it has the same issue and will end up orbiting the sun, or easily peturbed from other bodies in the solar system.
Also, our moon is rather lopsided. A more suitable situation would be to have the moon be especially symmetric. Perhaps it could be liquid? That would allow the sattelite to orbit close in and remain stable.
Throw in some other reason to remain stable, like the all-powerful resonance. Make it slightly eccentric, make the sub-sattelite off-ballance and in an odd half multiple of its period, which is also a small multiple of the moon’s period, and furthermore have another large moon with a period an exact integral multiple of the moon’s.
If that’s not quite right, it’s at least believable to the audience, if they don’t solve the math for real.
A few years ago I would have said stable lunar satellites weren't possible.
High orbits near the Hill Sphere boundary get destabilized by the earth's influence.
Low orbits are destabilized by lunar mass concentrations (mascons for short.)
Then I read the Keck proposal for parking an asteroid in lunar orbit. I was surprised when they mentioned the possibility of parking the rock in a stable lunar orbit that would need no station keeping.
Then I learned Distant Retrograde Orbits (DROs) are stable even when approaching the boundaries of the Hill Sphere.
One example of a body in a DRO is Jupiter's Moon S/2003 J2. This moon's semi-major axis is nearly 30 million kilometers. Jupiter's Hill Sphere has a radius of of 52 million kilometers. The S/2003 J2 Wikipedia article says
The limits of Jupiter's gravitational influence are defined by its Hill sphere, whose radius is 52 gigametres (0.35 AU). Retrograde moons with axes up to 67% of the Hill radius are believed to be stable. Consequently, it is possible that even more distant moons of Jupiter may be discovered.
Our Moon's Hill Sphere has a radius of about 60,000 kilometers. In my orbital sims I have placed objects in a retrograde lunar orbit having semi-major axis 50,000 km. These orbits have lasted centuries. I would imagine a DRO at 40,000 kilometers could last eons. And this is high enough that lunar mascons wouldn't destabilize the orbit.
In a science fiction setting, a moon with a larger Hill Sphere is plausible. DROs are long term stable in the outer regions of the Hill Sphere.
Yes, they can. However, generally satellites of moons will get pulled out of orbit.
NASA has orbited spaceships and lunar modules around moons, proving that it can be done. However, the tidal forces of the planet will soon pull the moon's satellite out of orbit, probably into orbit around the planet. Maybe a large moon far away from its planet could support a satellite, since its own gravitational field would be stronger than the field of the planet at that distance.
Source: http://www.popsci.com/scitech/article/2008-04/could-moon-have-moons
Let's assume this is the Earth-Moon system.
If the Moon's moon is very small, you can easily have one. But the problem is it wouldn't be visible from Earth.
If you want the Moon's satellite be visible from Earth with the naked eye, it has to be some decent fraction of the size of the Moon. But now you will have a 3-body system. This is not good.
This is because the Moon's moon is large enough that its gravity can't be ignored. Usually, 3-body systems are unstable. So you would either have a collision or one of the bodies (probably the smallest will be flung out)
The solution to your problem might be placing the smaller moon in one of Lagrangian points. Maybe L4.
Having said that, it still may not work, as placing a large object in L4 might destabilize the system.
Another solution maybe placing the smaller moon in close orbit around Earth.
moon is a satellite of earth, earth is a satellite from sun, so 2nd level satellites allready exist, but this is possible because sun/earth and earth/moon are very different and moon is not much perturbated by sun.
I just thought of something when I read the question again. Assuming that being physically small and low-mass compared to its primary makes an improvement, it could be small but still visible for reasons other than reflected sunlight on common rock.
If you can accept an unstable system, yes.
From the perspective of a lifeform, the motion of the planets is unchanging, but in reality it is always shifting and eventually unstable. So you could permit a situation that was not stable given some plausible story about how it came to be - most systems are accretion-based, so the orbit has to be stable enough for the orbiting debris to accrete and become a moon.
As an example, the currently accepted theory is that a smaller proto-Earth collided with a Mars-sized body, leaving a larger planet (the current Earth) and a vast debris field from the second body which has accreted into our Moon. The Moon is slowly moving away from Earth as the Earth's spin slows, so this is not permanently stable either.
A possible story could be that a stable Planet+Moon pair meets an impactor flung out by a complex path around the giants in the system, which collides with the planet as above. If the original Moon was in an inclined orbit compared to the impactor's path, and suffered a glancing blow, there could be a period of time in which both moons orbited each other and the planet. Albeit this would not be long-lived, and would involve a lot of debris raining on the planet for a while.
Fun products of this regarding stories would be:
