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Lyril
2010-Jan-15, 05:41 AM
Just wondering - how complex can orbits become? For instance, a hypothetical planet of a hypothetical star has a number of moons or satellites. Could an outer moon have a satellite of its own - a moon of a moon? If so, how far down that track could you go? Then devising the terminology - moonlettes? mini-moonlets? Perhaps some of Saturn's many moons have smaller bits of debris orbiting them, even if only briefly. Would they be moons of a moon?

Murphy
2010-Jan-15, 06:08 AM
An interesting question. Technically since the Earth is a satellite of the Sun, then the Moon is a satellite of a satellite. And it is of course possible to put something in orbit around the Moon, spacecraft for instance. Potentially you could place an asteroid in Lunar orbit, thus giving the Moon a moon.

Having said that, I don't know of any instances in the solar system where a moon has its own moon. I may be wrong, but it doesn't seem to occur naturally (at least not here). I don't know the details, but I assume it has something to do with which body in the system is gravitationally dominant, i.e. the Moon stays orbiting the Earth because it is sufficiently inside Earth's gravity well that it doesn't orbit the sun itself. So if a moon somehow formed around an already existing moon, the first moon probably wouldn't have enough gravity to hold on to it in the face of the much greater gravity of the planet. Thus the "moon-moon" should start orbiting the planet at some point, no idea how long it would last for, but I'm sure it can be calculated.

Anybody want to present the formulas and give a mathematical explanation of this?

grant hutchison
2010-Jan-15, 11:15 AM
Moons of moons are unlikely to persist for long periods of time, because of tidal evolution.
The major moons of the solar system become tidally locked to their parent body in a fairly short period of time, astronomically speaking. A moonlet close enough to orbit a tide-locked moon without being perturbed away by the gravity of the parent planet will necessarily be in a low orbit, and will therefore revolve around the moon faster than the tide-locked moon rotates. So the tidal bulge the moonlet raises in the moon will make the moonlet evolve steadily to a lower orbit, until it hits the surface. All that will happen in a "short" space of time: a few million years after the formation of the moon and moonlet would be a typical time course, IIRC.

So it's not unexpected to find that there are no moonlets around the regular moons of the solar system. It's certainly possible that some of the outer irregular satellites of the gas giants could have moonlets or companions that could persist for long periods of time, however, since they're not as tightly controlled by tidal forces.

Grant Hutchison

aurora
2010-Jan-15, 04:58 PM
There are two moons of Saturn (small ones, in the rings) that periodically swap orbits.

If I recall correctly, that is.

That's about as close to the situation described in the OP as I'm aware of.

grant hutchison
2010-Jan-15, 05:08 PM
There are two moons of Saturn (small ones, in the rings) that periodically swap orbits.

If I recall correctly, that is.Epimetheus and Janus. They're just outside the main ring system.

Grant Hutchison

a1call
2010-Jan-15, 05:34 PM
A satellite/moonlet crash scenario can be seen in the "Kaguya" footage:

http://www.huffingtonpost.com/2009/06/23/japanese-kaguya-satellite_n_219393.html

neilzero
2010-Jan-15, 06:34 PM
Likely rare solar systems have only 3 bodies with more mass than Earth's moon but billions of small, low mass bodies. Other massive bodies come close enough to facilitate capture of an asteroid or comet, perhaps 20 times in 10 billion years, by the moon of the only planet. Typically the timing is wrong, but a rare capture could occur once and might persist for a billion years or so, as subsequent massive visitors would also typically have the wrong timing to perturb the tiny moon away from orbiting the moon. The mass, distance and resonances of the three massive bodies must be in a narrow range, so a moon of a moon that persists for even one billion years is likely very rare. Neil

Lyril
2010-Jan-16, 09:54 PM
Assuming that the universe is stranger than we can imagine, and that impossibilities are possible somewhere - I am just curious about whether really complex systems might be possible.
For instance - a large moon of a planet. Tidally locked? - I don't know if that would make a difference. At least one moon (moonlet?) in an orbit perpendicular to the plane of the moon. So the gravitational influence of the larger moon might not cause its destruction. Perhaps it is stable. Then put some smaller bits (moonlettes?) around the moonlet. Imagine the view from the moonlette - and the amount of maths involved in working out orbits.

Kinda speculating again - if Pluto/Charon are more like twin planets than a planet/moon system (ex-planet and moon) I wonder if a twin moon system would be possible somewhere. I guess the two shepherd moons of Saturn discovered some years ago are twin moons, but are large ones possible? Imagine twin moons, each with a moonlet or two orbiting a gas giant around a binary star.
Tardis - where are you?

grant hutchison
2010-Jan-17, 01:10 AM
For instance - a large moon of a planet. Tidally locked? - I don't know if that would make a difference. At least one moon (moonlet?) in an orbit perpendicular to the plane of the moon. So the gravitational influence of the larger moon might not cause its destruction. Perhaps it is stable.It would still evolve inwards tidally, as previously described. In such a strongly inclined orbit it would be subject to the Kozai mechanism, driven by the parent planet, which would drive its orbital eccentricity higher so that it would strike the moon's surface sooner rather than later.

Grant Hutchison

chornedsnorkack
2010-Jan-17, 07:34 PM
Where is the Hill limit for a satellite of a satellite?

Moon has orbital period of over 27 days. Only slightly more than 13 months in a year.

Moon is heavily perturbed by Sun. The dragon moves fast, changing the angle between Moon´s orbit and Earth´s equator, and the apsides also move fast.
Nevertheless Moon stays in a pretty steady orbit in long term and does not escape Earth.

If Moon had, say, Phobos sized satellite at an orbit with 48 hour period, would Earth and Sun manage to perturb it?

Sure, there would be tidal decay. Phobos orbits Mars in less than 8 hours. Mars duly slows it down - slowly.

How long could a satellite of Moon in 48 hour orbit last?

tony873004
2010-Jan-18, 08:12 AM
The Hill Sphere is at sma*(m/(3M))^(1/3), where sma is the distance from the moon to the planet, M is the mass of the planet, and m is the mass of the moon.

With a period of 48 hours, the satellite would need a semi-major axis of 15500 km from Earth's moon. The Moon's Hill Sphere with respect to the Earth is about 61500 km. For a stable orbit, it should be within 1/3 of the Hill Sphere distance. 15500 km is satisfies this, and it's far enough from the Moon that lunar mascons won't significantly alter its orbit. So such a moon around the Moon should be stable for a long time. But probably not for the life of the Moon. The Moon was once much closer to Earth, with a much smaller Hill Sphere. So if such an object formed with the Moon, it would probably be gone by now. But if you're talking about placing an asteroid in a 48-hour orbit today, it would probably survive millions of years.

Murphy
2010-Jan-18, 05:22 PM
I thought I would do a little tinkering around in Gravity Simulator to see if I could make a moon orbit another moon and indeed it's not difficult.

I started with a small Red Dwarf star (0.2 Solar masses) orbited by a large Gas Giant planet (160,000 km diameter, ~630 Earth masses) at 10 AUs. Then this gas giant is orbited by a large rocky moon (24,800 km diameter, 10 Earth masses) at 20,000,000 km. This system seems stable, so then I added in a medium sized moon (4,000 km diameter, 0.025 Earth masses) to orbit the bigger moon at 50,000 km.

It works fine, they don't immediately crash into each other or go flying off into space. Of course, I've only run the simulation for a few thousand years, so I can't tell if it’s stable over very long periods. But it works in principal, so theoretically yes, a moon can have a moon of its own. Even if it only lasts for a small percentage of the lifetime of the solar system, it's still a moon of a moon for however long it exists. If we explore the galaxy I would not be surprised to find such an occurrence at least some of the time.

IsaacKuo
2010-Jan-18, 07:54 PM
I would guess the following would be very stable over long time scales:

Star is the Sun.

Planet is a heavy gas giant at maybe 3000AU.

Moon and Moonlet are similar to Earth-Moon.

EDG
2010-Jan-19, 12:56 AM
I thought I would do a little tinkering around in Gravity Simulator to see if I could make a moon orbit another moon and indeed it's not difficult.

I started with a small Red Dwarf star (0.2 Solar masses) orbited by a large Gas Giant planet (160,000 km diameter, ~630 Earth masses) at 10 AUs. Then this gas giant is orbited by a large rocky moon (24,800 km diameter, 10 Earth masses) at 20,000,000 km. This system seems stable, so then I added in a medium sized moon (4,000 km diameter, 0.025 Earth masses) to orbit the bigger moon at 50,000 km.

It works fine, they don't immediately crash into each other or go flying off into space. Of course, I've only run the simulation for a few thousand years, so I can't tell if it’s stable over very long periods. But it works in principal, so theoretically yes, a moon can have a moon of its own. Even if it only lasts for a small percentage of the lifetime of the solar system, it's still a moon of a moon for however long it exists. If we explore the galaxy I would not be surprised to find such an occurrence at least some of the time.

Keep in mind that GravSim doesn't account for tides (that affect the rotation of the bodies and also the orbital evolution) - it just accounts for secular effects from other masses. Solar tides should affect the GG-moon system quite significantly, which will affect the evolution of the moon's orbit around the jovian - that won't be shown in the simulation.

AtomicHorror
2010-Jan-19, 01:30 AM
This is a question that I've been searching for an answer to for some time. Does anyone know whether there is any combination of masses and orbital radii that would allow for such a "moon of a moon" to be relatively stable with the two constraints that a) the planet orbits within the habitable zone of the star and b) the moon has a mass and composition similar to Earth? After all, it's nice to have all that astronomical wonderment happening somewhere, but even better if you can view it from a habitable Earth-like moon right in the middle of it.