Moons of moons

[Moontanman]

Is it possible for a planet to have a satellite that also has it's own satellite? And example would be our Moon having it's own moon. If it is possible what would be the size limits of the moons moon and distances involved?

[InfiniteNow]

Why, yes sir, it is very much possible, indeed.

 

Curious About Astronomy: Can moons have moons?

[CraigD]

As the link InfiniteNow provided describes, an orbit is at least possible for a satellite within its primary’s Hill sphere. There’s no limit, in principle, to the mass of a satellite (other than if it exceeds the mass of the primary, then it’s the primary, and the other body its satellite).

 

However, I’m pretty sure there are a lot of complicating factors contribute to a satellite-of-a-satellite’s long-term orbital stability, such as an orbital period that is some small whole number ratio of its primary’s orbital period. These conditions are, I suspect, very rarely met - according the this wikipedia article, no natural satellite of a satellite has been observed – though a faint, banded ring system has been observed around Saturn’s little (0.03 moon masses) satellite Rhea, suggesting it may have several very small moons.

[Boerseun]

'Course it's possible.

 

After all, the Earth is one of the Sun's moons. Or it's a planet. There's no fundamental difference to how you want to see it - the core requirement here is simply the mass of the "moon" under discussion.

 

Besides, the lunar orbiter in the Apollo missions was a perfectly valid moon to the moon.

[Moontanman]

'Course it's possible.

 

After all, the Earth is one of the Sun's moons. Or it's a planet. There's no fundamental difference to how you want to see it - the core requirement here is simply the mass of the "moon" under discussion.

 

Besides, the lunar orbiter in the Apollo missions was a perfectly valid moon to the moon.

 

Ok I understand that under current circumstances our moon couldn't have a perminant moon but could the moon orbit the Earth in our present solar system so it could rotate independant of the Earth so it could have it's own moon. Possibly about 600 miles in diameter or so. also how long could such a body orbit the moon under it's present circumstanaces? since the moon is slowly moving away from the earth it may one day be far enough away to have it's own moon.

[Boerseun]

It's already perfectly able to have a natural satellite of 600kms - but only under a particular orbital altitude. If above that altitude, the Earth would start interfering and destabilise the orbit. Don't ask me what that altitude is, however...

 

But seeing as the moon has no atmosphere, I'd imagine a satellite 600kms in diameter (a moon's moon, if you will) that barely skims the surface will be relatively safe from the Earth's grubby claws for quite a while. It won't be a perfectly stable orbit, however, but then again, such an orbit doesn't exist.

 

For instance, the moon is slowly moving away from the Earth, and the Earth's orbit around the Sun wobbles because of Jupiter, Saturn (to a much lesser degree) and Venus and Mars playing a very complicated role in determining our exact position in space at any given moment in time.

 

Kepler's orbital equations will work perfectly in a two-body system. It works just as well in multi-body systems, it just becomes increasingly difficult to calculate.

[CraigD]

It's [Earth’s moon is] already perfectly able to have a natural satellite of 600kms - but only under a particular orbital altitude. If above that altitude, the Earth would start interfering and destabilise the orbit. Don't ask me what that altitude is, however...

 

But seeing as the moon has no atmosphere, I'd imagine a satellite 600kms in diameter (a moon's moon, if you will) that barely skims the surface will be relatively safe from the Earth's grubby claws for quite a while.

The Moon’s Hill sphere is about 61,500 km radius, or 49,700 km altitude, or 35.4 Moon radii, or 0.16 of its orbital distance from Earth. It’s actually larger, as a ratio to the Moon’s radius, than Earth’s Hill sphere of 150,000 km, or 23.6 Earth radii, so staying within it doesn’t require a surface-skimming orbit.

It won't be a perfectly stable orbit, however, but then again, such an orbit doesn't exist.

Though Boer’s right that a perfectly stable orbit in the real universe doesn’t exist, quite a few that are pretty stable for billions of years (such as Earth’s and the Moon’s) obviously do. Yet despite no shortage of suitable easily observable bodies (including, it’s now believed, a debris ring about equal in total mass to the Moon that persisted for about 100 years after the Moon was formed about 4.5 billion years ago by a giant impact with the Mars-size Thea), we don’t observe any moons of the Moon, or of various other moons we’ve observed closely, except maybe Rhea (and her’s, if they exist, are likely recent and destined to be short-lived).

 

Some sort of orbital mechanical phenomena appears to be preventing long-lived moons of moons, while permitting numerous moons of much smaller bodies, ie: asteroid moons. My guess is it has to do with a moon of a moon being significantly part of a 3+ body systems consisting of its primary (eg: the Moon), its primary (eg: Earth) and its primary (the Sun). Consider, for example, that the Moon’s Hill sphere relative to the Sun is about 35,600 km, smaller than its Hill sphere with respect to Earth. A moon of the Moon is subject to much more complicated orbital mechanics than an effectively two-body system.

Kepler's orbital equations will work perfectly in a two-body system. It works just as well in multi-body systems, it just becomes increasingly difficult to calculate.

I’d go as far as saying that Kepler’s equations, which are fundamentally 2-body equations (and not, really, even that, but rather geometric laws describing a body following an ellipse that just happen to have a large body at one of their foci) not only can’t be used to calculate the motion of a small body with more than one primary, but are intuitively misleading for 3+ body systems.

 

We can make a sensible corollary to Newton’s reformulation of Kepler’s laws along the lines of:

If you take 2 bodies and just throw them together at random, they’ll either not orbit one another (that is, follow hyperbolas), or orbit one another stably (that is, follow elipses).

This is very clear-cut and simple, even if complicated slightly by allowing the bodies to have non-zero radii and angular momentum.

 

With 3+ bodies, no such nice corollary exists. The system may very closely follow Kepler’s laws, then suddenly do something strange and dramatic, such as ejecting a smaller body from the system.

[Moontanman]

The Moon’s Hill sphere is about 61,500 km radius, or 49,700 km altitude, or 35.4 Moon radii, or 0.16 of its orbital distance from Earth. It’s actually larger, as a ratio to the Moon’s radius, than Earth’s Hill sphere of 150,000 km, or 23.6 Earth radii, so staying within it doesn’t require a surface-skimming orbit.Though Boer’s right that a perfectly stable orbit in the real universe doesn’t exist, quite a few that are pretty stable for billions of years (such as Earth’s and the Moon’s) obviously do. Yet despite no shortage of suitable easily observable bodies (including, it’s now believed, a debris ring about equal in total mass to the Moon that persisted for about 100 years after the Moon was formed about 4.5 billion years ago by a giant impact with the Mars-size Thea), we don’t observe any moons of the Moon, or of various other moons we’ve observed closely, except maybe Rhea (and her’s, if they exist, are likely recent and destined to be short-lived).

 

Some sort of orbital mechanical phenomena appears to be preventing long-lived moons of moons, while permitting numerous moons of much smaller bodies, ie: asteroid moons. My guess is it has to do with a moon of a moon being significantly part of a 3+ body systems consisting of its primary (eg: the Moon), its primary (eg: Earth) and its primary (the Sun). Consider, for example, that the Moon’s Hill sphere relative to the Sun is about 35,600 km, smaller than its Hill sphere with respect to Earth. A moon of the Moon is subject to much more complicated orbital mechanics than an effectively two-body system.I’d go as far as saying that Kepler’s equations, which are fundamentally 2-body equations (and not, really, even that, but rather geometric laws describing a body following an ellipse that just happen to have a large body at one of their foci) not only can’t be used to calculate the motion of a small body with more than one primary, but are intuitively misleading for 3+ body systems.

 

We can make a sensible corollary to Newton’s reformulation of Kepler’s laws along the lines of:

If you take 2 bodies and just throw them together at random, they’ll either not orbit one another (that is, follow hyperbolas), or orbit one another stably (that is, follow elipses).

This is very clear-cut and simple, even if complicated slightly by allowing the bodies to have non-zero radii and angular momentum.

 

With 3+ bodies, no such nice corollary exists. The system may very closely follow Kepler’s laws, then suddenly do something strange and dramatic, such as ejecting a smaller body from the system.

 

 

I visited this site Curious About Astronomy: "Can moons have moons?" recomened by "infinitenow" and it said the main problem was the tidal lock of the moon with the earth, this would make any orbiting body impact the moon eventually, even if it was inside the moons Hill sphere. I got the impression the bigger the object the quicker the impact would occure.

[CraigD]

I visited this site Curious About Astronomy: "Can moons have moons?" recomened by "infinitenow" and it said the main problem was the tidal lock of the moon with the earth, this would make any orbiting body impact the moon eventually, even if it was inside the moons Hill sphere.

As far as I know, any satellite with an orbital period less (faster orbit) than its primary’s period of rotation, or one that orbits in the opposite direction of its primary’s rotation, etc, will lose kinetic energy, eventually spiraling into its primary. A Satellite with orbital period greater (slower orbits) than its primary (such as the Moon orbiting Earth) gains energy, spiraling outward.

 

Since the Moon’s rotation is gravitationally locked to Earth, it’s period is about 27.3 days. For the moon, this requires a circular orbit of radius (semimajor axis) greater than about 88,400 km, which is outside the Moon’s Hill sphere of about 61,500 km.

 

If the Moon’s orbit were about 1.44 times its present (about 553,000 km, well within Earth’s Hill sphere of about 1,500,000 km), it would be possible for it to have a satellite that spiraled outward.

I got the impression the bigger the object the quicker the impact would occure.

I don’t believe this is the case, unless the difference in mass is so great that it can transfer energy to its primary in different way, such as breaking its crust and “kneading” it, etc.

 

Rotation complicates the stability of orbits. A rare example of a dwarf planet binary system that avoids this problem is the Pluto-Charon system, each of which is tidally locked to the other. Charon never sets on Pluto.